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Economic Quarterly—Volume 93, Number 3—Summer 2007—Pages 201–227
Inflation and
Unemployment: A
Layperson’s Guide to the
Phillips Curve
Jeffrey M. Lacker and John A. Weinberg
W
hat do you remember from the economics class you took in college? Even if you didn’t take economics, what basic ideas do you
think are important for understanding the way markets work? In
either case, one thing you might come up with is that when the demand for a
good rises—when more and more people want more and more of that good—
its price will tend to increase. This basic piece of economic logic helps us
understand the phenomena we observe in many specific markets—from the
tendency of gasoline prices to rise as the summer sets in and people hit the
road on their family vacations, to the tendency for last year’s styles to fall in
price as consumers turn to the new fashions.
This notion paints a picture of the price of a good moving together in the
same direction with its quantity—when people are buying more, its price is rising. Of course supply matters, too, and thinking about variations in supply—
goods becoming more or less plentiful or more or less costly to produce—
complicates the picture. But in many cases such as the examples above, we
might expect movements up and down in demand to happen more frequently
than movements in supply. Certainly for goods produced by a stable industry
in an environment of little technological change, we would expect that many
movements in price and quantity are driven by movements in demand, which
would cause price and quantity to move up and down together. Common sense
This article first appeared in the Bank’s 2006 Annual Report. The authors are Jeffrey M.
Lacker, President of the Federal Reserve Bank of Richmond, and John A. Weinberg, a Senior
Vice President and Director of Research. Andreas Hornstein, Thomas Lubik, John Walter, and
Alex Wolman contributed valuable comments to this article. The views expressed are those of
the authors and do not necessarily reflect those of the Federal Reserve System.
202
Federal Reserve Bank of Richmond Economic Quarterly
suggests that this logic would carry over to how one thinks about not only the
price of one good but also the prices of all goods. Should an average measure
of all prices in the economy—the consumer price index, for example—be
expected to move up when our total measures of goods produced and consumed rise? And should faster growth in these quantities—as measured, say,
by gross domestic product—be accompanied by faster increases in prices?
That is, should inflation move up and down with real economic growth?
The simple intuition behind this series of questions is seriously incomplete
as a description of the behavior of prices and quantities at the macroeconomic
level. But it does form the basis for an idea at the heart of much macroeconomic policy analysis for at least a half century. This idea is called the
“Phillips curve,” and it embodies a hypothesis about the relationship between
inflation and real economic variables. It is usually stated not in terms of the
positive relationship between inflation and growth but in terms of a negative
relationship between inflation and unemployment. Since faster growth often
means more intensive utilization of an economy’s resources, faster growth will
be expected to come with falling unemployment. Hence, faster inflation is associated with lower unemployment. In this form, the Phillips curve looks like
the expression of a tradeoff between two bad economic outcomes—reducing
inflation requires accepting higher unemployment.
The first important observation about this relationship is that the simple
intuition described at the beginning of this essay is not immediately applicable
at the level of the economy-wide price level. That intuition is built on the
workings of supply and demand in setting the quantity and price of a specific
good. The price of that specific good is best understood as a relative price—
the price of that good compared to the prices of other goods. By contrast,
inflation is the rate of change of the general level of all prices. Recognizing
this distinction does not mean that rising demand for all goods—that is, rising
aggregate demand—would not make all prices rise. Rather, the important
implication of this distinction is that it focuses attention on what, besides
people’s underlying desire for more goods and services, might drive a general
increase in all prices. The other key factor is the supply of money in the
economy.
Economic decisions of producers and consumers are driven by relative
prices: a rising price of bagels relative to doughnuts might prompt a baker to
shift production away from doughnuts and toward bagels. If we could imagine
a situation in which all prices of all outputs and inputs in the economy, including wages, rise at exactly the same rate, what effect on economic decisions
would we expect? A reasonable answer is “none.” Nothing will have become
more expensive relative to other goods, and labor income will have risen as
much as prices, leaving people no poorer or richer.
The thought experiment involving all prices and wages rising in equal
proportions demonstrates the principle of monetary neutrality. The term refers
J. M. Lacker and J. A. Weinberg: Inflation and Unemployment
203
to the fact that the hypothetical increase in prices and wages could be expected
to result from a corresponding increase in the supply of money. Monetary
neutrality is a natural starting point for thinking about the relationship between
inflation and real economic variables. If money is neutral, then an increase
in the supply of money translates directly into inflation and has no necessary
relationship with changes in real output, output growth, or unemployment.
That is, when money is neutral, the simple supply-and-demand intuition about
output growth and inflation does not apply to inflation associated with the
growth of the money supply.
The logic of monetary neutrality is indisputable, but is it relevant? The
logic arises from thinking about hypothetical “frictionless” economies in
which all market participants at all times have all the information they need
to price the goods they sell and to choose among the available goods, and in
which sellers can easily change the price they charge. Against this hypothetical benchmark, actual economies are likely to appear imperfect to the naked
eye. And under the microscope of econometric evidence, a positive correlation
between inflation and real growth does tend to show up. The task of modern
macroeconomics has been to understand these empirical relationships. What
are the “frictions” that impede monetary neutrality? Since monetary policy
is a key determinant of inflation, another important question is how the conduct of policy affects the observed relationships. And finally, what does our
understanding of these relationships imply about the proper conduct of policy?
The Phillips curve, viewed as a way of capturing how money might not
be neutral, has always been a central part of the way economists have thought
about macroeconomics and monetary policy. It also forms the basis, perhaps
implicitly, of popular understanding of the basic problem of economic policy;
namely, we want the economy to grow and unemployment to be low, but if
growth is too robust, inflation becomes a risk. Over time, many debates about
economic policy have boiled down to alternative understandings of what the
Phillips curve is and what it means. Even today, views that economists express
on the effects of macroeconomic policy in general and monetary policy in
particular often derive from what they think about the nature, the shape, and
the stability of the Phillips curve.
This essay seeks to trace the evolution of our understanding of the Phillips
curve, from before its inception to contemporary debates about economic policy. The history presented in the pages that follow is by no means exhaustive. Important parts of economists’ understanding of this relationship that
we neglect include discussions of how the observed Phillips curve’s statistical
relationship could emerge even under monetary neutrality.1 We also neglect
the literature on the possibility of real economic costs of inflation that arise
1 King and Plosser (1984).
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even when money is neutral.2 Instead, we seek to provide the broad outlines
of the intellectual development that has led to the role of the Phillips curve in
modern macroeconomics, emphasizing the interplay of economic theory and
empirical evidence.
After reviewing the history, we will turn to the current debate about the
Phillips curve and how it translates into differing views about monetary policy.
People commonly talk about a central bank seeking to engineer a slowing of
the economy to bring about lower inflation. They think of the Phillips curve
as describing how much slowing is required to achieve a given reduction in
inflation. We believe that this reading of the Phillips curve as a lever that
a policymaker might manipulate mechanically can be misleading. By itself,
the Phillips curve is a statistical relationship that has arisen from the complex
interaction of policy decisions and the actions of private participants in the
economy. Importantly, choices made by policymakers play a large role in
determining the nature of the statistical Phillips curve. Understanding that
relationship—between policymaking and the Phillips curve—is a key ingredient to sound policy decisions. We return to this theme after our historical
overview.
1.
SOME HISTORY
The Phillips curve is named for New Zealand-born economist A.W. Phillips,
who published a paper in 1958 showing an inverse relationship between (wage)
inflation and unemployment in nearly 100 years of data from the United Kingdom.3 Since this is the work from which the curve acquired its name, one might
assume that the economics profession’s prior consensus on the matter embodied the presumption that money is neutral. But this in fact is not the case. The
idea of monetary neutrality has long coexisted with the notion that periods
of rising money growth and inflation might be accompanied by increases in
output and declines in unemployment. Robert Lucas (1996), in his Nobel
lecture on the subject of monetary neutrality, finds both ideas expressed in the
work of David Hume in 1752! Thomas Humphrey (1991) traces the notion of
a Phillips curve tradeoff throughout the writings of the classical economists
in the 18th and 19th centuries. Even Irving Fisher, whose statement of the
quantity theory of money embodied a full articulation of the consequences of
neutrality, recognized the possible real effects of money and inflation over the
course of a business cycle.
In early writings, these two opposing ideas—that money is neutral and
that it is associated with rising real growth—were typically reconciled by
the distinction between periods of time ambiguously referred to as “short
2 Cooley and Hansen (1989), for instance.
3 Phillips (1958).
J. M. Lacker and J. A. Weinberg: Inflation and Unemployment
205
run” and “long run.” The logic of monetary neutrality is essentially longrun logic. The type of thought experiment the classical writers had in mind
was a one-time increase in the quantity of money circulating in an economy.
Their logic implied that, ultimately, this would merely amount to a change in
units of measurement. Given enough time for the extra money to spread itself
throughout the economy, all prices would rise proportionately. So while the
number of units of money needed to compensate a day’s labor might be higher,
the amount of food, shelter, and clothing that a day’s pay could purchase would
be exactly the same as before the increase in money and prices.
Against this logic stood the classical economists’observations of the world
around them in which increases in money and prices appeared to bring increases in industrial and commercial activity. This empirical observation did
not employ the kind of formal statistics as that used by modern economists
but simply the practice of keen observation. They would typically explain
the difference between their theory’s predictions (neutrality) and their observations by appealing to what economists today would call “frictions” in the
marketplace. Of particular importance in this instance are frictions that get in
the way of price adjustment or make it hard for buyers and sellers of goods and
services to know when the general level of all prices is rising. If a craftsman
sees that he can sell his wares for an increased price but doesn’t realize that
all prices are rising proportionately, he might think that his goods are rising in
value relative to other goods. He might then take action to increase his output
so as to benefit from the perceived rise in the worth of his labors.
This example shows how frictions in price adjustment can break the logic
of money neutrality. But such a departure is likely to be only temporary. You
can’t fool everybody forever, and eventually people learn about the general
inflation caused by an increase in money. The real effects of inflation should
then die out. It was in fact in the context of this distinction between long-run
neutrality and the short-run tradeoff between inflation and real growth that
John Maynard Keynes made his oft-quoted quip that “in the long run we are
all dead.” 4
Phillips’ work was among the first formal statistical analyses of the relationship between inflation and real economic activity. The data on the rate
of wage increase and the rate of unemployment for Phillips’ baseline period
of 1861–1913 are reproduced in Figure 1. These data show a clear negative
relationship—greater inflation tends to coincide with lower unemployment.
To highlight that relationship, Phillips fit the curve in Figure 1 to the data. He
then examined a number of episodes, both within the baseline period and in
other periods up through 1957. The general tendency of a negative relationship
persists throughout.
4 Keynes (1923).
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Federal Reserve Bank of Richmond Economic Quarterly
Figure 1 Inflation-Unemployment Relationship in the United
Kingdom, 1861–1913
Rate of Change of Wage Rate (% Per Year)
10
8
6
4
2
0
-2
-4
0
1
2
3
4
5
6
7
Unemployment Rate (%)
8
9
10
11
Source: Phillips (1958).
Crossing the Atlantic
A few years later, Paul Samuelson and Robert Solow, both eventual Nobel
Prize winners, took a look at the U.S. data from the beginning of the 20th
century through 1958.5 A similar scatter-plot to that in Figure 1 was less
definitive in showing the negative relationship between wage inflation and
unemployment. The authors were able to recover a pattern similar to Phillips’
by taking out the years of the World Wars and the Great Depression. They also
translated their findings into a relationship between unemployment and price
inflation. It is this relationship that economists now most commonly think of
as the “Phillips curve.”
Samuelson and Solow’s Phillips curve is reproduced in Figure 2. They interpret this curve as showing the combinations of unemployment and inflation
available to society. The implication is that policymakers must choose from
the menu traced out by the curve. An inflation rate of zero, or price stability,
5 Samuelson and Solow (1960).
J. M. Lacker and J. A. Weinberg: Inflation and Unemployment
207
Figure 2 Inflation-Unemployment Relationship in the United States
around 1960
11
Average Increase in Price (% Per Year)
10
9
8
7
6
5
B
4
3
2
1
A
0
-1
1
2
3
4
5
6
7
8
9
Unemployment Rate (%)
Source: Samuelson and Solow (1960).
appears to require an unemployment rate of about 5 21 percent. To achieve unemployment of about 3 percent, which the authors viewed as approximately
full employment, the curve suggests that inflation would need to be close to 5
percent.
Samuelson and Solow did not propose that their estimated curve described
a permanent relationship that would never change. Rather, they presented it
as a description of the array of possibilities facing the economy in “the years
just ahead.” 6 While recognizing that the relationship might change beyond
this near horizon, they remained largely agnostic on how and why it might
change. As a final note, however, they suggest institutional reforms that might
produce a more favorable tradeoff (shifting the curve in Figure 2 down and
to the left). These involve measures to limit the ability of businesses and
unions to exercise monopoly control over prices and wages, or even direct
6 Ibid., p. 193.
208
Federal Reserve Bank of Richmond Economic Quarterly
wage and price controls. Their closing discussion suggests that they, like many
economists at the time, viewed both inflation and the frictions that kept money
and inflation from being neutral as at least partly structural—hard-wired into
the institutions of modern, corporate capitalism. Indeed, they concluded their
paper with speculation about institutional reforms that could move the Phillips
curve down and to the left. This was an interpretation that was compatible
with the idea of a more permanent tradeoff that derived from the structure of
the economy and that could be exploited by policymakers seeking to engineer
lasting changes in economic performance.
By the 1960s, then, the Phillips curve tradeoff had become an essential
part of the Keynesian approach to macroeconomics that dominated the field
in the decades following the Second World War. Guided by this relationship,
economists argued that the government could use fiscal policy—government
spending or tax cuts—to stimulate the economy toward full employment with
a fair amount of certainty about what the cost would be in terms of increased
inflation. Alternatively, such a stimulative effect could be achieved by monetary policy. In either case, policymaking would be a conceptually simple
matter of cost-benefit analysis, although its implementation was by no means
simple. And since the costs of a small amount of inflation to society were
thought to be low, it seemed worthwhile to achieve a lower unemployment
rate at the cost of tolerating only a little more inflation.
Turning the Focus to Expectations
This approach to economic policy implicitly either denied the long-run neutrality of money or thought it irrelevant. A distinct minority view within the
profession, however, continued to emphasize limitations on the ability of rising inflation to bring down unemployment in a sustained way. The leading
proponent of this view was Milton Friedman, whose Nobel Prize award would
cite his Phillips curve work. In his presidential address to the American Economics Association, Friedman began his discussion of monetary policy by
stipulating what monetary policy cannot do. Chief among these was that it
could not “peg the rate of unemployment for more than very limited periods.” 7
Attempts to use expansionary monetary policy to keep unemployment persistently below what he referred to as its “natural rate” would inevitably come at
the cost of successively higher inflation. Key to his argument was the distinction between anticipated and unanticipated inflation. The short-run tradeoff
between inflation and unemployment depended on the inflation expectations
of the public. If people generally expected price stability (zero inflation), then
monetary policy that brought about inflation of 3 percent would stimulate the
7 Friedman (1968), p. 5.
J. M. Lacker and J. A. Weinberg: Inflation and Unemployment
209
economy, raising output growth and reducing unemployment. But suppose the
economy had been experiencing higher inflation, of say 5 percent, for some
time, and that people had come to expect that rate of increase to continue.
Then, a policy that brought about 3 percent inflation would actually slow the
economy, making unemployment tend to rise.
By emphasizing the public’s inflation expectations, Friedman’s analysis
drew a link that was largely absent in earlier Phillips curve analyses. Specifically, his argument was that not only is monetary policy primarily responsible
for determining the rate of inflation that will prevail, but it also ultimately determines the location of the entire Phillips curve. He argued that the economy
would be at the natural rate of unemployment in the absence of unanticipated
inflation. That is, the ability of a small increase in inflation to stimulate economic output and employment relied on the element of surprise. Both the
inflation that people had come to expect and the ability to create a surprise
were then consequences of monetary policy decisions.
Friedman’s argument involved the idea of a “natural rate” of unemployment. This natural rate was something that was determined by the structure
of the economy, its rate of growth, and other real factors independent of monetary policy and the rate of inflation. While this natural rate might change
over time, at any point in time, unemployment below the natural rate could
only be achieved by policies that created inflation in excess of that anticipated
by the public. But if inflation remained at the elevated level, people would
come to expect higher inflation, and its stimulative effect would be lost. Unemployment would move back toward its natural rate. That is, the Phillips
curve would shift up and to its right, as shown in Figure 3.
The figure shows a hypothetical example in which the natural rate of
unemployment is 5 percent and people initially expect inflation of 1 percent.
A surprise inflation of 3 percent drives unemployment down to 3 percent.
But sustained inflation at the higher rate ultimately changes expectations, and
the Phillips curve shifts back so that the natural rate of unemployment is
achieved but now at 3 percent inflation. This analysis, which takes account of
inflation expectations, is referred to as the expectations-augmented Phillips
curve. An independent and contemporaneous development of this approach
to the Phillips curve was given by Edmund Phelps, winner of the 2006 Nobel
Prize in economics.8 Phelps developed his version of the Phillips curve by
working through the implications of frictions in the setting of wages and prices,
which anticipated much of the work that followed.
The reasoning of Friedman and Phelps implied that attempts to exploit
systematically the Phillips curve to bring about lower unemployment would
succeed only temporarily at best. To have an effect on real activity, monetary
8 Phelps (1967).
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Federal Reserve Bank of Richmond Economic Quarterly
Figure 3 Expectations-Augmented Phillips Curve
8
7
Inflation Rate (%)
6
5
4
3
2
1
1
2
3
4
5
u*
Unemployment Rate (%)
6
7
8
Notes: When expected inflation is 1 percent, an unanticipated increase in inflation will
initially bring unemployment down. But expectations will eventually adjust, bringing unemployment back to its natural rate (u∗ ) at the higher rate of inflation.
policy needed to bring about inflation in excess of people’s expectations. But
eventually, people would come to expect higher inflation, and the policy would
lose its stimulative effect. This insight comes from an assumption that people
base their expectations of inflation on their observation of past inflation. If,
instead, people are more forward looking and understand what the policymaker
is trying to do, they might adjust their expectations more quickly, causing the
rise in inflation to lose much of even its temporary effect on real activity. In
a sense, even the short-run relationship relied on people being fooled. One
way people might be fooled is if they are simply unable to distinguish general
inflation from a change in relative prices. This confusion, sometimes referred
to as money illusion, could cause people to react to inflation as if it were a
change in relative prices. For instance, workers, seeing their nominal wages
rise but not recognizing that a general inflation is in process, might react as if
their real income were rising. That is, they might increase their expenditures
on goods and services.
J. M. Lacker and J. A. Weinberg: Inflation and Unemployment
211
Robert Lucas, another Nobel Laureate, demonstrated how behavior resembling money illusion could result even with firms and consumers who
fully understood the difference between relative prices and the general price
level.9 In his analysis, confusion comes not from people’s misunderstanding,
but from their inability to observe all of the economy’s prices at one time. His
was the first formal analysis showing how a Phillips curve relationship could
emerge in an economy with forward-looking decisionmakers. Like the work of
Friedman and Phelps, Lucas’ implications for policymakers were cautionary.
The relationship between inflation and real activity in his analysis emerged
most strongly when policy was conducted in an unpredictable fashion, that is,
when policymaking was more a source of volatility than stability.
The Great Inflation
The expectations-augmented Phillips curve had the stark implication that any
attempt to utilize the relationship between inflation and real activity to engineer
persistently low unemployment at the cost of a little more inflation was doomed
to failure. The experience of the 1970s is widely taken to be a confirmation of
this hypothesis. The historical relationship identified by Phillips, Samuelson,
and Solow, and other earlier writers appeared to break down entirely, as shown
by the scatter-plot of the data for the 1970s in Figure 4. Throughout this decade,
both inflation and unemployment tended to grow, leading to the emergence of
the term “stagflation” in the popular lexicon.
One possible explanation for the experience of the 1970s is that the decade
was simply a case of bad luck. The Phillips curve shifted about unpredictably
as the economy was battered by various external shocks. The most notable
of these shocks were the dramatic increases in energy prices in 1973 and
again later in the decade. Such supply shocks worsened the available tradeoff,
making higher unemployment necessary at any given level of inflation.
By contrast, viewing the decade through the lens of the expectationsaugmented Phillips curve suggests that policy shared the blame for the disappointing results. Policymakers attempted to shield the real economy from
the effects of aggregate shocks. Guided by the Phillips curve, this effort often
implied a choice to tolerate higher inflation rather than allowing unemployment to rise. This type of policy choice follows from viewing the statistical
relationship Phillips first found in the data as a menu of policy options, as suggested by Samuelson and Solow. But the arguments made by Friedman and
Phelps imply that such a tradeoff is short lived at best. Unemployment would
ultimately return to its natural rate at the higher rate of inflation. So, while
the relative importance of luck and policy for the poor macroeconomic perfor9 Lucas (1972).
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Federal Reserve Bank of Richmond Economic Quarterly
Figure 4 Inflation-Unemployment Relationship in the United States,
1961–1995
14
80
12
Inflation Rate (%)
10
8
75
90
6
70
4
85
95
2
65
61
0
3
4
5
7
6
Unemployment Rate (%)
8
9
10
Notes: Inflation rate is seasonally-adjusted CPI, Fourth Quarter.
Source: Bureau of Labor Statistics/Haver Analytics.
mance of the 1970s continues to be debated by economists, we find a powerful
lesson in the history of that decade.10 The macroeconomic performance of
the 1970s is largely what the expectations-augmented Phillips curve predicts
when policymakers try to exploit a tradeoff that they mistakenly believe to be
stable.
The insights of Friedman, Phelps, and Lucas pointed to the complicated
interaction between policymaking and statistical analysis. Relationships we
observe in past data were influenced by past policy. When policy changes,
people’s behavior may change and so too may statistical relationships. Hence,
the history of the 1970s can be read as an illustration of Lucas’ critique of what
was at the time the consensus approach to policy analysis.11
10 Velde (2004) provides an excellent overview of this debate. A nontechnical description of
the major arguments can be found in Sumo (2007).
11 Lucas (1976).
J. M. Lacker and J. A. Weinberg: Inflation and Unemployment
213
Focusing attention on the role of expectations in the Phillips curve creates
a challenge for policymakers seeking to use monetary policy to manage real
economic activity. At any point in time, the current state of the economy
and the private sector’s expectations may imply a particular Phillips curve.
Assuming that the Phillips curve describes a stable relationship, a policymaker
might choose a preferred inflation-unemployment combination. That very
choice, however, can alter expectations, causing the tradeoff to change. The
policymaker’s problem is, in effect, a game played against a public that is
trying to anticipate policy. What’s more, this game is repeated over and over,
each time a policy choice must be made. This complicated interdependence of
policy choices and private sector actions and expectations was studied by Finn
Kydland and Edward C. Prescott.12 In one of the papers for which they were
awarded the 2005 Nobel Prize, they distinguish between rules and discretion
as approaches to policymaking. By discretion, they mean period-by-period
decisionmaking in which the policymaker takes a fresh look at the costs and
benefits of alternative inflation levels at each moment. They contrast this
with a setting in which the policymaker makes a one-time decision about the
best rule to guide policy. They show that discretionary policy would result in
higher inflation and no lower unemployment than the once-and-for-all choice
of a policy rule.
Recent work by Thomas Sargent and various coauthors shows how discretionary policy, as studied by Kydland and Prescott, can lead to the type of
inflation outcomes experienced in the 1970s.13 This analysis assumes that the
policymaker is uncertain of the position of the Phillips curve. In the face of this
uncertainty, the policymaker estimates a Phillips curve from historical data.
Seeking to exploit a short-run, expectations-augmented Phillips curve—that
is, pursuing discretionary policy—the policymaker chooses among inflationunemployment combinations described by the estimated Phillips curve. But
the policy choices themselves cause people’s beliefs about policy to change,
which causes the response to policy choices to change. Consequently, when
the policymaker uses new data to update the estimated Phillips curve, the curve
will have shifted. This process of making policy while also trying to learn
about the location of the Phillips curve can lead a policymaker to choices that
result in persistently high inflation outcomes.
In addition to the joint rise in inflation and unemployment during the
1970s, other empirical evidence pointed to the importance of expectations.
Sargent studied the experience of countries that had suffered from very high
inflation.14 In countries where monetary reforms brought about sudden and
rapid decelerations in inflation, he found that the cost in terms of reduced
12 Kydland and Prescott (1977).
13 Sargent (1999), Cogley and Sargent (2005), and Sargent, Williams, and Zha (2006).
14 Sargent (1986).
214
Federal Reserve Bank of Richmond Economic Quarterly
output or increased unemployment tended to be much lower than standard
Phillips curve tradeoffs would suggest. One interpretation of these findings
is that the disinflationary policies undertaken tended to be well-anticipated.
Policymakers managed to credibly convince the public that they would pursue
these policies. Falling inflation that did not come as a surprise did not have
large real economic costs.
On a smaller scale in terms of peak inflation rates, another exercise in
dramatic disinflation was conducted by the Federal Reserve under Chairman
Paul Volcker.15 As inflation rose to double-digit levels in the late 1970s,
contemporaneous estimates of the cost in unemployment and lost output that
would be necessary to bring inflation down substantially were quite large.
A common range of estimates was that the 6 percentage-point reduction in
inflation that was ultimately brought about would require output from 9 to 27
percent below capacity annually for up to four years.16 Beginning in October
1979, the Fed took drastic steps, raising the federal funds rate as high as 19
percent in 1980. The result was a steep, but short recession. Overall, the costs
of the Volcker disinflation appear to have been smaller than had been expected.
A standard estimate, which appears in a popular economics textbook, is one
in which the reduction in output during the Volcker disinflation amounted to
less than a 4 percent annual shortfall relative to capacity.17 This amount is a
significant cost, but it is substantially less than many had predicted before the
fact. Again, one possible reason could be that the Fed’s course of action in this
episode became well-anticipated once it commenced. While the public might
not have known the extent of the actions the Fed would take, the direction of
the change in policy may well have become widely understood. By the same
token, and as argued by Goodfriend and King, remaining uncertainty about
how far and how persistently the Fed would bring inflation down may have
resulted in the costs of disinflation being greater than they might otherwise
have been.
The experience of the 1970s, together with the insights of economists
emphasizing expectations, ultimately brought the credibility of monetary policy to the forefront in thinking about the relationship between inflation and
the real economy. Credibility refers to the extent to which the central bank
can convince the public of its intention with regard to inflation. Kydland and
Prescott showed that credibility does not come for free. There is always a
short-run gain from allowing inflation to rise a little so as to stimulate the real
economy. To establish credibility for a low rate of inflation, the central bank
must convince the public that it will not pursue that short-run gain.
15 Goodfriend and King (2005).
16 Ibid.
17 Mankiw (2007).
J. M. Lacker and J. A. Weinberg: Inflation and Unemployment
215
The experience of the 1980s and 1990s can be read as an exercise in building credibility. In several episodes during that period, inflation expectations
rose as doubts were raised about the Fed’s ability to maintain its commitment to
low inflation. These episodes, labeled inflation scares by Marvin Goodfriend,
were marked by rapidly rising spreads between long-term and short-term interest rates.18 Goodfriend identifies inflation scares in 1980, 1983, and 1987.
These tended to come during or following episodes in which the Fed responded
to real economic weakness with reductions (or delayed increases) in its federal funds rate target. In these instances, Fed policymakers reacted to signs of
rising inflation expectations by raising interest rates. These systematic policy
responses in the 1980s and 1990s were an important part of the process of
building credibility for lower inflation.
2. THE “MODERN” PHILLIPS CURVE
The history of the Phillips curve shows that the empirical relationship shifts
over time, and there is evidence that those movements are linked to the public’s inflation expectations. But what does the history say about why this
relationship exists? Why is it that there is a statistical relationship between
inflation and real economic activity, even in the short run? The earliest writers
and those that followed them recognized that the short-run tradeoff must arise
from frictions that stand in the way of monetary neutrality. There are many
possible sources of such frictions. They may arise from the limited nature of
the information individuals have about the full array of prices for all products
in the economy, as emphasized by Lucas. Frictions might also stem from
the fact that not all people participate in all markets, so that different markets
might be affected differently by changes in monetary policy. One simple type
of friction is a limitation on the flexibility sellers have in adjusting the prices of
the goods they sell. If there are no limitations all prices can adjust seamlessly
whenever demand or cost conditions change, then a change in monetary policy
will, again, affect different markets differently.
Deriving a Phillips Curve from Price-Setting Behavior
This price-setting friction has become a popular device for economists seeking
to model the behavior of economies with a short-run Phillips curve. To see
how such a friction leads to a Phillips curve, think about a business that is
setting a price for its product and does not expect to get around to setting the
price again for some time. Typically, the business will choose a price based
on its own costs of production and the demand that it faces for its goods. But
18 Goodfriend (1993).
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Federal Reserve Bank of Richmond Economic Quarterly
because that business expects its price to be fixed for a while, its price choice
will also depend on what it expects to happen to its costs and its demand
between when it sets its price this time and when it sets its price the next time.
If the price-setting business thinks that inflation will be high in the interim
between its price adjustments, then it will expect its relative price to fall. As
average prices continue to rise, a good with a temporarily fixed price gets
cheaper. The firm will naturally be interested in its average relative price
during the period that its price remains fixed. The higher the inflation expected
by the firm up until its next price adjustment, the higher the current price it
will set. This reasoning, applied to all the economy’s sellers of goods and
services, leads directly to a close relationship between current inflation and
expected future inflation.
This description of price-setting behavior implies that current inflation
depends on the real costs of production and expected future inflation. The real
costs of production for businesses will rise when the aggregate use of productive resources rises, for instance because rising demand for labor pushes up
real wages.19 The result is a Phillips curve relationship between inflation and
a measure of real economic activity, such as output growth or unemployment.
Current inflation rises with expected future inflation and falls as current unemployment rises relative to its “natural” rate (or as current output falls relative
to the trend rate of output growth).
A Phillips Curve in a “Complete” Modern Model
The price-setting frictions that are part of many modern macroeconomic models are really not that different from arguments that economists have always
made about reasons for the short-run nonneutrality of money. What distinguishes the modern approach is not just the more formal, mathematical derivation of a Phillips curve relationship, but more importantly, the incorporation
of this relationship into a complete model of the macroeconomy. The word
“complete” here has a very specific meaning, referring to what economists
call “general equilibrium.” The general equilibrium approach to studying
economic activity recognizes the interdependence of disparate parts of the
economy and emphasizes that all macroeconomic variables such as GDP, the
level of prices, and unemployment are all determined by fundamental economic forces acting at the level of individual households and businesses. The
completeness of a general equilibrium model also allows for an analysis of
the effects of alternative approaches to macroeconomic policy, as well as an
evaluation of the relative merits of alternative policies in terms of their effects
on the economic well-being of the people in the economy.
19 There are a number of technical assumptions needed to make this intuitive connection
precisely correct.
J. M. Lacker and J. A. Weinberg: Inflation and Unemployment
217
The Phillips curve is only one part of a complete macroeconomic model—
one equation in a system of equations. Another key component describes how
real economic activity depends on real interest rates. Just as the Phillips curve
is derived from a description of the price-setting decisions of businesses, this
other relationship, which describes the demand side of the economy, is based
on households’ and business’ decisions about consumption and investment.
These decisions involve people’s demand for resources now, as compared to
their expected demand in the future. Their willingness to trade off between
the present and the future depends on the price of that tradeoff—the real rate
of interest.
One source of interdependence between different parts of the model—
different equations—is in the real rate of interest. A real rate is a nominal
rate—the interest rates we actually observe in financial markets—adjusted
for expected inflation. Real rates are what really matter for households’ and
firms’ decisions. So on the demand side of the economy, people’s choices
about consumption and investment depend on what they expect for inflation,
which comes, in part, from the pricing behavior described by the Phillips
curve. Another source of interdependence comes in the way the central bank
influences nominal interest rates by setting the rate charged on overnight,
interbank loans (the federal funds rate in the United States). A complete model
also requires a description of how the central bank changes its nominal interest
rate target in response to changing economic conditions (such as inflation,
growth, or unemployment).
In a complete general equilibrium analysis of an economy’s performance,
all three parts—the Phillips curve, the demand side, and central
bank behavior—work together to determine the evolution of economic variables. But many of the economic choices people make on a day-to-day basis
depend not only on conditions today, but also on how conditions are expected
to change in the future. Such expectations in modern macroeconomic models are commonly described through the assumption of rational expectations.
This assumption simply means that the public—households and firms whose
decisions drive real economic activity—fully understands how the economy
evolves over time and how monetary policy shapes that evolution. It also
means that people’s decisions will depend on well-informed expectations not
only of the evolution of future fundamental conditions, but of future policy
as well. While discussions of a central bank’s credibility typically assume
that there are things related to policymaking about which the public is not
fully certain, these discussions retain the presumption that people are forward
looking in trying to understand policy and its impact on their decisions.
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Federal Reserve Bank of Richmond Economic Quarterly
Implications and Uses of the Modern Approach
A Phillips curve that is derived as part of a model that includes price-setting
frictions is often referred to as the New Keynesian Phillips curve (NKPC).20
A complete general equilibrium model that incorporates this version of the
Phillips curve has been referred to as the New Neoclassical Synthesis model.21
These models, like any economic model, are parsimonious descriptions of
reality. We do not take them as exact descriptions of how a modern economy
functions. Rather, we look to them to capture the most important forces at
work in determining macroeconomic outcomes. The key equations in new
neoclassical or new Keynesian models all involve assumptions or approximations that simplify the analysis without altering the fundamental economic
forces at work. Such simplifications allow the models to be a useful guide to
our thinking about the economy and the effects of policy.
The modern Phillips curve is similar to the expectations-augmented Phillips
curve in that inflation expectations are important to the relationship between
current inflation and unemployment. But its derivation from forward-looking
price-setting behavior shifts the emphasis to expectations of future inflation.
It has implications similar to the long-run neutrality of money, because if inflation is constant over time, then current inflation is equal to expected inflation.
Then, whatever that constant rate of inflation, unemployment must return to
the rate implied by the underlying structure of the economy, that is, to a rate
that might be considered the “natural” unemployment. Money is not truly
neutral in these models, however. Rather, the pricing frictions underlying the
models imply that there are real economic costs to inflation. Because sellers of
goods adjust their prices at different times, inflation makes the relative prices
of different goods vary, and this distorts sellers’ and buyers’ decisions. This
distortion is greater, the greater the rate of inflation.
The expectational nature of the Phillips curve also means that policies that
have a short-run effect on inflation will induce real movements in output or
unemployment mainly if the short-run movement in inflation is not expected to
persist. In this sense, the modern Phillips curve also embodies the importance
of monetary policy credibility, since it is credibility that would allow expected
inflation to remain stable, even as inflation fluctuated in the near term.
A more general way of emphasizing the importance of credibility is to say
that the modern Phillips curve implies that the behavior of inflation will depend
crucially on people’s understanding of how the central bank is conducting
monetary policy. What people think about the central bank’s objectives and
strategy will determine expectations of inflation, especially over the long run.
Uncertainty about these aspects of policy will cause people to try to make
20 Clarida, Galı́, and Gertler (1999).
21 Goodfriend and King (1997).
J. M. Lacker and J. A. Weinberg: Inflation and Unemployment
219
inferences about future policy from the actual policy they observe. Even if
the central bank makes statements about its long-run objectives and strategy,
people will still try to make inferences from the policy actions they see. But in
this case, the inference that people will try to make is slightly simpler: people
must determine if actual policy is consistent with the stated objectives.
Does this newest incarnation of the Phillips curve present a central bank
with the opportunity to actively manage real economic activity through choosing more or less inflationary policies? The assumption that people are forward
looking in forming expectations about future policy and inflation limits the
scope for managing real growth or unemployment through Phillips curve tradeoffs. An attempt to manage such growth or unemployment persistently would
translate into the public’s expectations of inflation causing the Phillips curve
to shift. This is another characteristic that the modern approach shares with
the older expectations-augmented Phillips curve.
What this modern framework does allow is the analysis of alternative
monetary policy rules—that is, how the central bank sets its nominal interest
rate in response to such economic variables as inflation, relative to the central
bank’s target, and the unemployment rate or the rate of output growth relative to
the central bank’s understanding of trend growth.22 A typical rule that roughly
captures the actual behavior of most central banks would state, for instance,
that the central bank raises the interest rate when inflation is higher than its
target and lowers the interest rate when unemployment rises. Alternative rules
might make different assumptions, for instance, about how much the central
bank moves the interest rate in response to changes in the macroeconomic
variables that it is concerned about. The complete model can then be used to
evaluate how different rules perform in terms of the long-run levels of inflation
and unemployment they produce, or more generally in terms of the economic
well-being generated for people in the economy. A typical result is that rules
that deliver lower and less variable inflation are better both because low and
stable inflation is a good thing and because such rules can also deliver less
variability in real economic activity. Further, lower inflation has the benefit
of reducing the costs from distorted relative prices.
While low inflation is a preferred outcome, it is typically not possible,
in models or in reality, to engineer a policy that delivers the same low target
rate of inflation every month or quarter. The economy is hit by any number
of shocks that can move both real output and inflation around from month to
month—large energy price movements, for example. In the presence of such
shocks, a good policy might be one that, while not hitting its inflation target
each month, always tends to move back toward its target and never stray too
far.
22 We use the term “monetary policy rule” in the very general sense of any systematic pattern
of choice for the policy instrument—the funds rate—based on the state of the economy.
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Federal Reserve Bank of Richmond Economic Quarterly
Complete models incorporating a modern Phillips curve also allow
economists to formalize the notion of monetary policy credibility. Remember
that credibility refers to what people believe about the way the central bank
intends to conduct policy. If people are uncertain about what rule best describes the behavior of the central bank, then they will try to learn from what
they see the central bank doing. This learning can make people’s expectations
about future policy evolve in a complicated way. In general, uncertainty about
the central bank’s policy, or doubts about its commitment to low inflation, can
raise the cost (in terms of output or employment) of reducing inflation. That
is, the short-run relationship between inflation and unemployment depends on
the public’s long-run expectations about monetary policy and inflation.
The modern approach embodies many features of the earlier thinking about
the Phillips curve. The characterization of policy as a systematic pattern of behavior employed by the central bank, providing the framework within which
people form systematic expectations about future policy, follows the work
of Kydland and Prescott. And the focus on expectations itself, of course,
originated with Friedman. Within this modern framework, however, some
important debates remain unsettled. While our characterization of the framework has emphasized the forward-looking nature of people’s expectations,
some economists believe that deviations from this benchmark are important
for understanding the dynamic behavior of inflation. We turn to this question
in the next section.
We have described here an approach that has been adopted by many contemporary economists for applied central bank policy analysis. But we should
note that this approach is not without its critics. Many economists view the
price-setting frictions that are at the core of this approach as ad hoc and unpersuasive. This critique points to the value of a deeper theory of firms’
price-setting behavior. Moreover, there are alternative frictions that can also
rationalize monetary nonneutrality. Alternatives include frictions that limit
the information available to decisionmakers or that limit some people’s participation in some markets. So while the approach we’ve described does not
represent the only possible modern model, it has become a popular workhorse
in policy research.
3.
HOW WELL DOES THE MODERN PHILLIPS CURVE FIT
THE DATA?
The Phillips curve began as a relationship drawn to fit the data. Over time,
it has evolved as economists’ understanding of the forces driving those data
has developed. The interplay between theory—the application of economic
logic—and empirical facts has been an important part of this process of discovery. The recognition of the importance of expectations developed together
with the evidence of the apparent instability of the short-run tradeoff. The
J. M. Lacker and J. A. Weinberg: Inflation and Unemployment
221
modern Phillips curve represents an attempt to study the behavior of both
inflation and real variables using models that incorporate the lessons of Friedman, Phelps, and Lucas and that are rich enough to produce results that can
be compared to real world data.
Attempts to fit the modern, or New Keynesian, Phillips curve to the data
have come up against a challenging finding. The theory behind the short-run
relationship implies that current inflation should depend on current real activity, as measured by unemployment or some other real variable, and expected
future inflation. When estimating such an equation, economists have often
found that an additional variable is necessary to explain the behavior of inflation over time. In particular, these studies find that past inflation is also
important.23
Inflation Persistence
The finding that past inflation is important for the behavior of current and future inflation—that is, the finding of inflation persistence—implies that movements in inflation have persistent effects on future inflation, apart from any
effects on unemployment or expected inflation. Such persistence, if it were
an inherent part of the structure and dynamics of the economy, would create a
challenge for policymakers to reduce inflation by reducing people’s expectations. Remember that we stated earlier the possibility that if the central bank
could convince the public that it was going to bring inflation down, then the
desired reduction might be achieved with little cost in unemployment or output. Inherent inflation persistence would make such a strategy problematic.
Inherent persistence makes the set of choices faced by the policymaker closer
to that originally envisioned by Samuelson and Solow. The faster one tries to
bring down inflation, the greater the real economic costs.
Inherent persistence in inflation might be thought to arise if not all pricesetters in the economy were as forward looking as in the description given
earlier. If, instead of basing their price decisions on their best forecast of
future inflation behavior, some firms simply based current price choices on
the past behavior of inflation, this backward-looking pricing would impart
persistence to inflation. Jordi Galı́ and Mark Gertler, who took into account
the possibility that the economy is populated by a combination of forwardlooking and backward-looking participants, introduced a hybrid Phillips curve
in which current inflation depends on both expected future inflation and past
inflation.24
23 Fuhrer (1997).
24 Galı́ and Gertler (1999).
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Federal Reserve Bank of Richmond Economic Quarterly
An alternative explanation for inflation persistence is that it is a result primarily of the conduct of monetary policy. The evolution of people’s inflation
expectations depends on the evolution of the conduct of policy. If there are
significant and persistent shifts in policy conduct, expectations will evolve as
people learn about the changes. In this explanation, inflation persistence is not
the result of backward-looking decisionmakers in the economy but is instead
the result of the interaction of changing policy behavior and forward-looking
private decisions by households and businesses.25
Another possibility is that inflation persistence is the result of the nature of
the shocks hitting the economy. If these shocks are themselves persistent—that
is, bad shocks tend to be followed by more bad shocks—then that persistence
can lead to persistence in inflation. The way to assess the relative importance
of alternative possible sources of persistence is to estimate the multiple equations that make up a more complete model of the economy. This approach, in
contrast with the estimation of a single Phillips curve equation, allows for explicitly considering the roles of changing monetary policy, backward-looking
pricing behavior, and shocks in generating inflation persistence. A typical
finding is that the backward-looking terms in the hybrid Phillips curve appear
considerably less important for explaining the dynamics of inflation than in
single equation estimation.26
The scientific debate on the short-run relationship between inflation and
real economic activity has not yet been fully resolved. On the central question
of the importance of backward-looking behavior, common sense suggests that
there are certainly people in the real-world economy who behave that way.
Not everyone stays up-to-date enough on economic conditions to make sophisticated, forward-looking decisions. People who do not may well resort
to rules of thumb that resemble the backward-looking behavior in some economic models. On the other hand, people’s behavior is bound to be affected
by what they believe to be the prevailing rate of inflation. Market participants
have ample incentive and ability to anticipate the likely direction of change in
the economy. So both backward- and forward-looking behavior are grounded
in common sense. However the more important scientific questions involve
the extent to which either type of behavior drives the dynamics of inflation
and is therefore important for thinking about the consequences of alternative
policy choices.
25 Dotsey (2002) and Sbordone (2006).
26 Lubik and Schorfheide (2004).
J. M. Lacker and J. A. Weinberg: Inflation and Unemployment
223
The Importance of Inflation Persistence for
Policymakers
Related to the question of whether forward- or backward-looking behavior
drives inflation dynamics is the question of how stable people’s inflation expectations are. The backward-looking characterization suggests a stickiness
in beliefs, implying that it would be hard to induce people to change their expectations. If relatively high inflation expectations become ingrained, then it
would be difficult to get people to expect a decline in inflation. This describes
a situation in which disinflation could be very costly, since only persistent evidence of changes in actual inflation would move future expectations. Evidence
discussed earlier from episodes of dramatic changes in the conduct of policy,
however, suggests that people can be convinced that policy has changed. In
a sense, the tradeoffs faced by a policymaker could depend on the extent to
which people’s expectations are subject to change. If people are uncertain
and actively seeking to learn about the central bank’s approach to policy, then
expectations might move around in a way that departs from the very persistent, backward-looking characterization. But this movement in expectations
would depend on the central bank’s actions and statements about its conduct
of policy.
The periods that Goodfriend (1993) described as inflation scares can be
seen as periods when people’s assessment of likely future policy was changing rather fluidly. Even very recently, we have seen episodes that could be
described as “mini scares.” For instance, in the wake of Hurricane Katrina
in late 2005, markets’ immediate response to rising energy prices suggested
expectations of persistently rising inflation. Market participants, it seems,
were uncertain as to how much of a run-up in general inflation the Fed would
allow. Inflation expectations moved back down after a number of FOMC
members made speeches emphasizing their focus on preserving low inflation.
This episode illustrates both the potential for the Fed to influence inflation expectations and the extent to which market participants are at times uncertain
as to how the Fed will respond to new developments.
4.
MAKING POLICY
While the scientific dialogue continues, policymakers must make judgments
based on their understanding of the state of the debate. At the Federal Reserve Bank of Richmond, policy opinions and recommendations have long
been guided by a view that the short-term costs of reducing inflation depend on expectations. This view implies that central bank credibility—that
is, the public’s level of confidence about the central bank’s future patterns of
behavior—is an important aspect of policymaking. Central bank credibility
makes it less costly to return inflation to a desirable level after it has been
pushed up (or down) by energy prices or other shocks to the economy. This
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Federal Reserve Bank of Richmond Economic Quarterly
view of policy is consistent with a view of the Phillips curve in which inflation
persistence is primarily a consequence of the conduct of policy.
The evidence is perhaps not yet definitive. As outlined in our argument,
however, we do find support for our view in the broad contours of the history
of U.S. inflation over the last several decades. At a time when a consensus
developed in the economics profession that the Phillips curve tradeoff could
be exploited by policymakers, apparent attempts to do so led to or contributed
to the decidedly unsatisfactory economic performance of the 1970s. And
the improved performance that followed coincided with the solidification of
the profession’s understanding of the role of expectations. We also see the
initial costs of bringing down inflation in the early 1980s as consistent with
our emphasis on expectations and credibility. After the experience of the
1970s, credibility was low, and expectations responded slowly to the Fed’s
disinflationary policy actions. Still, the response of expectations was faster
than might be implied by a backward-looking Phillips curve.
We also view policymaking on the basis of a forward-looking understanding of the Phillips curve as a prudent approach. A hybrid Phillips curve with
a backward-looking component presents greater opportunities for exploiting
the short-run tradeoff. In a sense, it assumes that the monetary policymaker
has more influence over real economic activity than is assumed by the purely
forward-looking specification. Basing policy on a backward-looking formulation would also risk underestimating the extent to which movements in inflation can generate shifts in inflation expectations, which could work against
the policymaker’s intentions. Again, the experience of past decades suggests
the risks associated with policymaking under the assumption that policy can
persistently influence real activity more than it really can. In our view, these
risks point to the importance of a policy that makes expectational stability its
centerpiece.
5.
CONCLUSION
One key lesson from the history of the relationship between inflation and real
activity is that any short-run tradeoff depends on people’s expectations for
inflation. Ultimately, monetary policy has its greatest impact on real activity
when it deviates from people’s expectations. But if a central bank tries to
deviate from people’s expectations repeatedly, so as to systematically increase
real output growth, people’s expectations will adjust.
There are also, we think, important lessons in the observation that overall
economic performance, in terms of both real economic activity and inflation,
was much improved beginning in the 1980s as compared to that in the preceding decade. While this improvement could have some external sources
related to the kinds of shocks that affect the economy, it is also likely that
improved conduct of monetary policy played a role. In particular, monetary
J. M. Lacker and J. A. Weinberg: Inflation and Unemployment
225
policy was able to persistently lower inflation by responding more to signs of
rising inflation or inflation expectations than had been the case in the past. At
the same time, the variability of inflation fell, while fluctuations in output and
unemployment were also moderating.
We think the observed behavior of policy and economic performance is
directly linked to the lessons from the history of the Phillips curve. Both
point to the importance of the expectational consequences of monetary policy
choices. An approach to policy that is able to stabilize expectations will be
most able to maintain low and stable inflation with minimal effects on real
activity. It is the credible maintenance of price stability that will in turn allow
real economic performance to achieve its potential over the long run. This
will not eliminate the business cycle since the economy will still be subject
to shocks that quicken or slow growth. We believe the history of the Phillips
curve shows that monetary policy’s ability to add to economic variability by
overreacting to shocks is greater than its ability to reduce real variability, once
it has achieved credibility for low inflation.
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Economic Quarterly—Volume 93, Number 3—Summer 2007—Pages 229–250
A Taylor Rule and the
Greenspan Era
Yash P. Mehra and Brian D. Minton
T
here is considerable interest in determining whether monetary policy
actions taken by the Federal Reserve under Chairman Alan Greenspan
can be summarized by a Taylor rule. The original Taylor rule relates
the federal funds rate target to two economic variables: lagged inflation and the
output gap, with the actual federal funds rate completely adjusting to the target
in each period (Taylor 1993).1 The later assumption of complete adjustment
has often been interpreted as indicating the policy rule is “non-inertial,” or
the Federal Reserve does not smooth interest rates. Inflation in the original
Taylor rule is measured by the behavior of the GDP deflator and the output
gap is the deviation of the log of real output from a linear trend. Taylor (1993)
shows that from 1987 to 1992 policy actions did not differ significantly from
prescriptions of this simple rule. Hence, according to the original Taylor rule,
the Federal Reserve, at least during the early part of the Greenspan era, was
backward looking, focused on headline inflation, and followed a non-inertial
policy rule.
Recent research, however, suggests a different picture of the Federal Reserve under Chairman Greenspan. English, Nelson, and Sack (2002) present
evidence that indicates policy actions during the Greenspan period are better
explained by an “inertial” Taylor rule reflecting the presence of interest rate
smoothing.2 Blinder and Reis (2005) state that the Greenspan Fed focused on
We would like to thank Andreas Hornstein, Robert Hetzel, Roy Webb, and Nashat Moin for
their comments. The views expressed in this article are those of the authors and do no
necessarily reflect those of the Federal Reserve Bank of Richmond or the Federal Reserve
System.
1 Taylor (1993) did not estimate the policy rule but chose specific values for the policy
response coefficients, the real rate, and the inflation target.
2 English, Nelson, and Sack (2002) provide empirical evidence for the hypothesis that the
Greenspan Fed smoothed interest rates. Woodford (2005) suggests the Federal Reserve under
Greenspan, in fact, communicated its interest-smoothing intentions to financial markets by including descriptive, forward-looking sentences in its policy statements to ensure that policy expectations
of the financial sector remain aligned with its own outlook for policy. For example, in order to
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a “core” measure of inflation in adjusting its federal funds rate target. Clarida,
Galı́, and Gertler (2000), among others, have shown that a forward-looking
Taylor rule that relates the current funds rate target to “expected” inflation and
output developments appears to fit the data quite well over the period spanning the tenures of Chairmen Paul Volcker and Alan Greenspan. Orphanides
(2001) argues that policy evaluations using policy rules estimated with the
final revised data may be misleading.
This article estimates a Taylor rule that address three key features of the
Greenspan period highlighted in recent research: the Federal Reserve under
Greenspan was forward looking, focused on core inflation, and smoothed
interest rates. Furthermore, this article uses the real-time data for economic
variables and investigates whether results based on the final, revised data
change when the real-time data are used. We also examine whether the use
of real-time data leads to a better explanation of policy actions during the
Greenspan period.
A Taylor rule incorporating the above-noted three features is shown below
in equation (1.3).
∗
F Rt∗ = α 0 + α π π ct,j + α y (ln yt,k − ln yt,k
),
∗
F Rt = ρF Rt−1 + (1 − ρ)F Rt + vt ,
F Rt = ρF Rt−1 + (1 − ρ){α 0 + α π π ct,j
∗
)} + vt ,
+α y (ln yt,k − lnyt,k
(1.1)
(1.2)
(1.3)
where F Rt is the actual federal funds rate, F Rt∗ is the federal funds rate
target, π ct,j is the j -period ahead forecast of core inflation made at time t,
ln y is the log of actual output, ln y ∗ is the log of potential output, and vt
∗
) is the k-period
is the disturbance term. Thus, the term (ln yt,k − ln yt,k
ahead forecast of the output gap. Equation (1.1) relates the federal funds
rate target to expected values of two economic fundamentals: core inflation
and the output gap. The funds rate target is hereafter called the policy rate.
The coefficients α π and α y measure the long-term responses of the funds
rate target to the expected inflation and the output gap. They are assumed to
be positively signed, indicating that the Federal Reserve raises its funds rate
deal with the threat of deflation in 2003, policy statements in that year included sentences such
as “. . . policy accommodation can be maintained for a considerable period of time,” meaning the
Federal Reserve would not raise its funds rate target in response to increases in real growth given
the threat of deflation. The intent was to hold long-term interest rates low by quashing expectations that the Fed was on the verge of increasing the funds rate. In 2004, policy statements
included phrases such as “. . . the Committee believes that it can be patient in removing policy
accommodation,” and “. . . the Committee believes that policy accommodation can be removed at
a pace that is likely to be measured.” The latter came to mean 25 basis points at each FOMC
meeting. These considerations suggest the Greenspan policy rule should be estimated allowing for
the presence of interest-rate smoothing. Blinder and Reis (2005) also argue that the Greenspan
Fed used frequent small changes in the funds rate to hit its target for the policy rate suggested
by economic fundamentals such as inflation and unemployment.
Y. P. Mehra and B. D. Minton: Taylor Rule and the Greenspan Era
231
target if inflation rises and/or the output gap is positive. Equation (1.2) is the
standard partial adjustment equation, expressing the current funds rate as a
weighted average of the current funds rate target F Rt∗ and last quarter’s actual
value F Rt−1 . If the actual funds rate adjusts to its target within each period,
then ρ equals zero, which suggests that the Federal Reserve does not smooth
interest rates. Equation (1.2) also includes a disturbance term, indicating that
in the short run, the actual funds rate may deviate from the value implied by
economic determinants specified in the policy rule. If we substitute equation
(1.1) into (1.2), we get (1.3), a forward-looking “inertial” Taylor rule.3
This article estimates the Taylor rule (1.3) using final as well as real-time
data. The real-time data consists of the Greenbook forecasts of core CPI
inflation and the Congressional Budget Office (CBO) estimates of the output
gap.4 The policy rule estimated using the final data covers all of the Greenspan
period from 1987:1 to 2005:4, whereas the rule estimated using the Greenbook
forecasts spans part of the Greenspan period from 1987:1 to 2000:4, given the
five-year lag in release of the Greenbook forecasts to the public.5
The empirical work presented here suggests several conclusions. First,
policy response coefficients in the estimated inertial Taylor rule (α π , α y , ρ )
are all positively signed and statistically significant. The key points to note
are: (a) the estimated long-term inflation response coefficient α π is well above
unity, which suggests that the Greenspan Fed responded strongly to expected
inflation; (b) the estimated output gap response coefficient α y is generally
below unity, suggesting the presence of a relatively weak response to the output
gap; and (c) the estimated partial adjustment coefficient ρ is well above zero,
indicating the presence of interest-rate smoothing. The conclusion suggested
by the estimated Taylor rule, namely, the Greenspan Fed responded strongly to
expected inflation developments (α π > 1) but relatively weakly to the output
gap (α y < 1), is in line with the recent work by Boivin (2006), who, using a
different estimation methodology, reports time-varying estimates of inflation
and the output gap response coefficients from 1970 to 1995. For the period
3 As is well known, the constant term in the Taylor rule has embedded in it the Federal
Reserve’s estimates of the short-term real rate and the inflation target. For further explantion,
∗ )
rewrite equation (1.1) of the text as F Rt∗ = rr ∗ + π ∗ + α π (π ct,j − π ∗ ) + α y (ln yt,k − ln yt,k
∗
∗
where rr is the real rate and π is the inflation target. If we substitute the above equation
into equation (1.2) of the text, we get equation (1.3) of the text, where the constant term is
now defined as α 0 = rr ∗ + (1 − α π )π ∗ . However, one cannot recover estimates of both rr ∗ and
π ∗ without bringing some additional information. See footnote 17.
4 The preferred measure of real economic activity (say, the output gap) should be the one
used in generating the Greenbook forecasts. However, for a major part of the sample period
covered here, the Greenbook has not published estimates of the output gap. Hence, it is quite
common in this literature to estimate the policy rules using the CBO estimates of the output (or
unemployment) gap.
5 We lose observations at the beginning and end of the sample period due to leads and lags
of inflation in the policy rule. The effective sample period is 1988:1 to 2004:4.
232
Federal Reserve Bank of Richmond Economic Quarterly
since the mid-1980s, the reported estimated policy coefficients are stable and
close to values as reported in this article.6
Second, the hypothesis that the Greenspan Fed paid attention to expected
inflation and output gap developments is supported by additional test results.
Those tests favor a forward-looking inertial Taylor rule over the one in which
the Federal Reserve focuses on lagged inflation and the output gap. Furthermore, the results somewhat support the hypothesis that the Greenspan Fed
was focused on core rather than on headline inflation.
Third, the Taylor rule estimated using the Greenbook core CPI inflation
forecasts and the CBO’s estimates of real-time output gap has a lower standard
error of estimate and predicts policy actions better than the Taylor rule estimated using actual future inflation and the final, revised data on the output gap.
However, there still remain several periods during which policy actions differ
significantly from prescriptions of the simple Taylor rule. Hence, despite its
better fit, the forward-looking inertial Taylor rule estimated here may not be
considered a complete description of policy actions taken by the Greenspan
Fed.
The rest of the article is organized as follows. Section 1 discusses estimation of the Greenspan policy rule and the real-time data that underlie the
estimated policy rule. Section 2 discusses estimation results, and concluding
observations are in Section 3.
1.
EMPIRICAL METHODOLOGY
Estimation of the Forward-Looking Inertial Taylor
Rule
One key objective of this article is to investigate whether monetary policy
actions taken by the Federal Reserve under Chairman Greenspan can be summarized by a Taylor rule according to which the Federal Reserve was forward
looking, focused on core inflation, and smoothed interest rates. We model
the forward-looking nature of the policy rule by relating the current value of
the funds rate target to the four-quarter-average expected inflation rate and the
contemporaneous output gap. The policy rule incorporating these features is
reproduced below in equation (2.3).
6 In Boivin (2006), the main objective is to investigate whether policy coefficients have
changed over time. For expected inflation, the Greenbook forecasts of GNP and GDP deflator
are employed. The level of economic activity is proxied using the difference between the natural
unemployment rate and the Greenbook forecast of the unemployment rate. The article, however,
also uses the real-time output gap measure constructed by Orphanides (2001). For the period
1985 to 1995, the point estimates of the long-run inflation response coefficients are well above
unity and those for the long-run output gap response coefficient are well below unity.
Y. P. Mehra and B. D. Minton: Taylor Rule and the Greenspan Era
F Rt
233
= ρ F Rt−1 + (1 − ρ){α 0 + α π π ct,4 + α y (ln yt − ln yt∗ )}, (2.3)
+vt
where π ct,4 is the average of one-to-four-quarter-ahead forecasts of core CPI
inflation made at time t and other variables as previously defined.7
The estimation of the policy rule in equation (2.3) raises several issues.
The first issue relates to how we measure expected inflation and the output
gap. The second issue relates to the nature of data used in estimation, namely,
whether it is the real-time or final, revised data. As discussed earlier, the
use of revised as opposed to the real-time data may affect estimates of policy
coefficients and may provide a misleading historical analysis of policy actions
(Orphanides 2001, 2002). The third issue is an econometric one, arising as
a result of the potential presence of serial correlation in the error term vt .
Rudebusch (2006) points out that the Federal Reserve may respond to other
economic factors besides expected inflation and the output gap, and hence a
Taylor rule estimated omitting those other factors is likely to have a serially
correlated error term. The presence of serial correlation in the disturbance
term, if ignored, may spuriously indicate that the Federal Reserve is smoothing
interest rates.
To further explain that a serially correlated disturbance term may mistakenly indicate the presence of partial adjustment, note first that if the funds rate
does partially adjust to the policy rate as shown in (1.2) and the disturbance
term has no serial correlation, then the reduced-form policy rule in (1.3 or
2.3) has the lagged funds rate as one of the explanatory variables. Hence, the
empirical finding of a significant coefficient on the lagged funds rate in the
estimated policy rule may be interpreted as indicating the presence of interestrate smoothing. Now assume that there is no partial-adjustment, ρ = 0 in
(2.3), but instead the disturbance term is serially correlated as shown below
in equation (3.1).
vt
F Rt
= svt−1 + ε t ,
= sF Rt−1 + {α 0 + α π π ct,4 + α y (ln yt − ln yt∗ )}
∗
)} + ε t .
−s{α 0 + α π π ct−1,4 + α y (ln yt−1 − ln yt−1
(3.1)
(3.2)
If we substitute equation (3.1) into (2.3), it can be easily shown that we get the
reduced-form policy rule in equation (3.2), in which among other variables
lagged funds rate also enters the policy rule. Hence, the empirical finding of
7 In particular, the four-quarter-average inflation forecast is defined as π c
=
t,4
(π ct,1 +π ct,2 +π ct,3 +π ct,4 )
. We have also dropped the subscript 0 in the output gap term (ln
4
∗ ).
yt,0 − ln yt,0
234
Federal Reserve Bank of Richmond Economic Quarterly
a significant coefficient on the lagged funds rate in the estimated policy rule
may be interpreted arising as a result of interest rate smoothing when in fact,
it is not present. In view of these considerations, this policy rule is estimated
allowing for the presence of both interest rate smoothing and serial correlation,
namely, we allow both partial adjustment and a serially correlated disturbance
term. It can be easily shown that the policy rule incorporating both partial
adjustment and serial correlation can be expressed as in equation (4).
F Rt
= α 0 (1 − s)(1 − ρ) + (s + ρ)F Rt−1 + (1 − ρ)
{α π π ct,4 + α y (ln yt − ln yt∗ )} − s{(1 − ρ)α π π ct−1,4
∗
+(1 − ρ)α y (ln yt−1 − ln yt−1
)} − sρF Rt−2 + ε t .
(4)
Note that if there is no serial correlation (s = 0 in [4]), we get the reducedform policy rule shown in equation (2.3), and if there is no partial adjustment
(ρ = 0 in [4]), we get the policy rule shown in (3.2). Of course, if both s and
ρ are not zero, we have a policy rule with both partial adjustment and serial
correlation.
In previous research, the forward-looking policy rule similar to the one
given in equation (2.3) has often been estimated assuming rational expectations and using a generalized method of moments procedure (Clarida, Galı́, and
Gertler 2000). We follow this literature and estimate the policy rule assuming
rational expectations; namely, we substitute actual future core inflation and
actual current output gap for the expected inflation and output gap terms and
use an instrumental variables procedure to estimate policy coefficients. However, we also estimate the policy rule using the Greenbook inflation forecasts
as proxy for expected inflation. In contrast to previous work, we estimate the
policy rule allowing for the presence of both interest-rate smoothing and serial
correlation as in equation (4). We use a nonlinear instrumental variables procedure when rational expectations are assumed and nonlinear ordinary least
squares procedure when the Greenbook forecasts are used. The instruments
used are three lagged values of inflation, the federal funds rate, levels and first
differences of the output gap, and the spread between the ten-year Treasury
bond yield and the federal funds rate.
In previous work, as in Boivin (2006), ordinary least squares have been employed to estimate the Taylor rule that uses the Greenbook forecasts. However,
the use of ordinary least squares requires the assumption that the Greenbook
forecasts are contemporaneously uncorrelated with the policy shock εt . As
noted in Boivin (2006), while some casual arguments can be made to support
this assumption,8 they cannot be directly verified, and hence would not be
8 Reifschneider, Stockton, and Wilcox (1997) provide some information about the conditioning assumptions of the Greenbook forecasts over the last ten years. The first feature is that these
forecasts are made under the typical assumption that the federal funds rate will remain unchanged
Y. P. Mehra and B. D. Minton: Taylor Rule and the Greenspan Era
235
enough to convince a skeptic that the Greenbook forecasts may potentially be
correlated with the policy surprise. This correlation may arise if the Greenbook forecasts reflect some contemporaneous information and the FOMC also
reacts to such information by adjusting the policy rate, as argued in Rudebusch
(2006). This endogeneity could introduce some bias in parameter estimates.
In view of this consideration, we check the robustness of our results to the
presence of potential endogeneity, using instrumental variables. In particular,
we also estimate the Taylor rule, using the Greenbook forecasts made in previous quarters as instruments. We find our main results are robust with respect
to this change in the estimation procedure.
Data
We estimate the policy rule in equation (4) over the period from 1987:1 to
2005:4 using the data on core CPI inflation and the output gap. For expected
inflation, we also use the Greenbook inflation forecasts of core CPI inflation,
prepared by the Board staff for the Federal Open Market Committee (FOMC)
meeting held near the second month of the quarter. There is considerable
evidence that the Greenbook forecasts are most appropriate in capturing policymakers’ real-time assessment of future inflation developments. Romer and
Romer (2000) show that the Federal Reserve has an informational advantage
over the private sector, producing relatively more accurate forecasts of inflation than does the private sector. Bernanke and Boivin (2003) argue one needs
a large set of conditional information to properly model monetary policy. In
that respect, the Greenbook forecasts include real-time information from a
wide range of sources, including the Board staff’s “judgment,” not otherwise
directly measurable. The policy rule that uses the Greenbook forecasts is
estimated over the period from 1988:1 to 2000:4.
Unlike inflation forecasts the Board staff’s estimates of the output gap are
not readily available. Here we follow the previous research using estimates
of potential output prepared by the Congressional Budget Office (CBO).9
during the next six to eight quarters. This neutral assumption about the path of monetary policy
may reflect the desire of the Board staff to avoid being construed as making policy recommendations, suggesting that for most of that period, the forecasts were not conditioned on the policy
surprise. The second feature of these forecasts is a large “judgmental” component, making it hard
for these forecasts to be mechanically reproduced by any particular forecasting model, thereby lessening the probability of a contemporaneous correlation between forecasts and the policy surprise.
9 Potential output is defined as trend in the productive capacity of the economy and is estimated by the level of GDP attainable when the economy is operating at a high rate of resource
use. The CBO estimates potential output for the economy, using a production function approach
applied to each of five major sectors (nonfarm business, government, farm, household and nonprofit
institutions, and residential housing) and then aggregating sectoral estimates of potential output. For
example, for the nonfarm business sector CBO uses a neoclassical production function that relates
output produced in that sector to labor (hours worked), capital, and total factor productivity. Potential output in nonfarm business sector is an estimate of output attainable when labor, capital,
236
Federal Reserve Bank of Richmond Economic Quarterly
Figure 1 Vintage 2006 and Real-Time Output Gap (Congressional
Budget Office)
4
2006
Real-time
Output Gap
2
0
-2
-4
-6
1987
1989
1991
1993
1995
1997
1999
2001
2003
2005
However, we also construct a real-time series on the output gap using the
Congressional Budget estimates of actual and potential output series available
in real time.10 Unlike the data on the output gap, the data on CPI is not
significantly revised, and hence we use the 2006 vintage dataset for core CPI.
Figure 1 charts real-time estimates of the output gap from 1987 to 2005.
The most recent vintage (2006) estimates of the output gap are also charted.
The main observation is that the real-time estimates of the output gap are not
too different from their recent vintage estimates with the exception of periods
1990 to 1993 and 1995 to 1998. The real-time estimates of the output gap
during the period surrounding the 1990–1991 recession indicate the presence
of considerably more slack in the economy than what is indicated by current
and total factor productivity variables in the production function are set at their cyclically adjusted
levels (Congressional Budget Office 2001).
10 In January of each year from 1991 to 2006, the Congressional Budget Office has released
the historical data on actual and potential output. For the period 1987 to 1990, the output gap
is constructed using the series on actual and potential output given in the 1991 vintage data file.
For 1991, we have used the pertinent series on actual and potential output from the 1992 vintage
data file and for each year thereafter. So, the potential output estimate for 2005 is constructed
using the data file released in January 2006.
Y. P. Mehra and B. D. Minton: Taylor Rule and the Greenspan Era
237
Figure 2 Greenbook Forecasts and Actual Core CPI Inflation
(Four-Quarter Average)
5.5
Greenbook
Actual
5.0
Core CPI Inflation
4.5
4.0
3.5
3.0
2.5
2.0
1.5
1987
1989
1991
1993
1995
1997
1999
estimates. Hence, a policy rule that uses the real-time estimates of the output
gap is likely to prescribe a lower funds rate target than what is indicated
by the use of revised estimates. Similarly, real-time estimates of the output
gap from 1995 to 1998 indicate far less slack in the economy than what is
suggested by the current vintage estimates, due to the ongoing productivity
acceleration that was not recognized by most economists at the time. Hence,
for the subperiod 1995 to 1998 the funds rate target prescribed by the policy
rule with the real-time output gap is higher than what is suggested by the
current vintage estimate of the output gap, ceteris paribus. Given the size of
output gap revisions, policy evaluation is likely to be affected whether one
uses the real-time or revised data on the output gap.
Figure 2 charts the actual and Greenbook forecasts of the four-quarteraverage core CPI inflation rate. As shown, the Greenbook forecasts track
actual inflation fairly well, with the exception of periods, 1988:2 to 1989:2 and
1995 to 1997. In both these subperiods, the Greenbook was “too pessimistic”
about future inflation. As some analysts have noted, during the first subperiod
the Board staff may have worried about future inflation because the Greenspan
Fed had kept interest rates low following the stock market crash of October
238
Federal Reserve Bank of Richmond Economic Quarterly
1987. During the second subperiod, productivity acceleration was underway,
and most economists, including the Board staff, were slow in recognizing the
favorable effects of productivity acceleration on inflation.
2.
EMPIRICAL RESULTS
This section presents and discusses estimates of a Taylor rule fitted over the
Greenspan period.
Estimates of Policy Response Coefficients
Table 1 presents estimates of policy response coefficients (α π , α y , ρ) from the
Taylor rule in equation (4) estimated using the final as well as the real-time
data on core CPI inflation and the output gap. Row 1 contains estimates derived using the current vintage data on the output gap, whereas row 2 contains
estimates derived using the real-time data on the output gap. Row 3 contains
ordinary least squares estimates using the Greenbook core CPI inflation forecasts and the real-time data on the output gap. We also present estimates of the
first-order serial correlation coefficient s. The estimates in rows 1 through 3 of
Table 1 suggest the following observations. First, all estimated policy response
coefficients are correctly signed and statistically significant. In particular, the
inflation response coefficient α π is generally well above unity and the output
response coefficient α y is below unity, which suggests that the Greenspan Fed
responded strongly to expected inflation and relatively weakly to output.
Second, the estimated serial correlation coefficient s is generally positive
and statistically significant, indicating the presence of serially correlated errors
in the estimated policy rules. As noted in Rudebusch (2006), the presence
of serial correlation may reflect influences on the policy rate of economic
variables to which the Federal Reserve may have responded but which are
omitted from the estimated policy rule.
Third, even after allowing for the presence of serial correlation, the estimated partial adjustment coefficient ρ is positive and well above zero, which
suggests the continued role of partial adjustment in generating a significant
coefficient on the lagged value of the funds rate. This result is similar to that of
English, Nelson, and Sack (2002). However, the magnitude of the estimated
partial adjustment coefficient ρ reported here is somewhat smaller than what
is found in previous research. As discussed later in this article, the point estimates of the partial adjustment coefficient range from .5 to .7 when the Taylor
rule is alternatively estimated using the Greenbook forecasts of headline CPI
and GDP inflation rates.
2005:4
2000:4
2000:4
2005:4
2
3
4
5
Real-time
Real-time
Real-time
Real-time
Gap
Revised
(Actual, BW)
(Actual, BW)
(GB, FW)
(Actual, FW)
Inflation
(Actual, FW)
OLS
OLS
OLS
IV
Estimation
IV
απ
1.5
(3.7)
2.2
(8.2)
1.7
(8.8)
1.0
(1.8)
0.71
(0.8)
αy
.78
(3.2)
.68
(5.5)
.64
(6.4)
.73
(2.6)
.51
(1.5)
ρ
.73
(6.7)
.66
(6.4)
.70
(13.1)
.75
(5.9)
0.66
(2.8)
s
.59
(4.3)
.49
(3.6)
.35
(2.5)
.59
(3.5)
.84
(3.9)
.98
.97
.98
.98
2
R
.98
.345
.329
.257
.315
SER
.326
(a)
(c)
The instruments used are three lagged values of the inflation rate, the funds rate, the output gap (final or real-time), the growth
gap, and the spread between nominal yields on ten-year Treasury bonds and the federal funds rate. Parentheses contain t-values.
SER is the standard error of estimate. Estimation was done allowing for the presence of first-order serial correlation in vt ,
and s is the estimated first-order serial correlation coefficient. The sample periods begin in 1988:1 and end in the year shown
in the column labeled “period.”
∗ )} + v .
F Rt = ρF Rt−1 + (1 − ρ){α 0 + α π π ct−1 + α y (ln yt−1 − ln yt−1
t
Row 4 contains nonlinear ordinary least squares (OLS) estimates of policy coefficients from the backward-looking (BW) policy
rule given below in (c).
t,4
Row 3 contains nonlinear ordinary least squares estimates (OLS) of policy coefficients from the forward-looking (FW) policy
rule given below in (b) and use the Greenbook (GB) inflation forecasts of core CPI inflation and real-time CBO estimates of
the output gap.
F Rt = ρF Rt−1 + (1 − ρ){α 0 + α π GBπ c + α y (ln yt − ln yt∗ )} + vt .
(b)
F Rt = ρF Rt−1 + (1 − ρ){α 0 + α π π c + α y ( ln yt − ln yt∗ )} + vt .
t,4
Notes: Rows 1 and 2 contain nonlinear instrumental variables (IV) estimates of policy coefficients from the forward-looking
(FW) policy rule given below in (a) and use revised or real-time data on the output gap.
Period
2005:4
Row
1
Table 1 Estimated Taylor Rules: Core CPI Inflation
Y. P. Mehra and B. D. Minton: Taylor Rule and the Greenspan Era
239
240
Federal Reserve Bank of Richmond Economic Quarterly
These estimates indicate a faster convergence of the funds rate to its desired
level over this sample period (see Panels A and B in Table 3).11
Forward- Versus Backward-Looking Specifications
The maintained hypothesis in this article is that the Greenspan Fed was forward
looking, responding to expected inflation rather than lagged inflation. As noted
at the outset, the original Taylor rule relates the actual federal funds rate to
lagged inflation and the output gap. In order to investigate which specification
better explains the Greenspan period, we also estimate the backward-looking
specification. Rows 4 and 5 in Table 1 contain estimates of policy response
coefficients from this backward-looking specification, using core CPI inflation
and the real-time data on the output gap. Row 4 reports estimates for the
subperiod 1988:1 to 2000:4, as does row 5 for the complete sample period
1988:1 to 2005:4.
One key feature of the backward-looking specifications reported in Table
1 is that the estimated inflation response coefficient α π is close to or below
unity and not always statistically significant. These estimates suggest that
the Greenspan Fed did not respond strongly to inflation.12 This conclusion
is in sharp contrast to the one suggested by forward-looking specifications,
according to which the Greenspan Fed responded strongly to inflation.
How does one decide which one of these two alternative specifications
better describes the Greenspan period? The first to note is that the forwardlooking specification better fits the data, because the forward-looking specification based on the Greenbook forecasts has a lower standard error of estimate
than the backward-looking specification, (compare SERs across rows 3 and 4
in Table 1). We investigate this issue further by testing the validity of alternative specifications, using a general specification that nests both backward- and
forward-looking specifications. In particular, consider a general specification
11 As illustrated in Rudebusch (2006), the typical estimate of the partial adjustment coefficient
ρ for this sample period is .8, suggesting that if in response to changed economic conditions the
Federal Reserve wanted to raise the funds rate by one percentage point, it would raise it by about
20 basis points in the first three months and by about 60 basis points after one year. Focusing
on the Taylor rule, which is estimated using Greebook forecasts and real-time data on the output
gap, the mid-point of the estimated range of the partial adjustment coefficient is .6, suggesting the
adjustment of the actual funds rate to its desired level will be complete well before a year. See
also English, Nelson, and Sack (2002), in which the use of real-time data in a forward-looking
policy rule yields an estimate of the partial adjustment coefficient that is also quite low.
12 Blinder and Reis (2005) report a similar finding. For the period from 1987:3 to 2000:1,
they estimate a Taylor rule that relates the funds rate target to current inflation and the unemployment gap. The inflation response coefficient estimated during that time is .57, leading them
to conclude that the Greenspan Fed did not respond strongly to inflation.
Y. P. Mehra and B. D. Minton: Taylor Rule and the Greenspan Era
241
given in equation (5.1).
F Rt∗ = a + α π GBπ ct,j + α y (ln yt − ln yt∗ ) + α π2 π ct−1
F Rt
vt
∗
),
+α y2 (ln yt−1 − ln yt−1
∗
= ρF Rt−1 + (1 − ρ)F Rt + vt , and
= svt−1 + ε t ,
(5.1)
(5.2)
where all variables are defined as before. Equation (5.1) relates the federal
funds rate target to variables suggested by both the specifications. The key
assumption underlying the general specification (5.1) is that lagged inflation
and the output gap may directly influence the current federal funds rate target,
in addition to influencing it indirectly through the Greenbook inflation forecast.
The backward-looking specification allows for the direct influence of lagged
inflation and the output gap on the current funds rate target. If α π and α y
are zero in (5.1), we get the backward-looking specification, and if α π2 and
α y2 are zero, we get the forward-looking specification.
Table 2 contains nonlinear ordinary least squares estimates of policy response coefficients from the general policy rule (5) estimated over the period
from 1988:1 to 2000:4. In addition to using the four-quarter-average Greenbook inflation forecast, we also report estimates using the one-quarter and
two-quarter-average inflation forecasts. As shown, estimated coefficients on
the Greenbook forecast α π and the current output gap α y are correctly signed
and statistically significant, whereas estimated coefficients on lagged inflation
α π2 and lagged output gap α y2 are not. The p-value of the null hypothesis that
α π2 and α y2 are zero is .89 to .94, leading to the conclusion that the data favors
the forward-looking specification.13
Robustness Issues: Core Versus Headline Inflation
and Ordinary Least Squares Versus Instrumental
Variables
Another key aspect of the maintained hypothesis is that the Greenspan Fed was
focused on core rather than headline inflation. Furthermore, the analysis using
the Greenbook forecasts used ordinary least squares to estimate the Taylor
rule. We now investigate the robustness of our results to a few changes in the
specification of the Taylor rule and the choice of the estimation procedure.
Table 3 presents the Taylor rule estimated using the Greenbook forecasts
of three alternative measures of inflation: core CPI, headline CPI, and the
GDP implicit deflator. The measure of real-time output gap used is from
13 The results do not change if the general specification is estimated including current val-
ues of inflation and the output gap, instead of lagged values of inflation. That is, the estimated
coefficient on expected inflation remains significant and that on current inflation is not.
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Federal Reserve Bank of Richmond Economic Quarterly
Table 2 Estimates of Policy Response Coefficients From a General
Policy Rule: Core CPI Inflation
Row
1
GB Forecasts
1-q average
2
2-q average
3
4-q average
απ
1.49
(1.9)
1.85
(2.0)
1.99
(2.5)
αy
.91
(1.9)
0.86
(1.9)
0.71
(2.0)
ρ
.75
(8.4)
0.75
(8.5)
0.72
(8.3)
α π2
.29
(.3)
.16
(.1)
0.33
(.3)
α y2
-.1
(.2)
-.1
(.3)
-.1
(.3)
2
SER
.284
R
.97
p-value
.89
.275
.97
.94
.262
.97
.93
Notes: The coefficients reported are nonlinear least squares estimates of the policy rule
given below in (a) and use the Greenbook forecasts (GB) and real-time data on the output
gap.
∗ ),
F Rt∗ = a + α π GBπ c + α y (ln yt −ln yt∗ ) + α π2 π t−1 + α y2 (ln yt−1 −ln yt−1
(a.1)
t,4
F Rt = ρF Rt−1 + (1 − ρ)F Rt∗ + vt ,
(a.2)
where all variables are defined as in Table 1. Parentheses below coefficients contain tvalues. The p-value reported is for the test of the null hypothesis that α π2 and α y2 are
zero. The sample period is from 1988:1 to 2000:4. We do not report the estimated serial
correlation coefficient, though the equations are estimated assuming the presence of serial
correlation.
the Congressional Budget Office and remains the same across these three inflation specifications. Panel A presents ordinary least squares estimates and
Panel B, instrumental variables estimates. For a comparison, Panel C reports
the Taylor rule estimated using actual future inflation and the final data on
the output gap. The estimates presented in Table 3 indicate three main observations. First, focusing on the Taylor rule with the Greenbook forecasts,
the hypothesis—the Greenspan Fed responded strongly to expected inflation
and relatively weakly to the output gap—is robust with respect to the use of
headline inflation forecasts and the instrumental variables procedure. The estimated inflation response coefficient is well above unity and the output gap
response coefficient is below unity for all three measures of inflation. The
instrumental variables estimates of key policy response coefficients yield conclusions that are qualitatively similar to those based on ordinary least squares
estimates (compare estimates across Panels A and B). These results suggest
that the bias in ordinary least squares estimates, introduced as a result of the
potential endogeneity of the Greenbook forecasts, may be very small.
Second, as expected, the fit of the estimated Taylor rule as measured by the
standard error of regression (SER) is somewhat worse if instrumental variables
are used. However, the Taylor rule estimated with the Greenbook forecasts
always has a lower standard error of regression than the Taylor rule estimated
using actual future inflation and the revised data on inflation and on the output
gap (compare the SERs across Panels A, B, and C).
Y. P. Mehra and B. D. Minton: Taylor Rule and the Greenspan Era
243
Table 3 Estimated Taylor Rules
Panel A: Greenbook Forecasts/Ordinary Least Squares
2
Sample Period
Inflation
α0
απ
αy
ρ
s
R
1988:1–2000:4
Core CPI
.35
(2.5)
.46
(3.3)
.45
(3.3)
.253
GDP
.69
(13.1)
.74
(14.4)
.66
(10.9)
.98
1988:1–2000:4
.64
(6.4)
.81
(5.5)
.66
(6.5)
.257
CPI
1.7
(8.8)
2.1
(6.4)
1.9
(8.5)
.98
1988:1–2000:4
0.12
(0.20)
-0.80
(0.70)
0.70
(1.20)
.98
.252
.98
.270
.98
.273
.97
.278
.97
.314
.98
.324
.96
.332
SER
Panel B: Greenbook Forecasts/Instrumental Variables
1988:1–2000:4
Core CPI
1988:1–2000:4
CPI
1988:1–2000:4
GDP
-0.20
(0.30)
-1.50
(1.20)
0.29
(0.40)
1.8
(9.3)
2.3
(6.0)
2.1
(9.0)
.62
(6.6)
.78
(5.5)
.64
(7.2)
.60
(6.9)
0.64
(7.8)
.51
(4.5)
.45
(3.2)
.60
(4.3)
.55
(4.1)
Panel C: Actual Future Inflation/Instrumental Variables
1988:1–2000:4
Core CPI
1988:1–2000:4
CPI
1988:1–2000:4
GDP
2.70
(1.30)
1.80
(1.00)
1.30
(0.80)
1.0
(1.5)
1.3
(2.2)
1.9
(2.9)
.85
(1.9)
.80
(2.0)
.67
(1.8)
.80
(5.6)
.78
(7.3)
.72
(4.3)
.60
(3.2)
.61
(3.4)
.63
(2.7)
Notes: Panels A, B, and C contain nonlinear estimates of policy coefficients from the
policy rule given below in (a). Panels A and B use the Greenbook inflation forecasts
and the CBO real-time estimates of the output gap. Panel C uses actual future inflation
and the final revised data on the output gap.
F Rt = ρF Rt−1 + (1 − ρ){α 0 + α π π c + α y (ln yt − ln yt∗ )} + vt .
t,4
(a)
The instruments used are three lagged values of the pertinent inflation variable: the federal funds rate, the output gap (real-time or final), the growth gap, and the spread between
nominal yields on ten-year Treasury bonds and the federal funds rate. See notes in Table 1.
Third, regarding core versus headline inflation, the results are mixed.
When the Greenbook forecasts are used, instrumental variables estimates favor
the core CPI, whereas ordinary least squares estimates favor the headline GDP
inflation (compare the SERs across Panels A and B in Table 3). However, as
reported in the next section, when we compare the relative accuracy of the
within-sample dynamic forecasts of the funds rate generated by these different
Taylor rules, the Taylor rule with core CPI inflation forecasts yields slightly
more accurate forecasts of the funds rate than the Taylor rule with headline
244
Federal Reserve Bank of Richmond Economic Quarterly
inflation forecasts, supporting the maintained hypothesis that the Greenspan
Fed was focused on core inflation.14
Predicting the Actual Path of the Federal Funds Rate
Using the Greenbook Inflation Forecasts and the
Real-Time Output Gap
In order to evaluate how well the forward-looking inertial Taylor rule estimated
here predicts actual policy actions, we focus on the policy rule estimated
using Greenbook core CPI inflation forecasts and the real-time CBO estimates
of the output gap from 1987:4 to 2000:4. For this exercise we focus on
ordinary least squares estimates. We carry out this evaluation in two alternative
ways. According to the inertial Taylor rule estimated here, expected inflation
(approximated by Greenbook inflation forecasts) and the output gap are two
major determinants of the federal funds rate target. In order to see how well
the actual funds rate is predicted by these two economic fundamentals, we
generate the within-sample dynamic predictions of the funds rate from 1987:4
to 2000:4, using the estimated policy rule shown in equation (6).
F Rt = ρ̂F Rt−1 + (1 − ρ̂){α̂ 0 + α̂ π GBπ ct,4 + α̂ y (ln yt − ln yt∗ )},
p
p
(6)
where F R p is the predicted funds rate and other variables are defined as before.
The key feature of the prediction equation (6) is that in generating the currentquarter predicted value of the funds rate, we use last quarter’s predicted, but
not actual value of the federal funds rate, in addition to using current-period
values of two other economic fundamentals.
Figure 3 charts the within-sample dynamic predictions of the funds rate.15
Actual values of the funds rate and the prediction errors are also charted. Two
observations need to be highlighted. First, the actual funds rate has generally
moved in the direction suggested by these two economic fundamentals (see
Panel A). Second, the estimated policy rule predicts very well the actual level
of the funds rate. The mean absolute error is .29 percentage points and the root
mean squared error is .40 percentage points. Despite this good fit, however,
there are few periods when the actual funds rate is far away from the value
prescribed by economic fundamentals. Significant deviations, at least twice
the root mean squared error, occur in 1988 and 1995 (see Panel B, Figure 3).
14 We did not consider the consumption expenditure deflator (PCE) in this comparison, because the Federal Reserve only recently started focusing on core PCE. In fact, the Greenbook
started producing forecasts of core PCE beginning in 2000, suggesting the Greenspan Fed was
focused on core CPI for most of the period covered.
15 The predictions begin in 1987:4. For generating the prediction for 1987:4, we use the
preceding quarter’s actual funds rate. For later periods, the predicted values are generated using
the preceding period’s predicted value and the current period estimates of expected inflation and
the output gap.
Y. P. Mehra and B. D. Minton: Taylor Rule and the Greenspan Era
245
Figure 3 Predicting the Actual Funds Rate
Panel A: Actual and Predicted Funds Rate (Dynamic Predictions, Core CPI)
10.0
Actual
Predicted
7.5
5.0
2.5
1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000
Panel B: Residual
1.00
0.75
0.50
0.25
0.00
-0.25
-0.50
-0.75
-1.00
-1.25
1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000
Figure 4 charts the static predictions of the federal funds rate, generated
using the same policy rule but feeding in last quarter’s actual value of the funds
rate as shown below in equation (7).
F Rt = ρ̂F Rt−1 + (1 − ρ̂){α̂ 0 + α̂ π GBπ ct,4 + α̂ y (ln yt − ln yt∗ )}.
p
(7)
In static forecasts the current-period forecast of the funds rate is determined,
in part, by the current-period value of the desired policy rate suggested by
economic fundamentals and, in part, by the one-period lagged value of the
actual funds rate. So, in the static exercise the current forecast is influenced, in
part, by actual policy actions, with the magnitude of the influence of policy on
the forecast being determined by the size of the partial adjustment coefficient
ρ̂. Hence, the actual funds rate is likely better predicted by static than dynamic
forecasts, because the latter are generated ignoring the recent history of actual
funds rate changes.
A visual check of actual values of the funds rate and its static predictions
charted in Figure 4 is consistent with the estimated policy rule. The mean
absolute error is now .20 percentage points and the root mean squared error is
246
Federal Reserve Bank of Richmond Economic Quarterly
Figure 4 Predicting the Actual Funds Rate
Panel A: Actual and Predicted Funds Rate (Static Predictions, Core CPI)
10.0
Actual
Predicted
7.5
5.0
2.5
1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000
Panel B: Residual
0.54
0.36
0.18
0.00
-0.18
-0.36
-0.54
-0.72
-0.90
1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000
.26 percentage points. Panel B charts the residuals. As shown, there are still
a few periods of significant deviations. We see deviations at least as large as
twice the root mean squared error occurring in 1988, 1989, 1995, and 1998:4.
Thus, Figures 3 and 4 suggest that the Taylor rule estimated using Greenbook
inflation forecasts and the real-time data on the output gap well predict actual
policy actions, with the caveat that few episodes remain when the actual funds
rate is significantly far from what is prescribed by this policy rule.
Using Actual Future Core Inflation and the Revised Output
Gap
It is worth pointing out that in the prediction exercise the Taylor rule estimated
using the Greenbook inflation forecasts and the real-time data on the output
gap predicts actual policy actions better than the Taylor rule estimated using
actual future inflation (core CPI) and the current vintage estimate of the output
gap. In particular, we re-estimate the Taylor rule over the period from 1988:1
to 2000:4 and generate the within-sample, static and dynamic predictions
of the funds rate, using the current vintage estimate of the output gap. For
static predictions, the mean absolute error and root mean squared error are
.30 and .37 percentage points, respectively. For dynamic predictions, the
Y. P. Mehra and B. D. Minton: Taylor Rule and the Greenspan Era
247
corresponding mean absolute error and the root mean squared errors are .72
and .84 percentage points. These prediction errors are substantially higher
than those generated using the Greenbook inflation core CPI forecasts and the
real-time output gap.
Core Versus Headline Inflation
The use of core inflation forecasts in the estimated Taylor rule produces slightly
more accurate forecasts of the funds rate than those based on the headline inflation. For dynamic predictions of the funds rate generated using alternatively
the Taylor rules based on core CPI, CPI, and GDP inflation forecasts, the mean
absolute errors are .29, .35, and .33 percentage points, respectively. The corresponding root mean squared errors are .40, .44, and .41 percentage points.
These summary statistics do favor core CPI, though the Taylor rule based on
GDP inflation forecasts is a serious contender.16,17
Policy Residuals: Role of Additional Factors in the
Estimated Taylor-Type Rule
As stated above, even though the use of Greenbook inflation forecasts and
real-time data on the output gap enables the estimated policy rule to predict
policy actions very well, there remain few periods when the actual funds rate
is significantly away from values prescribed by the rule, with significant deviations occurring in 1988, 1989, 1995, and 1998:4. Many analysts contend that
16 If the Taylor rules based on the Greenbook forecasts of three alternative measures of
inflation—core CPI, CPI, and GDP—are estimated with instrumental variables, then the root mean
squared errors generated by the dynamic prediction exercise are .46, .59, and .49 percentage points,
respectively.
17 It will be interesting to derive an estimate of the Greenspan Fed’s inflation target under
the additional assumption that the Fed’s estimate of the short-term real rate can be approximated
by the sample mean of the ex post real yield on three-month Treasury bills over a longer sample
period, the latter defined as the nominal yield minus the lagged value of the four-quarter-average
GDP inflation rate. By this metric, the short-term real rate is 1.9 percent if we use the sample
period 1961:1–2005:4, and 2.1 percent if we use only the Greenspan period 1987:1–2005:4. These
calculations suggest it is reasonable to assume that the Greenspan Fed’s estimate of the short-real
rate is approximately 2.0 percent. Given rr ∗ = 2.0 percent and given an estimate of the constant
term from the estimated Taylor rule based on the Greenbook forecasts of core CPI inflation, the
Greenspan Fed’s inflation target calculated using the relationship α̂ 0 = rr ∗ + (1 − α̂ π )π ∗ → .12 =
2.0 + (1 − 1.7)π ∗ is 2.7 percent. The result above—the Greenspan Fed’s inflation target is 2.7
percent—may at first appear at odds with the 2.0 percent value assumed in the original Taylor rule,
where inflation is measured by the behavior of GDP inflation. During the Greenspan era, GDP
inflation has exhibited a somewhat different trend behavior than the core CPI inflation measure.
Using the metric of comparing means, the sample mean of GDP inflation rates over 1987:1–
2005:4 is 2.4 percent, which is lower compared with the value 3.0 percent computed using core
CPI inflation over the same period. If we were to adjust the inflation targets for the presence
of different means, then the Greenspan Fed having an inflation target of 2.7 percent based on
the behavior of the core CPI inflation measure is equivalent to its having, instead, an inflation
target of 2.1 percent based on the GDP inflation measure. The latter value is close to 2.0 percent
assumed in the original Taylor rule.
248
Federal Reserve Bank of Richmond Economic Quarterly
significant deviations represent episodes when the Greenspan Fed responded
to a variety of macroeconomic developments that are not included in the simple policy rule (Blinder and Reis 2005, Rudebusch 2006). To illustrate this
point, consider the following narrative history of those developments.
The first episode occurs in 1988 and 1989. Following the stock market
crash of October 1987, the Greenspan Fed kept interest rates low as an insurance against the heightened risk of a recession, so that in 1988 the actual funds
rate is below what is prescribed by the Taylor-type rule. Inflation worries then
may have led the Greenspan Fed to tighten more in 1989, which suggests that
greater-than-policy-rule tightening in 1989 followed a somewhat looser policy of the previous year. Some support for this view emerges if we examine
the Greenbook inflation forecasts in the period leading to 1989. As shown
in Figure 2, for the period surrounding mid-to-late 1988 and early 1989, the
Greenbook inflation forecasts turned out to be too pessimistic.
The second episode occurs in 1995 when the actual funds rate is higher than
what is prescribed by the rule. The reasons for this greater-than-policy-rule
tightening are not very clear. Taylor (2005) notes this may reflect preemptive
policy tightening that began in 1994, whereas Rudebusch (2006) attributes it
to an inflation scare that occurred at the end of 1994 evidenced by a rapid
rise in long-term interest rates. Some limited support for the inflation scare
argument appears in Figure 2, which shows that beginning in 1994:3, the
Greebook inflation forecasts turned somewhat pessimistic about inflation.18
Finally, in 1998:4 the actual funds rate is below what is prescribed by
the policy rule. This is the period when the international financial system
was rocked by the Russian default and the demise of the Long-Term Capital
Management (LTCM), which led the Greenspan Fed to lower interest rates.
Together, these episodes suggest that the particular Taylor rule estimated in
this article may not be considered a complete description of policy actions
taken by the Greenspan Fed.
18 Another factor that explains the greater-than-policy tightening in 1995 and in 1996–1997, as
in some previous work that uses actual future inflation and the current vintage output gap measure,
is the remarkable increase in productivity and potential output. At the time, most economists did
not recognize these changes and, hence, may have overestimated the degree of utilization in product
and labor markets, which likely reflected in tighter policy. However, a visual check of Figures 1
and 2 suggests that productivity acceleration may not be relevant in explaining the greater-thanpolicy tightening in 1995. As shown in Figure 1, real-time estimates of the output gap indicate far
less slack in the economy than what is suggested by its 2006-vintage-only data in the subperiod
following the year 1995. Similarly, the Greenbook forecasts become significantly pessimistic only
in the years 1996–1997. Thus, these considerations suggest that while productivity acceleration
may be relevant in explaining the post-1995 greater-than-policy tightenings documented in some
previous work, its role in explaining the 1995 policy episode is in doubt.
Y. P. Mehra and B. D. Minton: Taylor Rule and the Greenspan Era
3.
249
CONCLUDING OBSERVATIONS
The main objective of this article is to investigate whether monetary policy
actions taken by the Greenspan Fed can be summarized by a Taylor rule.
Recent research highlights three aspects of the policy rule followed by the
Greenspan Fed; namely, the Greenspan Fed was forward looking, focused on
core inflation, and smoothed interest rates. The empirical work presented here
supports the above-noted general characterization of the policy rule followed
by the Greenspan Fed.
Using the Greenbook inflation forecasts and real-time Congressional Budget estimates of the output gap, this article reports evidence indicating that the
Greenspan Fed reacted strongly to expected inflation and relatively weakly
to the output gap. The evidence also indicates the Greenspan Fed smoothed
interest rates, though the degree of interest-rate smoothing exhibited is considerably less than what is documented in previous research. The hypothesis that
the Greenspan Fed was focused on core CPI inflation receives some support,
as the Taylor rule based on the Greenbook forecasts of core CPI inflation does
produce slightly more accurate forecasts of the funds rate than the Taylor rule
that uses the Greenbook forecasts of headline CPI or GDP inflation.
This article finds that a Taylor rule estimated using the Greenbook core
CPI inflation forecasts and real-time Congressional Budget estimates of the
output gap predicts very well the actual path of the federal funds rate from
1987 to 2000. The Taylor rule estimated alternatively with the Greenbook
GDP inflation forecasts seems to do as well. However, there are few periods
when the Greenspan Fed is off the estimated rule, arising perhaps as a result
of the Federal Reserve response to special macroeconomic developments not
captured by the simple rule.
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Blinder, Alan S., and Ricardo Reis. 2005. “Understanding the Greenspan
Standard.” Paper presented at the Federal Reserve Bank of Kansas City
Economic Symposium, “The Greenspan Era: Lessons for the Future.”
Jackson Hole, WY.
Boivin, Jean. 2006. “Has U.S. Monetary Policy Changed? Evidence from
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and Banking 38 (4): 1,149–173.
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Clarida, Richard, Jordi Galı́, and Mark Gertler. 2000. “Monetary Policy
Rules and Macroeconomic Stability: Evidence and Some Theory.”
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“Econometric Models and the Monetary Policy Process.”
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Rudebusch, Glenn D. 2002. “Term Structure Evidence on Interest Rate
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Taylor, John B. 1993. “Discretion Versus Policy Rules in Practice.”
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Economic Quarterly—Volume 93, Number 3—Summer 2007—Pages 251–286
Quantitative Models of
Sovereign Default and the
Threat of Financial
Exclusion
Juan Carlos Hatchondo, Leonardo Martinez, and Horacio Sapriza
B
usiness cycles in small emerging economies differ from those in developed economies. Emerging economies feature interest rates that are
higher, more volatile, and countercyclical (interest rates are usually
acyclical in developed economies). These economies also feature higher output volatility, higher volatility of consumption relative to income, and more
countercyclical net exports.1 Recent research is trying to develop a better
understanding of these facts, as has been done for U.S. business cycles.
Because of the high volatility and countercyclicality of the interest rate,
the (state-dependent) borrowing-interest rate menu is a key ingredient in any
model designed to explain the cyclical behavior of quantities and prices in
emerging economies. Some studies assume an exogenous interest rate.2 Others provide microfoundations for the interest rate based on the risk of default.3
This is the approach taken by recent quantitative models of sovereign default,
which are based on the framework proposed by Eaton and Gersovitz (1981).4
These articles build on the assumption that lenders can punish defaulting counThe authors would like to thank Kartik Athreya, Kevin Bryan, Huberto Ennis,
and Ned Prescott for helpful comments.
E-mails: JuanCarlos.Hatchondo@rich.frb.org;
Leonardo.Martinez@rich.frb.org; and hsapriza@andromeda.rutgers.edu. The views expressed in
this article do not necessarily reflect those of the Federal Reserve Bank of Richmond or the
Federal Reserve System.
1 See Aguiar and Gopinath (2007), Neumeyer and Perri (2005), and Uribe and Yue (2006).
2 See, for example, Aguiar and Gopinath (2007), Neumeyer and Perri (2005), Schmitt-Grohé
and Uribe (2003), and Uribe and Yue (2006).
3 Default episodes are not exceptional. Many nations have experienced episodes of sovereign
default, some of the latest being Russia in 1998, Ecuador in 1999, and Argentina in 2001.
4 See Aguiar and Gopinath (2006); Arellano (forthcoming); Arellano and Ramanarayanan
(2006); Bai and Zhang (2006); Cuadra and Sapriza (2006a, b); Lizarazo (2005a,b); and Yue (2005).
252
Federal Reserve Bank of Richmond Economic Quarterly
tries by excluding them from international financial markets. The assumption
is controversial on several grounds. First, it appears to be at odds with the
existence of competitive international capital markets (which is assumed in
these models). It is not obvious that competitive creditors would be able to
coordinate cutting off credit to a country after a default episode.5 Second,
empirical studies suggest that once other variables are used as controls, market access is not significantly influenced by previous default decisions (see,
for example, Gelos, Sahay, and Sandleris 2004, Eichengreen and Portes 2000,
and Meyersson 2006).6
1.
SUMMARY OF RESULTS
This article studies the role of the exclusion assumption for business cycle
properties of emerging economies. It first describes the business cycle properties of a sovereign default model with exclusion and compares them with
those of the same model without exclusion. The article finds that the presence
of exclusion punishment is responsible for a high fraction of the sovereign
debt that can be sustained in equilibrium. It also finds that the business cycle
statistics of the model are not significantly affected by the exclusion punishment. The model without exclusion generates annual debt-output ratios of
less than 2 percent. Whereas, the model with exclusion generates debt-output
ratios between 4.8 and 6.3 percent. On the other hand, the cyclical behavior
of consumption, output, interest rate, and net exports are not fundamentally
different in the models with and without exclusion. An additional limitation
shared by both model environments is that the volatility of the interest rate
and (to a lesser extent) of the trade balance are too low compared to the data.
This suggests that the exclusion assumption does not play an important role
in these dimensions, and therefore future studies that do not rely on the threat
of financial exclusion will not necessarily be handicapped in explaining the
business cycle in emerging economies.
5 This point is also raised by Cole, Dow, and English (1995) and Athreya and Janicki (2006).
6 Sturzenegger and Zettelmeyer (2005) discuss how holders of defaulted bonds succeeded in
interfering with cross-border payments to other creditors who had previously agreed to a debt
restructuring. From this, they infer that holders of defaulted bonds may have been able to exclude
defaulting economies from international capital markets. On the other hand, they conclude that
“legal tactics are updated all the time, and new ways are discovered both to extract payment
from a defaulting sovereign as well as to avoid attachments.” In particular, they expect that “the
threat of exclusion may be less relevant for some countries or to all countries in the future.” For
example, they explain that after Argentina defaulted in 2001, “attempts to actually attach assets
have so far turned out to be fruitless.” In any case, other forms of financing are always available to
defaulting economies (issuing bonds at home, aid, official credit, multilateral or bilateral financing,
etc.). The discussion in Sturzenegger and Zettelmeyer (2005) suggests, therefore, that defaulting
economies might face at most a higher borrowing cost, though it is not clear how important this
cost differential may be.
J. C. Hatchondo, L. Martinez, and H. Sapriza: Quantitative Models
253
The model studied in this article builds on the framework studied in Aguiar
and Gopinath (2006), which in turn, quantifies the model presented by Eaton
and Gersovitz (1981). The most appealing feature about this setup is that it
reduces the default decision to a simple tradeoff between current and future
consumption without a major departure from the workhorse model used for
real business cycle analysis in the last decades. Recent quantitative studies on
sovereign default have shown that this environment can potentially account
for important business cycle features in emerging economies and that it can
be extended to address other issues (such as the optimal maturity structure
of sovereign debt).7 The framework studied in Aguiar and Gopinath (2006)
is the simplest among the ones presented in recent studies. This has the
advantage of making the discussion of the role of the exclusion assumption
more transparent.8 On the other hand, this has the disadvantage of hurting the
performance of the model along several dimensions. Where appropriate, the
article explains how the simplifying assumptions hurt the performance of the
model.
This article studies a small open economy endowed with a single tradable good. As in Aguiar and Gopinath (2006), two endowment processes
are considered: a process with shocks to the endowment level and a process
with shocks to the endowment growth rate. The objective of the government
is to maximize the present value of future utility flows of the representative
agent. The government has only one financial instrument available: it can
save or borrow using one-period bonds. These assets are priced in a competitive market inhabited by a large number of identical, infinitely lived, risk
neutral-lenders. Lenders have perfect information regarding the economy’s
endowment. The government makes two decisions in every period. First, it
decides whether to refuse to pay previously issued debt. Second, it decides
how much to borrow or save. The baseline model features two costs of defaulting. First, the country may be excluded from capital markets. Second, it
faces an “output loss.” The endowment is reduced in a fixed percentage in the
period following a default. The assumption that countries experience an output loss after a default intends to capture the disruptions in economic activity
entailed by a default decision. IMF (2002), Kumhof (2004), and Kumhof and
Tanner (2005) discuss how financial crises that lead to severe recessions are
triggered by sovereign default.
7 Arellano (forthcoming); Arellano and Ramanarayanan (2006); Bai and Zhang (2006); Cuadra
and Sapriza (2006a,b); Lizarazo (2005a,b); and Yue (2005) extend the framework in Aguiar and
Gopinath (2006) but maintain the basic assumptions (including the exclusion assumption).
8 The only difference between the model presented in this article and the model in Aguiar
and Gopinath (2006) is that here it is assumed that there is a unique period of output loss after default—in contrast with the stochastic number of periods of output loss assumed by Aguiar
and Gopinath (2006). This allows us to eliminate the threat of exclusion without increasing the
dimensionality of the state space. The Appendix shows that this departure does not have sizable
effects on the results.
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This article solves the model with and without the exclusion threat and
compares their behavior. Mechanically, in the model with shocks to the endowment level, the default decision becomes relatively more sensitive to the
endowment shock once the exclusion threat is eliminated and, therefore, less
sensitive to the debt level. In turn, bond prices become less sensitive to the borrowing level. On the other hand, in the model with shocks to the growth rate
the default decision becomes relatively less sensitive to the endowment shock,
which increases the sensitivity of the bond price to the borrowing level. Given
that in this class of models the high sensitivity of the default probability to
the borrowing level limits their quantitative performance, the previous effects
slightly improve the performance of the model with shocks to the endowment
level and deteriorate the performance of the model with shocks to the growth
rate. In spite of this, both models still do not replicate the default rates, the
volatility of the trade balance, nor the volatility of the spread observed in the
data.
The rest of the article proceeds as follows. Section 2 introduces the model.
Section 3 presents the parameterization. Section 4 discusses the case in which
the economy can be excluded from capital markets. Section 5 studies how
the implications of the model change when the economy cannot be threatened
with financial exclusion. Section 6 concludes the article.
2. THE MODEL
The environment studied in this article builds on the framework presented
by Aguiar and Gopinath (2006), who study the quantitative performance of
a model of sovereign default based on Eaton and Gersovitz (1981). Relative
to Aguiar and Gopinath (2006), the only difference is that it is assumed here
that there is a single period of output loss after default—in contrast with the
stochastic number of periods of output loss assumed in their article. The
Appendix shows that the results are not sensitive to this assumption.
The economy receives a stochastic endowment stream of a single tradable
good. The endowment process has two components: a transitory shock and a
trend shock, namely,
yt = ezt t ,
(1)
where yt denotes the endowment realization in period t, zt denotes the transitory shock, and t denotes the trend component.
The transitory shock zt follows
an AR(1) process with long-run mean μz ,
and autocorrelation coefficient ρ z < 1, that is,
2
zt = 1 − ρ z μz + ρ z zt−1 + ε zt ,
where zt ∼ N 0, σ z .
(2)
J. C. Hatchondo, L. Martinez, and H. Sapriza: Quantitative Models
255
The trend component evolves according to
t = gt t−1 ,
(3)
where
ln (gt ) = 1 − ρ g ln μg − m + ρ g ln (gt−1 ) + ε t ,
(4)
2
σ
|ρ g | < 1, εt ∼ N 0, σ 2g , and μg = 21 1−ρg 2 .9
g
The objective of the government is to maximize the present value of future utility flows of the representative agent. The representative agent has
preferences that display a constant coefficient of relative risk aversion:
c(1−σ ) − 1
,
1−σ
where σ denotes the coefficient of relative risk aversion. Let β denote the discount factor.
To ensure a well-defined problem it is assumed that
u (c) =
E lim β t (yt )(1−σ ) = 0.
t→∞
The government makes two decisions in each period. First, it decides
whether to refuse to pay previously issued debt. Second, it decides how much
to borrow or save. As in previous quantitative studies, it is assumed that the
government faces two penalties if it decides to default. One penalty is that it
may be excluded from capital markets. The second penalty is that it faces an
exogenous “output loss” of λ percent in the period following a default.
The exclusion state evolves as follows. In the default period, the economy
is excluded from capital markets with probability 1 − φ 1 , with φ 1 ∈ [0, 1]. In
every period that follows a period of exclusion, the economy regains access
to capital markets with probability φ ∈ [0, 1] or remains excluded for one
more period with probability 1 − φ.10 This implies that the expected length of
1
exclusion is given by 1−φ
. If the economy was not excluded from financial
φ
markets at the end of the previous period, it is not excluded at the beginning
of the current period.
The government can choose to save or borrow using one-period bonds.
There is a continuum of risk-neutral lenders with “deep pockets.” Each lender
can borrow or lend at the risk-free rate r. Lenders have perfect information
9 The endowment process is motivated by the work of Aguiar and Gopinath (2007). They
find that shocks to trend growth (rather than transitory fluctuations around a stable trend) are the
primary source of fluctuations in emerging markets.
10 Previous quantitative studies of sovereign default assume that the government cannot borrow in the period it defaults (φ 1 = 0), and it regains access to capital markets with a constant
probability (φ) after that. In order to accommodate this possibility, it is assumed that φ 1 can be
different from φ.
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Federal Reserve Bank of Richmond Economic Quarterly
regarding the economy’s endowment. The bond price is determined as follows.
First, the government announces how many bonds it wants to issue. Then,
lenders offer a price for these bonds. Finally, the government sells the bonds
to one of the lenders who offered the highest price.
Let b denote the current position in bonds. A negative value of b denotes
that the government was an issuer of bonds in the previous
period.
Each bond
delivers one unit of good next period for a price of qd b , z, , g this period.
The price depends on the current default decision, d. This is due to the fact that
a current default decreases future output and affects future default decisions.
The government compares two continuation values in order to decide
whether to default or pay back the previously issued debt. The present discounted utility after a default is represented by V1 (z, , g, h). The variable h
denotes the credit history of the government. It takes a value of 1 when the government defaulted in the previous period, and it takes a value of 0 when the government did not default in the previous period. The present discounted utility
when all previously issued debt is paid back is represented by V0 (b, z, , g, h).
The government defaults if the continuation value V1 (z, , g, h) is larger than
V0 (b, z, , g, h) and does not default otherwise.
Let x denote the exclusion state. The variable x takes a value of 1 when the
economy is excluded, and takes a value of 0 otherwise. Let V (b, z, , g, h, x)
denote the government’s value function at the beginning of a period.
In the period it defaults, the economy can or cannot be excluded from
financial markets. Let Ṽ1 (z, , g, h, 0) denote the continuation value when
the economy defaulted and is not excluded. Let Ṽ1 (z, , g, h, 1) denote the
continuation value when it is excluded. Thus,
V1 (z, , g, h) = φ 1 Ṽ1 (z, , g, h, 0) + (1 − φ 1 ) Ṽ1 (z, , g, h, 1) .
(5)
The timing of the decisions within a period is summarized in Figure 1. At
the beginning of the period the endowment shocks are realized. The realization
in period t of a state variable x is denoted by xt . After observing the endowment
realization, the government decides whether to pay back previously issued
debt. If it decides to pay the debt back, the government
ND issues an amount
ND
bt+1
of bonds and faces a continuation value of V0 bt+1
, zt , t , gt , 0 . If
the government defaults, it may or may not be excluded from capital markets
today. If it is not excluded, it faces a continuation value of Ṽ1 (zt , t , gt , 1, 0, ).
If it is excluded, it faces a continuation value of Ṽ1 (zt , t , gt , 1, 1, ). If the
government defaults and is not excluded today from capital markets, it issues
D
an amount bt+1
of bonds. After a default, the government faces an output loss
of λ percent in period t + 1 regardless of whether it was excluded from capital
markets in period t.
The value function of a defaulting economy that is excluded in the default
period is computed as follows:
Ṽ1 (z, , g, h, 1) = u (y (1 − hλ)) + βE V (0, z , g , g , 1, e) ,
(6)
J. C. Hatchondo, L. Martinez, and H. Sapriza: Quantitative Models
257
Figure 1 Order of Events and Alternative Continuation Values in
Period t
V0 (b tND
+1 ,zt , t , gt , 0)
Issue b tND
+1
Pay back b t
t +1
~
V1 (zt , t , gt , 1, 0)
Issue b tD+1
Not excluded
t
Endowment shocks
are realized
t +1
Default on bt
Excluded
t +1
Cannot issue: b t +1 =0
~
V1 (zt , t ,gt ,1 , 1)
Output loss
of %
where
φV (0, z , g , g , 1, 0)+
(1–φ) V (0, z , g , g , 1, 1)
E V (0,z ,g ,g ,1,e) =
Fz dz | z Fg dg | g .
If the government has decided to default and is excluded in the period of
default, it consumes the aggregate endowment (there are no financial transfers
from or to the rest of the world) and carries zero debt to the next period. At
the beginning of the following period, exclusion finishes with probability φ .
The expected continuation value of this scenario is V (0, z, g, g, 1, 0). If the
exclusion time is extended, the expected continuation value
is V (0, z, g, g, 1, 1).
The dynamic programming problem for a defaulting economy that is not
excluded in the default period is
Ṽ1 (z, , g, h, 0) = max
b
u y (1 − hλ) − q1 b , z, , g b +
βE V (b , z , g , g , 1, 0)
where
E V (b , z , g , g , 1, 0) =
V (b , z , g , g , 1, 0)Fz dz | z Fg dg | g .
(7)
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Federal Reserve Bank of Richmond Economic Quarterly
In this case, the government must choose how much debt it will issue.
The value function of the government when it has decided to pay back its
debt is obtained from the following Bellman equation:
V0 (b, z, , g, h) = max
b
u y (1 − hλ)
q0 b , z, , g b +
+ b −
,
βE V (b , z , g , g , 0, 0)
(8)
where
V (b , z , g , g , 0, 0)Fz dz | z Fg dg | g .
E V (b , z , g , g , 0, 0) =
The function V (b, z, , g, h, x) is computed as follows:
V (b, z, , g, h, 0) = max{V1 (z, , g, h) , V0 (b, z, , g, h)},
and
(9)
V (b, z, , g, h, 1) = u (y (1 − hλ)) + βE φV (0, z , g , g , 0, e) ,
where
φV (0, z , g , g , 0, 0)+
(1–φ) V (0, z , g , g , 0, 1)
E V (0,z ,g ,g , 0,e) =
Let
d (b, z, , g, h) =
Fz dz | z Fg dg | g .
1 if V1 (z, , g, h) > V0 (b, z, , g, h)
0 if V1 (z, , g, h) ≤ V0 (b, z, , g, h)
(10)
denote the equilibrium default decision.
The price of a bond if a default decision d was made in the current period
satisfies the lenders’ zero profit condition. It is given by
qd b , z, , g =
1
1 − E d | b , z, , g, d ,
1+r
(11)
where
E d | b , z, , g, d =
d b , z , g , g , d Fz dz | z Fg dg | g
denotes the probability that the government decides to default if it purchases
b bonds, and the current default decision is d .
Equilibrium Concept
Definition 1 A recursive competitive equilibrium is characterized by
1. a set of value functions V (b, z, , g, h, x), V1 (z, , g, h),
and V0 (b, z, , g, h);
J. C. Hatchondo, L. Martinez, and H. Sapriza: Quantitative Models
259
2. a set of policies for asset holdings b0 (b, z, , g, h) and b1 (b, z, , g, h),
and a default decision d (b, z, , g, h); and
3. a bond price function qd b , z, , g ,
such that
(a) V (b, z, , g, h, x), V1 (z, , g, h), and V0 (b, z, , g, h) satisfy the system of functional equations (5)–(9);
(b) the default policy d (b, z, , g, h) and the policies for asset holdings
b0 (b, z, , g, h) and b1 (b, z, , g, h) solve the dynamic programming problem
specified by equations (5)–(9); and
(c) the bond price function qd b , z, , g, h is given by equation (11).
Discussion of the Environment
The model analyzed in this article relies on several simplifying assumptions.
This has the advantage that the model remains tractable and that the main
mechanisms can be presented in a more transparent way. The disadvantage
of using such a stylized framework is that the model is ill-suited to account
for the quantitative behavior of some key variables.11 The rest of this section
discusses several simplifications embedded in the environment presented in
the previous section and extensions that have been studied in the literature.
Focusing on an endowment economy simplifies the analysis. A more comprehensive study of the business cycle would require incorporating capital and
labor into the model. Aguiar and Gopinath (2006) also consider an extension
of the basic model with labor as the only input in the production function.
The results do not change significantly. More recently, Bai and Zhang (2006)
study a production economy with capital.
The model assumes that the government issues one-period bonds. Allowing the government to issue long-term bonds would introduce nontrivial
complications to the analysis. For instance, if the government can issue twoperiod bonds, it is necessary to keep track of how much debt was issued two
periods ago (which is due today) and how much debt was issued one period ago
(which will be due tomorrow). Alternatively, if the government only issues
annuities there would only be one state: how many annuities have been issued
since the last default. However, the pricing of the annuities issued today would
be more complex than the price of a one-period bond. Lenders would not only
need to compute the probability of a default in the following period, but also
the probability of a default two-periods ahead, conditional on not observing a
default tomorrow; the probability of observing a default three-periods ahead;
11 Other authors have studied different extensions of this framework, which have improved its
quantitative performance. See, for example, Arellano (forthcoming); Arellano and Ramanarayanan
(2006); Bai and Zhang (2006); Cuadra and Sapriza (2006a, b); Lizarazo (2005a, b); and Yue (2005).
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Federal Reserve Bank of Richmond Economic Quarterly
conditional on not observing a default in the next two periods; and so on.
Arellano and Ramanarayanan (2006) allow the government to issue short and
long bonds.
It was assumed that the government cannot issue bonds contingent on the
future realization of its endowment. Even if creditors have perfect information
regarding the economy’s endowment, this would not imply that contracts contingent on the endowment realization could be written (the endowment may
not be verifiable). In reality, one limitation for writing contracts contingent
on real variables is that the government could manipulate the measurement
of these variables (see Borensztein and Mauro 2004). Determining to what
extent bonds can be state contingent in reality and studying some degree of
state contingency in quantitative models of sovereign default are interesting
avenues for future research.
The assumption that countries experience an exogenous output loss after
defaulting intends to capture the disruptions in economic activity entailed by
a default decision. In general, default episodes are not observed in economic
booms but in recessions. This means that a fraction of the low economic
activity that is observed after a default episode can be explained by weak fundamentals pre-existing the default decision. Thus, not all of the decrease in
economic activity observed after a default is related to the default decision
and cannot be considered as a cost of defaulting. On the other hand, default
decisions are likely to introduce disruptions in economic activity of the defaulting economy. IMF (2002), Kumhof (2004), and Kumhof and Tanner (2005)
discuss how financial crises that lead to severe recessions are triggered by
sovereign default. This is due to the fact that government debt is not only held
by foreigners but also by locals, and in particular by local banks—something
that is not explicitly considered in the stylized model studied in this article.
Thus, government default may hurt financial intermediation significantly (see
IMF 2002 for a discussion of recent episodes).12
In the model, the output loss triggered by the default decision is independent of the size of the default. If the output loss represents the damage made
by the default decision through the local financial system, it could be argued
that the loss should depend (positively) on the amount that is not repaid by the
government (in particular, it should depend on the amount held by the locals;
see, for example, IMF 2002). Considering this would introduce additional
complications to the analysis though it is an interesting avenue to be pursued
12 In the stylized model discussed in this article, the output loss of λ percent in the period
after a default intends to capture the cost of defaulting implied by the disruptions in economic
activity triggered by the declaration of default. The calibration of the parameter λ should capture
these disruptions and does not intend to match the overall decrease in output observed after a
default. In contrast to the exclusion from capital markets, the output loss does not intend to
capture a punishment imposed by creditors. Eaton and Gersovitz (1981) discuss output loss as the
result of punishments.
J. C. Hatchondo, L. Martinez, and H. Sapriza: Quantitative Models
261
in future work. If the output loss depends on the amount not paid by the
government, it can be argued that the government should also be allowed to
choose the size of the default.13 Arellano (forthcoming) argues that the output
loss depends on the state of the economy and, thus, introduces this into the
model.
Previous quantitative studies assume that after default, the economy suffers the output loss for a stochastic number of periods (the periods in which the
economy is excluded from capital markets). For simplicity, this assumption
is modified in this article. Assuming that the output loss lasts for a stochastic
number of periods in a context in which there is no financial exclusion raises
the possibility of scenarios in which the government defaults before the duration of output losses triggered by the previous default has ended. This would
require keeping track of the number of output losses the economy is suffering
and would increase the dimensionality of the state space. The Appendix shows
that the results are not sensitive to the modification of the output loss process
utilized in this article.
The assumption that countries are excluded from capital markets after a
default episode is motivated by evidence of a drainage in capital flows into
countries that defaulted (see, for example, Gelos, Sahay, and Sandleris 2004).
However, it very well may be that the difficulties in market access observed
after a default episode respond to the same factors that triggered the default
decision itself.14 In support of this, Gelos, Sahay, and Sandleris (2004) document that once other variables are used as controls, market access is not
significantly influenced by previous defaults (see also Eichengreen and Portes
2000 and Meyersson 2006). Moreover, it is not obvious that after a default
episode competitive creditors would be able to coordinate cutting off credit to
defaulting countries. Thus, the study of an environment in which a defaulting
economy cannot be excluded from capital markets is the first building block
of any work that attempts to explain the exclusion outcome as an endogenous
outcome of the model.
13 In this article, the government must decide whether it honors all the debt issued in the
previous period or whether it defaults on all of it. But this is not a restrictive assumption given
that the costs of defaulting are orthogonal to the amount of debt that is repudiated. In this case,
the government would never find it optimal to default on less than a 100 percent of the outstanding
debt. This would not be the case if the cost of defaulting depends on the amount repudiated. Yue
(2005) studies partial default in an environment in which the defaulted amount is decided in a
bargaining process between the government and the lenders.
14 For example, Hatchondo, Martinez, and Sapriza (2006b) analyze a model in which both
default and the difficulties in market access after default may be triggered by a change in the
policymaker in power.
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Federal Reserve Bank of Richmond Economic Quarterly
Table 1 Parameter Values Specific to Models I and II
Model I
−
0%
0.90
3.4%
ρg
σg
ρz
σz
Model II
0.17
3%
−
0%
Notes: A period in the model corresponds to a quarter.
3.
PARAMETERIZATION
The model is solved numerically using value function iteration and interpolation as in Hatchondo, Martinez, and Sapriza (2006a).15 Whenever possible,
this article considers the same parameter values as in Aguiar and Gopinath
(2006), which facilitates the comparison of the results. To solve the model
numerically, Bellman equations are first recast in detrended form. All variables are normalized by μg t−1 as in Aguiar and Gopinath (2006). This
normalization implies that the mean of the detrended endowment is one.
Even thoughAguiar and Gopinath (2007) argue that the best representation
of the output process for emerging economies is characterized by equations
(1) through (4), this specification requires keeping track of z and g as state
variables. The computational method used in previous articles in the literature
does not allow solving for this specification without incurring sizable approximation errors. Instead, they consider two alternative endowment processes.
In Model I, the economy is hit only with transitory shocks (z shocks). In
Model II, the economy is hit with shocks to the trend only (g shocks). Table
1 reports the parameter values specific to each of the two model alternatives.
Parameters values that are common across models are presented in Table
2. Aguiar and Gopinath (2006) assume an output loss of 2 percent during
the exclusion period. This is based on empirical estimates of the output loss
triggered by a default decision (see Chuhan and Sturzenegger 2005). As
explained above, for simplicity this article assumes that all output loss occurs
only in one period, the period that follows the decision. The value of λ is
calibrated to make the output-loss cost of defaulting in this article equivalent
to the one in Aguiar and Gopinath (2006). In particular, the value of λ is
chosen to be such that for Model I, the mean debt level in the simulations is
the same as the one in the original formulation of Aguiar and Gopinath (2006).
We show that this value (of λ) enables Model II to generate a similar level of
debt as in Aguiar and Gopinath (2006).
15 The value functions V and V are approximated using Chebychev polynomials.
0
1
Fifteen
polynomials on the asset space and ten on the endowment shock are used. Results are robust to
using more polynomials.
J. C. Hatchondo, L. Martinez, and H. Sapriza: Quantitative Models
263
Table 2 Parameter Values Common to Models I and II
Risk Aversion
International Interest Rate
Probability of Redemption in the Same Period of Default
Probability of Redemption
Mean Growth Rate
Mean (log) Transitory Productivity
Discount Factor
Loss of Output
σ
r
φ1
φ
μg
μz
β
λ
2
1%
0%
10%
1.006
−0.5σ 2z
0.8
8.3%
Notes: A period in the model corresponds to a quarter.
Except for the value of λ, the remaining parameters take the same values as
in Aguiar and Gopinath (2006). The coefficient of relative risk aversion of 2 is
within the range of accepted values. The probability of redemption implies an
average autarky duration of 2.5 years (in the model, a period refers to a quarter),
similar to the value estimated by Gelos, Sahay, and Sandleris (2004)—Section
5 presents the results when creditors cannot exclude a defaulting economy. The
process of output is calibrated to match the process for Argentina from 1983 to
2000. The subjective discount factor is set to 0.8. This departs from standard
macro models. As in Aguiar and Gopinath (2006), in the stylized framework
discussed in this article, a low discount factor is needed to induce the economy
to accumulate debt and be willing to accept a higher spread over the risk-free
interest rate (the international interest rate). The limitations faced by the
stylized framework to generate default with more reasonable discount factors
may be a consequence of its simplifying assumptions.16 As was mentioned
previously, recent articles study different extensions of this framework that
improve its quantitative performance (assuming that lenders can use financial
exclusion as a punishment).
4.
RESULTS WITH EXCLUSION
This section presents the results obtained when the parameters that determine
the exclusion process are chosen as in Aguiar and Gopinath (2006), that is,
φ 1 = 0 and φ = 0.1. This means that the government cannot issue bonds in the
period it defaults, and after that it faces a constant probability φ of regaining
access to capital markets.
16 For example, the end of Section 4 describes how the assumption that the government
can only issue one-period bonds increases the marginal issuance cost. If it were not for the low
discount factor, the issuance volume and spreads observed in equilibrium would be even lower
than what is observed in the data.
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Federal Reserve Bank of Richmond Economic Quarterly
Figure 2 Default Regions
0.20
0.15
0.10
z
0.05
0.00
-0.05
-0.10
-0.15
-0.20
-0.30
-0.28
-0.26
-0.24
-0.22
-0.20
b
1.08
1.06
1.04
g
1.02
1.00
0.98
0.96
0.94
0.92
-0.25
-0.20
-0.15
b
Notes: Default region when the endowment is hit with transitory shocks (top panel) and
growth trend shocks (bottom panel).
J. C. Hatchondo, L. Martinez, and H. Sapriza: Quantitative Models
265
Equilibrium Default Region and Bond Prices with
Exclusion
The shaded areas in Figure 2 display the default regions (i.e., the combinations
of endowment shocks and debt levels for which the economy would choose to
default) of the model with transitory and trend shocks.17 Both graphs show that
the higher the endowment shock, the higher the minimum debt level at which
it is optimal to declare a default. From another perspective, for a given initial
debt level, the government finds it optimal to default only if the endowment
shock is sufficiently low.
The benefit of defaulting is that resources that would have been allocated
to pay back previously issued bonds are, instead, allocated to current consumption. There are two costs entailed by a default decision: a loss in output
and the inability of the government to use international capital markets to
smooth out domestic endowment shocks. It should be noticed that the “costs”
of defaulting do not depend on the debt level at the time of default. Thus, a
higher initial debt level increases the benefits of a default without increasing
the costs. For sufficiently large debt levels, the benefits of defaulting offset the
“fixed” costs. This explains why in Figure 2 it is optimal for the government
to default on relatively large values of debt (low b).
A low endowment shock implies that there are less resources available in
the current and subsequent periods.18 Given that the output loss that follows
a default decision is a constant fraction of the underlying potential output,
it is more costly to default for high endowment realizations than for low
endowment realizations. In the model with transitory shocks, this is the main
force behind the negative relationship between the shock to the endowment and
the debt threshold at which the government is indifferent between defaulting
and not defaulting.19 However, in the model with trend shocks, a high shock
today signals higher growth rates in the future. This increases the desire to
borrow as it allows bringing future resources to the current period. The fact
that the ability to borrow is more valuable in good than in bad times helps
explain why the government defaults only on larger debt volumes in good
times.
Figure 3 shows the equilibrium bond prices faced by the government as
a function of the current issuance level (−b) and the endowment shock. The
17 The detrended output process has a mean of 1. This implies that the debt levels b in
Figure 2 correspond to the ratio of debt-to-mean output.
18 Both the trend shocks and the transitory shocks display positive autocorrelation.
19 If the endowment is low, the marginal utility of consumption is high, and therefore the
gain from defaulting is high. However, if the model with transitory shocks is solved assuming that
the output loss is a fixed amount instead of a percentage of output, the default region becomes
almost vertical but with a positive slope. This is due to the fact that with a high endowment
shock the economy displays a less intense desire to issue debt, and therefore it assigns a lower
value to retaining access to capital markets.
266
Federal Reserve Bank of Richmond Economic Quarterly
Figure 3 Bond Price Menus
1.0
0.9
z = -0.23458
z = 0.23343
0.8
0.7
q
0.6
0.5
0.4
0.3
0.2
0.1
0.0
-0.30
-0.29
-0.28
-0.27
-0.26
-0.25
-0.24
-0.23
-0.22
-0.19
-0.18
-0.17
b
1.0
0.9
g = 0.91467
g = 1.0973
0.8
0.7
q
0.6
0.5
0.4
0.3
0.2
0.1
0.0
-0.25
-0.24
-0.23
-0.22
-0.21
-0.20
b
Notes: Equilibrium bond price menu faced by the government at low and high endowment realizations. The low endowment realization is three standard deviations to the left
of the unconditional mean. The high endowment realization is three standard deviations
to the right of the unconditional mean. The top panel shows the equilibrium bond price
in the model with shocks to the level. The bottom panel shows the equilibrium bond
price in the model with shocks to the trend.
J. C. Hatchondo, L. Martinez, and H. Sapriza: Quantitative Models
267
curves have a waterfall shape. For relatively low issuance levels there is no
risk of default. In this case, competitive investors demand the risk-free rate in
compensation for purchasing the government’s bonds. For issuance volumes
for which there is a positive probability of default tomorrow, the rate of return
demanded for holding bonds is higher than the risk-free rate, i.e., the price
1
offered is lower than 1+r
. Finally, for sufficiently high issuance volumes, it
is common knowledge that the government would default in the following
period for almost any endowment realization. In this case, investors offer a
zero price for each bond issued today.
It should be noted that price q is nondecreasing in the current endowment
realization. In other words, the higher the endowment, the higher the issuance
level at which the price starts to fall. This is due to the persistence in the
endowment process and the shape of the default regions. A higher endowment
today implies that it is more likely to observe high endowments in the following
period, and therefore it makes the default probability lower.
Business Cycle Properties With the Exclusion
Punishment
The model is simulated for 750,000 periods (500 samples of 1,500 observations
each). In order to compute business cycle statistics, 400 samples of the last
72 periods before a default episode are used. The samples selected are such
that the last exclusion period was observed at least two periods before the first
period in the sample. The number of periods in each sample is equal to the
number of periods in the data compared with the simulations (Argentina 1983–
2000). Restricting to samples at least two periods away from the last exclusion
period helps avoid extreme observations that may distort the results.20 The
moments reported below correspond to the average across the 400 samples.
The behavior of four series is analyzed: the logarithm of income (y ), the
logarithm of consumption (c), the ratio of the trade balance to output (tb), and
the annualized spread (Rs ). All series are filtered using the Hodrick-Prescott
filter with a smoothing parameter of 1600. Standard deviations are denoted
by σ and are reported in percentage terms; correlations are denoted by ρ .
Table 3 reports business cycle moments observed in the data (Argentina
1983–2000) and in Models I and II. With the exception of the debt-to-output
20 In the periods that follow an exclusion period, the government inherits little or no debt
from previous periods. The consequence is that in these periods the government borrows a relatively
low amount, and thus it pays relatively low spreads compared to what is observed in the remaining
observations. In the simulations, these outliers may appear up to two periods after the end of an
exclusion period. It is judged that it is more appropriate to present results computed without
considering these outliers. Simulation results are contrasted against data from Argentina during a
period in which the economy was not excluded from capital markets. Moreover, these outliers can
alter the calculations of business cycle statistics (see Hatchondo, Martinez, and Sapriza 2006a).
268
Federal Reserve Bank of Richmond Economic Quarterly
Table 3 Business Cycle Statistics
Data
σ (y)
σ (c)
σ (tb)
σ (Rs )
ρ (c, y)
ρ (tb, y)
ρ (Rs , y)
ρ (Rs , tb)
Mean Debt Output Ratio (%)
Rate of Default
4.08
4.85
1.36
3.17
0.96
-0.89
-0.59
0.68
Model I
Transitory Shocks
4.14
4.23
0.20
0.006
0.99
-0.43
-0.80
0.85
Model II
Trend Shocks
4.15
4.38
0.63
0.013
0.99
-0.29
-0.06
0.89
51
75
6.3
6.6
4.8
24
Notes: The moments correspond to the average across 400 samples. The debt output
ratio is measured as the stock of debt divided by the annual output level.
ratio, the business cycle moments for Argentina are taken from Aguiar and
Gopinath (2006). The moments are chosen so as to evaluate the ability of
the models to replicate the distinctive business cycle properties of emerging
economies that were described in the beginning of the article. It must be said
that the sample moments for Argentina display the same qualitative features
observed in other emerging markets.21
The moments in the simulated samples generated by Models I and II are
different from the moments reported inAguiar and Gopinath (2006). The main
reason is that they use a different computational method from the one used
in this article. While, Aguiar and Gopinath (2006) use a discrete state space
method, we use interpolation methods and a nonlinear optimization routine to
find the optimal issuance levels. Hatchondo, Martinez, and Sapriza (2006a)
demonstrate that the numerical errors incurred by the discrete state space
technique may lead to misleading conclusions in some dimensions. The most
important one is that the spread volatility becomes negligible once the model
is solved using a more accurate method. Other statistics about the behavior
of the spread over the business cycle are also susceptible to numerical errors
when the model is solved using a discrete state space technique.22
21 As previously mentioned, emerging economies feature interest rates that are high, volatile,
and countercyclical; high volatility of consumption relative to income (typically, higher than one);
and countercyclical net exports (see, for example, Aguiar and Gopinath 2007; Neumeyer and Perri
2005; and Uribe and Yue 2006).
22 A second reason behind the discrepancy between the moments in Table 3 and in Aguiar
and Gopinath (2006) is that the setups are not exactly the same. In their model, the output loss
lasts as long as the exclusion punishment. In the present setup, the output loss lasts for only
one period. The Appendix shows that this difference accounts for only a small fraction of the
discrepancy in the performance of the two models.
J. C. Hatchondo, L. Martinez, and H. Sapriza: Quantitative Models
269
Figure 4 The Effect of the Bond Price Menu on the Objective Function
1.0
-4.8
0.8
-4.9
0.6
-5.0
0.4
-5.1
0.2
-5.2
0.0
-0.270
-0.265
-0.260
-0.255
-0.250
-0.245
Objective Function
Bond Price
Bond Price
Objective Function
-5.3
-0.240
b
Notes: Objective function and price function faced by the government when z = μz and
b = −0.25 (which is within the range observed in the simulations). The vertical line
represents the optimal issuance level.
The table shows that both models fail to generate the volatilities of the trade
balance and spread observed in the data. In particular, the standard deviations
of the spread are two orders of magnitude lower than the value observed in the
data. This is an important limitation of both models. Moreover, Models I and
II generate 6.6 and 24 defaults in 10,000 periods, respectively. These values
are below the ratio of 75 defaults in 10,000 periods computed by Reinhart,
Rogoff, and Savastano (2003) using a sample of emerging markets from 1824
to 1999, though it is not clear that this is the frequency that the model should
replicate.23 An alternative procedure is to compare the default rate generated
by the model with the default rate implicit in the average spread observed over
the sample period (under the assumption of risk-neutral lenders). The value
23 The model is calibrated to match the macroeconomic behavior of Argentina between 1983
and 2000, while the default rate computed in Reinhart, Rogoff, and Savastano (2003) is based on
a different time period and a sample of various countries.
270
Federal Reserve Bank of Richmond Economic Quarterly
of the latter is 243 defaults for every 10,000 periods, which is even further
away from the model predictions.
On the other hand, the models are able to generate a high volatility of
consumption relative to income and the sign of the co-movements between
the trade balance, spread, and output that are observed in the data.24
Discussion of the Results With the Exclusion
Punishment
This section describes the tradeoffs the government faces when it decides how
much debt to issue. This helps in understanding the logic behind the results
presented in Table 3. The section focuses on the model with transitory shocks
(z), though the same logic applies to the model with trend shocks.
Given the monotonicity of the default decisions (see Figure 2), the bond
price function faced by the government when it decides how much to borrow
can be written as
1 − F z∗ b | z
,
(12)
q b ,z =
1+r
where z∗ b denotes the next period endowment shock that makes the government indifferent between defaulting and not defaulting on a debt level b ,
and F denotes the cumulative distribution function for the next period shock.
If the endowment shock in the following period is lower than z∗ , the government will default on b . If it is higher
than
z∗ , the government will pay back
b . In the top panel of Figure 2, z∗ b represents the frontier of the shaded
area. Equation (12) shows that the shape of price q mirrors the
shape
of the
probability of observing a default the next period, namely, F z∗ b | z .
The solid line of Figure 4 displays the bond price menu faced by the
government in a period in which the endowment realization is equal to the
unconditional mean of the endowment process (μz ) and the economy is not
excluded from capital markets. The sensitivity of the bond price to the issuance
volume (b ) is given by
−f z∗ b | z ∂z∗ b
q b , z
=
,
(13)
1+r
∂b
∂b
where f denotes the density function of future shocks. This equation shows
that the shape of the bond price depends on two factors: the probability dis
tribution f and the sensitivity of z∗ to changes in b (the shape of the default
region). The assumption that future endowment shocks are drawn from a
24 The table does not report statistics about the current account. Given that both models
generate a relatively stable debt level and a low volatility of the interest rate, interest payments also
display low volatility. Therefore, the balance of the current account is almost perfectly correlated
with the trade balance and inherits the statistical properties of the latter.
J. C. Hatchondo, L. Martinez, and H. Sapriza: Quantitative Models
271
Gaussian distribution accounts for the flat portion of the price curve. The thin
tails of f explain why the price is almost invariant to b at issuance volumes
such that the threshold z∗ takes extreme values.
The bond price plays a central role in understanding the shape of the
objective function of the government represented in Figure 4. Formally, the
objective function is given by the right-hand side of the Bellman equation:
RH S b = u y (1 − λ) + b − q0 b , z b + β
V (b , z , 0, 0)Fz dz | z .
For the range of values of b such that there is no default risk, the present
discounted welfare increases with the issuance level, i.e., the burden of starting
tomorrow with higher liabilities does not compensate for the extra resources
collected for current consumption.25 As the price per bond starts to fall,
there is an extra factor that appears in the tradeoff between current and future
consumption: an extra dollar of borrowing implies a lower bond price. In
particular, an extra dollar of borrowing implies a decrease in price q received
for all the bonds issued in the current period.
If the price function is steep, borrowing an extra dollar is quite costly due
to the decrease in bond price received for all bonds issued in the current period.
In the stylized model presented in this article, the price function becomes very
steep at borrowing levels at which the government pays an interest rate close to
the risk-free rate. Consequently, the borrowing levels observed in equilibrium
are such that the economy pays low spreads. This explains the low default
frequency reported in Table 3.
The top panel of Figure 3 shows that a higher endowment realization enables the government to borrow more without paying a higher spread, but
the price function becomes steep at borrowing levels for which the spread
is low independently of whether the endowment shock is “low” or “high.”
This feature contributes to the explanation of why in equilibrium the government chooses to pay low spreads at all endowment realizations, and thus the
volatility of the spread is low.
The inability of the model to generate a higher default rate and spread
volatility may be a consequence of its simplifying assumptions. Consider,
for instance, the assumption that the government can only issue one-period
bonds. Recall that as illustrated in Figure 4, the interest rate increases with
the borrowing level (the bond price decreases). The assumption of one-period
bonds implies that in every period the economy has to roll over its entire stock
of debt. Thus, the increase in the interest rate that is due to an extra dollar of
borrowing affects the entire stock of bonds and not only the last unit issued.
More precisely, consider the decision of whether to borrow x + 1 dollars or x
25 It should be stressed that this result is not general and critically depends on the parameter
values chosen, especially the value of the subjective discount factor.
272
Federal Reserve Bank of Richmond Economic Quarterly
dollars. When the government is renewing its entire stock of debt, the higher
interest implied by borrowing x +1 instead of x applies to the x +1 units issued.
This is trivially larger than the cost induced by an increase in the interest rate
paid for the last bond issued. This argument illustrates how restricting the
government to issue one-period bonds increases the marginal issuance cost,
and thus accounts for a fraction of the low spreads generated by the model.
Even though the government is risk averse and lenders are risk neutral,
the volatility of consumption is higher than the volatility of output in both
models. As discussed in the beginning of Section 4, price q is nondecreasing
in the current endowment realization. That is, a higher endowment enables the
government to issue more bonds without necessarily paying a higher spread.
Given the low value of the discount factor, the economy will seize the opportunity to borrow more whenever it appears, explaining why the economy
borrows more in good times. This explains why the model is able to generate a higher volatility of consumption relative to income. Formally, current
consumption is determined by current income and net borrowing, namely,
c = y − qb − b .
Therefore,
σ 2 (c) = σ 2 (y) + 2σ [y − (qb − b)] + σ 2 qb − b .
The positive covariance between net borrowing (b − qb ) and income
increases the volatility of consumption relative to income.
Table 3 shows that both models are able to replicate the sign of the comovements between trade balance, spread, and output observed in the data.
The fact that the government borrows more in good times leads to a negative
correlation between trade balance and output (as observed in the data).26 The
mechanics that determine the sign of the correlation between the spread and
output are more complex. On the one hand, if the bond price function faced
by the government is kept constant, a higher income realization today reduces
the need to borrow, and therefore it reduces the spread that the government
is willing to pay for its debt. This generates a negative correlation between
income and spread. But the bond price function also changes with the income
realization. If the price of the bond becomes less sensitive to the borrowing
level at higher income levels, the government would be willing to pay a higher
spread at higher income levels. The latter may change the sign of the correlation between the spread and income. For example, the next section shows that
26 The trade balance is defined as
tb = y − c = qb − b.
Thus, the positive correlation between net borrowing and income translates into a negative correlation between trade balance and income.
J. C. Hatchondo, L. Martinez, and H. Sapriza: Quantitative Models
273
once the exclusion punishment is eliminated, the spread becomes pro-cyclical
in Model II.
5.
RESULTS WITHOUT EXCLUSION
This section studies the implications of removing the threat of financial exclusion. Formally, this implies setting the value of φ 1 equal to 1. The section
describes how the default and saving decisions change when the government
cannot be threatened with financial exclusion. This helps to understand how
the business cycle statistics change when the exclusion assumption is abandoned, which is discussed later in the section entitled “Business Cycle Properties.”
Equilibrium Choices Without the Exclusion
Punishment
The common feature across Models I and II is that they are able to sustain
a lower debt level when the government does not face the threat of financial
exclusion. In other dimensions, the model with transitory shocks without
exclusion features higher equilibrium spreads (lower equilibrium issuance
prices) and spreads that are more responsive to the endowment shock compared
to the model with transitory shocks and exclusion. On the other hand, the
model with trend shocks features lower equilibrium spreads and spreads that
are less responsive to trend shocks compared to the model with exclusion.
Figure 5 illustrates how the default decisions change when exclusion cannot be used as a punishment in Models I and II. The graphs illustrate that the
government defaults at lower debt levels when the threat of financial exclusion
is eliminated. The result is not surprising though. The possibility of being
excluded from capital markets imposes a cost to every default decision (regardless of the size of the default). Once the threat of financial exclusion is
eliminated, it becomes less costly to default, and thus the government finds it
optimal to default at lower debt levels.
The top panel of Figure 5 shows that in Model I the default decision
becomes relatively more sensitive to the endowment shock (and less sensitive
to the debt level) when the threat of exclusion is eliminated. This is due to
the fact that the possibility of going into financial autarky is more painful at
lower endowment realizations than at higher endowment realizations. When
the current shock to the endowment level is higher, the need to smooth out
consumption by borrowing is weaker, and therefore the value assigned to
retaining access to capital markets is lower. In other words, the government
would suffer less from being excluded from capital markets if its endowment
level is higher. When the threat of financial exclusion is eliminated, the overall
cost of defaulting decreases more at lower endowment realizations than at
274
Federal Reserve Bank of Richmond Economic Quarterly
Figure 5 Default Regions With and Without Exclusion
b (Without Exclusion)
-0.09
-0.08
-0.07
-0.10
-0.06
-0.05
0.20
0.20
0.15
0.15
0.10
0.10
0.05
0.05
0.00
0.00
-0.05
-0.05
-0.10
-0.10
z
z
-0.11
-0.15
-0.15
With Exclusion
-0.20
-0.28
-0.10
-0.27
-0.26
-0.25
b (With Exclusion)
b (Without Exclusion)
-0.09
-0.08
-0.07
-0.24
-0.23
-0.06
-0.05
1.08
1.08
1.06
1.06
1.04
1.04
1.02
1.02
1.00
1.00
0.98
0.98
0.96
0.96
0.94
g
g
-0.11
-0.20
Without Exclusion
0.94
With Exclusion
Without Exclusion
0.92
0.92
-0.24
-0.23
-0.22
-0.21
-0.20
b (With Exclusion)
-0.19
-0.18
Notes: Endowment shocks at which the government is indifferent between defaulting and
not defaulting in the model with transitory shocks (top panel) and in the model with
trend shocks (bottom panel). The scale on the bottom corresponds to the models with
exclusion. The scale on the top corresponds to the models without exclusion.
J. C. Hatchondo, L. Martinez, and H. Sapriza: Quantitative Models
275
higher endowment realizations. This accounts for the flatter default region in
the top panel of Figure 5.
The picture looks different in the model with trend shocks. The bottom
panel of Figure 5 shows that the default region becomes steeper without exclusion. In this case, the mechanism described in the previous paragraph is
also present, but there is an additional effect. A higher growth rate in the current period not only means that there are more resources available for current
consumption but also that future growth rates are likely to be high—recall
that there is persistence in growth rates. Consequently, unlike a higher transitory shock, a higher growth shock introduces an incentive to borrow more
on account of the future increases in the endowment. This means that the
value assigned to retaining access to capital markets is larger when the current
growth rate is higher. When the threat of financial exclusion is eliminated, the
overall cost of defaulting decreases more at higher endowment realizations
than at lower endowment realizations. This explains the change in the slope
of the default regions in the model with trend shocks.
The change in the shape of the default region plays an important role
in understanding the change in the shape of the price function. The formal
link between the two is described in equation 13. For
example, the steeper
∂z∗ (b )
the default region (the higher the expression ∂b ), the steeper the price
function.
Figure 6 shows the price functions faced by the economy in Model I with
and without exclusion.27 The charts in Figure 6 show that when the threat of
exclusion is eliminated, the bond price starts to decrease at a lower issuance
level. This mirrors the shift of the default region due to a lower cost of default.
The graphs show that the moderate change in the slope of the default regions
observed in the top panel of Figure 5 translate into a moderate change in the
slope of the price functions.
Figure 7 shows the price function faced by the economy in Model II with
and without exclusion.28 The charts show that the steeper default regions that
are observed when the threat of financial exclusion is eliminated translate into
steeper price functions.
27 Notice that the top panel of Figure 6 represents the same functions as the top panel
of Figure 3 but with different scales. The graph is reproduced again in order to facilitate the
comparison of the shape of the price functions in the models with and without exclusion.
28 The top panel of Figure 6 represents the same functions as the bottom panel of Figure 3
but with different scales.
276
Federal Reserve Bank of Richmond Economic Quarterly
Figure 6 Bond Price Menus in Model I With and Without Exclusion
-0.285
1.0
0.9
-0.280
Range of b for max(z)
-0.275
-0.270
-0.265
min(z)
-0.260
1.0
0.9
0.8
0.8
0.7
0.7
0.6
0.6
0.5
0.5
0.4
0.4
0.3
0.3
0.2
0.2
0.1
0.1
0.0
-0.256
-0.251
-0.246
-0.241
Range of b for min(z)
-0.236
q
q
max(z)
0.0
-0.231
Range of b for max(z)
-0.105
1.0
-0.095
-0.090
-0.085
-0.080
1.0
0.9
min(z)
max(z)
0.8
0.8
0.7
0.7
0.6
0.6
0.5
0.5
0.4
0.4
0.3
0.3
0.2
0.2
0.1
0.1
0.0
-0.075
-0.070
-0.065
-0.060
-0.055
q
q
0.9
-0.100
0.0
-0.050
Range of b for min(z)
Notes: Bond price as a function of the issuance level in the model with transitory shocks
and exclusion (top panel) and in the model with transitory shocks and without exclusion
(bottom panel). The high (low) shock is three standard deviations higher (lower) than the
unconditional mean of z. The scale of bond issuances when the endowment shock is low
is described by the bottom horizontal axes. Likewise, the scale of bond issuances when
the endowment shock is high is described by the top horizontal axes. The different scales
used in the horizontal axes facilitate the comparison of the shape of the price functions.
J. C. Hatchondo, L. Martinez, and H. Sapriza: Quantitative Models
277
Figure 8 displays the equilibrium issuance price in Model I as a function
of the endowment shock realization in the specifications with and without
exclusion. The graphs show that the price at which the government issues
debt is lower and more sensitive to the endowment shock in the setup without
exclusion.
Figure 9 shows the bond prices paid in equilibrium in the model with
shocks to the trend with and without exclusion. The graphs show that the
prices at which the government issues debt are higher in the setup without
exclusion. The correlation with the endowment shock also changes. When
the government can be threatened with financial exclusion the spread decreases
with respect to the shock to the trend. But when the government cannot be
threatened with financial exclusion, the spread increases with respect to the
shock to the trend.29
The Mechanics of the Equilibrium Behavior of the Spread
This section discusses the differential behavior of the spread in Models I and II
once the exclusion assumption is abandoned. Consider first the Euler equation
that determines the optimal borrowing level
u (c) q0 (b , z, , g) =
β
∂V (b ,z , ,g ,h)
F (dz | z)F (dg
∂b
u (c)b ∂q0 (b∂b,z,,g)
.
| g)−
(14)
The left-hand side of the equation captures the marginal benefit of issuing
one more bond today, i.e., the increase in current consumption. The right-hand
side captures the marginal costs. The first term represents the “future marginal
cost.” Issuing one more unit of debt today makes the economy poorer in the
future—the government will either have to pay back its debt or face the cost
of defaulting. The second term on the right-hand side represents the “present
marginal cost.” This is the cost derived from decreasing the price of all the
bonds issued today. The role of the latter was discussed more extensively in
the end of Section 4.
In both models the optimal issuance volume is lower when the government
does not face the threat of default. An immediate consequence is that it
depresses the present marginal cost (the second term in the right-hand side of
equation (14) is the product of the borrowing level times the sensitivity of the
price to the borrowing level). The decrease in the marginal cost induced by
a lower borrowing level may be compensated, in part, by accepting a lower
price for each bond issued, which reduces the marginal benefit of borrowing.
This can explain the lower equilibrium bond prices (higher spread) that are
observed in Model I when the threat of exclusion is eliminated (see Figure 8).
29 The beginning of Section 5 provides some intuition for the differential behavior of the
spread displayed by Models I and II once the exclusion assumption is abandoned.
278
Federal Reserve Bank of Richmond Economic Quarterly
Figure 7 Bond Price Menus in Model II With and Without Exclusion
Range of b for max(g)
-0.225
-0.215
-0.205
-0.195
-0.185
1.0
0.9
0.9
0.8
0.8
0.7
0.7
0.6
0.6
0.5
0.5
0.4
0.4
0.3
0.3
0.2
0.2
0.1
min(g)
max(g)
0.0
-0.23
-0.22
0.1
0.0
-0.102
-0.21
-0.20
Range of b for min(g)
Range of b for max(g)
-0.092
-0.082
-0.19
-0.072
-0.18
-0.062
1.0
0.9
0.9
0.8
0.8
0.7
0.7
0.6
0.6
0.5
0.5
0.4
0.4
0.3
0.3
0.2
0.1
0.2
min(g)
max(g)
0.1
0.0
-0.11
q
q
-0.112
1.0
q
q
-0.235
1.0
0.0
-0.10
-0.09
-0.08
Range of b for min(g)
-0.07
-0.06
Notes: Bond price as a function of the issuance level in the model with trend shocks
and exclusion (top panel) and in the model with trend shocks and without exclusion (bottom panel). The high (low) shock is three standard deviations higher (lower) than the
unconditional mean of g. The scale of bond issuances when the trend shock is low is
described by the bottom horizontal axes. Likewise, the scale of bond issuances when the
trend shock is high is described by the top horizontal axes. The different scales used in
the horizontal axes facilitate the comparison of the shape of the price functions.
J. C. Hatchondo, L. Martinez, and H. Sapriza: Quantitative Models
279
Figure 8 Bond Prices Observed in Equilibrium in Model I
0.9896
0.9894
0.9892
0.9890
q
0.9888
0.9886
0.9884
0.9882
0.9880
b = -0.24221
b = -0.25427
0.9878
0.9876
-0.20
-0.15
-0.10
-0.05
0.00
0.05
0.10
0.15
0.20
z
b = -0.060302
b = -0.074774
0.9896
0.9894
0.9892
0.9890
q
0.9888
0.9886
0.9884
0.9882
0.9880
0.9878
0.9876
-0.20
-0.15
-0.10
-0.05
0.00
0.05
0.10
0.15
0.20
z
Notes: Bond price observed in equilibrium in the model with transitory shocks and exclusion (top panel) and in the model with transitory shocks and without exclusion (bottom
panel).
280
Federal Reserve Bank of Richmond Economic Quarterly
Figure 9 Bond Prices Observed in Equilibrium in Model II
b = -0.18518
b = -0.18769
0.9896
0.9894
0.9892
0.9890
q
0.9888
0.9886
0.9884
0.9882
0.9880
0.9878
0.9876
0.92
0.94
0.96
0.98
1.00
1.02
1.04
1.06
1.08
g
b = -0.072727
b = -0.069091
0.9896
0.9894
0.9892
0.9890
q
0.9888
0.9886
0.9884
0.9882
0.9880
0.9878
0.9876
0.92
0.94
0.96
0.98
1.00
1.02
1.04
1.06
1.08
g
Notes: Bond price observed in equilibrium in the model with trend shocks and exclusion
(top panel) and in the model with trend shocks and without exclusion (bottom panel).
J. C. Hatchondo, L. Martinez, and H. Sapriza: Quantitative Models
281
Table 4 Business Cycle Statistics Computed With and Without
Exclusion Punishment
Transitory Shocks
Data
σ (y)
σ (c)
σ (T B/Y )
σ (Rs )
ρ (c, y)
ρ (T B/Y, y)
ρ (Rs , y)
ρ (Rs , T B/Y )
Mean Debt
Output Ratio (%)
Rate of Default
4.08
4.85
1.36
3.17
0.96
-0.89
-0.59
0.68
51
75
With
Exclusion
4.14
4.23
0.20
0.006
0.99
-0.43
-0.81
0.85
6.3
6.6
Without
Exclusion
4.10
4.19
0.21
0.05
0.99
-0.43
-0.95
0.69
1.7
25
Trend Shocks
With
Exclusion
4.15
4.38
0.63
0.013
0.99
-0.29
-0.06
0.89
4.8
24
Without
Exclusion
4.16
4.23
0.23
0.015
0.99
-0.29
0.40
-0.96
1.8
20
Notes: The debt output ratio is measured as the stock of debt divided by the annual
output level.
A similar effect is present in Model II. But in this case the bond price
becomes steeper in the setup without exclusion. This effect alone tends to
increase the present marginal cost of borrowing, and therefore unlike Model I,
a lower bond price is not necessary to satisfy equation (14). This can explain
why the levels of the equilibrium bond prices in Model II do not change
significantly when the threat of exclusion is eliminated (see Figure 9).
The forces behind the changes in the slope of the spread with respect to the
endowment shock are more difficult to tease out. As explained in the end of
Section 4, the equilibrium relationship between the spread and the endowment
shock depends on various effects, and the sign of the relationship does not
necessarily need to be negative. In fact, Figure 9 shows that in the model with
trend shocks and no exclusion, the spread increases with the growth shock.
Business Cycle Properties Under No Exclusion
The business cycle statistics reported in Table 3 are recalculated for an economy without the exclusion punishment and presented in Table 4 (the statistics
in Table 3 are reproduced in order to facilitate comparison).
The implications of removing the exclusion punishment reported in Table
4 are consistent with the discussion of equilibrium choices in the beginning
of Section 5. Table 4 shows that the assumption of exogenous exclusion is
responsible for a high fraction of the debt level supported in the model with
exclusion. Recall that in this model the government chooses borrowing levels
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Federal Reserve Bank of Richmond Economic Quarterly
that allow the government to pay very low spreads. These levels are lower
when the default cost raised by the threat of financial exclusion is removed.
Table 4 shows that both models quantitatively fail along important dimensions with or without the assumption of financial exclusion: the default rate,
the volatility of the spread, and the volatility of the trade balance are too low
compared with the data. Even though the overall performance is poor, the
behavior of the model with transitory shocks shows a moderate improvement,
while the behavior of the model with trend shocks deteriorates when the exclusion assumption is eliminated. The model with endowment shocks and
no exclusion displays a higher default rate and spread volatility compared to
the model with exclusion (but still far below the data), while the remaining
business cycle statistics are not substantially different. On the other hand, the
sign of the correlation between output and the spread, and between the spread
and the trade balance are reversed and become counterfactual in the model
with trend shocks and no exclusion.
The higher default rate generated by Model I when the threat of financial
exclusion is eliminated is consistent with the higher equilibrium spread described in Figure 8. The higher spread volatility observed in the setup without
exclusion is also consistent with Figure 8, which shows a higher sensitivity of the spread with respect to output in the model without exclusion. The
lower default rate and similar spread volatility generated by Model II when the
threat of financial exclusion is eliminated are consistent with the adjustments
illustrated in Figure 9.
6.
CONCLUDING REMARKS
This article discusses the quantitative performance of sovereign default models
and explains how the performance is affected by the assumption that countries can be exogenously excluded from capital markets after a default. The
article compares the performance of a stylized model with and without the
threat of exclusion. It is shown that the exclusion assumption explains a high
fraction of the sovereign debt that can be sustained in equilibrium but does
not significantly alter the remaining business cycle statistics of the model. In
effect, the model without exclusion generates annual debt-output ratios of less
than 2 percent. The model with exclusion generates annual debt-output ratios
of 4.8 percent when the shocks hit the growth rate and of 6.3 percent when
the shocks hit the endowment level. The article shows that in the model with
shocks to the endowment level, the default decision becomes slightly more
sensitive to the endowment shock and, therefore, less sensitive to the debt
level. This helps reduce the sensitivity of the bond price to the borrowing
level. On the other hand, in the model with shocks to the trend the default
decision becomes relatively less sensitive to the endowment shock, which increases the sensitivity of the bond price to the borrowing level. Given that
J. C. Hatchondo, L. Martinez, and H. Sapriza: Quantitative Models
283
in this class of models the excessive sensitivity of the default probability to
the borrowing level limits the models’ quantitative performance, the previous
effects may help explain why the performance of the model with shocks to the
endowment level shows moderate improvement and why the performance of
the model with shocks to the trend deteriorates. In spite of this, both models
still fail along important dimensions. The default rate, the volatilities of the
trade balance and of the spread, and the debt levels are too low compared to
the data. These shortcomings suggest that the exclusion assumption does not
play an important role, and therefore future studies that do not rely on the
threat of financial exclusion will not necessarily be handicapped in explaining
the business cycle in emerging economies. These shortcomings also suggest
that other assumptions of the model must be modified in order to bring the
model closer to the data.
284
APPENDIX:
Federal Reserve Bank of Richmond Economic Quarterly
THE MODEL WITH STOCHASTIC
DURATION OF OUTPUT LOSS
As mentioned before, the model introduced in Section 2 does not exactly
coincide with the model presented in Aguiar and Gopinath (2006). They
assume that following a default episode, the duration of lower output lasts as
long as the time of exclusion. Table 5 shows that the business cycle statistics
presented in Table 3 are not greatly affected by the choice of the process of
output loss—statistics computed with a stochastic duration of output loss are
taken from Hatchondo, Martinez, and Sapriza (2006a) who solve the model
in Aguiar and Gopinath (2006) with the computational method used in this
article.
Table 5 Business Cycles Under Different Specifications of the
Output Loss
Transitory Shocks
One-Period
Output Loss
σ (y)
σ (c)
σ (T B/Y )
σ (Rs )
ρ (c, y)
ρ (T B/Y, y)
ρ (Rs , y)
ρ (Rs , T B/Y )
Mean Debt
Output Ratio (%)
Rate of Default
4.14
4.23
0.20
0.006
0.99
-0.43
-0.81
0.85
6.8
6.6
Stochastic
Duration of
Output Loss
4.13
4.25
0.24
0.007
0.99
-0.43
-0.74
0.89
6.8
7.8
Trend Shocks
One-Period
Output Loss
4.16
4.38
0.63
0.013
0.99
-0.29
-0.06
0.89
4.7
24
Stochastic
Duration of
Output Loss
4.16
4.39
0.65
0.015
0.99
-0.29
-0.09
0.91
4.8
22
Notes: Business cycle statistics from models with output loss in one period and models
with a stochastic duration of the output loss. The debt output ratio is measured as the
stock of debt divided by the annual output level.
J. C. Hatchondo, L. Martinez, and H. Sapriza: Quantitative Models
285
REFERENCES
Aguiar, Mark, and Gita Gopinath. 2006. “Defaultable Debt, Interest Rates
and the Current Account.” Journal of International Economics 69 (1):
64–83.
Aguiar, Mark, and Gita Gopinath. 2007. “Emerging Markets Business
Cycles: The Cycle is the Trend.” Journal of Political Economy 115 (1):
69–102.
Arellano, Cristina. Forthcoming. “Default Risk and Income Fluctuations in
Emerging Economies.” American Economic Review.
Arellano, Cristina, and Ananth Ramanarayanan. 2006. “Default and the Term
Structure in Sovereign Bonds.” Working Paper, University of Minnesota.
Athreya, Kartik B., and Hubert P. Janicki. 2006. “Credit Exclusion in
Quantitative Models of Bankruptcy: Does It Matter?” Federal Reserve
Bank of Richmond Economic Quarterly 92 (1): 17–50.
Bai, Yan, and Jing Zhang. 2006. “Financial Integration and International
Risk Sharing.” Working Paper, University of Michigan.
Borensztein, Eduardo, and Paolo Mauro. 2004. “The Case for GDP-Indexed
Bonds.” Economic Policy 19 (38): 165–216.
Chuhan, Punam, and Federico Sturzenegger. 2005. “Defaults Episodes in the
1980s and 1990s: What Have We Learned?” In Managing Economic
Volatility and Crises, eds. Joshua Aizenman and Brian Pinto, New York,
NY: Cambridge University Press: 471–519.
Cole, Harold L., James Dow, and William B. English. 1995. “Default,
Settlement, and Signalling: Lending Resumption in a Reputational
Model of Sovereign Debt.” International Economic Review 36 (2):
365–85.
Cuadra, Gabriel, and Horacio Sapriza. 2006a. “Sovereign Default, Interest
Rates and Political Uncertainty in Emerging Markets.” Banco de
México, Working Paper 2006-02.
Cuadra, Gabriel, and Horacio Sapriza. 2006b. “Sovereign Default, Terms of
Trade, and Interest Rates in Emerging Markets.” Banco de
México,Working Paper 2006-01.
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Repudiation: Theoretical and Empirical Analysis.” Review of Economic
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Eichengreen, Barry, and Richard Portes. 2000. “Debt Restructuring With and
Without the IMF.” Manuscript, University of California, Berkeley.
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Gelos, Gaston, Ratna Sahay, and Guido Sandleris. 2004. “Sovereign
Borrowing by Developing Countries: What Determines Market Access?”
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Reserve Bank of Richmond, Working Paper No. 06-11.
Hatchondo, Juan Carlos, Leonardo Martinez, and Horacio Sapriza. 2006b.
“Heterogeneous Borrowers in Quantitative Models of Sovereign
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IMF. 2002. “Sovereign Debt Restructurings and the Domestic Economy
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Department, February 21.
Kumhof, Michael. 2004. “Fiscal Crisis Resolution: Taxation Versus
Inflation.” Manuscript, Stanford University.
Kumhof, Michael, and Evan Tanner. 2005. “Government Debt: A Key Role
in Financial Intermediation.” IMF Working Paper 05/57.
Lizarazo, Sandra. 2005a. “Sovereign Risk and Risk Averse International
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Lizarazo, Sandra. 2005b. “Contagion of Financial Crises in Sovereign Debt
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Meyersson, Erik. 2006. “Debt Intolerance and Institutions, an Empirical
Investigation into the Institutional Effect of Sovereign Debt.” Mimeo,
Institute for International Economic Studies, Stockholm University.
Neumeyer, Pablo A., and Fabrizio Perri. 2005. “Business Cycles in
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Reinhart, Carmen M., Kenneth S. Rogoff, and Miguel A. Savastano. 2003.
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Schmitt-Grohé, Stephanie, and Martin Uribe. 2003. “Closing Small Open
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Sturzenegger, Federico, and Jeromin Zettelmeyer. 2005. “Has the Legal
Threat to Sovereign Debt Restructuring Become Real?” Working Paper,
Harvard University.
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Yue, Vivian. 2005. “Sovereign Default and Debt Renegotiation.” Working
Paper, New York University.
Economic Quarterly—Volume 93, Number 3—Summer 2007—Pages 287–315
Barriers to Foreign Direct
Investment Under Political
Instability
Marina Azzimonti and Pierre-Daniel G. Sarte
F
oreign direct investment (FDI), as pointed out by Kindleberger (1969),
arises when the host country has an investment opportunity that it cannot exploit by itself because it lacks the means or technical know-how,
or because of market incompleteness (that is, access to capital markets is restricted). A multinational corporation (MNC) may be able to exploit such
an opportunity because it has the necessary capital, technology, and managerial skills to do so. Even though the return to foreign direct investment is
potentially large in many developing countries (for example, the opening up
of Eastern Europe provided advantages to multinational firms because of the
low cost of labor, low levels of capital in place, and the proximity to major
markets), the flow of direct investment is concentrated in just a few countries.1 Lucas (1990) attributes this lack of FDI in countries with potentially
large marginal returns to capital to the fact that many developing countries
face higher political risk than industrialized ones.
A distinctive characteristic of FDI is that once an investment has been
made, a foreign investor cannot prevent the government in the host country
from changing the environment in which the investment decision was made.
Despite attempts to establish international tribunals, contracts between multinational corporations (MNCs) and sovereign countries are almost impossible
to enforce. The quality of institutions, and in particular, the degree of protection of property rights, are key in determining the expected return to foreign
We would like to thank Andreas Hornstein, Leonardo Martinez, Borys Grochulski, and Nashat
Moin for their comments. Also, we would like to thank Kevin Bryan for excellent research
assistance. The views expressed in this article are those of the authors and do not necessarily reflect those of the Federal Reserve Bank of Richmond or the Federal Reserve System.
E-mails: marina-azzimonti@uiowa.edu and pierre.sarte@rich.frb.org.
1 The United Nations (1996) reports that 80 percent of the total investment flowing to developing countries in 1995 was received by only ten countries.
288
Federal Reserve Bank of Richmond Economic Quarterly
investors. Countries with relatively poor legal protection of assets, and a
high degree of political instability, generally exhibit high rates of expropriation and this makes investment less attractive. In practice, expropriation can
take different forms. A direct act of expropriation involves nationalization of
foreign-owned corporations, in which the government simply takes control
of the capital stock (Kobrin 1980, 1984). There are also indirect forms of
expropriation that multinational corporations face. Examples include excessive taxation, capital controls, manipulation of exchange rates, and bribes and
permits demanded by government officials.
In this article, we describe some stylized facts about expropriation episodes
and other lessons learned from the empirical literature on FDI. We then summarize some of the main theories attempting to explain the effects of expropriation on investment and growth. Finally, we develop a theory that relates
each type of expropriation to political instability and concentration of power.
A simple two-period political economy model is presented in which groups
with access to an expropriation technology alternate in power according to
an exogenous probability. The group that controls the government in the
first period has the ability to obtain bribes from foreign investors who are
attempting to gain access to production in the host country. This form of
indirect expropriation is analogous to an investment tax, in the sense that it
distorts the optimal allocation of international capital by imposing additional
costs to potential investors. After investment decisions have been made (in
the second period), the group in office decides how much capital should be
seized or nationalized, a direct form of expropriation.
Following the literature on FDI, we will assume that any capital expropriated by the host country becomes unproductive. This stylized representation
tries to characterize the empirical observation that MNCs are usually more
efficient in running production than the host country. For example, Minor
(1994) documents that about 35 percent of all enterprises that were expropriated between 1960 and 1979 have been privatized between 1980 and 1992,
indicating public “disillusion with the typical result of expropriation, the stateowned enterprise” (see Biais and Perotti 2002 for more on recent trends on
privatizations). Theoretically, the costs associated with expropriation arise
mainly because of two reasons. First, there is usually a reduction in the technological spillovers embodied in foreign capital. Second, because the capital
installed by foreign investors may be specific to the manager’s skills, it may
take time for domestic workers to acquire the know-how needed to operate the
foreign technology. As a consequence, reductions in the capital stock installed
by MNCs imply productivity losses and depressed domestic wages.
At any point in time, the benefit associated with expropriation is given by
the amount of goods that can be transferred from MNCs to domestic agents.
The tradeoff faced by policymakers is, therefore, given by the redistributive
gains of expropriation versus the income loss suffered by local workers.
M. Azzimonti and P. D. Sarte: Barriers to FDI
289
A key assumption is that there are no institutional barriers to discretionary
redistribution, so any group can appropriate all expropriated resources. Because the group in power is not forced to transfer resources to other groups, a
“tragedy of the commons” arises: there is too much expropriation in equilibrium. A tragedy of commons occurs when property rights of an asset cannot
be enforced; a typical example is fishing on a lake. Typically this gives rise to
over-consumption or under-investment (see Gordon 1954 or Lancaster 1973).
In our model, it is precisely the fact that groups cannot ensure ex ante that
they will receive the benefits of expropriation in the future that cause overexpropriation in the first period, making the level of bribes inefficiently large.
The degree of such inefficiency is related to how likely it is that the current
group in government retains power in the second period. That is, the degree
of such inefficiency is related to the political instability.
While countries that have higher political instability are predicted to exhibit higher levels of indirect expropriation, direct expropriation levels are
lower. The intuition is as follows: because each group finds its chances of
being in power in the second period very unlikely, it becomes shortsighted
and demands a large quantity of bribes when in power (i.e., in the first period). This discourages investment, and the reduction of capital decreases the
marginal cost of direct expropriation, encouraging more expropriation in the
second period. The marginal benefit is reduced as well because the tax base
shrinks, which reduces the incentives to expropriate. Under a Cobb-Douglas
technology assumption, the latter effect dominates and direct expropriation
goes down.
A second interesting result derived in this article is related to the concentration of power. Following Tornell and Lane (1999), power is concentrated
when there are few groups competing for government. They find that the
relation between indirect expropriation and the number of groups in power is
non-monotonic. When there is high concentration of power initially, a dilution
of concentration results in more indirect expropriation, but this relationship
reverts when concentration is small (i.e., there is a large number of groups to
begin with). Direct expropriation, on the contrary, always increases with the
number of groups. We provide some details on the intuition behind this result
at the end of Section 4.
The organization of the paper is as follows. We define the different types
of expropriation in Section 1 and summarize the main empirical findings in
the literature in Section 2. We then proceed to describe some of the most
influential theoretical articles on expropriation in Section 3. In Section 4, our
model is described and the main results are derived. Section 5 concludes.
290
1.
Federal Reserve Bank of Richmond Economic Quarterly
DEFINING EXPROPRIATION
Expropriation refers, in general, to policies that adversely affect the private
value of the stock and/or returns of foreign investment. As mentioned in the
previous section, we can distinguish between “direct” and “indirect” expropriation.
OECD (2004) provides an extensive analysis of the concept of expropriation, where jurisprudence, state practice, and literature on international
investment law are considered. According to the survey, direct expropriation
is “. . . an act where there is a compulsory transfer of property rights by the
host state. . . . An investment is nationalised or otherwise directly expropriated
through formal transfer of title or outright physical seizure. In addition to the
term expropriation, terms such as ‘dispossession,’ ‘taking,’ ‘deprivation,’or
privation’ are also used.” Kobrin (1980, 1984) and Minor (1994) define direct
expropriation as the “forced divestment of equity ownership of a foreign direct
investor.” The principal characteristic is that such divestment is involuntary,
against the will of the owners and/or managers of the enterprise, and must
entail managerial control through equity ownership across national borders.
Indirect expropriation stands for other forms of change in the institutional
environment that reduce the value of an investment, but in which property
is not necessarily seized. Schlemmer-Schulte (1999) characterizes indirect
expropriation “. . . as excessive and repetitive tax or regulatory measures that
have a de facto confiscatory effect in that their combined results deprive the
investor in fact of his ownership, control or interests in the investment . . .” This
may be accomplished, in addition to the raising of taxes, through manipulation
of exchange rates (i.e., devaluations), fees or bribes charged to the enterprise,
the return of the firm to public ownership at unfair terms, the stiffening of
regulation, or the institution of non-tariff barriers, such as restrictions in the
repatriation of profits or other capital transactions (referred to as “transfer
risk” by insurance companies). This form of indirect expropriation is also
referred to as “disguised” or “creeping expropriation.” In contrast to the case
of direct expropriation, there is no generally accepted definition of indirect
expropriation in international law. Moreover, the distinction between this
form of expropriation and non-compensable regulation (i.e., antitrust laws,
environmental protection, etc.) is not clear.2
2.
LESSONS FROM THE EMPIRICAL LITERATURE
In this section, we will analyze alternative forms of expropriation and describe
their changes over the past 30 years. Afterward, we summarize some of the
2 See Organization for Economic Cooperation and Development (2004) for an extensive discussion on the issue.
M. Azzimonti and P. D. Sarte: Barriers to FDI
291
empirical articles documenting the relationship between expropriation (and
other measures of the quality of institutions) and FDI.
Direct Expropriation
According to Minor (1994), there were 575 expropriation acts between 1960
and 1992, committed by 79 developing host countries against foreign multinationals. Africa was the region with the highest concentration of expropriation
events in the 1960s and 1970s, but Latin America and Asia became more
active during the 1980s. The manufacturing and petroleum sectors were the
most affected by direct expropriation: they account for about 40 percent of
all expropriation events between 1960 and 1964, and this percentage rises to
almost 50 percent in the period 1976–1979. Jensen (2005) points out that
another industry recently affected by major political events was privately financed infrastructure, in which some projects have been directly expropriated
(for example, the government of Thailand’s seizure of a private expressway
in 1993). Li (2004) documents that out of 520 expropriation acts committed
between 1960 and 1990, autocratic governments committed 423 acts while
democratic governments committed only 97 acts. This finding relates to the
fact that democratic governments have stronger institutions protecting property rights.
Minor shows a decline in the number of expropriation events after the
1970s. This is explained by the fact that international conditions in the late
1970s increased the benefits of FDI inflows and the freedom of action over
some multinational corporations was limited. For example, in 1990 a paragraph in the Chinese-Foreign Joint Venture Law added a “no nationalization”
clause (Robertson and Chen 1990). Tanzania adopted the National Investment Protection Policy Act that offers legal protection against nationalization
(Corkran 1991). Of course, whether host countries respect such agreements
ex post is not obvious. A more important factor that reduced the incentives
to nationalize multinational corporations was the failure of state-owned enterprises. As mentioned earlier, more than 35 percent of the enterprises that
were expropriated prior to 1980 were subsequently privatized. This indicates
that multinational corporations have an advantage over domestic governments
in running production (because investments are specific to the skills of their
foreign managers, for example), an assumption that will be made in the theoretical section of the article.
According to the Organization for Economic Cooperation and Development (OECD), “Disputes on direct expropriation—mainly related to nationalization that marked the 1970s and 1980s—have been replaced by disputes
related to foreign investment regulation and ‘indirect expropriation’ ” (OECD
2004, 2). The following section describes the particular form that this type of
expropriation has taken in recent years.
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Federal Reserve Bank of Richmond Economic Quarterly
Indirect Expropriation
Indirect expropriation acts are more difficult to document in a consistent manner because of the lack of a formal or legal definition. In this subsection,
we will restrict attention to a set of examples to highlight the nature of these
expropriation acts.
Argentina’s financial crisis of 2001–2002, when the “corralito” was imposed, provides a good example of indirect expropriation: the government
restricted capital transactions and “pesified” contracts and financial assets.
Foreign firms’ funds were converted into pesos, and many contracts, especially in infrastructure, were rewritten or canceled. At the same time, capital
was not allowed to leave the country (hence the name, “corralito,” which
means “little fence”).
Janeba (2002) provides some other examples of indirect expropriation. In
1995, China announced the dissolution of various benefits that foreign firms
received in the form of exemptions from custom duties or tax rebates when using local materials. Russia frequently considered introducing a “super profits
tax” for foreign oil companies investing in Russia. Government renegotiation
of power, electricity, and water contracts after financial crises in Argentina, Indonesia, Pakistan, and the Philippines constitute further examples (see Moran
2003). More recent examples include foreign oil companies being forced out
of their joint venture contracts, for example, such as the company, TNK-BP
in Russia.
Shleifer and Vishny (1993) argue that indirect expropriation is particularly
distortive for countries with unstable governments in which an entrepreneur
may have to bribe several public officials and still face the possibility that none
of them really has the power to allow the project to proceed.
Stylized Facts
Trends
Researchers at the World Bank’s Multilateral Investment Guarantee Agency
(MIGA) found that U.S. investors in emerging markets were subject to both
direct and indirect acts of expropriations between 1970 and 2001. The researchers note that between 1971 and 1980, U.S. investors were exposed to
restrictions on transferring and repatriating funds (transfer risk) and also subject to a number of direct expropriations. During the period of 1981–1990, an
even greater increase in the number of transfer risks claims as well as major
reductions in the number of expropriations occurred. Chifor (2002) notes, “In
the past two decades, indirect expropriation has supplanted direct takings as
the dominant form of state interference with foreign investment, as host countries have learned that more value can be extracted from foreign enterprises
through the more subtle instrument of regulatory control rather than outright
M. Azzimonti and P. D. Sarte: Barriers to FDI
293
seizures.” The period of 1996–2000 was risky for multinational corporations,
mainly because political violence and civil war claims increased dramatically.
For most firms, however, direct expropriation was the most damaging. As
Jensen (2005) notes, “Of all the dollars paid out by OPIC from 1970-1978,
96% of these claims were for expropriation. From 1991-2004, even after the
major financial crises that triggered a number of transfer claims, 84% of the
settlement amounts of OPIC claims were for expropriation.”3
FDI, Expropriation, and Institutions
There are a large number of empirical articles that attempt to assess the quantitative importance of expropriations and the quality of institutions on FDI
inflows. Most studies make no distinction between the effects of direct and
indirect forms of expropriation. An exception to this are articles focusing on
corruption, a form of creeping expropriation. Mauro (1995) finds that corruption has a negative effect on total and private investment, thus hindering
growth. Wei (2000), using data on OECD countries, shows that corruption
indices are strongly and negatively correlated with FDI inflows. For example, he estimates that an increase in Singapore’s level of corruption to that of
Mexico’s would have the same negative effect on inward FDI as raising the
tax rate on multinational corporations by 50 percentage points. Hines (1995)
documents a reduction in U.S. FDI in the period following the 1977 U.S. Foreign Corrupt Practices Act, which stipulated penalties for U.S. multinational
firms found to be bribing foreign officials. Asiedu (2006), using a panel data
for 22 countries over the period 1984–2000, shows that a decline in Nigeria’s
level of corruption to that of South Africa’s has the same positive effect on
FDI as increasing the share of fuels and minerals in total exports by about 35
percent. He concludes that countries that are small or lack natural resources
can attract FDI by improving their institutions and policy environment.
Variables contained in the Political Risk Services/International Country
Risk Guide (PRS/ICRG) political risk dataset, such as corruption in government, expropriation risk, bureaucratic quality, risk of repudiation of contracts
by the government, and law and order, are used in other studies to explain
differences in FDI inflows across countries. These variables are collected
in order to provide a comparable measure across countries of how expected
returns to capital investment are reduced by direct and indirect forms of expropriation. While some components such as expropriation risk, for example,
only incorporate the probability that capital is expropriated after investment,
others such as corruption in government, for example, refer to reductions in
profitability that will occur almost with certainty (i.e., bribes).
3 The United States Overseas Private Investment Corporation (OPIC) provides investment insurance for U.S. firms.
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Federal Reserve Bank of Richmond Economic Quarterly
Daude and Stein (2001), using a simple average of the variables in the
PRS/ICRG dataset mentioned previously (for the year 1995), find that a one
standard deviation improvement in the quality of institutions increases FDI
by a factor of 2.2. When focusing on risk of repudiation of contracts by the
government, an improvement of one standard deviation—for example, from
the level of Egypt to that of Finland—increases FDI by a factor of 1.4. They
also find that variables measuring economic policy predictability are positively
correlated with FDI inflows. Busse and Hefeker (forthcoming), using the
same dataset for the period 1984–2005, find that the quality of institutions is
a relevant factor for determining FDI inflows. The degree of ethnic tensions,
law and order, and government stability are all statistically significant factors
affecting net FDI inflows.
Hausmann and Fernández-Arias (2000) analyze the effects of institutional
variables in the composition of capital inflows using variables compiled by
Kaufmann, Kraay, and Zoido-Lobatón (1999). They find that lack of regulatory quality, government effectiveness and shareholder rights are significant
factors explaining reductions in the share of inflows represented by FDI. Using
the Institutional Investor Index as a measure of country risk, Raff and Srinivasan (1998) find that in the manufacturing sector there is a -0.55 correlation
between country risk and inward FDI. Li and Resnick (2003) find that both
property rights protection and democracy-related property rights protection
encourage FDI inflows.
In summary, there is concrete evidence from the empirical literature that
(1) poor quality of institutions, (2) alternative forms of expropriation, and (3)
lack of commitment of policy all have negative effects on FDI inflows. In the
next section, we will describe how the theoretical literature attempts to explain
these correlations.
3.
LESSONS FROM THE THEORETICAL LITERATURE
Most of the theoretical literature assumes that local governments’ incentives to
expropriate depend on the difference between the benefits of obtaining income
from foreign capital (or the ownership of capital) and the opportunity costs of
expropriation. Affiliate operation is frequently less successful when managed
by the host government rather than by the MNC. This applies specifically
to projects in which the hosts import not only physical capital but also foreign entrepreneurship, either in the form of managerial skills or technological
know-how.
Under these assumptions, Eaton and Gersovitz (1984) present one of the
most influential articles on expropriation theory. They analyze a static economy where competitive investors decide on the amount of foreign investment
to be placed in a small open economy. The host country decides whether to
expropriate the whole stock of physical capital in order to maximize national
M. Azzimonti and P. D. Sarte: Barriers to FDI
295
income. The cost of such policy is given by the loss in productivity suffered
because managerial services are no longer available after expropriation occurs.
Foreseeing that their capital might be expropriated ex post, foreign investors
will never increase their investment to the level where expropriation becomes
optimal. As a result, even though no expropriation occurs in equilibrium, the
international allocation of capital is distorted, and FDI remains inefficiently
low. Consequently, the ability of the government to expropriate when it lacks
the commitment to make binding promises on policy may actually reduce the
government’s welfare. Empirically, this explains why domestic factor prices
may not reflect social returns when the supply of investment is affected by the
threat of expropriation. This also supports the finding that commodity trade
fails to equate the returns to capital across countries.
Thomas and Worrall (1994) extend this idea to an infinite-horizon economy and characterize the set of self-enforcing agreements between the host
government and an MNC (i.e., in a bilateral monopoly environment). The
contract specifies the level of investment the MNC should make each period
and the amount of output that must be transferred to the host country. The
key is that the host government may have a short-term gain by reneging on
the contract and expropriating output or capital at any point. In this case, the
MNC retaliates by not investing in the future which entails a long-run cost
because the domestic economy returns to “autarky.” The sustainable contract
prescribes that investments should be inefficiently low in the initial periods
with no transfers to the host country. Investment rises afterward to a stationary level, in which the host country starts receiving transfers. Investment
is pro-cyclical, and transfers are positively serially correlated. Because the
temptation to expropriate is larger when output is high, the optimal contract
offers more transfers in the future. The back-loading result can be interpreted
as a tax holiday, in which the host country exempts investors from tax obligations. It provides some direct transfers and allows for duty-free imports.
Thomas and Worrall’s article is closely related to Doyle and van Wijnbergen (1994) who find tax holidays as the outcome of a bargaining game
between a foreign investor and a small country, but in which the host country
can commit to tax rates for one period. Schnitzer (1999) obtains a similar
result by assuming that the foreign investor can switch to production facilities
in other countries, rather than assuming commitment to taxes. In contrast to
the previous articles, the self-enforcing contract may exhibit overinvestment.
While the previous studies were mostly concerned with explaining the
level of expropriation, Aguiar, Amador, and Gopinath (2006) focus on its
cyclical properties. The role of the government is to insure the wages of domestic workers, who do not have access to financial markets and are subject
to output risk. The government can obtain resources from taxing the MNC’s
profits (which the authors interpret as an indirect form of expropriation) and
redistributing them as lump sum transfers to workers. They show that the
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combination of lack of commitment and incomplete markets results in policy that generates amplification and prolongation of shocks to output. The
government’s credibility not to expropriate is scarcest when the economy is
in a recession, which depresses investment and prolongs downturns. If the
government had the ability to commit to a policy sequence, it would use countercyclical and undistortionary taxes. When it lacks commitment, it distorts
foreign investment in bad times and cannot achieve full insurance.
The articles mentioned previously have a common characteristic: governments are benevolent. Policymakers want to maximize welfare (or national
output), but they cannot achieve the first best because they are tempted to
expropriate too much ex post. The lack of commitment to policy is the main
friction in these studies. One aspect that they do not address is that such
policies cause redistribution within agents in the host country. Interaction between powerful groups that compete to gain control and appropriate national
resources can lead to another source of inefficiencies that distort investment
decisions. The political economy game in which a “tragedy of commons”
arises, resulting in suboptimal investment levels, is studied in a series of articles by Tornell and co-authors. Tornell and Velasco (1992) explain why, even
though poor countries have a higher marginal productivity of capital, they are
subject to capital flights toward richer countries. Their main idea is that in
countries with weak institutions and poor protection of property rights, some
groups can appropriate the returns of other groups by controlling fiscal policy. By investing some of their assets in foreign markets, domestic agents can
ensure private access and avoid “overappropriation” (i.e., indirect expropriation) from other groups. Tornell and Lane (1999) use a similar environment
to explain how this dynamic interaction between groups leads to a slowdown
in economic growth. They show that dilution in the concentration of power
ameliorates this problem, a result in contrast to the traditional wisdom in models with a common pool problem. The explanation is based on the fact that
groups do not cooperate. So as the number of groups increases, each group
must reduce its appropriation rate to make sure its rate of return is no lower
than that of its outside option (i.e., investing in the more inefficient informal
sector). These articles are closer to ours, due to their emphasis on political
factors such as disagreement over redistributive policy across the population
of the host country.
Our article is also closely related to Amador (2003), who finds that government borrowing is inefficiently high if there is some probability of losing
power in the future. It is also related to Azzimonti (2005), who provides
microfoundations in a probabilistic voting model for the shortsightedness of
parties in an environment in which the government chooses public investment
and the provision of a consumable public good. The underlying force driving
the inefficiency of policy is common to all three articles; the difference being
that in Azzimonti’s environment, investment is chosen by the party in power
M. Azzimonti and P. D. Sarte: Barriers to FDI
297
and taxes are imposed on the domestic group. In the current article, investment
is made by foreign investors who have an outside option and the proceeds of
expropriating part of it are distributed to a specific group. The article is also
related to a body of literature characterizing equilibria that rules out reputation. See, for example, Azzimonti, Sarte, and Soares (2006); Quadrini (2005);
or Klein, Krusell, and Rı́os-Rull (2004), which characterize Markov-perfect
equilibria (the analogous to our equilibrium concept in an infinite-horizon
economy). Finally, it is related to a set of political economy models in which
redistributive uncertainty results in inefficiencies (see Lizzeri 1999, Alesina
and Tabellini 1990, or Battaglini and Coate forthcoming).
4. THE EXPROPRIATION GAME
In this section, we describe the environment and derive our main results. We
proceed by specifying the timing and then solving for the subgame-perfect
equilibrium through backward induction.
The Environment
The economy is populated by a government, domestic agents, and foreign capitalists. Agents live for two periods. They are endowed with both one unit of
time each period and e units of the only consumption good in the economy. We
can interpret e as an agent’s share of local production (which is not explicitly
modeled). Additional output can be produced by identical firms interacting in
competitive markets. Shares of these firms are owned by foreign investors who
supply capital (denoted by K ) but not labor. The opportunity cost of installing
capital is given by the world interest rate r ∗ that could be obtained by investing the funds in riskless bonds in international financial markets. Following
Eaton and Gersovitz (1984), we will assume that “managerial services” are
the intangible assets that foreign investors bring to the production process:
organizational skills, technological knowledge, access to overseas markets,
etc. The main difference between managerial skills and physical capital is
that the former cannot be expropriated by the government. More importantly,
if expropriation occurs, the managerial services of the foreign capitalist are no
longer available for production. This implies that any capital expropriated by
the government becomes unproductive, because either the domestic worker
does not have the necessary skills to run production by himself or because the
capital installed by the foreign investor was specific to the manager’s skills.
Therefore, it cannot be used to produce using the foreign technology.
Production requires two inputs, domestic labor L and capital K and uses
the following technology:
Assumption 1 The production function satisfies
f (K, L) = AK α L1−α .
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Domestic agents (the workers) supply labor inelastically at the competitive
wage rate w , and have no international mobility. Each belongs to one of n
groups (we can also interpret a group as a collection of individuals residing
in one of n districts), with total population normalized to one. Agents are
identical, so for symmetry we will assume that there is a measure n1 of agents
per group or district. Their preferences over consumption satisfy standard
assumptions, as shown below.
Assumption 2 Instantaneous utility is logarithmic and additively separable,
and agents discount the future at rate β ∈ (0, 1). Thus,
u(c1 , c2 ) = log(c1 ) + β log(c2 ).
As described in Section 2, expropriation can take two forms: (1) direct
expropriation, in which the government takes part or all of the already installed
capital, and (2) creeping expropriation, in which transnational corporations are
required to pay bribes or licenses that allow them to produce in the host country.
Notice that while the former takes place after investment decisions have been
made, the latter takes place beforehand. This asymmetry will have important
implications regarding the effects of electoral uncertainty on expropriation
rates.
We will model both forms of expropriation as proportional rates. The
government will demand a proportion τ out of total investment to be paid by
any firm that intends to produce in the country. Notice that we refer to it as a
bribe, but in terms of the modeling technique, it is observationally equivalent
to an investment tax. The rate at which installed capital is expropriated ex post
will be denoted by θ . Notice that activities are homogeneous in this model,
so the host country expropriates all activities at the same rate.4
The resources collected by either form of expropriation are used to provide lump sum transfers that can be targeted toward different groups in the
population. We will denote the transfer that group i receives, as a function of
the expropriation rate, by T i (θ).
Assumption 3 A group’s objective, when in power, is to maximize the utility
of its members.
The government expropriates FDI and distributes the proceeds between
agents residing in different districts in the country. Two remarks are relevant
at this point.
First, even though the expropriation rate by acting as an investment tax
distorts the optimal allocation of capital, it serves as an instrument to transfer
resources from foreign investors to local workers. The government, who only
4 We are abstracting from the fact that some sectors are more vulnerable to expropriation
than others.
M. Azzimonti and P. D. Sarte: Barriers to FDI
299
cares about the well-being of domestic agents, might be willing to compromise future production (that will be reduced because inflows of K decrease)
in order to collect part of the dividends that would otherwise go to the hands
of foreigners. This tradeoff will determine the optimal level of creeping expropriation chosen over time. Notice that the dynamic nature of the game
implies that, in general, it would not be optimal for the government to require
bribes at a level where investment in the country drops to zero (that is, a τ that
drives I = 0). Given the assumptions on technology, it would also never be
optimal to expropriate capital completely ex post. An important assumption
behind this result is the fact that domestic agents cannot produce with the
transnational corporation’s technology, as described previously.
This environment is a stylized version of an economy where output can
be produced with a domestic technology and a (possibly superior) foreign
technology. Because we want to focus on the problem of expropriation, rather
than on the dynamics of the labor market, we assume that agents are simply
endowed with e units of the good and supply labor, inelastically, to foreign
firms. It would be interesting to analyze, as an extension, the case in which
labor decisions are endogenous and domestic firms compete with transnational
corporations for domestic labor. Reallocation of workers from one sector to
another after expropriation will cause some distortions—and probably benefit
some types of workers while hurting others—that are ignored in the following
analysis.
Secondly, since transfers can be targeted toward specific districts, it is
reasonable to expect each region to lobby in order to obtain them. The disagreement over how the budget should be allocated across districts can be
resolved by some form of voting. One way to model this would be by assuming that there are n parties, each one representing a district that alternates in
power according to a Markov process. Amador (2003) presents a model with
symmetric parties that want to maximize the group’s consumption and face
some probability of being in power at each point in time (election dates are
uncertain). Once in power, the elected party chooses policy so as to maximize
the utility of its constituency. Azzimonti (2005) provides microfoundations
for the probabilities in a model of endogenous voting (but in which elections
occur at regular intervals). An alternative approach, presented in Battaglini
and Coate (forthcoming), assumes that legislators representing a district bargain in congress over redistribution of the budget. These approaches share the
property that redistributive uncertainty—captured by the probability of being
the decisionmaker in the following period—plays a key role in the level of
distortions imposed by policy because of the shortsightedness it introduces.
The sequence of events can be divided into four stages as described below.
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Timing
• Period 1:
1. Creeping Expropriation Stage: the group in power decides the level
of bribes they will demand from foreign investors, τ .
2. Investment Stage: foreign firms decide how much to invest, I , in
the host country. Bribes are collected, targeted transfers T1i are
made, and consumption c1 takes place.
• Period 2:
1. Expropriation Stage: one of the groups gains control of the government and expropriates a proportion θ of already installed capital.
2. Post-Expropriation Stage: the good is produced, wages are paid,
targeted transfers T2i are made, and consumption c2 takes place.
Notice that we are assuming that there is no transnational corporation in
Period 1, so consumption at that point will be the sum of the endowment an
agent possesses and the transfers it obtains from the government (that collected
resources in the form of creeping expropriation). We made this assumption
to simplify the exposition, but the model can easily be extended to a case in
which the government can also expropriate capital installed in the first period
of a firm that invested in the country at some point in the past.
We will solve the problem by backward induction, starting from the last
stage in Period 2.
The Second Period
Post-Expropriation Stage
This subsection describes the optimization problem faced by the manager of a
representative firm. Considering a particular specification for technology and
preferences, it characterizes a competitive equilibrium given the expropriation
rate and transfers for this economy.
At this stage, the government has already expropriated θK out of the total
capital stock, hence the firm produces with the remaining amount of capital
(1 − θ )K ≡ K̃. Firms take prices (the wage rate for local workers w) as given,
and demand labor in the local market to maximize profits
max f (K̃, L) + (1 − δ)K̃ − wL,
where δ denotes the depreciation rate of capital.
M. Azzimonti and P. D. Sarte: Barriers to FDI
301
The FOC is
fL (K̃, L) = w,
so labor is paid its marginal productivity. For our given production function,
this is equivalent to
(1 − α) AK̃ α L−α = w.
Notice that since K̃ ≤ K, the wage rate goes down after an expropriation.
This occurs because with a lower level of capital installed, workers are less
productive (this would hold for any arbitrary function that satisfies fLK > 0).
Recall that agents do not have access to capital markets, so their only
income is wage income wl , where l = 1 is the individual labor supply, plus
any transfers T2i received from the government. Their budget constraint can
be written as
c2i = e + w + T2i .
Proposition 1 A competitive equilibrium given policy {θ, {T2i (θ)}ni=1 }, is a
set of prices {w} and allocations {L, {c2i }ni=1 } such that
1. consumption of agent i satisfies
c2i = e + w + T2i (θ),
2. labor supply is L = 1,
3. wages are competitive
w = (1 − α) AH η K̃ α L−α , and
(1)
4. the government’s budget constraint holds
n
1
i=1
n
T2i (θ) = θK.
Expropriation Stage
This is the stage in which after a group gains power, it chooses the proportion
θ of total capital to be expropriated.5 A group’s objective is to maximize the
utility of its supporters. This implies that, while they do not put any weight on
the welfare of other regions or groups, policymakers are “benevolent planners”
for their own region.6
5 Because groups are homogeneous, we can focus on the problem of a representative one.
6 In the political economy literature, these policymakers are referred to as partisan. An al-
ternative approach, also studied in the literature, assumes that the leaders’ sole objective is to
maximize their probability of controlling the government because they either obtain some egorents from being in power or they can redistribute resources to themselves (kleptocrats).
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Federal Reserve Bank of Richmond Economic Quarterly
It is assumed that there is no commitment technology: once in power, the
group will choose what is best for its constituency from that point on, taking
the capital stock as given. This implies that promises made before the political
uncertainty is resolved are not credible. In particular, groups cannot credibly
promise to transfer resources to other regions in the future. As a result, it is in
no group’s interest to provide transfers to regions different than its own once
it is in power. Mathematically, this implies that group i will optimally set
j
T2 = 0 for j = i.
This is the case because (1) groups do not derive utility from the wellbeing of other regions, and (2) because they cannot sign binding contracts
with other groups over policy.
The government balances its budget, so the total amount expropriated is
divided among the members of the group controlling the government. In other
words,
1 i
T = θK.
n 2
The maximization problem of the group in power at this point (where we
have omitted the i subscripts for clarity) is
max u(c2 )
θ
s.t.,
c2 = e + w + T 2 ,
T2 = nθK, and
θ ≤ 1,
where w satisfies equation (1). Replacing the constraints above, we can simplify the objective function to u(e +w +nθK). This implies that at the second
stage the government maximizes utility by maximizing per capita consumption of the group it represents, so the problem becomes simply
max{e + w + nθK}.
θ ≤1
The first-order condition is
∂w ∂T2
+
≤0
(= 0 if θ < 1) .
∂θ
∂θ
The marginal benefit of increasing the expropriation rate is given by the
extra consumption that can be afforded by an increase in the transfer,
MB ≡
∂T2
= nK > 0.
∂θ
M. Azzimonti and P. D. Sarte: Barriers to FDI
303
Figure 1 Marginal Benefits (MB) and Costs of Expropriation (MC)
θ
θΕ
– Expropriated rate in the x-axis
– Defined in Proposition 2
MC
MB, MC
MB
θΕ
1
θ
Notice that the marginal benefit is independent of the level of θ . Graphically,
it can be represented by a horizontal line (see Figure 1).
The marginal cost is given by a decrease in the agent’s labor income due
to a reduction in the domestic wage rate,
∂w ∂ K̃
∂w
=−
, and
∂θ
∂ K̃ ∂θ
= (1 − α) αA (1 − θ)α−1 K α .
MC ≡ −
This function is increasing and convex in the rate of expropriation as long
as α < 1, as typically assumed with a Cobb-Douglas production technology.
Moreover, because the MC becomes infinitely large as θ → 1, the intersection
between the two curves will occur at an interior point (again, refer to Figure
1).
The optimal level of expropriation is found by equating the marginal costs
and benefits of increasing θ .
(1 − α) αA (1 − θ )α−1 K α = nK.
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Federal Reserve Bank of Richmond Economic Quarterly
Proposition 2 The optimal expropriation rate is given by
1
1−α
1 1
E
.
θ =1−
(1 − α) αA
K n
Thus, it is not optimal for any group in power to fully expropriate foreign
investment. That is, θ E < 1.
Since all other groups are identical, the amount of expropriation in this
economy is independent of the identity of the group in power. An interesting
extension would be to analyze the case in which sectors were heterogeneous,
either in their capital intensity or in the ability of the government to expropriate
them. In this case, workers would also be heterogeneous and disagree on the
rate of expropriation (and not only on where to target the transfers).
The First Period
Recall that there are two relevant stages in this period: investment and creeping
expropriation stages. We discuss them in the following section.
Investment Stage
We now move to the decision problem of a foreign firm considering whether
the project is worth pursuing in the host country. Expropriation affects this
decision on two margins. On the one hand, the cost of investment is increased
by the proportion of bribes that will need to be paid to the group in power. On
the other hand, the future returns of such investment will be reduced by the
fact that some proportion of capital will be expropriated in the second period.
1
∗
Firms discount the future at the rate 1+r
∗ , as r represents their outside
option. The maximization problem faced by an investor at this stage is
1
π(I ) s.t.,
I
1 + r∗
π(I ) = f (I˜, L) + (1 − δ)I˜ − wL, and
I˜ = (1 − θ)I.
max − I (1 + τ ) +
The cost of the investment is incurred today, while the benefits π(I ) are
received next period, which is why they are discounted. The investor knows
that for each unit of investment, he will need to pay a proportion τ today in
bribes or permits. He also knows that for each unit of capital installed, only a
fraction (1−θ ) will be productive: the rest is expropriated by the host country.
The assumption of atomistic competitive investors implies that the action
of one of them does not affect the level of expropriation. In other words, each
takes θ and τ as given (for the case where the transnational corporation has
monopoly, and hence bargaining power, see Doyle and van Wijnbergen 1984
M. Azzimonti and P. D. Sarte: Barriers to FDI
305
or Thomas and Worrall 1994). The first-order condition for an investor is
1 ∂π(I )
−(1 + τ ) +
= 0.
1 + r ∗ ∂I
MC
MB
Therefore, the transnational corporation equates the marginal cost of investment to the discounted value of the marginal benefit received from its
investment opportunity. A marginal increase in installed capital causes an
increase in benefits of
∂π(I )
= (1 − θ) fI (I˜, L) + (1 − δ) .
∂I
The right-hand side is the marginal increase in production, plus the marginal
increase in undepreciated capital, allmultiplied by the proportion
(1 − θ) that
˜
can be utilized. We can interpret θ fI (I , L) + (1 − δ) as the opportunity
cost of expropriation: it represents the amount of potential benefits that the
foreign investor could have obtained if it was not expropriated.
Notice that this value introduces a wedge-distorting investment decision:
it produces inefficiencies. This can be seen more clearly from the following
equation in which we have replaced the marginal benefit and rearranged the
optimality condition:
1
fI (I˜, L) + (1 − δ) = 1 + r ∗ (1 + τ )
.
(1 − θ)
Under our functional forms and noting that in equilibrium I = K, the
optimality condition becomes
α ((1 − θ )K)α−1 A + (1 − δ) =
(1 + r ∗ )(1 + τ )
.
(1 − θ)
Lemma 1 The optimal level of investment under expropriation is
1
1−α
αA (1 − θ)α
E
.
K =
(1 + r ∗ ) (1 + τ ) − (1 − δ)(1 − θ)
If there was no expropriation, a foreign firm would invest K N E (where
NE stands for “no expropriation”).
1
1−α
αA
NE
K
=
> KE.
∗
(1 + r ) (1 + τ ) − (1 − δ)
As expected, expropriation discourages investment in the host country.
We can now replace θ by θ E to find the value of FDI in equilibrium,
KE =
φ(n)
,
1+τ
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Federal Reserve Bank of Richmond Economic Quarterly
where
1
n
1
(1 − α) 1−α
.
Aα
1
−
δ
+
φ(n) =
1 + r∗
n
1−α
(2)
Creeping Expropriation Stage
At this stage, it is the group in power in Period 1 that decides the level of
bribes τ , which it will demand from potential investors. There are two main
differences between the tradeoffs faced by policymakers at this point, relative
to those faced in the second period, when choosing (ex post) direct expropriation. First, because capital has not yet been installed, FDI is more “elastic.”
Given the outside opportunities faced by investors, this imposes a constraint
on the level of bribes, which in principle, should decrease the temptation to
extract too many resources from multinational corporations. Because of this,
we would expect creeping expropriation to be less harmful than direct expropriation. On the other hand, the group decides on the level of τ without
knowing whether it will be in power next period. This introduces uncertainty
over who will have control of the expropriation technology in the second period. More importantly, it introduces uncertainty on the identity of the group
receiving the benefits of such expropriation. With probability 1 − p , another
group gains control and distributes resources only toward its own region. This
second difference with respect to direct expropriation, given by the existence
of redistributional uncertainty, induces greater expropriation in the present
through bribes by any group in power in Period 1. Therefore, it is not clear
which type of expropriation is more distortive at the end.
Before solving for the optimal level of τ , we need to specify the process by
which groups gain control of the government. In this article, we will assume
that groups alternate in power according to a stochastic Markov process: the
probability of being the decisionmaker next period, given that the group in
power today is denoted by p . Notice that this reduced-form specification
is silent on whether groups gain control via a democratic process in which
parties compete for elections, or the turnover follows from revolutions and
coups following a nondemocratic (and possibly violent) process.
Consider the problem faced by a representative group in power in Period
1. It needs to choose the creeping expropriation rate τ on FDI inflows, taking
as given the behavior of the domestic sector and foreign firms, as well as
competitive prices and aggregates. In particular, it needs to take into account
the effects of the bribes and other forms of creeping expropriation chosen
based on the following:
1. The consumption of its constituency when the group is in power, because it is maximizing its utility
c1 = e + T1 , and
M. Azzimonti and P. D. Sarte: Barriers to FDI
307
c2 = e + w + T 2 .
2. The consumption of its constituency when the group is out of power,
because there is a probability that next period a different group is in
power,
c̃2 = e + w.
3. FDI inflows, I = K E (in equilibrium), because foreign investors decide
after knowing the level of τ
φ(n)
KE =
,
1+τ
where φ(n) is defined in equation (2).
4. Transfers to the region it represents, via the government budget constraint
T1 = τ nK E and
T2 = θ E nK E .
5. Second period’s expropriation rate θ E ,
1
1−α
1 1
E
θ =1− E
.
(1 − α) αA
K
n
6. Equilibrium prices, because they affect their constituency’s consumption
w = (1 − α) A[(1 − θ E )K E ]α .
The group solves
maxu(c1 ) + β{pu(c2 ) + (1 − p)u(c̃2 )},
τ
subject to the conditions listed above.
The first-order condition reads as
dc1
dc2
d c̃2
uc (c1 )
+ β puc (c2 )
+ (1 − p)uc (c̃2 )
= 0.
dτ
dτ
dτ
When the rate of creeping expropriation increases today, there is a direct
effect in agents’ consumption—captured in the first term of the expression—
since those favored by the group in control receive an increase in the transfer
of
nK E
dT1
=
.
dτ
1+τ
Firms react to a larger τ by cutting FDI,
KE
dI
.
=−
1+τ
dτ
308
Federal Reserve Bank of Richmond Economic Quarterly
This reduces the amount of capital available for production next period (recall
E
dI
that dτ
= dK
dτ ), which modifies tomorrow’s consumption because the next
policymaker will face a lower tax base, and thus be forced to reduce the level
of transfers T2 . Moreover, from condition 5 this triggers a reduction in direct
expropriation (θ E ) as well. The total effect in transfers is given by
E
E
dT2
E dθ
EK
= n K
+θ
and
dτ
dτ
dτ
nK E
= −
.
1+τ
Notice that since (1 − θ E )K E is independent of τ (see condition 5 above),
then from condition 6 so is w . Because second period wages are unaffected
by creeping expropriation, the level of consumption when a group is out of
power is independent of τ . In other words, ddτc̃2 = 0, so the last term in the
first-order condition cancels out. The fact that c2 is independent of the level
of bribes is a result of the particular assumption on preferences, because under
logarithmic utility income and substitution effects cancel out. This results in
optimal direct expropriation rates being inversely proportional to the stock
of capital, so (1 − θ )K is constant and independent of τ . Replacing u by a
logarithmic utility, we obtain the following lemma:
Lemma 2 Under assumption 2, redistributional uncertainty introduces a
wedge in the efficient growth rate of consumption since, in the political equilibrium
c2 = βpc1 .
Absent the redistributional uncertainty (i.e., where groups act in a coordinated fashion) the government would choose policy so that c2 = βc1 . Because
p < 1, the equation above shows that the ratio of consumption between the
two periods is suboptimally low. In other words, the political uncertainty
makes policymakers too impatient.
Proposition 3 Under assumptions 1 and 2, the optimal rate of creeping expropriation is given by
τ=
where
γ (n) − eβp
,
(1 + βp)nφ(n) − γ (n) + eβp
⎡
γ (n) = nφ(n) ⎣1 +
(1 + r ∗ )(1 − α)
α 1−δ+
n
1−α
⎤
⎦ + e.
M. Azzimonti and P. D. Sarte: Barriers to FDI
309
Expropriation and Political Instability
Political instability refers to the frequency by which groups alternate in power.
Countries facing high turnover rates are those where p is relatively small.
Why is this the case? Because the probability that any given group remains
in control of the government in the second period is low.
In this section, we analyze the implications of political instability on the
level of expropriation predicted by the model and contrast it to what the empirical literature has found.
Proposition 4 characterizes how each rate of expropriation changes
with p .
Proposition 4 Under assumptions 1 and 2, we can show that
1. creeping expropriation is larger in countries with greater political instability (i.e., low p)
dτ
< 0, and
dp
2. direct expropriation is lower in countries with greater political instability
dθ
> 0.
dp
We can understand the intuition behind the negative relationship between
the amount of bribes and permits demanded by foreign investors τ , and the
probability of keeping control of the government p , by looking at the expression in Lemma 2. When the group in power faces relatively low political
instability, the chances of being able to appropriate transfers next period are
large. In this case, policymakers want to increase relative consumption (i.e.,
the ratio cc21 ). The change in p is equivalent to an increase in the degree of
patience of the group in power. Consumption in the second period becomes
relatively cheaper, creating a substitution effect toward less consumption today and more consumption tomorrow. Due to market incompleteness, the
only way to achieve this transfer of resources is via a reduction in the degree of creeping expropriation today, by lowering T1 and, thus, c1 . Because
transnational corporations bring human capital and technology, they are more
efficient in production than the local country. It is then optimal for any group
to wait and expropriate after investments have been made when p increases,
because the proportion of investment that will not be expropriated ex post
will be productive: K E increases with lower τ rates. If the country had access to borrowing and lending, this effect would be reduced, but nonetheless,
present. Therefore, we should expect that countries with low turnover impose
310
Federal Reserve Bank of Richmond Economic Quarterly
relatively low barriers to FDI inflows—that is, require lower bribes and make
construction and production permits cheaper to foreign investors.
The effect of p on direct expropriation is more subtle and has to do with
inter-group manipulation. Because θ is chosen after the political uncertainty
has been resolved, it is, in principle, unaffected by p . There is no direct
effect of turnover on expropriation ex post. Indirectly, however, increases in
p reduce creeping expropriation in the first period and attract more FDI. In
other words, K E increases. Because there is a larger tax base, the MB of
expropriating in Period 2 increases. The marginal cost also increases but in a
lower proportion (this is due to the Cobb-Douglas technology assumption). As
a result, θ goes up. Another way to understand the intuition behind this second
result is to consider the costs and benefits of the group deciding today. If p is
relatively low, another group will gain control in Period 2 with high probability.
If the current group happens to be out of power tomorrow (a likely event),
direct expropriation imposes large costs in terms of reduced production and
no benefits, because no transfers are received. There are incentives, therefore,
to manipulate future decisions by affecting the stock of capital inherited by
tomorrow’s policymaker and make direct expropriation less attractive. From
the expression in condition 5, Section 4, this can be achieved by decreasing
K E . How can the group controlling the government in Period 1 reduce future
capital? This can be accomplished by making FDI less attractive—increasing
the barriers to its entrance. We should, therefore, expect a negative correlation
between political instability and direct expropriation rates.
Notice that this analysis is partial in the sense that we are only considering
a once-and-for-all investment decision. There is no action that a government
in the second period can take to undo the manipulation of the first period
policymaker. In an economy with a longer horizon, in which investment
decisions were made every period, the group in power in Period 2 could also
demand bribes and permits, and thus break the link between first period bribes
and the allocation of foreign capital in the country. That possibility would give
groups controlling the government in Period 2 an extra degree of freedom. It
would then be interesting to extend the analysis to a case with an infinitehorizon economy.
Expropriation and Concentration of Power
The previous section assumed that differences in political instability only correspond to political factors and were independent of other fundamentals of
the economy. In a model where such probability was endogenized, we would
expect p to be related to the number of groups in the economy, n. If there were
many groups fighting for power, given the same aggregate size of the population, the probability of keeping control of the government would probably
be low, and we already know the effects this reduction has on expropriation.
On the other hand, a larger value of n implies that if a given group happened
M. Azzimonti and P. D. Sarte: Barriers to FDI
311
Figure 2 Expropriation and Concentration of Power
2.22
0.8
Creeping Expropriation
Direct Expropriation
0.7
2.20
0.6
2.18
0.5
(n)
2.16
0.4
0.3
2.14
0.2
2.12
0.1
2.10
0.0
2.08
-0.1
2
4
6
8
10
2
4
6
8
10
n
n
to gain control, then the benefits of expropriation per member in the group
would increase because per capita transfers would be larger. This implies that,
in principle, the relation between concentration of power and expropriation
could be non-monotonic.
We have calculated how creeping expropriation changes as we reduce the
concentration of power for a numerical example (the parameter values were
not calibrated but rather chosen to illustrate our point). The probability of
staying in power faced by any group is assumed to satisfy
p=
1
+ ξ,
n
where ξ represents an “incumbency advantage” term, reflecting the fact that the
group in power has greater chances to gain control next period than any other
group in the opposition. The political economy literature has documented the
existence of such an advantage in democratic elections. In more authoritarian
systems, we often see groups or families in control of the government for long
periods of time because they have access to military force and other means of
repression. Increases in ξ can be interpreted as changes in political instability
not related to the concentration of power, which were studied in the previous
section, whereas the effects of concentration can be analyzed separately by
looking at the effects of changes in n.
312
Federal Reserve Bank of Richmond Economic Quarterly
Inspection of Figure 2 tells us that when there is relatively large concentration of power (i.e., n close to 2), increases in the number of groups result
in more expropriation of both types. This happens because larger values of
n reduce p and, from the intuition in the previous section, this encourages
creeping expropriation activities, that is, rises in τ . On the other hand, when
there is little concentration of power, increases in the number of groups in a
given economy result in lower levels of τ . While the probability of remaining in power decreases with n, transfers per capita increase, but in a larger
proportion and, therefore, dominate. Even though each group is less likely to
stay in power, the benefits of expropriating in Period 1 more than compensate
the costs driven by an increase in the risk of losing control of the government
in Period 2. This result is different from the one found in the previous section, and it gives a direct testable implication of the model. If countries have
greater political instability because there is low incumbency advantage, more
creeping expropriation is to be expected. If, on the other hand, it is due to the
composition of competing groups, and there is a relatively large number of
them, then we should expect less creeping expropriation as political instability
increases.
5.
CONCLUSIONS
We reviewed the empirical evidence on the effects of expropriation on FDI
inflows, mainly focusing on developing countries. We then discussed theoretical models explaining how the quality of institutions affects FDI and growth.
In particular, we described how the different frictions present in the political
process result in policies that discourage FDI inflows. Finally, we presented
a simple model that sheds some light on the effects of expropriation on FDI
under: (1) lack of commitment to policy from the government, (2) redistributional uncertainty resulting from stochastic alternation of groups in power,
and (3) the interaction between alternative forms of expropriation. The main
contribution of this work is twofold: the analysis of a model in which both
direct and indirect forms of expropriation are present and the study of how
the two types of expropriation relate to political instability. We also discussed
the effects of the concentration of power on the incentives to use each type of
expropriation and their resulting effects on investment.
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