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Central Banking:
Then and Now
J. Alfred Broaddus, Jr.

T

hank you very much for that kind introduction. It is very nice indeed to
be here in the Shenandoah Valley. Like Woodrow Wilson, I’m a native
son of Virginia. Unlike him, I can’t claim to have begun life in this
magnificent Valley. But I did have the pleasure of completing my undergraduate studies not too far from here at Washington and Lee. So I feel very much
at home here, and I appreciate your invitation to be with you.
The theme of this conference is “Facing Economic Issues: Clinton and
Wilson.” And this is a quite appropriate theme, because there are obvious parallels. President Clinton and the country face pressing economic problems today,
many of which have been discussed by previous speakers at this conference.
President Wilson also faced substantial economic challenges in his Administrations. One of President Wilson’s greatest achievements—which occurred in his
first year in office—was his orchestration of the difficult compromise, among
a number of powerful and conflicting groups in the country, that culminated
in passage of the Federal Reserve Act in December 1913 and the creation of
our central bank, including its regional arms, the Federal Reserve Banks, the
following year.
Against this background, what I would like to do this morning is to tell you
a story: an historical story, if I may, which seems appropriate in this setting.
It is the story of the Federal Reserve, inflation, deflation and the relationship

This article is adapted from an address given by J. Alfred Broaddus, Jr., president of the Federal Reserve Bank of Richmond, to the Woodrow Wilson Forum sponsored by the Woodrow
Wilson Birthplace Foundation, Staunton, Virginia, on April 2, 1993. Marvin Goodfriend,
senior vice president and director of research at the Richmond Fed, contributed substantially
to the preparation of the article.

Federal Reserve Bank of Richmond Economic Quarterly Volume 79/2 Spring 1993

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Federal Reserve Bank of Richmond Economic Quarterly

between the three. Probably everyone here knows that the Fed is supposed to
maintain the purchasing power of the American dollar and to prevent inflation.
It is also supposed to prevent deflation, which is not much on people’s minds
today, but was at times in Wilson’s day and certainly in the 1930s. Another way
of saying this is that the Fed is supposed to keep the aggregate level of prices—
not the individual prices of particular goods and services, but the aggregate
price level—reasonably stable over time. A stable price level by definition
implies the absence of both persistent inflation and persistent deflation.
That the Fed is in some sense responsible for stabilizing the price level
presupposes some benefit from doing so. As many of you know, there has been
far less than complete agreement in the United States, both in the distant past
and more recently, on the desirability of price-level stability—particularly the
desirability of controlling inflation. Some people, especially those who borrow
money regularly, benefit from inflation, at least temporarily and partially. But
I think it’s fair to say that a majority of Americans value a stable price level
and a sound dollar, even if they don’t think about it a lot. In general they
don’t want the frequently high and typically variable inflation rates that have
plagued so many other countries in the past and now. Americans sense that stable prices and stable money prevent the arbitrary redistributions of real income
and wealth that accompany inflation and weaken societies. They sense also that
stable prices and stable money eliminate the confusion, uncertainty, risk and
inefficiency that inflation introduces into the nation’s free market system.
Now while most Americans believe that the Fed is supposed to “fight”
inflation and deflation in some general sense, they are also aware that the fight
has been an uneven one and by no means fully successful in all periods of our
history. On the contrary, the country went through a cataclysmic deflation in
the 1930s. Subsequently it went through a substantial inflation in the late 1970s
and early 1980s—not as traumatic and damaging as the experience in the ’30s,
but a very bad time nonetheless.
What’s the problem? Why hasn’t the Fed done a better job? I am going to
argue today that one reason—and maybe the main reason—is that the Fed does
not now have, and it never has had, a clear congressional mandate to stabilize
the price level. Consequently, the Fed’s success in stabilizing the price level
in at least some periods of its history has been and continues to be a function largely of (1) prevailing general economic conditions, (2) the strength of
the Federal Reserve’s leaders, and (3) old-fashioned luck. The implication, of
course, is that something probably should be done to strengthen the Fed’s hand
so that its performance would be less dependent on fortuitous circumstances.
And let me make it clear that I personally feel strongly that something should
be done. I am well aware that in today’s relatively low inflation climate, many
people do not see this as a pressing issue, such as the federal budget deficit or
health care reform, that requires immediate attention. I disagree for reasons I
hope to make clear in the remainder of my comments.

Alfred Broaddus: Central Banking: Then and Now

3

There are probably several ways one could make this argument, but, as
I suggested earlier, I want to take an historical approach, which seems appropriate here. I’ll proceed as follows. First, I want briefly to describe the
monetary conditions that led to the creation of the Fed—with the assistance of
Woodrow Wilson. Then I will try to indicate exactly what the framers of the
Federal Reserve Act expected the Fed to do—its mandate in 1913 and 1914,
as it were. A particular point here is that the mandate did not include, in any
explicit way, stabilizing the price level. Next, I’ll indicate how the rapid and
substantial change in circumstances during and after World War I, shortly after
the Fed was created, forced the Fed to confront the problem of stabilizing the
price level early on in the 1920s, a challenge it met with some success until
the stock market crash in 1929. All of this is the “then” part of my remarks.
Finally, I’ll skip over to the late 1970s and 1980s—the “now” part—and show
that the Federal Reserve has faced many of the same inflation challenges in
recent years that it faced in the 1920s. It has achieved some success in this
later period also, for remarkably similar reasons. However, the absence of a
clear price-level stability mandate today presents the nation with some—not
all, but some—of the same kinds of risks it faced in its early years. We are
much better equipped to deal with these risks now than we were then. But we
can and should reduce them by clarifying the Fed’s price stability mandate,
preferably through legislation.
That’s my introduction, and it has been a long one. But let me proceed,
and I will try to make the remainder of my points as compactly as I can.

1. THE GOLD STANDARD AND PRICE STABILITY BEFORE
THE FEDERAL RESERVE
As I suggested a minute ago, the Federal Reserve was established in 1914
to remedy banking and currency problems that had been recurring since the
Civil War. The country had no central bank during this period, which is known
to economic historians as the National Banking Era. The United States left
the gold standard to help finance the Civil War, but returned to it in 1879.
Thereafter, monetary conditions were largely governed by the flow of gold to
and from the United States as part of the international balance of payments
adjustment mechanism under the international gold standard.
Under the gold standard, the national money supply was closely linked
to the nation’s stock of monetary gold, which included gold coin, Treasury
currency backed by gold, and gold reserves held by banks. When the country
ran a balance of trade surplus, for example, the excess of foreign receipts over
expenditures was received in gold. The gold inflow set in train a multiple
expansion of deposits that increased the money supply. The increase in the
money supply then increased domestic demand for goods and services and put

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Federal Reserve Bank of Richmond Economic Quarterly

upward pressure on domestic prices. The reverse occurred when the country
ran a trade deficit. For our purposes, the point is that under a gold standard
without a central bank, the nation’s stock of money was automatically regulated
by conditions in world markets.
This system had good features and not-so-good features. On the good side,
the gold standard did keep the aggregate price level under control over the very
long run. The aggregate level of prices in 1914, for example, was not very
different from the level 30 years before in the early 1880s. By comparison,
the price level rose 270 percent between 1960 and 1985. So the gold standard
provided an anchor for the price level over the long run—that is, it provided
a means of stabilizing the price level over the long run. Moreover, it was a
credible anchor; the public understood the mechanism and knew it worked.
But the gold standard had significant limitations in the short and intermediate terms. First, while the gold standard anchored the price level over the very
long run, it nonetheless allowed it to drift upward and downward by significant
amounts over fairly long periods. For example, slow growth in the world gold
supply caused the price level to decline at over 1 percent per year from 1879
to 1897, which provoked William Jennings Bryan’s famous plea not to crucify
mankind on a cross of gold. Subsequently, new gold discoveries and improved
mining techniques caused the metal’s supply to increase rapidly in the late
1890s and early 1900s. Consequently, the price level rose at over 2 percent
per year from about 1897 to 1914. A second limitation was that the strict
discipline of the gold standard did not allow the money supply to increase
rapidly in response to domestic disturbances such as a banking panic or a stock
market crash.

2. SHORT-TERM INTEREST RATE BEHAVIOR BEFORE
THE FEDERAL RESERVE
Let me expand just a little on that last point and shift the focus temporarily
from prices to interest rates, since it was really a concern about financial problems and sharp interest rate movements under the gold standard that led to the
Federal Reserve Act. Because the nation’s monetary gold stock was relatively
unresponsive to domestic economic conditions in the short run, the National
Banking Era was characterized by considerable short-term interest rate variability. Sudden sustained short-term interest rate spikes of over 10 percentage
points occurred on eight occasions during this period. Some, though not all,
of these spikes were associated with banking panics, which involved a loss
of confidence in the banking system and a rush to convert bank deposits into
currency. Since banks held only a fractional reserve of coin and currency in
their vaults, “bank runs” generated a scramble for liquidity that could not be
satisfied in the short run. Major banking panics occurred in 1873, 1884, 1890,
1893 and 1907.

Alfred Broaddus: Central Banking: Then and Now

5

In addition to the recurring interest rate spikes, there was a pronounced
seasonal pattern in short-term interest rates. This pattern resulted from the relatively strong demand for currency during the fall harvest and Christmas holiday
seasons. It was exacerbated by the reserve requirement provisions of the National Bank Act, which led to a phenomenon known as “pyramiding”—the
concentration of reserves in big-city banks. The practice of counting correspondent balances as legal reserves, combined with the payment of interest on
interbank balances, caused reserves to concentrate in the larger cities, especially in New York. The withdrawal of interbank balances in peak agricultural
and holiday periods tended to exacerbate seasonal pressures on the banking
system. Consequently, short-term interest rates varied seasonally by as much
as 6 percentage points over the course of a year.

3. THE FEDERAL RESERVE’S MANDATE IN 1914
This background information is essential in understanding what President Wilson and the Congress had in mind when they passed the Federal Reserve Act.
The Federal Reserve was established in 1914 in large part to alleviate the
two main problems of the National Banking Era: (1) recurrent interest rate
spikes associated with liquidity crises and banking panics, and (2) interest
rate seasonals exacerbated by reserve pyramiding. Specifically, as stated in
its preamble, the purposes of the Federal Reserve Act were “to provide for
the establishment of Federal Reserve banks, to furnish an elastic currency, to
afford means of rediscounting paper, to establish a more effective supervision
of banking in the United States, and for other purposes.”
Under the Act, 12 Federal Reserve Banks (including ours in Richmond)
were established around the country as depositories for the required reserves
that previously had been held at correspondent banks in New York City and
elsewhere. By requiring that private banks hold reserves directly in a Federal
Reserve Bank, the Act eliminated reserve pyramiding and eased the seasonal
strain on the banking system.
The most important power given the new central bank, however, was the
authority to issue currency and to create bank reserves at least partly independently of the nation’s monetary gold reserves. The Fed could create currency
and reserves as long as the Federal Reserve Banks kept a minimum 40 percent
gold reserve against Federal Reserve notes, which were paper currency, and
a 35 percent gold reserve against deposits held by private banks at Federal
Reserve Banks. These minimum gold reserve ratios made the Fed respect the
discipline of the gold standard; however, the monetary gold stock was so large
during the Fed’s early years that these requirements were not “binding.” In
other words, they did not constrain the volume of Federal Reserve notes that
could be issued nor the volume of bank reserve deposits that could be created
by Reserve Bank discount window lending. The power to create currency and

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Federal Reserve Bank of Richmond Economic Quarterly

bank reserves enabled the Fed to do what it had been established to do: eliminate both the seasonal in interest rates and the periodic spikes in rates that had
plagued the country during the National Banking Era.

4. PRICE STABILITY IN THE FED’S EARLY YEARS
The Expectation
As we have just seen, the new central bank was well equipped to deal with
both seasonal and special liquidity pressures and their effects on interest rates.
But we need now to shift our focus back to the price level and ask: What did
the Federal Reserve System and its ability to create currency and bank reserves
imply for the stability of the price level—that is, the stability of the purchasing
power of money? The answer is that it was taken for granted that the minimum
gold reserve ratio under the gold standard would continue to provide what
economists call a nominal anchor for the monetary system, which is a fancy
way of saying that it would provide for a reasonably stable price level over
time. (As a footnote, I should point out here that the framers of the Federal
Reserve Act apparently did not give much attention to the intermediate drift
of the price level upward and downward which, as I mentioned earlier, can
and did occur under the gold standard.) The clear presumption underlying the
Act was that the new central bank would concern itself mainly with making
liquidity available on a timely basis to smooth short-term movements in interest
rates. Any discretionary injection of currency or bank reserves for this purpose,
however, was expected to be only temporary, so that the nation’s money supply
and price level would, over the long term, be governed by the nation’s stock
of monetary gold, much as it had been before the establishment of the Fed.
Given this presumption—and this is a crucially important point about the
history of central banking in the United States—the Federal Reserve Act did
not include a mandate for price stability because everyone expected that the
price level in fact would be stable over time as long as the Federal Reserve
respected its minimum gold reserve ratio. The gold standard would guarantee
price stability and the new central bank could focus on stabilizing the banking
system and interest rates. No separate mandate to resist inflation or deflation
was needed.
Federal Reserve Policy in the Aftermath of World War I
This was the expectation. Let me turn now to the reality of the early years of the
Fed—more specifically, the period between 1914 and 1929. The presumptions
about the gold standard and price-level stability implicit in the Federal Reserve
Act were tested swiftly and severely during these years. In one of the great
ironies of monetary history, by the time the Federal Reserve Banks actually

Alfred Broaddus: Central Banking: Then and Now

7

opened for business in 1914, the outbreak of World War I in Europe had
brought about widespread suspensions of national commitments to maintain
the fixed currency price of gold. Because the United States remained neutral
until 1917, it was able to remain on the gold standard throughout the War, and,
although it embargoed gold exports, it continued to fix the dollar price of gold
at $20.67 per ounce.
As it turned out, United States participation in the War and the large federal
deficits that accompanied it—yes, there were deficits back then too—occasioned
the first major use of the fledgling central bank’s power to create currency and
bank reserves. Most of the federal deficit was covered by sales of U.S. government bonds to the public. The additional supply of bonds, naturally, put
upward pressure on interest rates, which would have greatly increased the cost
of financing the War had the pressures been allowed to persist. Consequently,
the Reserve Banks held short-term interest rates down by keeping their discount
rates low and accommodating credit demand at these rates—which they were
able to do because of the excess gold reserves I mentioned earlier. The discount
window lending by Federal Reserve Banks, in turn, increased the supply of bank
reserves and caused the U.S. money supply to rise.
Now, as you are no doubt aware, rapid money growth produces inflation
over time. Consequently, the highly accommodative monetary policy during
the War caused the U.S. price level approximately to double. Although the
War ended in 1918, Federal Reserve policy remained accommodative in 1919
in an effort to cushion the negative economic impact of demobilization. The
continued rapid growth in Federal Reserve notes and in bank reserves that
resulted from this policy, along with the lifting of the wartime gold embargo
that allowed gold to flow abroad again, finally mopped up the excess gold and
caused the Federal Reserve’s gold reserve ratio to become binding in mid-1920,
toward the end of President Wilson’s second term.
At this point, the Fed finally had to confront the constraints of the gold
standard, and it responded affirmatively and aggressively. Faced with the need
to defend its gold reserve ratio, the Fed raised its discount rate from 4 percent
to 7 percent in 1920, a near doubling. In today’s terminology this constituted
a sharp “tightening” of monetary policy, and it was strong medicine. The deflationary impact was swift and extraordinary. Prices fell precipitously, and by
June 1921 about half of the earlier wartime increase in the price level had been
reversed. Unfortunately, the sharp decline in the price level was accompanied
by a severe economic contraction and rising unemployment lasting from early
1920 to mid-1921. But by acting as it did, the Fed essentially validated the implicit assumption underlying the Federal Reserve Act—that the country would
remain on the gold standard, which would maintain a stable price level over
the long run if not the shorter run. To use some current jargon, the Fed attained
credibility for its commitment to the gold standard and price stability by its stiff
tightening of policy in 1920. As a postscript, many monetary historians would

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Federal Reserve Bank of Richmond Economic Quarterly

argue that the Fed could have achieved greater credibility with less economic
disruption if it had tightened policy sooner. Regrettably, the cost of failure to
resist inflation promptly and decisively when it arises is a lesson the nation has
had to learn repeatedly.
Price Stability in the 1920s
After validating the country’s commitment to the gold standard in the early ’20s,
and once it had obtained a cushion of gold reserves above its legal minimum,
the Fed began to use its monetary policy powers to achieve a greater degree of
short-term price-level stability. Under the able leadership of Benjamin Strong,
Governor of the Federal Reserve Bank of New York, the Fed deliberately began to offset the effect of temporary gold inflows on the U.S. money supply by
selling equivalent amounts of securities from its portfolio. Likewise, temporary
short-term outflows of gold were offset by security purchases. Such “sterilization” insulated the U.S. economy from the money supply and aggregate demand
instability that gold flows would have caused had they been allowed to affect
currency and bank reserves.
Aggregate economic conditions were favorable during most of the period
from 1922 to 1929, in my view, partly because the Fed recently had won at
least belated credibility for its commitment to price stability by defending the
gold reserve ratio in 1920 and 1921, partly because of Strong’s extraordinarily skillful discretionary containment of inflation, and partly because of the
absence of severe economic shocks. Unfortunately, at the end of the decade,
these foundations began to crumble. After having been partially restored in the
’20s, the international gold standard became increasingly fragile and deflationary. Moreover, Governor Strong died an untimely death in 1928, which robbed
the Fed of strong leadership. Thus the Fed—bereft of any explicit price stability mandate—was simply unable to maintain a discretionary monetary policy
aimed at price stability. The consequence was a 30 percent decline in prices in
the early 1930s and the most terrible economic depression in American history.
Before moving to my concluding comments about the “now” period in the
title of this talk, it may be helpful to summarize briefly the principal points
about the “then” period. The main point is that the Federal Reserve Act did not
mandate the Federal Reserve System to control inflation or stabilize the price
level; instead, it instructed the Fed, in effect, to smooth interest rates. The reason
for the omission of a price stability mandate was that it was assumed that the
gold standard would produce long-run price stability because the Fed would
adhere to its minimum gold reserve ratio over time. The Federal Reserve was
successful in pursuing price stability in the 1920s in part because of favorable
underlying economic and financial conditions in the period between 1921 and
1929. But prices were also stable because the Fed had made its price stability
objective credible by strongly defending its minimum gold reserve ratio early
in the decade. Subsequently, the Fed reinforced its commitment by sterilizing

Alfred Broaddus: Central Banking: Then and Now

9

gold inflows under the skillful leadership of Benjamin Strong. Once Strong and
the favorable economic climate were removed, however, the absence of a price
stability mandate led inexorably to the debacle of the 1930s.
While what happened during the Depression decade of the 1930s obviously
is very important in U.S. monetary history, I must move on now from the
“then” part of my talk to the concluding “now” part. We shall see that at least
some of the deficiencies in the institutional structure of American monetary
policymaking that existed in 1929 still exist, and that they present some risks,
although the risks are different from those of the earlier period.

5. INFLATION IN THE 1970s AND 1980s
We pick up our story a half-century later in the mid-1970s. At the time, inflation
had been rising slowly but steadily since the early 1960s. The U.S. dollar and,
through it, the world’s other major currencies, had been linked to gold under
an arrangement known as the Bretton Woods System after the town in New
Hampshire where the agreement had been forged at the end of World War II.
Under the arrangement, the U.S. had pledged to maintain convertibility of the
dollar into gold at $35 per ounce. But when excessively accommodative monetary policy and gold outflows caused the Federal Reserve’s then 25 percent
gold reserve ratio to become binding in the mid-’60s, in sharp contrast to the
Fed’s behavior in 1920 and 1921, the gold reserve requirement was eliminated.
After some attempts to repair the Bretton Woods System, it finally collapsed
in 1973.
The year 1973 is generally remembered as the year of the first oil price
shock, but it was also a watershed in U.S. monetary history. Before 1973 there
was a sense that both the domestic and international monetary systems should
retain at least some link to gold, even though the country had not really permitted the gold standard rules to constrain monetary policy for some time. Since
1973, however, there has been a general—although not universal—belief that
the gold standard is a thing of the past. Consequently, for the last 20 years the
Fed has lacked even the weak Bretton Woods commitment to gold that would
have anchored the price level at least over the very long run and helped it deliver
price stability. Since the Federal Reserve was originally designed to operate in
an institutional environment with at least some such commitment, one might
have expected Congress, as a matter of logic, to give the Fed an explicit price
stability mandate when the Bretton Woods System fell apart. Unfortunately, no
clear mandate has been forthcoming, although Congressman Stephen Neal of
North Carolina introduced an amendment to the Federal Reserve Act in 1989
and has reintroduced it every year since that would provide such a mandate.
The Neal Amendment (sometimes referred to as the “zero inflation amendment”) would require the Fed, over a period of time, to eliminate inflation as
a significant factor in economic and business decisions. The Fed supports this

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Federal Reserve Bank of Richmond Economic Quarterly

Amendment, and I personally believe its passage would benefit the American
economy enormously.
As you probably know, Congress did pass legislation in the late 1970s that
requires the Fed to set and report targets for the growth of the U.S. money
supply. Many people, including your speaker, were hopeful at the time that this
legislation would yield more stable and noninflationary money growth rates,
and, hence, a more stable price level. But, frankly, it did not work well in this
period. As measured by the Consumer Price Index, the inflation rate rose from
4.9 percent in 1976 to 13.3 percent in 1979 and 12.5 percent in 1980. To be
sure, the higher inflation partly reflected the continued sharp increases in oil
prices in this period. But it is also true that money supply growth exceeded
its targets almost continuously throughout the late 1970s. This performance
created doubts about the Fed’s commitment to the targets, which encouraged
inflationary price- and wage-setting behavior even before the oil price shock.
Congress’ willingness to accept the inflationary money growth rates, and its
failure to mandate the Federal Reserve to stabilize prices, further undermined
the public’s confidence that inflation would be resisted. In short, by the late
1970s the Fed had little if any credibility as an inflation fighter or as a defender
of the purchasing power of the dollar.

6. AGGRESSIVE INFLATION FIGHTING IN THE 1980s
By the time Paul Volcker became Federal Reserve Chairman in August 1979,
the inflation outlook had begun to deteriorate rapidly. The widely publicized
announcement on October 6, 1979, of the Federal Reserve’s intention to control
money growth more closely inaugurated a period of aggressive inflation fighting. The announcement signaled financial markets and the country that the Fed
was prepared to take responsibility for delivering low inflation, even without
an explicit mandate for price stability from Congress.
But the announcement was just the beginning. Because the Fed’s credibility
as an inflation fighter had been so badly compromised, the System had to follow
the announcement with strong actions to demonstrate its intent, much as the
Fed had had to do in the early 1920s. And strong action was taken in the form
of a severe tightening of policy that took short-term interest rates from around
11 percent in late 1979 to 17 percent by April 1980 and ultimately to around 20
percent by early 1981. This was the sharpest tightening the Federal Reserve had
ever engineered in so short a time. The action succeeded in bringing inflation
down to around 4 percent in 1982. In addition, in a manner similar to the early
1920s, it greatly enhanced the Fed’s credibility as a defender of the purchasing
power of the dollar, although—in another parallel to the ’20s—it was accompanied by a sharp and costly contraction. This credibility, combined with (in yet
another parallel to the ’20s) the able leadership of Chairman Volcker and his

Alfred Broaddus: Central Banking: Then and Now

11

successor, Alan Greenspan, has enabled the Fed to maintain the low inflation
rate in subsequent years and, indeed, to reduce it somewhat further to a trend
rate currently of approximately 3 percent.

7. IMPLICATIONS OF THE PARALLELS BETWEEN THE
’20s AND THE ’80s: A CONCLUDING COMMENT
As we have seen, Federal Reserve policy in the early 1980s had much in common with that of the 1920s. Both decades opened with periods of exceedingly
tight monetary policy in response to earlier accelerations of inflation, and the
restrictive policies succeeded in bringing inflation sharply downward in both
periods. Beyond this, the Fed’s strong actions in each instance conferred upon
it an enhanced credibility that helped keep inflation low for the remainder of
the decade. Moreover, unusually capable central bankers in both periods took
advantage of this credibility to pursue price stability with essentially discretionary actions, even though Strong was acting within the overall framework
of the gold standard in the earlier period.
There is one final, less comforting comparison between the two periods,
however, that needs to be drawn. As I have indicated, the Fed entered the 1930s
without Benjamin Strong, with an eroding and exceedingly deflationary gold
standard, and with no alternative, explicit price stability mandate. Currently, the
Fed is moving toward the end of this century and the beginning of the next in
a stronger and qualitatively different condition. Inflation, rather than deflation,
is the current concern. Economic conditions are more tranquil now than they
were at the end of 1929, despite the many problems we still face. Further,
in my opinion the Fed currently enjoys energetic and very capable leadership.
However, as in 1929, there is no clear mandate for the Fed to pursue price-level
stability. This makes many of us who work at the Fed uneasy, and it explains
why the Federal Reserve supports Congressman Neal’s Amendment, which, as
I noted earlier, would provide us with such a mandate.
In short, ladies and gentlemen, under present institutional arrangements
surrounding the conduct of American monetary policy, maintenance of a sound
dollar in the longer-term future will require continued strong leadership at the
Fed, an absence of major destabilizing economic shocks like the oil shocks
of the 1970s and, ultimately, a measure of good luck. The continuation of all
these circumstances indefinitely would be fortuitous. I don’t feel very comfortable in this situation, and you shouldn’t feel comfortable either—especially the
younger people in the audience. This economic issue may seem less immediate
and pressing than some of the others you’ve faced over the last day and a half.
But I can assure you that it is no less important. We need to resolve it promptly.

Unit Roots in
Macroeconomic Time
Series: Some Critical Issues
Bennett T. McCallum

A

n enormous amount of analytical literature has recently appeared on
the topic of “unit roots” in macroeconomic time series. Indeed, tests
for the presence of unit roots and techniques for dealing with them
have together comprised one of the most active areas, over the past decade, in
the entire field of macroeconomics. The issues at hand have involved substantive questions about the nature of macroeconomic growth and fluctuations in
developed economies and technical questions about model formulation and estimation in systems that include unit-root variables. The present paper attempts
to describe several of the main issues and to evaluate alternative positions. It
does not pretend to be a comprehensive survey of the literature or to provide
an “even-handed” treatment of issues, however.1 Instead, it attempts to develop
a convincing perspective on the topic, one that is consistent with the views of
many active researchers in the area but that may nevertheless be somewhat
idiosyncratic.
The exposition that is presented below is designed to be predominantly
nontechnical in nature. Indeed, it takes a rather old-fashioned approach to

This paper has been prepared for the Research Department of the Federal Reserve Bank of
Richmond. The author, H. J. Heinz Professor of Economics at Carnegie Mellon University
and research associate at the National Bureau of Economic Research, is indebted to John
Campbell, David DeJong, Marvin Goodfriend, Robert King, Peter Schmidt, and Mark Watson for suggestions and useful criticism. The views expressed do not necessarily reflect those
of the Federal Reserve Bank of Richmond or the Federal Reserve System.
1 For other recent survey articles, see Stock and Watson (1988) and Campbell and Perron
(1991).

Federal Reserve Bank of Richmond Economic Quarterly Volume 79/2 Spring 1993

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Federal Reserve Bank of Richmond Economic Quarterly

econometric issues and uses recently developed concepts only sparingly. It
does, however, rely extensively on notational conventions involving the time
series “lag operator,” L. Under these conventions the symbol L may be manipulated as if it were an algebraic symbol while its effect, when applied to a time
series variable, is to shift the variable’s date back in time by one period. Thus
Lxt = xt−1 while bLLxt = bL2 xt = bxt−2 , etc. In addition, the notation α(L)
will denote a polynomial expression in the lag operator as follows: α(L) =
.
.
α0 + α1 L + α2 L2 + α3 L3 + ˙.. Therefore, α(L)xt = α0 xt + α1 xt−1 + α2 xt−2 + ˙..
Using this notation, then, a distributed-lag regression relation of yt on current and lagged values of xt could be written as yt = α(L)xt + t , with t a
stochastic disturbance term. Furthermore, polynomials in L, which are often
restricted to have only a finite number of terms, may be “multiplied” as in the
following example:2 if α(L) = α0 + α1 L + α2 L2 and β(L) = β0 + β1 L, then
α(L)β(L) = β0 α0 + β0 α1 L + β0 α2 L2 + α0 β1 L + α1 β1 L2 + α2 β1 L3 . Finally,
“division” by a lag polynomial means that the implied inverse, α−1 (L), is a
polynomial such that α−1 (L)α(L) = 1. Thus α(L)β −1 (L) yields a polynomial
γ(L) such that β(L)γ(L) = α(L). It should be mentioned that the first coefficient
of a lag polynomial, such as α0 , is often normalized so as to equal one.
A brief outline of our discussion is as follows. In Section 1, the distinction
between trend stationarity and difference stationarity of time series is introduced. That distinction is then related to the “unit root” concept in Section
2, which is primarily devoted to a description of attempts by researchers to
determine whether the time series of real GNP values for the United States
is difference or trend stationary (i.e., does or does not have an autoregressive
unit root). Two approaches, involving different strategies for the specification
of maintained and tested hypotheses, are discussed. Then in Section 3 a third
approach, which presumes that the real GNP series is a sum of trend-stationary
and difference-stationary components, is considered. From the discussion in
Sections 2 and 3 together, it is concluded that the relevant question is not
whether the GNP series is difference stationary, but what is the relative contribution of the two components. It is also concluded that an accurate answer is
not obtainable with the amount of data available.
In Section 4 the topic changes to the question of how to process trending
data before conducting regression studies relating two or more variables. The
answer that is developed is that the choice between differencing and deterministic trend removal is normally of secondary importance, the principal relevant
consideration being the serial correlation properties of the regression residuals.
This regression context is continued in Section 5, which concerns the topic of
cointegration. It is argued that strict cointegration is probably rather rare, since
relationship disturbances will usually be—like shocks to univariate series—

2 The proper term is “convolution.” Any reader who desires a more rigorous description of
lag operators may consult Dhrymes (1971).

B. T. McCallum: Unit Roots in Macroeconomic Time Series

15

a sum of stationary and difference-stationary processes. Examples relating to
money demand and purchasing-power-parity studies are provided. In Section
6, finally, some conclusions are tentatively put forth.

1. STOCHASTIC VS. DETERMINISTIC TRENDS
As most readers are well aware, many macroeconomic data series display upward tendencies or “trends” when observations are plotted against time. For
many purposes it is useful and/or conventional to work with detrended values of these variables—i.e., versions from which trend components have been
removed. Traditionally, most researchers would effect this detrending step by
subtracting from the raw numbers (or their logs) a deterministic3 trend expression such as α0 + α1 t, where t is a time index. For various reasons it
is often useful to express the basic series in terms of logarithms of the raw
data, in which case α1 becomes a measure of the per-period growth rate of the
variable in question. Thus if yt is the basic variable, the traditional detrending
procedure implicitly splits yt into two components, one representing the trend
and the other a cyclical or non-trend component.4 With yt the basic variable
and t a white-noise5 disturbance, we have
yt = α0 + α1 t + γ(L) t ,

(1)

where α0 + α1 t is the trend component and γ(L) t is the non-trend component
(or the detrended series). In this traditional decomposition, it is assumed that
the detrended series γ(L) t is a stationary stochastic process, which requires
(among other things) that the population means E[γ(L) t ], variances E[γ(L) t ]2 ,
and autocovariances E[γ(L) t γ(L) t−j ] are the same for all t. (Here the variance and covariance expressions are written under the presumption that the
means equal zero.) Accordingly, yt is said to be a trend-stationary variable; it
may have a trend component but its deviations from a deterministic trend are
stationary. A variable’s status with regard to stationarity is of importance in
its own right, as we shall see in a moment, and also because there is a large
body of statistical techniques whose validity depends upon stationarity of the
variables being analyzed.
At least since 1982,6 however, many researchers have preferred an alternative model of the trend vs. non-trend decomposition. Instead of (1), they use
3 That

is, non-stochastic.
our discussion will ignore seasonal components.
5 A white-noise random variable is one generated by a process that specifies that each period’s
value, t , is drawn from a population with mean zero and finite variance σ 2 , and is not dependent
on previous values.
6 This was the year in which the article by Nelson and Plosser (1982) was published. The
popularity of differencing had been growing gradually, however, at least since the much earlier
publication of Box and Jenkins (1970).
4 Throughout,

16

Federal Reserve Bank of Richmond Economic Quarterly

a formulation such as (2),
∆yt = β + A(L) t ,

(2)

where A(L) t is stationary and β represents the average per-period change (or
growth rate) of the variable yt (or the variable whose log is yt ). In this formulation yt is said to be a difference-stationary variable, i.e., one that is generated by
a difference-stationary time series. Such a variable cannot in general be made
stationary by the removal of a deterministic trend; instead, the series needs to
be first-differenced prior to processing.
The basic distinction between trend-stationary (TS) and difference-stationary (DS) variables is that the former do, and the latter do not, tend to return to
a fixed deterministic trend function. Since the non-trend component γ(L) t in
(1) is stationary with mean zero, the process is such that yt tends to fluctuate
about the fixed trend function α0 + α1 t. In formulation (2), by contrast, the
tendency is for yt to grow at the rate β from its current position, whatever
that might be. There is, except in a special limiting case, no tendency for yt to
return to any fixed trend path.
The distinction between TS and DS series was emphasized in a highly influential paper by Nelson and Plosser (1982). In this paper, the authors clearly
described the TS vs. DS distinction and also discussed the undesirable statistical consequences of detrending by the traditional technique of removing
a deterministic time function when in fact the series is generated by a DS
process. In addition, Nelson and Plosser (1982) presented evidence suggesting
that many important U.S. time series are of the DS class and went on to argue
that evidence indicates that U.S. business cycles are largely real as opposed
to monetary in nature, i.e., that real shocks have been the principal sources
of cyclical variability with the contribution of monetary shocks being entirely
of secondary importance. The last of these arguments was not found convincing by the macroeconomics profession—see, e.g., McCallum (1986) and West
(1988)—but the hypothesis that many important series (including real GNP)
reflect DS processes became quite widely accepted. More recently, opinion has
partially reversed itself—as we shall see below—but for the past eight to ten
years the idea that real GNP is not trend stationary has been viewed by a large
number of researchers as true (and important). It will be useful, consequently, to
devote some attention to the logic of the statistical tests that led researchers to
that position. In the process of presenting this logic, several relevant points of
importance will be brought out—including the meaning of the term “unit root.”

2. A UNIT ROOT IN U.S. GNP?
Consider now the TS representation (1) with the lag polynomial γ(L) written
as the ratio of two other polynomials θ(L) and φ(L), both assumed with little

B. T. McCallum: Unit Roots in Macroeconomic Time Series

17

loss of generality to be finite7 of order q and p, respectively. Thus we have
yt = α0 + α1 t + θ(L)φ−1 (L) t .

(3)

Now suppose that 1/ρ is the smallest root of the polynomial φ(L), i.e., is the
smallest number8 that satisfies the equation 1 + φ1 z + · · · + φp zp = 0.9 Then
˜
φ(L) could be written as (1 − ρL)φ(L) and multiplication of (3) by (1 − ρL)
10
would give
˜
(1 − ρL)yt = α0 (1 − ρ) + ρα1 + α1 (1 − ρ)t + θ(L)φ−1 (L) t .

(4)

And in the special case in which ρ = 1, the latter collapses to
˜
(1 − L)yt = α1 + θ(L)φ−1 (L) t .

(5)

Since (1 − L)yt equals ∆yt , then, the latter is of the same form as (2). Consequently, when there is a unit root to φ(L)—when 1/ρ = 1.0—representation
(1) yields, as a special case, the DS formulation (2).11
In light of the foregoing result, a natural test procedure is suggested for
determining whether “yt has a unit root”—i.e., whether the AR polynomial
φ(L) has a unit root so that yt is DS. What is involved is that the researcher
maintains the hypothesis that (1) is true, represents it as in equation (4), and
then tests the (“null”) hypothesis that ρ in (4) is equal to one. If the latter
hypothesis is rejected, then one concludes that yt is not a DS series. But if
the hypothesis ρ = 1.0 is not rejected, then one can in a sense conclude that
yt is a DS variable—or that the behavior of yt is not significantly different
from that of a DS variable. Because ordinary asymptotic distribution theory
breaks down in the case in which ρ is precisely equal to one, a consistent test
requires that the relevant “t-statistic” on the coefficient of yt−1 be compared
with a critical value taken from a nonstandard distribution. But this can readily
be done, since Dickey and Fuller (1979) have provided the profession with the
pertinent tables.
The foregoing procedure was in fact employed by Nelson and Plosser
(1982) to test for unit roots in over a dozen important U.S. time series. In
only one of these could the tested hypothesis that ρ = 1.0 be rejected at a
7 That

is, to include only a finite number of terms with nonzero coefficients. Any stationary
stochastic process can be closely approximated by an expression of the form θ(L)φ−1 (L) t .
8 Perhaps a complex number.
9 Consider, for example, the second-order case. Then 1 + φ z + φ z2 = 0 could equivalently
1
2
be written as (1 − α1 z)(1 − α2 z) = 0, where φ1 = −(α1 + α2 ) and φ2 = α1 α2 . But the latter
equation is satisfied by the two values z1 = 1/α1 and z2 = 1/α2 . So the lag polynomial 1 +
φ1 L + φ2 L2 could as well be expressed as (1 − α1 L)(1 − α2 L). The roots of the polynomial φ(L)
1
are said to be 1/α1 and 1/α2 .
10 Here (1 − ρL)(α + α t) = α − ρα L + α t − ρα (t − 1) = α (1 − ρ) + α t − ρα t +
0
1
0
0
1
1
0
1
1
ρα1 = α0 (1 − ρ) + α1 (1 − ρ)t + ρα1 .
11 If ρ > 1.0, then y will have explosive behavior of a type that seems unlikely and that
t
will become easily detectable after a few years.

18

Federal Reserve Bank of Richmond Economic Quarterly

conventional significance level (i.e., 0.01 or 0.05), so the authors’ tentative
conclusion was that most U.S. macroeconomic data series are of the DS class,
i.e., are unit-root variables.
There was, however, one rather obvious difficulty with this tentative conclusion,12 as follows: while it was not possible to reject the hypothesis that the
series’ roots like ρ were equal to one, it would also have been impossible to
reject hypotheses asserting that these roots equaled 0.99, for example, or even
0.95. But with ρ equal to 0.99 or 0.95, the model would be one of the TS class.
Continuing with this perspective, it might be argued that it is highly implausible
that the tested hypothesis of ρ equal to unity would hold precisely, as opposed
to approximately. The data, that is, could do no more than show that the value
of ρ is close to one. Consequently, this entire testing approach, which begins
with a TS representation and posits the DS model as a special case, seemed
highly unconvincing to a number of analysts.13
An alternative approach would be to begin with a maintained hypothesis
implying difference stationarity and then express trend stationarity—the absence of an AR unit root—as a special case. Thus the time series process for
yt could be written as in (2) but with A(L) = θ(L)φ−1 (L):
∆yt = β + θ(L)φ−1 (L) t .

(6)

Then if the moving-average lag polynomial θ(L) were to have a unit root so
˜
that θ(L) = (1 − L)θ(L), expression (6) could be operated on by (1 − L)−1 to
yield
˜
yt = β0 + βt + θ(L)φ−1 (L) t .

(7)

(That [1−L]−1 β equals β0 +βt can be justified by multiplying each by [1−L].)
Consequently, it would be possible to express (6) as
˜
φ(L)∆yt = βφ(L) + (1 − γL)θ(L) t ,

(8)

estimate the latter, and test the hypothesis that γ = 1. If it were possible to reject the latter, then the outcome might be viewed as providing more convincing
evidence in favor of the DS view.14
In fact, the influential paper by Campbell and Mankiw (November 1987)
proceeded in precisely this fashion, using quarterly postwar data for the United
States, 1947–1985. So what did these authors find? As it happens, the answer
is not straightforward because it is unclear how many terms should be included
in estimation of the φ(L) and θ(L) polynomials in (8). In their paper, Campbell
and Mankiw reported results for 16 different cases representing all possible
12 The

difficulty was recognized, but not emphasized, by Nelson and Plosser (1982).
e.g., McCallum (1986, pp. 405–6).
14 It would, however, be possible to object that expressing trend stationarity as a zero-measure
special case effectively biases the procedure in favor of a DS finding. Note, incidentally, that a
unit root in the MA polynomial does not imply a process of the “unit root” type.
13 See,

B. T. McCallum: Unit Roots in Macroeconomic Time Series

19

Table 1 Test Statistics from Campbell and Mankiw (November 1987,
Table I)
Number of MA Parameters

Number of AR
Parameters

1

2

3

1
2
3

22.96*
2.06
0.95

11.73*
4.02*
1.31

0.00
0.00
0.00

Notes: Tabulated entries are values of 2 log (SSE0 /SSE), where SSE denotes the sum of squared
residuals and SSE0 indicates imposition of the constraint that makes A(1) = 0. The ARMA models
are estimated for ∆yt where yt is the log of U.S. real GNP, seasonally adjusted, quarterly for
1947:1–1985:4. Asterisks indicate values that are significantly different from zero (0.05 significance level) under the usual test, but this test is inappropriate (as discussed in the text).

combinations of zero to three AR parameters and zero to three MA parameters.
Of these, it is arguable that only those with at least one AR and one MA term
should be seriously entertained. The usual test statistics for those nine cases
are given in Table 1. For each case, the reported number is the likelihood ratio
statistic for a test of the hypothesis that θ(L) has a unit root—i.e., that the TS
hypothesis is true. In most cases this statistic has asymptotically,15 under the
null hypothesis, a chi-square distribution with one degree of freedom, so that
the critical value is 3.84 for a test with significance level 0.05 (or 6.63 for a
0.01 level). Based on these values, the table indicates that in three of the nine
cases—i.e., for three of the nine specifications—the null TS hypothesis can be
rejected at the 0.05 level. Described in this fashion, then, the Campbell and
Mankiw (November 1987) results did not provide strong evidence against the
TS hypothesis (or, in favor of the unit root hypothesis). But under the particular
hypothesis of concern in this case, that θ(L) has a unit root, the usual asymptotic
distribution theory breaks down—as it does when testing for a unit root in the
AR polynominal φ(L). This breakdown tends to reduce the critical level for
the likelihood ratio statistics and to produce an excessive number of extreme
values such as those in the final column of Table 1. Thus the figures in that
table are actually more unfavorable for the TS hypothesis than they appear to
be at first glance.
Furthermore, Campbell and Mankiw did not describe the results as in the
previous paragraph. Instead, they suggested that the ARMA (2,2) model16 —the
case with two autoregressive and two moving average parameters—commands
special attention because it is not significantly worse than the (2,3) or (3,2)
15 I.e.,

in the limit as the sample size grows without bound.
ARMA model is one that admits both autoregressive and moving average polynomials. The notation ( p, q) indicates how many terms ( p and q) are included in the AR and MA
polynomials. Sometimes the number of times d that the basic variable has been differenced is
included in a ( p, d, q) notation.
16 An

20

Federal Reserve Bank of Richmond Economic Quarterly

models and is significantly better than the (2,1) model (and somewhat better than the [1,2] specification).17 But in this case, the results (see Table 1)
call for rejection of the TS null hypothesis, even given the test’s bias toward
acceptance. The suggestion of Campbell and Mankiw, consequently, was that
postwar quarterly evidence supports the notion that real GNP for the U.S. is
not trend stationary, but instead is generated by a DS (or unit root) process.
We shall return to the persuasiveness of this suggestion below. But first it will
be useful to discuss a different aspect of the Campbell and Mankiw analysis,
which their discussion emphasized.
In particular, a notable feature of the Campbell-Mankiw (November 1987)
paper is its presentation of an attractive measure of the ultimate or “long-run”
response of yt to a unit shock, i.e., a 1.0 realization of the disturbance t . To
define this measure, consider again the DS formulation (2), ∆yt = β + A(L) t ,
and write it out as
yt = yt−1 + β +

t

+ A1

t−1

+ A2

t−2

+ ···.

(9)

From the latter expression, it can be seen that the per-unit effect of t on yt is
1.0 (in the sense that if t were to equal some positive value instead of its mean
zero, then yt would be higher by the same amount.) But then the per-unit effect
of t on yt+1 would be 1 + A1 , with the part A1 occurring “directly” and the
remainder through its effect on yt . Continuing with this line of reasoning, it is
found that the (per-unit)18 effect on yt+k would be 1 + A1 + A2 + · · · + Ak . In the
limit as k → ∞, then, we would have 1 + A1 + A2 + · · · , which may be denoted
A(1). (That expression arises from writing A(L) = 1 + A1 L + A2 L2 + · · · and
inserting 1 wherever L appears.) Thus the measure A(1) reflects the ultimate or
long-run effect of t on yt when the process generating yt is of form (2).
An important property of the measure A(1) is that its value is zero for
any TS process. To see that, write A(L) = θ(L)φ−1 (L) and recall that for a TS
˜
variable the MA polynomial can be written as θ(L) = (1 − L)θ(L). Thus we
have
˜
A(L) = (1 − L)θ(L)φ−1 (L) ≡ (1 − L)a(L) = a(L) − La(L),

(10)

˜
where a(L) ≡ θ(L)φ−1 (L). But then we obtain
A(1) = a(1) − La(1) = a(1) − a(1) = 0

(11)

since La(1) = L(1 + a1 + a2 + · · ·) = 1 + a1 + a2 + · · · . Thus if θ(L) can be
˜
written as (1 − L)θ(L), as it can when the process at hand is TS, it is true that
A(1) = 0.
17 Here the meaning of “model A is better than B” is that B is nested in A and can be
rejected with a significance level of 0.05.
18 Henceforth the words “per unit” will typically be omitted.

B. T. McCallum: Unit Roots in Macroeconomic Time Series

21

Table 2 Estimates of A(1) from Campbell and Mankiw (November
1987, Table IV)
Number of MA Parameters

Number of AR
Parameters

1

2

3

1
2
3

1.72
1.77*
1.36*

1.73
1.52
1.60*

0.03
0.00
0.00

Notes: See Table 1.

What about the values of A(1) implied by various DS processes? For each
of these A(1) will be nonzero, but will take on various values depending on the
response pattern. In particular, A(1) will exceed one if the ultimate impact on
yt of a shock is greater than the first-period impact. An important special case
is provided by the random-walk process in which ∆yt = β + t . In this case
A(L) = 1 + 0L + 0L2 + · · · = 1 so A(1) = 1. Next, the first-order MA case has
∆yt = β + t + θ t−1 so A(L) = 1 + θL and A(1) = 1 + θ. Then A(1) is greater
than or smaller than one depending on whether θ is positive or negative.
A somewhat more general process is the ARMA (1,1) model for ∆yt ,
namely,
(1 − φL)∆yt = (1 + θL) t .

(12)

In this case A(L) = (1+θL)(1−φL)−1 so A(1) = (1+θ)/(1−φ). An example application is provided by the Campbell-Mankiw (November 1987) estimates with
the U.S. GNP series. Their point estimates of φ and θ are 0.522 and −0.179,
respectively, so that A(1) = (1 − .179)/(1 − .522) = 0.821/0.478 = 1.717. Thus
the ARMA (1,1) model for ∆yt suggests that the long-run response of yt (log
of GNP) to a shock will be about 1.7 times as large as the immediate (within
one quarter) response.
In sum we see that the measure A(1) provides an attractive way of expressing the magnitude of the “long-run response” of a variable ( yt ) to a unit
shock ( t ).19 And in their study of postwar U.S. GNP, Campbell and Mankiw
(November 1987) find that for all but three of their nine cases20 A(1) is substantially larger than one, implying that the impact of shocks is to cumulate,
rather than dissipate, as time passes. Their values are reported in Table 2, where
it may be noted that for the ARMA (2,1), (3,1) and (3,2) cases (marked with
asterisks), the point estimates of A(1) are large even though the A(L) polynomials are not significantly different from ones with A(1) = 0 according to the
19 Another useful measure has been featured in the work of Cochrane (1988). It is described
below in text attached to footnote 26.
20 Recall that they actually reported 16 cases, but that we are focusing on 9.

22

Federal Reserve Bank of Richmond Economic Quarterly

usual test (compare Table 1). Consequently, although they are guarded in their
statements, Campbell and Mankiw seem to conclude that there are grounds for
being reasonably confident that the long-run response of a unit shock to U.S.
GNP is substantially greater than one. In this sense, shocks to GNP have no
trend-reversion tendency at all.21
This conclusion has not, however, held up to subsequent criticism. One major reason for skepticism was provided in a study by Christiano and Eichenbaum
(1990). Basically, their study emphasized that the different ARMA specifications considered by Campbell and Mankiw give rise to quite different values of
A(1)—as is evident in Table 2—and that there is very little reason to conclude
that any one of them is appropriate—or even that one of those with A(1) > 1 is.
The Christiano-Eichenbaum argument is that relevant inferences are sensitive
to the choice of ARMA specification employed, even within the set of those
that provide approximately equally good fits to the data.
One of the experiments conducted by Christiano and Eichenbaum will
illustrate their results. In this experiment they conducted simulations with a
model with parameters matching those estimated by Campbell and Mankiw in
the ARMA (3,3) case. In other words, they pretended that this case—which
implies A(1) = 0—is true, and then considered what would happen if it were
studied under the assumption that the ARMA (2,2) specification were correct.
For each simulation they would generate 150 “data” points using the (3,3)
parameters, then estimate a (2,2) model and test the hypothesis that A(1) = 0.
They conducted 2,000 such simulations and found that the hypothesis A(1) = 0,
which was true in the process studied, was nevertheless rejected in 74 percent
of the simulations.22 Similarly, in 2,000 more simulations, based on the ARMA
(1,3) parameter estimates from Campbell and Mankiw, it was found that the
true hypothesis A(1) = 0 was rejected in 38 percent of the simulations.
The conclusion reached by Christiano and Eichenbaum was as follows: on
the basis of 150 observations, about the number of quarterly postwar data periods, it is not possible to make accurate inferences about the long-run response
measure A(1). Equivalently, it is not possible to determine with high reliability
whether the stochastic process generating real GNP observations is of the TS
or DS class.
During the last few years, numerous additional papers on the topic have appeared; only a few can be mentioned. Sims (1988) has suggested that Bayesian
techniques of statistical inference are more appropriate than classical in this
particular context and DeJong and Whiteman (1989, 1991) have presented
Bayesian results that provide support for the view that the U.S. GNP process
is actually of the TS class. That conclusion has been strongly challenged by
Phillips (1991), in a paper that provided the basis for a symposium occupying an
21 It is sometimes said that they are highly “persistent,” but that terminology is inappropriate
for reasons clearly described by Cochrane (“Comments,” 1991, pp. 206–7).
22 With a test statistic designed to have a 0.05 significance level.

B. T. McCallum: Unit Roots in Macroeconomic Time Series

23

entire issue of the Journal of Applied Econometrics. The symposium includes
rejoinders by Sims and DeJong-Whiteman; it would be difficult to identify any
clear outcome. Others, including Stock (1991), Cochrane (April 1991), Sowell
(1992) and Rudebusch (1993), have reached the Christiano-Eichenbaum (1990)
conclusion—i.e., that it is not possible with existing data to settle the issue—by
alternative means. In my opinion, this last conclusion seems generally appropriate, but there is another way of approaching the issue that is conceptually
rather simple and perhaps illuminating.

3. THE UNOBSERVED COMPONENTS APPROACH
In the previous section two approaches were mentioned, based on equations
(3) and (6). In the first of these, the maintained hypothesis is trend stationarity
with difference stationarity viewed as a zero-measure23 special case, whereas
in (6) the DS hypothesis is maintained and TS is treated as the (zero-measure)
special case. Let us now consider an alternative approach that proceeds within
a framework in which both TS and DS components are presumed to play a role,
the implied statistical problem being to determine how much weight to give to
each. Aspects of this “unobserved components” approach have been developed
by Harvey (1985), Watson (1986), Clark (1987), and Cochrane (1988).
The analysis presented by Clark (1987) provides a useful introduction and
perspective. It begins by writing the observable variable under study, yt , as the
sum of a DS “trend” term zt and a stationary “cycle” term xt :
yt = zt + xt .

(13)

Although a more general specification would be possible, Clark assumes that
the cyclical component is a pure AR process so that φ(L)xt = vt , with vt
white noise. Indeed, in his empirical implementation with U.S. GNP data Clark
makes φ(L) a second-order polynomial, so that xt is an ARMA (2,0). The trend
component is assumed to obey
zt = zt−1 + d + wt ,

(14)

where wt is white noise, independent of vt . Actually Clark takes the drift term
d to be itself a random walk: dt = dt−1 + ut with ut white. But empirically he
finds the variability of ut to be very small, so we shall for simplicity view dt
as a constant, as in (14). The model at hand for yt is therefore
yt = (1 − φ1 L − φ2 L2 )−1 vt + (1 − L)−1 (d + wt ).

(15)

Let us consider, then, how (15) fits the U.S. quarterly postwar GNP data.
23 I.e., a case represented by parameter values that would be graphically represented as a
point (with zero area) in a region depicting all possible parameter values.

24

Federal Reserve Bank of Richmond Economic Quarterly

Table 3 Estimates of ARMA (2,2) Models from Clark (1987)
Parameters
and Statistics

Constrained

Unconstrained

φ1
φ2
θ1
θ2
SE
Q(10)
A(1)

1.548
−0.601
−1.214
0.248
0.0103
7.9
0.64

0.658
−0.420
−0.335
0.529
0.0103
4.8
1.57

Notes: ARMA models estimated for ∆yt (see Table 1) for 1948:1–1985:4. Q(10) denotes the
Box-Pierce Q-statistic for ten autocorrelations of the residuals; under the null hypothesis of white
noise it has asymptotically a chi-square distribution with ten degrees of freedom.

As a preliminary, it will be instructive to consider a comparison that begins
by expressing (15) as
(1 − φ1 L − φ2 L2 )∆yt = (1 − L)vt + (1 − φ1 L − φ2 L2 )(d + wt ).

(16)

Here the right-hand side is the sum of two independent MA processes, with
the higher-order one being an ARMA (0,2). Using Granger’s Lemma,24 then,
we can write (16) as
(1 − φ1 L − φ2 L2 )∆yt = δ + (1 + θ1 L + θ2 L2 ) t ,

(17)

where t is an implied, constructed white-noise disturbance and where δ =
d(1 − φ1 − φ2 ). But the representation in (17) has six parameters (φ1 , φ2 , θ1 , θ2 ,
2
2
σ 2 , and δ) whereas the basic model (15) has only five (φ1 , φ2 , σv , σw , and d).
So the particular components model at hand, which sums an AR (2) component
and a random-walk component, can be viewed as a constrained version of an
ARMA (2,2) model for ∆yt .
It is of course true that the unconstrained model (17) must fit the data at
least slightly better than the constrained version (15). But Clark’s estimates,
reported in Table 3, indicate that in the case at hand there is almost no difference, i.e., almost no deterioration in fit, from imposing the constraint. In
particular, the estimated residual variance for (15) is essentially the same as with
(17) and the Box-Pierce Q(10) statistic is not much worse. So the constrained
version—the components model (15)—could as well be the preferred choice.25
24 Granger’s

Lemma says that the sum of two independent ARMA processes, one ARMA
( p1 , q1 ) and the other ARMA ( p2 , q2 ), is an ARMA ( p∗ , q∗ ) where p∗ ≤ p1 + p2 and q∗ ≤
max( p1 + q2 , p2 + q1 ). For pure MA processes, then, q∗ ≤ max(q1 , q2 ).
25 Both Clark (1988) and Cochrane (1988) have developed arguments suggesting that unconstrained ARMA models with difference series tend to be poor at the job of estimating long-run
properties such as A(1).

B. T. McCallum: Unit Roots in Macroeconomic Time Series

25

But although the constrained and unconstrained ARMA models fit the data
about the same, they yield very different A(1) measures. Whereas the unconˆ
strained version gives A(1) = 1.57, virtually the same as estimated by Campbell
and Mankiw, for the (unconstrained) components model the estimate is 0.64.
In two diagrams, Clark (1987) presented evidence apparently suggesting
that for U.S. quarterly GNP the unobserved components model may provide a
better estimate than the unconstrained ARMA of the long-run response statistic
A(1). The first of these, denoted Figure V in Clark’s paper, plots the implied
autocorrelations at various lags for the two models (plus one more, an ARMA
[0,2]) and for the ∆yt sample. In that plot it will be seen that the unconstrained ARMA (denoted ARIMA 212) matches the sample somewhat better
at short lags (e.g., 1–5 quarters) but that the components model provides a
better match at lags of 5-20 quarters. More striking are the related results
shown in Clark’s Figure VI, which plots the variance ratios Vk /V1 , where
Vk ≡ (1/k) Var( yt − yt−k ), for lag lengths k up to 60 quarters.26 In this case,
the apparent superiority of the components model’s match to the sample data
is striking. But, as Campbell and Mankiw (May 1987) point out, sample values
of Vk provide biased estimates of their population counterparts. Accordingly,
Campbell and Mankiw suggest that the sample values should be multiplied by
T/(T − k), where T is the sample size. Here T = 148, so the adjusted sample
values of Vk are considerably larger than the unadjusted values for k ≥ 20.
With this bias adjustment incorporated, the match between sample and
components-model values of Vk would continue to be somewhat better than
between sample and unconstrained ARMA values, but not nearly to the same
extent as in Clark’s Figure VI. The same point applies, but with less force, to
his Figure V.
More generally, the unobserved components approach to modeling the trend
vs. cyclical decomposition seems conceptually attractive, in part because it does
not treat either TS or DS processes as (zero-measure) special cases. The implied
question is not whether one of these two possibilities can be rejected, but instead
is “How important quantitatively is the zt as opposed to the xt component?” That
question cannot be answered in precisely the stated form, since the variance of
the DS component zt depends on the horizon considered and goes to infinity
in the limit. But one type of answer is provided by the A(1) measure itself and
another by a comparison of the variances of vt and wt , i.e., the shocks to xt and
ˆ
ˆ
zt . In the case at hand, Clark’s estimates are σv = 0.0072 and σw = 0.0066.
An objection to the components approach as implemented by Clark (1987)
and Watson (1986) was expressed by Campbell and Mankiw (May 1987, p.
115). This objection is that with the DS component zt modeled as a random
walk, the estimated value of A(1) must lie between zero and one; thus values
26 As k → ∞, the limit V of the V sequence is the long-run response measure proposed
k
by Cochrane (1988) mentioned above in footnote 19. Its relation to A(1) is V = (1 − R2 )[A(1)]2 ,
where R2 is 1 − (σ 2 /Var ∆yt ).

26

Federal Reserve Bank of Richmond Economic Quarterly

greater than one are ruled out a priori. But while this important objection is
applicable to the Clark and Watson studies, it is not applicable to the approach
in general, for the latter can accommodate other DS processes for zt . Instead of
a random walk, for example, the zt process could be specified as a first-order
MA: ∆zt = d + wt + θwt−1 . For the zt component alone, A(1) would then equal
1 + θ so values in excess of one will be obtained if θ > 0. And if the variability
of zt is large in relation to that for xt , then the A(1) value for yt could easily
exceed one.27
Another objection is that it is unreasonable to assume that xt and zt components are independent, as the approach presumes. There is undoubtedly some
merit to this point, since technology shocks will presumably have both cyclical
and long-lasting effects. But the Campbell-Mankiw ARMA approach amounts
to use of an unobserved components model in which the shocks (like vt and wt
in [15]) are perfectly correlated,28 which property seems even less desirable.
Perhaps the most important objection to the unobserved components modeling of trend vs. cycle is that it is computationally much more difficult than
estimation of ARMA models, the necessary steps involving application of
Kalman filter techniques. For a discussion of such techniques, the reader is
referred to Harvey (1981).
On the basis of the foregoing discussion, it would seem reasonable to
conclude that the postwar U.S. quarterly real GNP process is most likely of
the DS class, since a sum of DS and TS components is itself a DS process.29
But it is far from clear that the long-run impact of shocks exceeds that of the
random-walk case in which A(1) = 1.0. Instead, a measure such as 0.6, which
attributes a substantial share of GNP variability to a stationary component, is
just as plausible. What does seem clear is that it is not possible, on the basis
of currently available data, to estimate A(1) with much accuracy or reliability.
Conceptually, the basic components-approach idea, of viewing a time series
as the sum of DS and TS processes, seems attractive as a framework for thinking
about the properties of univariate time series. In many cases, both components
would be presumed to be of non-negligible importance so many series will be
of the DS class. That does not imply, however, that any particular method can
be relied upon for trend vs. cyclical decomposition of time series data.

27 But with more parameters in the DS component, the components model may become
equivalent to an unconstrained ARMA.
28 See Watson (1986, p. 53).
29 Quite recently, Kwiatkowski, Phillips, Schmidt, and Shin (1992) have conducted tests of
the hypothesis that the DS component is of negligible importance in a components formulation.
For the real GNP series this hypothesis was found to be of borderline significance at the 0.05
level.

B. T. McCallum: Unit Roots in Macroeconomic Time Series

27

4. DETRENDING PRIOR TO ECONOMETRIC ANALYSIS
In this section we switch our attention away from trend estimation, conducted
for the purpose of isolating trend and cyclical components of a series, and toward trend removal (or “detrending”), conducted for the purpose of obtaining
series suitable for econometric analysis of relationships among variables. In this
context, then, the issue is whether to process variables prior to (say) regression
analysis by removal of an estimated deterministic trend30 or by differencing
of the series. A major reason for detrending is that the standard formulae
for standard errors, test statistics, etc., are in most cases based on asymptotic
distribution theory that assumes stationarity of the regressor variables.31 Belief
that some variable is generated by a process of the DS type—i.e., one with a
unit root—might then lead to the presumption that data differencing would be
preferable for that variable prior to its use in a regression study.
Other influential arguments for differencing of data prior to time series
econometric analysis were put forth by Granger and Newbold (1974) and
Nelson and Kang (1984). In the earlier of these papers it was shown that a
regression relating yt to xt would spuriously tend to find a relationship when in
fact yt and xt are generated independently but by random-walk processes. The
Nelson-Kang piece emphasized a tendency for trendless random-walk variables
to be spuriously related to time trends in estimated regressions.
As a result of these and other studies, considerable support developed during the mid-1980s for the position that differencing should routinely be carried
out prior to regression analysis involving time series data.32 The case for such
a practice was succinctly summarized by Plosser and Schwert (1978, p. 653)
as follows: “Ignoring the effects of underdifferencing can be a far more costly
error than ignoring the effects of overdifferencing.” More recently, there has
been significant counter-movement based on phenomena related to the concept
of “cointegration.” A consideration of that position will be presented below,
but it will be useful first to consider the merits of routine differencing, rather
than detrending, of variables with an apparent trend component.

30 In least-squares regression analysis the inclusion of a time trend among the regressors is
equivalent to the use of variables detrended by prior regression on the same time variable (i.e.,
using residuals, from these prior regressions on time, as the detrended variables).
31 The standard formulae do not rely on asymptotic distribution theory in cases in which
there are no lagged dependent variables in the system under study, but such cases are the exception
in applied macroeconomics.
32 A contrary argument is that differencing sacrifices information pertaining to levels or to
long-run relationships. Estimation of a levels relationship after differencing will not, of course,
provide any information about the constant term, but that is usually of little importance. The
argument developed below suggests that little is lost with regard to long-run multipliers unless
the variables are cointegrated, a topic that is taken up briefly in Section 6.

28

Federal Reserve Bank of Richmond Economic Quarterly

The issues at hand can be usefully introduced and illustrated in an example
similar to that used by Plosser and Schwert (1978). Consider a linear regression
relationship that is (by assumption) correctly specified in first differences, viz.,
∆yt = β∆xt + t ,

(18)

where t is a white-noise disturbance with variance σ 2 and where xt is exogenous, generated by a process independent of the process generating t . Now, if
instead of (18) the investigator estimates by ordinary least squares (OLS) the
relationship between xt and yt in levels, he is in effect applying OLS to
yt = α + βxt + ηt ,

(19)

in which the disturbance term ηt = t + t−1 +· · · is serially correlated and nonstationary. In this underdifferenced case, as Plosser and Schwert point out, the
OLS estimator of β could be inconsistent, depending on the process generating
xt . In any event, whether or not the OLS estimator is consistent, its sampling
distribution does not have finite moments. Inferences based on the usual OLS
formulae are likely, accordingly, to be highly inappropriate.
Next, suppose that instead the investigator applies OLS to the second
differences of yt and xt , estimating
∆(∆yt ) = β∆(∆xt ) + ∆ t .

(20)

In this case with overdifferencing the disturbance ∆ t is again serially correlated
but now its distribution is stationary. The OLS estimator of β will be unbiased
and consistent, but will be inefficient and its sampling variance will (except in
special cases) not be consistently estimated by the usual formulae.
These foregoing considerations, discussed by Plosser and Schwert (1978),
are of some interest but are actually relevant only under the presumption that the
investigator is wrong about the appropriate degree of differencing and makes
use of OLS estimators even though the implied disturbances are serially correlated. Of considerably greater interest, it would seem, are the consequences
of estimating β with underdifferenced or overdifferenced data when the investigator recognizes the presence of serial correlation in the OLS residuals
and responds by utilizing an estimator designed to take account of autocorrelated disturbances in the appropriate manner. In the overdifferenced case, for
example, the true relation can be written as
∆(∆yt ) = β∆(∆xt ) +

t

+θ

t−1 ,

(21)

with θ = −1.0. The interesting question, then, is whether the investigator will
be led seriously astray if he regresses ∆(∆yt ) on ∆(∆xt ) using an estimation
procedure designed for cases in which the disturbance process is a first-order
MA.

B. T. McCallum: Unit Roots in Macroeconomic Time Series

29

Now precisely this last question has been investigated via Monte Carlo
experimentation33 by Plosser and Schwert (1977). They find that even though
the absolute value of θ tends to be somewhat underestimated—with a sample
size of T = 100 the mean across 1,000 replications of the estimates of θ is about
−0.94—the estimates of β are not appreciably biased and the experimental
sampling distribution is not such as to lead frequently to incorrect inference.
Specifically, the frequency of rejection of a true hypothesis with a nominal
significance level of 0.05 is 0.063 in one experiment and 0.081 in the other.
Plosser and Schwert conclude, appropriately, that “the cost associated with
overdifferencing may not be large when care is taken to analyze the properties
of regression disturbances” (1978, p. 643).
The corresponding case of an investigation with underdifferencing arises
if we write the true relation as
yt = α + βxt + (1 − ρL)−1 t ,

(22)

with ρ = 1.0, and ask whether the investigator will be led seriously astray
(regarding β) if he regresses yt on xt under the assumption that the disturbance
process is a first-order AR. With respect to this possibility, Plosser and Schwert
(1978, p. 643) recognize that “if the resulting estimate of ρ is close to one,
as it should be in this case, differencing would be indicated leading to the
correct model˙ They do not, however, consider the effects on the estimation
...”
of β of concluding one’s investigation with the estimate provided by the levels
regression that takes account of AR disturbances—which is the situation corresponding to the presumed behavior of the investigator in the overdifferencing
case. This asymmetry in discussion prevents them from giving a comparison
of the relative costs of underdifferencing vs. overdifferencing when the investigator is intelligently taking account of the serial correlation properties of the
disturbances.
Some Monte Carlo results relevant to this type of procedure have, however,
been obtained by Harvey (1980) and Nelson and Kang (1984). The latter of
these papers is devoted primarily to emphasizing various ways in which investigators could be led to misleading results if they estimate underdifferenced
relationships and do not correct for serially correlated residuals, but it briefly
reports (on pp. 79–80) results of testing a true hypothesis analogous to β = 0
in (22) with β and ρ estimated jointly. With T = 100 and a significance level of
0.05, the frequency of rejection in 1,000 replications is 0.067, which compares
favorably with the Plosser-Schwert results for the case with overdifferencing.
The study by Harvey (1980) compares mean-squared-error (MSE) values34 for
33 This

approach is used because the usual asymptotic distribution theory breaks down in
cases with unit roots in either the MA or AR polynomial.
34 Across 200 replications.

30

Federal Reserve Bank of Richmond Economic Quarterly

estimates of β in (22) with ρ = 1.0 when estimated with first differences and
when estimated jointly with ρ using levels data (i.e., with underdifferencing and
an autocorrelation correction). Two specifications regarding the behavior of the
exogenous variable xt are considered by Harvey. In one of these the xt process
is stationary; in that case the MSE value for the estimator of β is 0.310 with
the (correct) first-difference specification and 0.309 with underdifferencing (and
autocorrelation correction).35 In the other case, which features strongly trending
xt data, the analogous MSE figures are 0.061 and 0.078.36
Also of relevance, though not conforming to the symmetric contrast provided by our specifications (18) and (20), is evidence provided by Harvey
relating to the estimation of a relation like (22) but with ρ = 0.9. The alternative estimators are based on application of maximum likelihood to the
(correct) levels specification and OLS to the first-differenced specification, the
latter amounting to estimation with ρ = 1.0 by constraint.37 The T = 100
MSE values are 0.263 and 0.262 for the two estimators with stationary xt ’s,
and 0.009 vs. 0.018 with trending xt ’s.
On the basis of the described Monte Carlo experiments, the appropriate conclusion would seem to be that neither overdifferencing nor underdifferencing leads to serious estimation or testing mistakes in regression models
with exogenous regressors, provided that the investigator takes intelligent account of serial correlation present in the regression residuals. It is perhaps
worth noting, given the tenor of their discussion, that this conclusion is not
contradicted in the least by the four studies involving actual data (and unknown
specifications) that are explored by Plosser and Schwert (1978).
Specifically, in each of these four cases the authors conclude that first
differencing is probably appropriate, but the point estimates and standard errors (for the parameter analogous to β) that are provided by regressions with
undifferenced data are virtually the same when the Cochrane-Orcutt procedure
is used to account for ρ = 0. In their Table 1 regression of (log) income on
the (log) money stock, for example, the slope coefficient (and standard error)
values are 1.127 (0.122) for the Cochrane-Orcutt levels regression and 1.141
(0.126) in the differenced case. The OLS regressions with data that have been
differenced twice give estimates that do not agree as well, but in each of these
cases there is evidence of uncorrected serial correlation in the residuals. In
Table 1, for example, the first residual autocorrelation is −0.36.
It is additionally worth noting that Plosser and Schwert (1978, p. 638)
also take the view that “the real issue is not differencing, but an appropriate
appreciation of the role of the error term in regression models.” Thus our
35 Actually the estimator “with autocorrelation correction” involves full maximum likelihood
estimation of (22).
36 These values are for sample size of T = 100; Harvey also gives results for T = 20 and
T = 50.
37 In the levels formulation, ρ is estimated jointly with β.

B. T. McCallum: Unit Roots in Macroeconomic Time Series

31

disagreement with Plosser and Schwert seems to be whether the “representative investigator” will, or will not, recognize and take steps in response to the
presence of autocorrelated residuals.
The foregoing evidence relates, however, principally to relations with exogenous regressors. In practice, it is much more common for equations of
interest to include one or more lagged endogenous variables. But if ∆yt−1
were to appear as an additional regressor in (18), then the situation regarding
estimation of β would be quite different. In order to obtain a bit of evidence as
to the validity of the suggestion—that the presence or absence of differencing
is not crucial when serial correlation corrections are applied—in situations in
which lagged endogenous variables are present, let us consider results pertaining to two example relationships (that may be of some substantive interest).
Specifically, let us first consider estimation of the rudimentary singleequation model of aggregate demand utilized in McCallum (1987), that is,
an equation relating growth of nominal GNP to growth rates of the monetary
base. Notationally, let xt and bt denote logarithms of nominal GNP and the
base, respectively, for period t and consider quarterly observations, seasonally
adjusted, for the sample period 1954:1–1991:3.38
As a starting point, consider the following updated version of the specification emphasized in McCallum (1987):
∆xt = 0.0078 + 0.3248 ∆xt−1 + 0.3190 ∆bt .
(.002) (.073)
(.104)
2

R = 0.196

SE = 0.0097

DW = 2.12

(23)
Q(10) = 8.3

Here parameter standard errors are shown in parentheses while the reported statistics are the unadjusted R2 , the estimated standard deviation of the disturbance
term, the Durbin-Watson statistic, and the Box-Pierce Q-statistic based on the
first ten autocorrelation terms.39 These statistics give no evidence of residual
autocorrelation and it is the case that ∆xt−2 would not provide additional explanatory power. As it happens, however, inclusion of ∆bt−1 would provide
additional explanatory power and would make ∆bt insignificant. Accordingly,
let us switch our attention to the variant of (23) in which ∆bt is replaced by
∆bt−1 , a variant also used in McCallum (1987). The 1954:1–1991:3 estimates
are as follows:
∆xt = 0.0076 + 0.2845 ∆xt−1 + 0.3831 ∆bt−1 .
(.002) (.075)
(.105)
2

R = 0.215
38 Data

SE = 0.0096

DW = 2.07

(24)
Q(10) = 8.0

for 1953-1990 are taken from the Citibase data set, while 1991 values come from the
Survey of Current Business (GNP) and the Federal Reserve Bank of St. Louis (adjusted monetary
base). Calculations are performed with version 7.0 of Micro TSP.
39 Under the assumption that the disturbances are white noise, Q(10) has asymptotically a
chi-squared distribution with eight degrees of freedom; its critical value for a 0.05 significance
level is therefore 18.3.

32

Federal Reserve Bank of Richmond Economic Quarterly

Here there is no evidence of residual autocorrelation and additional lagged
values of ∆xt and ∆bt would not enter significantly. The important properties
of the estimated relation are that ∆xt is mildly autoregressive and is positively
related to ∆bt , with a moderately large elasticity value that is not significantly
different from 0.5.
The first question to be answered, then, is “What would we have found
if we had estimated this same relation in (log) levels, using series with deterministic trends removed?” To develop an answer, first consider equation (25),
where the detrending is effected by inclusion of time as an additional regressor:
xt = 0.0273 + 0.00021 t + 1.0160 xt−1 − 0.0321 bt−1 .
(.072) (.0002)
(.020)
(.014)
R2 = 0.9999

SE = 0.0104

DW = 1.40

(25)
Q(10) = 23.1

Here the results are entirely different from those in (24), but there is distinct
evidence of residual autocorrelation. Re-estimation with the disturbance term
assumed to follow an AR(1) process yields
xt = 5.857 + 0.0067 t + 0.2763 xt−1 + 0.592 bt−1 + 0.996 ut−1 ,
(34.1) (.060)
(.081)
(.150)
(.023)
R2 = 0.9999

SE = 0.0095

DW = 2.14

(26)

Q(10) = 9.0

where ut is defined as (1 − ρL)−1 t . Now, with the AR(1) disturbance specification, we estimate the autocorrelation parameter to be very close to one
and the magnitude of the coefficients attached to xt−1 and bt−1 revert to the
neighborhood of the corresponding values in the differenced relation (24).40
The trend term is insignificant, as was the constant in (24), and qualitatively
the relation in (26) is quite similar to the version estimated in differences.
Next, we move in the opposite direction by differencing the variables one
more time than in the reference case (24). Let ∆∆xt ≡ ∆(∆xt ) for brevity.
Then with the disturbance treated as white noise, the result is
∆∆xt = 0.0002 − 0.3993 ∆∆xt−1 + 0.363 ∆∆bt−1 .
(.0009) (.074)
(.158)
R2 = 0.182

SE = 0.0110

DW = 2.12

(27)
Q(10) = 18.3

Here the estimated parameter on the lagged GNP variable is entirely unlike
that in (24), but the Q-statistic gives borderline evidence of serial correlation.
Estimated with a MA(1) specification for the disturbance, the results change
to:
∆∆xt = 0.00001 + 0.1666 ∆∆xt−1 + 0.3571 ∆∆bt−1 − 0.946 et−1 .
(.0008) (.065)
(.139)
(.032)
R2 = 0.370

SE = 0.0097

DW = 1.89

(28)

Q(10) = 9.5

40 The coefficient on the base variable is now somewhat larger than 0.5, rather than smaller,
but the difference is less than two standard errors.

B. T. McCallum: Unit Roots in Macroeconomic Time Series

33

Now the figures are again quite close to those in the once-differenced specification (24). Not only the estimated parameter values, but also the standard errors
are approximately the same—and there is no evidence of serial correlation.
Thus the results are similar for regressions using detrended levels, differences,
and second differences of the xt and bt variables, provided that autocorrelation
corrections are used.
A second example concerns spot and forward exchange rates. In a recent
paper (McCallum 1992), I have summarized some empirical regularities for the
post-1973 floating rate period, focusing on $/£, $/DM, and $/Yen rates over the
time span 1978:01–1990:07. Letting st and ft denote logs of the spot and 30day forward rates at the end of month t, one of the observed regularities is that
OLS regression of st on ft−1 provides a tight fit with a slope coefficient very
close to one—see the estimates reported in the first panel of Table 4. When ∆st
is regressed on ∆ft−1 , however, the relationship disappears and the estimated
slope coefficient becomes insignificantly different from zero—see the second
panel of Table 4. That contrast would seem to contradict the argument of the
preceding paragraphs since there is little indication of serial correlation in the
residuals in either case.
The results in panel three, however, support our previous argument. There
the levels equation relating st and ft−1 is reestimated with an AR(1) specification
for the disturbance process, even though the DW and Q-statistics in the top
panel do not clearly call for such a step. And for all three exchange rates the
result is the same—the AR parameter φ is estimated to be close to one with
the slope coefficient on ft−1 becoming indistinguishable from zero. The results
in panel three, in other words, are essentially equivalent to those in panel two,
even though differenced data are used in the latter and not in the former.
In addition, the specification using second differences together with a
MA(1) disturbance is implemented in the fourth panel of Table 4. There the
DM case differs slightly from the previous results, the slope coefficient on ft−1
being estimated as about 0.21 and significant, but for both the £ and Yen rates
the previous results are obtained again—the slope coefficient is close to zero
with the MA parameter being estimated in the vicinity of −1.0. For five out
of the six comparisons with the reference case of panel two, then, the results
are in strong agreement despite contrasting treatment in terms of differencing.
And even in the sixth case, the extent of disagreement is relatively minor.
Thus the evidence is again supportive of the general argument that the extent
of differencing is not crucial, in the context of detrending of variables prior
to econometric analysis, provided that residual autocorrelation corrections are
utilized.41
41 It should be said explicitly that this argument is not being made with regard to Granger
causality tests or variance decomposition statistics in vector-autoregression studies. It is my impression that these results are rather sensitive to the detrending procedure. But such results are, I
believe, of less importance than impulse response patterns.

34

Federal Reserve Bank of Richmond Economic Quarterly

Table 4 Spot on Forward Exchange Rate Regressions, Sample Period
1978:01–1990:07

Rate

Variables

$/DM

st on ft−1

$/£

''

''

$/Yen

''

''

$/DM

∆st on ∆ft−1

$/£

''

''

$/Yen

''

''

$/DM

st on ft−1

$/£

''

''

$/Yen

''

''

$/DM ∆∆st on ∆∆ft−1
$/£

''

''

$/Yen

''

''

Estimates (std. errors)
Const. Slope AR(1) MA(1)
−0.009
(.012)
0.014
(.009)
−0.046
(.067)

R2

Statistics
SE DW Q(10)

0.990
(.016)
0.977
(.016)
0.991
(.013)

0.963 0.0362 2.05

9.6

0.960 0.0359 1.82

5.9

0.975 0.0380 1.84

7.7

0.002 −0.063
(.003) (.081)
0.000 0.024
(.003) (.082)
0.003 0.038
(.003) (.082)

0.004 0.0358 1.96

7.5

0.000 0.0352 1.99

3.4

0.001 0.0374 1.99

4.8

0.964 0.0359 1.96

8.1

0.962 0.0351 1.99

3.8

0.976 0.0374 2.00

5.0

−0.887 0.526 0.0361 1.86
(.039)
−0.933 0.472 0.0357 1.96
(.035)
−0.956 0.468 0.0379 1.94
(.027)

4.1

−0.575 −0.057 0.991
(.510) (.083) (.015)
0.509 0.035 0.979
(.143) (.084) (.017)
−4.743 0.046 0.989
(.681) (.083) (.0l3)
0.000 −0.206
(.003) (.057)
0.000 −0.032
(.003) (.060)
0.000 −0.010
(.003) (.060)

3.1
4.0

Data source: Bank for International Settlements.

5. COINTEGRATION
Now suppose that xt and yt are two time series variables generated by DS
processes—i.e., their univariate series have AR unit roots—that are dynamically related by a distributed-lag relation with a stationary disturbance. In (29),
for example, we assume ut to be stationary:42
yt = α + β(L)xt + ut .

42 It

(29)

is not being assumed that xt is necessarily a predetermined variable, i.e., that ut is
uncorrelated with xt , xt−1 , · · · .

B. T. McCallum: Unit Roots in Macroeconomic Time Series

35

Under these conditions yt and xt are said to be cointegrated, the term arising because DS variables are referred to by many time series analysts as
“integrated.”43 Now it is a striking fact that when yt and xt are cointegrated, then
an OLS regression of yt on xt alone—with no lags—will yield a slope coefficient
b that is a consistent estimator of the “long-run” effect β(1) = β0 +β1 +· · · . This
result would appear to be of practical importance, as it promises to provide a
simple way of discovering features of long-run relationships between variables.
To demonstrate the result, let us express the residual et = yt − bxt as
et = α + β(L)xt + ut − bxt = α + [β(L) − b]xt + ut .

(30)

But with xt an integrated (DS) variable, et will then be integrated unless β(1) −
b = 0. And if et were integrated, then the sum of squared et values would
increase without limit as the sample size goes to infinity, so the OLS criterion
of picking b to minimize this sum forces b toward β(1).
There are numerous additional theoretical results concerning cointegrated
variables including extension to multivariate settings44 and close connections
between cointegration and the existence of “error correction” forms of dynamic
models.45 For present purposes, however, the main item of interest concerns
the frequently expressed contention that if two (or more) DS variables are not
cointegrated, then there exists no long-run relationship between (or among)
them. On the basis of this notion, various researchers have concluded that
purchasing-power-parity fails even as a long-run tendency (see, e.g., Taylor
[1988] and McNown and Wallace [1989]) whereas others have drawn analogous
conclusions regarding traditional money demand relations—see, e.g., Engle and
Granger (1987).46 Cuthbertson and Taylor (1990, p. 295) have stated the matter
thusly: “If the concept of a stable, long-run money demand function is to have
.
any empirical content whatsoever, then mt [log money]˙. must be cointegrated”
with log prices, log income, and interest rates.
Now clearly there is a technical sense in which these suggestions are correct: if yt and xt are both DS but not cointegrated, then the disturbance entering
any linear relationship between them must (by definition) be nonstationary. So
they can drift apart as time passes. I would argue, however, that it is highly
misleading to conclude that in any practical sense long-run relationships are
43 If a variable must be differenced d times to render it stationary, it is said to be integrated
of order d, abbreviated I(d). The term “integrated” was popularized by Box and Jenkins (1970),
its genesis being that a random-walk variable is at any time equal to the infinite sum (“integral”)
of all past disturbances. Cointegration analysis was developed by Granger (1983) and Engle and
Granger (1987).
44 See, for example, the expository piece by Dickey, Jansen, and Thornton (1991).
45 See Hendry (1986).
46 Other writers have apparently accepted this characterization prior to reaching the opposite
empirical conclusion. A few examples are Mehra (1989), Hoffman and Rasche (1991), Miller
(1991), Hafer and Jansen (1991), and Diebold, Husted, and Rush (1991).

36

Federal Reserve Bank of Richmond Economic Quarterly

therefore nonexistent. My argument is entirely interpretive; it includes no suggestion of technical error in the literature criticized. But its importance is not
thereby diminished.
To develop the argument at hand, let us take the example of a traditional
money demand function of the form
mt − pt = β0 + β1 yt + β2 Rt + ηt ,

(31)

where mt − pt is the log of real money balances, yt the log of a real transactions
variable (such as GDP), and Rt is an opportunity-cost variable relevant to the
measure of money being used. Let us suppose for the purpose of the argument
that mt − pt , yt , and Rt are all DS variables. And let us suppose that mt − pt ,
yt , and Rt have all been processed by removal of a deterministic trend.47 Then
the cointegration status of the relationship depends upon the properties of the
disturbance ηt —if its process is of the DS type, the variables in (31) will not
be cointegrated.
It is my contention that the traditional view of money demand theory,
represented for example by the New Palgrave entry by McCallum and Goodfriend (1987), would actually suggest that the variables in (31) are unlikely
to be cointegrated. The reason is that the rationale for (31) depends upon the
transactions-facilitating function of money, but the technology for effecting
transactions is constantly changing. And since technical progress cannot be
well represented by measurable variables, the effects of technical change not
captured by a deterministic trend show up in the disturbance term, ηt . But the
nature of technological progress is such that changes (shocks) are typically not
reversed. Thus one would expect there to be an important permanent component
to the ηt process, making it one of the DS type.
In such a situation, however, the “long-run” messages of traditional money
demand analysis may continue to apply. Provided that the magnitude of the
variance to the innovation in ηt is not large in relation to potential magnitudes
of ∆mt values, it will still be true that inflation rates will be principally determined by money growth rates, that long-run monetary neutrality will prevail,
that superneutrality will be approximately but not precisely valid, etc. That
the disturbance term in the money demand relationship is of the DS class is
simply not a source of embarrassment or special concern for supporters of the
traditional theory of money demand.48
Much the same can be said, furthermore, in the context of PPP doctrine.
Nominal exchange rates are probably not cointegrated with relative price levels
47 This step should not be at issue; the existence of technological change in the payments
industry is widely accepted.
48 Many of these supporters have been willing to estimate money demand functions in firstdifferenced form, thereby implicitly assuming a DS disturbance process.

B. T. McCallum: Unit Roots in Macroeconomic Time Series

37

because technological and taste shocks affecting real exchange rates have permanent components.49 But major differences among nations in money growth
and inflation rates may nevertheless dominate other effects on nominal exchange rates over long spans of time, leaving the practical messages of the PPP
doctrine entirely valid as a long-run matter.50 That such is the case in actuality
is indicated by the evidence collected by Gailliot (1970) and Officer (1980).
In both of the preceding examples, it was argued that one should expect
the disturbance term in a relation among levels of economic variables to include both permanent and transitory components, and therefore to possess an
autoregressive unit root. This argument—which is an application to disturbance
terms of the unobserved-components perspective put forth in Section 3—would
seem to be applicable quite broadly; indeed, to the disturbances of most behavioral relations. That point of view implies, unfortunately, that cointegrating
relationships will be rare51 and so the potentially beneficial estimation result
mentioned in the first paragraph of this section will not be forthcoming.52
The argument of the present section has a natural counterpart, it might
be added, in the context of debates concerning non-trend stationarity of the
price level. Some commentators, including Barro (1986) and Haraf (1986),
have emphasized uncertainty concerning future values of the price level and
have accordingly suggested that it is highly undesirable for pt (log of the price
level) to be generated by a unit-root process. The point of view expressed here
emphasizes, by contrast, the relative unimportance of pt nonstationarity per se,
given the existing magnitude of the disturbance variance for the pt process, in
comparison with recent values of the trend growth rate. One way to express
the point is to hypothesize that citizens and policymakers in the United States
would view price-level performance as highly satisfactory if it were generated
(in quarterly terms) as
pt = δ + pt−1 +

t

(32)

if δ = 0 and t were white noise with σ 2 = 0.00002. (The latter figure approximately equals the one-quarter forecast variance over 1954–1991.) Looking 20
years ahead, the forecast variance of pt would be 80(0.00002) = 0.0016, so a
95 percent confidence interval would be the current value plus or minus 0.08
49 As

suggested, for example, by Stockman (1987).
the interpretation of PPP is taken to agree with popular usage, although a good
case can be made for an alternative interpretation that expresses PPP as a form of a neutrality
proposition.
51 The s , f example in Section 5 is, however, a case in which cointegration evidently does
t t
obtain.
52 Campbell and Perron (1991, pp. 218-19) argues against this suggestion by means of a
reductio ad absurdum. The latter is not actually applicable, however, as my argument is directed
only toward variables that enter agents’ utility functions or budget constraints.
50 Here

38

Federal Reserve Bank of Richmond Economic Quarterly

(or ±8 percent in terms of the price level). That figure pales into insignificance
in comparison with the expected change in pt over 20 years if δ were nonzero
and equal to (e.g.) 0.011, a figure that corresponds to a 4.5 percent annual rate
of inflation.

6. CONCLUSIONS
In this final section we shall conclude the arguments. The discussion will not
be a summary of what has gone before—which is itself largely a condensation
of other work—but instead will attempt to reach conclusions in the sense of
“logical consequences” of what has gone before. In developing our arguments
it will be useful to distinguish the two different purposes of trend analysis
that were mentioned above: (i) isolating trend from cyclical components and
(ii) trend removal for the purpose of obtaining series suitable for econometric
analysis. We begin with subject (ii).
In the context of removing trends from time series so that relationships
among these series can be studied by conventional econometric methods, we
have seen that there is a tendency for similar results to be obtained from the two
methods, provided that serial correlation corrections are applied to the residuals
of the relationship being studied. This suggests that it is not crucial whether the
analyst differences the data or removes deterministic trends. The recommended
course of action would then be, evidently, to estimate the econometric model
both ways—with differenced and (deterministically) detrended data—and hope
that similar results will in fact be obtained. But emphasis in presentation will
usually be given to one set of results or the other, and in some cases the results
will not be similar. A natural basis for choice would then be to feature the
results that require the smaller amount of correction to remove autocorrelation
of the residuals. In the case of the GNP-monetary base example of Section 4,
for example, the preferred results would be those in equation (24), rather than
(26) or (28). And in the exchange rate example of Table 4, the results in the
second panel would be preferred, according to this criterion.
Now consider purpose (i), the estimation of trends so as to isolate trend
from cyclical components of a series. In Sections 2-4 above we have reviewed
various results all of which indicate that there is no reliable method for distinguishing among alternative trend/cycle decompositions even when these have
entirely different long-run response characteristics and different implications
about the relative importance of the two components. This seems, at first glance,
a discouraging conclusion.
Reflection on the issue suggests, however, that it actually makes very little
sense even to attempt to distinguish between trend and cycle on the basis
of a variable’s univariate time series properties alone. The reason is that the
separation of trend and cycle will in most cases be desired because the analyst

B. T. McCallum: Unit Roots in Macroeconomic Time Series

39

believes that the two components have different economic properties or significance. With regard to real GNP, for example, Nelson (1989, p. 74) emphasizes
that analysts “tend to think of the processes generating the two components as
quite different,” one being “due to growth in labor force and capital stock and
to technological change” and the other “arising largely from monetary [and
fiscal] disturbances.” But such components will be neither independent nor
perfectly correlated, as presumed by the two main trend estimation procedures
described above. And without knowledge of the extent of correlation, they are
not identified even under the assumption that the trend component is a random
walk. This latter assumption, moreover, is itself rather unsatisfactory.
More generally, the distinction between trend and cycle is by many economists viewed as pertaining to movements that are socially desirable and undesirable, respectively. But whether such is the case clearly depends upon the
economist’s theory of cyclical fluctuations, for some of these—the real business
cycle hypothesis, for example—will not view cyclical movements as something
that policy should attempt to mitigate. The nature of the cycle vs. trend distinction, in other words, depends upon the theory of macroeconomic fluctuations
adopted. But if that is the case, then it makes little sense to attempt to separate
out the cyclical component by means of a procedure that takes no account of
alternative theories but relies merely on a variable’s time series properties.53
The reader may have noticed that the remarks in this concluding section
have pertained exclusively to trend analysis, with the term “unit roots” failing
to appear. More generally, it may have been noted that there is no inevitable
connection between the two concepts—unit roots may be present in a series that
is entirely trendless (and vice versa). But the presence of trends is a constant
source of practical difficulties in the analysis of time series data, and the recent
interest in unit roots has stemmed largely from the notion of stochastic trends. It
is then for reasons of practicality that emphasis has here been given to the topic
of trends. Our principal messages regarding unit roots per se are implicit in our
conclusions regarding trends. But since those messages are somewhat negative
concerning the value of unit root testing, it needs to be mentioned explicitly
that introduction of the unit root concept, together with recognition that series
are likely to include DS components, has been a valuable corrective to the
earlier habit of presuming trend stationarity and has led to several analytical
insights.54

53 It should be noted that this argument does not imply that it is pointless to try to attempt
to reach substantive macroeconomic conclusions on the basis of analyses such as that of Blanchard and Quah (1989), which utilizes multiple time series and relies upon explicit substantive
assumptions for identification.
54 A recent example is provided by the related analyses of Fisher and Seater (1993) and
King and Watson (1992).

40

Federal Reserve Bank of Richmond Economic Quarterly

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Commercial Paper
Thomas K. Hahn

C

ommercial paper is a short-term unsecured promissory note issued by
corporations and foreign governments. For many large, creditworthy
issuers, commercial paper is a low-cost alternative to bank loans. Issuers are able to efficiently raise large amounts of funds quickly and without
expensive Securities and Exchange Commission (SEC) registration by selling
paper, either directly or through independent dealers, to a large and varied
pool of institutional buyers. Investors in commercial paper earn competitive,
market-determined yields in notes whose maturity and amounts can be tailored
to their specific needs.
Because of the advantages of commercial paper for both investors and
issuers, commercial paper has become one of America’s most important debt
markets. Commercial paper outstanding grew at an annual rate of 14 percent
from 1970 to 1991. Figure 1 shows commercial paper outstanding, which totaled $528 billion at the end of 1991.
This article describes some of the important features of the commercial
paper market. The first section reviews the characteristics of commercial paper.
The second section describes the major participants in the market, including
the issuers, investors, and dealers. The third section discusses the risks faced by
investors in the commercial paper market along with the mechanisms that are
used to control these risks. The fourth section discusses some recent innovations, including asset-backed commercial paper, the use of swaps in commercial
paper financing strategies, and the international commercial paper markets.

The author, a consultant with TKH Associates and former assistant economist at the Federal
Reserve Bank of Richmond, would like to thank Timothy Cook, Bob LaRoche, Jerome Fons,
and Mitchell Post for comments. The views expressed in this article are those of the author
and do not necessarily reflect those of the Federal Reserve Bank of Richmond or the Federal
Reserve System.

Federal Reserve Bank of Richmond Economic Quarterly Volume 79/2 Spring 1993

45

46

Federal Reserve Bank of Richmond Economic Quarterly

$ Billions

Figure 1 Commercial Paper Outstanding

Source: Board of Governors of the Federal Reserve System.

1. CHARACTERISTICS OF COMMERCIAL PAPER
The Securities Act of 1933 requires that securities offered to the public be
registered with the Securities and Exchange Commission. Registration requires
extensive public disclosure, including issuing a prospectus on the offering,
and is a time-consuming and expensive process.1 Most commercial paper is
issued under Section 3(a)(3) of the 1933 Act which exempts from registration
requirements short-term securities as long as they have certain characteristics.2
The exemption requirements have been a factor shaping the characteristics of
the commercial paper market.
1 Registration

for short-term securities is especially expensive because the registration fee is
a percent of the face amount at each offering. Thirty-day registered notes, rolled over monthly
for one year, would cost 12 times as much as a one-time issuance of an equal amount of one-year
notes.
2 Some commercial paper is issued under one of the two other exemptions to the Securities
Act. Commercial paper which is guaranteed by a bank through a letter of credit is exempt under
Section 3(a)(2) regardless of whether or not the issue is also exempt under Section 3(a)(3). Commercial paper sold through private placements is exempt under Section 4(2). See Felix (1987) for
more information on the legal aspects of commercial paper issuance.

T. K. Hahn: Commercial Paper

47

One requirement for exemption is that the maturity of commercial paper
must be less than 270 days. In practice, most commercial paper has a maturity
of between 5 and 45 days, with 30–35 days being the average maturity. Many
issuers continuously roll over their commercial paper, financing a more-or-less
constant amount of their assets using commercial paper. Continuous rollover of
notes does not violate the nine-month maturity limit as long as the rollover is
not automatic but is at the discretion of the issuer and the dealer. Many issuers
will adjust the maturity of commercial paper to suit the requirements of an
investor.
A second requirement for exemption is that notes must be of a type not
ordinarily purchased by the general public. In practice, the denomination of
commercial paper is large: minimum denominations are usually $100,000,
although face amounts as low as $10,000 are available from some issuers.
Because most investors are institutions, typical face amounts are in multiples
of $1 million. Issuers will usually sell an investor the specific amount of commercial paper needed.
A third requirement for exemption is that proceeds from commercial paper
issues be used to finance “current transactions,” which include the funding
of operating expenses and the funding of current assets such as receivables
and inventories. Proceeds cannot be used to finance fixed assets, such as plant
and equipment, on a permanent basis. The SEC has generally interpreted the
current transaction requirement broadly, approving a variety of short-term uses
for commercial paper proceeds. Proceeds are not traced directly from issue to
use, so firms are required to show only that they have a sufficient “current
transaction” capacity to justify the size of the commercial paper program (for
example, a particular level of receivables or inventory).3 Firms are allowed to
finance construction as long as the commercial paper financing is temporary and
to be paid off shortly after completion of construction with long-term funding
through a bond issue, bank loan, or internally generated cash flow.4
Like Treasury bills, commercial paper is typically a discount security: the
investor purchases notes at less than face value and receives the face value at
maturity. The difference between the purchase price and the face value, called
the discount, is the interest received on the investment. Occasionally, investors
request that paper be issued as an interest-bearing note. The investor pays the
3 Some SEC interpretations of the current transaction requirement have been established in
“no-action” letters. “No-action” letters, issued by the staff of the SEC at the request of issuers,
confirm that the staff will not request any legal action concerning an unregistered issue. See Felix
(1987, p. 39).
4 Past SEC interpretations of Section 3(a)(3) exemptions have also required that commercial
paper be of “prime quality” and be discountable at a Federal Reserve Bank (Release No. 334412). The discounting requirement was dropped in 1980. An increased amount of commercial
paper in the later 1980s was issued without prime ratings.

48

Federal Reserve Bank of Richmond Economic Quarterly

face value and, at maturity, receives the face value and accrued interest. All
commercial paper interest rates are quoted on a discount basis.5
Until the 1980s, most commercial paper was issued in physical form in
which the obligation of the issuer to pay the face amount at maturity is recorded
by printed certificates that are issued to the investor in exchange for funds. The
certificates are held, usually by a safekeeping agent hired by the investor, until
presented for payment at maturity. The exchanges of funds for commercial paper first at issuance and then at redemption, called “settling” of the transaction,
occur in one day. On the day the commercial paper is issued and sold, the
investor receives and pays for the notes and the issuer receives the proceeds.
On the day of maturity, the investor presents the notes and receives payment.
Commercial banks, in their role as issuing, paying, and clearing agents, facilitate the settling of commercial paper by carrying out the exchanges between
issuer, investor, and dealer required to transfer commercial paper for funds.
An increasing amount of commercial paper is being issued in book-entry
form in which the physical commercial paper certificates are replaced by entries in computerized accounts. Book-entry systems will eventually completely
replace the physical printing and delivery of notes. The Depository Trust Company (DTC), a clearing cooperative operated by member banks, began plans in
September 1990 to convert most commercial paper transactions to book-entry
form.6 By May 1992, more than 40 percent of commercial paper was issued
through the DTC in book-entry form.
The advantages of a paperless system are significant. The fees and costs
associated with the book-entry system will, in the long run, be significantly
less than under the physical delivery system. The expense of delivering and
verifying certificates and the risks of messengers failing to deliver certificates
on time will be eliminated. The problem of daylight overdrafts, which arise
from nonsynchronous issuing and redeeming of commercial paper, will be reduced since all transactions between an issuing agent and a paying agent will
be settled with a single end-of-day wire transaction.

2. MARKET PARTICIPANTS
Issuers and Uses of Commercial Paper
Commercial paper is issued by a wide variety of domestic and foreign firms,
including financial companies, banks, and industrial firms. Table 1 shows
5 The

Federal Reserve publishes in its H.15 statistical release daily interest rates for dealeroffered and directly placed commercial paper of one-month, three-month and six-month maturities.
All rates are based on paper with relatively low default risk. Commercial paper rates of various
maturities for select finance issuers and a dealer composite rate are also published daily in The
Wall Street Journal.
6 See The Depository Trust Company (1990).

T. K. Hahn: Commercial Paper

49

Table 1 Commercial Paper Outstanding by Major Issuer
Billions of dollars

Category

Major Issuer

Average
Amount
Outstanding Dealer

Finance

General Electric Capital
(subsidiary of GE)
Auto Finance
General Motors Acceptance
(subsidiary of GM)
Investment Banking Merrill Lynch
Commercial Banking J.P. Morgan
Industrial
PepsiCo
Foreign
Hanson Finance
Asset-Backed
Corporate Asset Funding

$36.9

Direct, Multiple

$23.6
$ 7.5
$ 4.4
$ 3.4
$ 3.5
$ 5.3

Direct
Dealer is subsidiary
Multiple
Multiple
Multiple
Goldman Sachs

Note: Quarterly Average Commercial Paper is for the first quarter of 1992, except GE, GMAC,
and PepsiCo, which are for the fourth quarter of 1991.
Source: Moody’s Global Short Term Record, June 1992.

Figure 2 Commercial Paper Outstanding by Issuer Type
End of 1991 Total $528.1 Billion
Billions of dollars

Source: Board of Governors of the Federal Reserve System.

examples of the largest commercial paper issuers. Figure 2 shows outstanding
commercial paper by type of issuer.
The biggest issuers in the financial firm category in Figure 2 are finance
companies. Finance companies provide consumers with home loans, retail automobile loans, and unsecured personal loans. They provide businesses with

50

Federal Reserve Bank of Richmond Economic Quarterly

a variety of short- and medium-term loans including secured loans to finance
purchases of equipment for resale. Some finance companies are wholly owned
subsidiaries of industrial firms that provide financing for purchases of the parent
firm’s products. For example, a major activity of General Motors Acceptance
Corporation (GMAC) is the financing of purchases and leases of General Motor’s vehicles by dealers and consumers. The three largest issuers—GMAC,
General Electric Capital, and Ford Motor Credit—accounted for more than 20
percent of the total nonbank financial paper outstanding at the end of 1991.
The financial issuer category also includes insurance firms and securities
firms. Insurance companies issue commercial paper to finance premium receivables and operating expenses. Securities firms issue commercial paper as a
low-cost alternative to other short-term borrowings such as repurchase agreements and bank loans, and they use commercial paper proceeds to finance a
variety of security broker and investment banking activities.
Commercial bank holding companies issue commercial paper to finance
operating expenses and various nonbank activities. Bank holding companies
have recently decreased their commercial paper issues following declines in
the perceived creditworthiness of many major domestic bank issuers.
More than 500 nonfinancial firms also issue commercial paper. Nonfinancial issuers include public utilities, industrial and service companies. Industrial
and service companies use commercial paper to finance working capital (accounts receivable and inventory) on a permanent or seasonal basis, to fund
operating expenses, and to finance, on a temporary basis, construction projects.
Public utilities also use commercial paper to fund nuclear fuels and construction. Figure 3 shows that commercial paper as a percent of commercial paper
and bank loans for nonfinancial firms rose from just 2 percent in 1966 to over
15 percent at the end of 1991.
The domestic commercial paper issuers discussed above include U.S. subsidiaries of foreign companies. Foreign corporations and governments also issue
commercial paper in the U.S. without use of a domestic subsidiary and these
foreign issues have gained increased acceptance by U.S. investors. Foreign
financial firms, including banks and bank holding companies, issue almost
70 percent of foreign commercial paper (Federal Reserve Bank of New York
1992). Industrial firms and governments issue the remainder. Japan, the United
Kingdom, and France are among the countries with a significant number of
issuers.
Investors
Money market mutual funds (MMFs) and commercial bank trust departments
are the major investors in commercial paper. MMFs hold about one-third of the
outstanding commercial paper, while bank trust departments hold between 15

T. K. Hahn: Commercial Paper

51

Percent

Figure 3 Commercial Paper as a Percent of Commercial Paper and Bank
Loans, Nonfinancial Firms

Source: Board of Governors of the Federal Reserve System.

and 25 percent.7 Other important investors, holding between 5 and 15 percent,
are nonfinancial corporations, life insurance companies, and private and government pension funds. Other mutual funds, securities dealers, and banks also
hold small amounts of commercial paper. Individuals hold little commercial
paper directly because of the large minimum denominations, but they are large
indirect investors in commercial paper through MMFs and trusts.
There have been major shifts in ownership of commercial paper during the
post-World War II period. Prior to World War II, the most important investors
in commercial paper were banks, which used commercial paper as a reserve
asset and to diversify their securities portfolios. In the fifties and sixties, industrial firms began to hold commercial paper as an alternative to bank deposits,
which had regulated interest rates that at times were significantly below the
market-determined rates on commercial paper. Historically high and variable
interest rates during the 1970s led households and businesses to hold more
7 Precise data on holdings of commercial paper by investor type, except by MMFs, are not
available. Some estimates are provided in Board of Governors of the Federal Reserve System
(1992, p. 52), Stigum (1990, p. 1027), and Felix (1987, p. 13).

52

Federal Reserve Bank of Richmond Economic Quarterly

Table 2 Money Market Mutual Funds and Commercial Paper

End of
1975
1980
1985
1990
1991

MMF
Assets
($ billions)

Commercial
Paper
Outstanding
($ billions)

MMF
Holdings
of CP
($ billions)

CP as Percent
of MMF
Assets

Percent of
CP Held
by MMFs

3.7
74.5
207.5
414.8
449.7

47.7
121.6
293.9
557.8
528.1

0.4
25.0
87.6
199.1
187.6

11
33
42
48
42

1
21
30
36
36

Note: MMFs exclude tax-exempt funds.
Source: Board of Governors of the Federal Reserve System.

of their funds in short-term assets and to transfer funds from bank deposits
with regulated interest rates to assets like MMF shares with market-determined
rates. At the same time, many large businesses found that they could borrow
in the commercial paper market at less expense than they could borrow from
banks. MMFs demanded the short-term, large-denomination, relatively safe,
and high-yield characteristics offered by commercial paper and hence absorbed
a major portion of new commercial paper issues. Table 2 shows that both
the commercial paper market and MMFs have experienced very rapid growth
since 1975. By the end of 1991, MMFs held 36 percent of the commercial paper
outstanding and commercial paper composed 42 percent of their total assets.
Placement and Role of the Dealer
Most firms place their paper through dealers who, acting as principals, purchase commercial paper from issuers and resell it to the public. Most dealers
are subsidiaries of investment banks or commercial bank holding companies.
A select group of very large, active issuers, called direct issuers, employ their
own sales forces to distribute their paper. There are approximately 125 direct
issuers, most of which are finance companies or bank holding companies. These
issuers sell significant amounts of commercial paper on a continuous basis.
When an issuer places its commercial paper through a dealer, the issuer decides how much paper it will issue at each maturity. The dealer is the issuer’s
contact with investors and provides the issuer with relevant information on
market conditions and investor demand. Dealers generally immediately resell
commercial paper purchased from issuers and do not hold significant amounts
of commercial paper in inventory. Dealers will temporarily hold commercial
paper in inventory as a service to issuers, such as to meet an immediate need
for a significant amount of funds at a particular maturity.
The difference between what the dealer pays the issuer for commercial
paper and what he sells it for, the “dealer spread,” is around 10 basis points

T. K. Hahn: Commercial Paper

53

on an annual basis. A large commercial paper program with $500 million in
paper outstanding for one year would cost the issuer $500,000 in dealer fees.
Because independent dealers are relatively inexpensive, only large and
well-recognized issuers distribute their own commercial paper. Direct issuers
are typically committed to borrowing $1 billion or more in the commercial
paper market on a continuous basis (Felix 1987, p. 20). Partly as a result of
the decline in dealer spreads over the last ten years, the percentage of total
commercial paper issued directly fell from almost 55 percent in 1980 to just 35
percent at the end of 1991. An additional factor in the growth of dealer-placed
commercial paper has been the entry into the market of smaller issuers who do
not have borrowing needs large enough to justify a direct sales force.
Competition among dealers significantly increased in the late 1980s after
the entrance into the market of bank dealers, which are subsidiaries of bank
holding companies. Prior to the mid-1980s, commercial banks mainly acted
as agents who placed commercial paper without underwriting and who carried
out the physical transactions required in commercial paper programs, including
the issuing and safekeeping of notes and the paying of investors at maturity.
Bank dealers entered the market after legal restrictions on underwriting by bank
holding companies were relaxed, and the increased competition led to declines
in profit margins and the exit from the market of some major investment bank
dealers. Salomon Brothers closed its dealership and Paine Webber sold its
dealership to CitiCorp. Goldman Sachs, another important dealer, responded to
increased competition by rescinding its longstanding requirement that it be the
sole dealer for an issuer’s commercial paper. Issuers have increased their use
of multiple dealers for large commercial paper programs, frequently including
a bank dealer in their team of dealers.
The largest commercial paper dealers are still the investment banks, including Merrill Lynch, Goldman Sachs, and Shearson Lehman. Commercial bank
holding companies with large commercial paper dealer subsidiaries include
Bankers Trust, CitiCorp, BankAmerica, and J.P. Morgan. Some foreign investment and commercial bank holding companies have also become significant
dealers.
The secondary market in commercial paper is small. Partly the lack of a secondary market reflects the heterogeneous characteristics of commercial paper,
which makes it difficult to assemble blocks of paper large enough to facilitate
secondary trading. Partly it reflects the short maturity of the paper: investors
know how long they want to invest cash and, barring some unforseen cash need,
hold commercial paper to maturity. Dealers will sometimes purchase paper from
issuers or investors, hold the paper in inventory and subsequently trade it. Bids
for commercial paper of the largest issuers are available through brokers.
Some direct issuers offer master note agreements which allow investors,
usually bank trust departments, to lend funds on demand on a daily basis at a
rate tied to the commercial paper rate. Each day the issuer tells the investor
the rate on the master note and the investor tells the issuer how much it will

54

Federal Reserve Bank of Richmond Economic Quarterly

deposit that day. At the end of 1991, approximately 10 percent of GMAC’s
short-term notes outstanding were master notes sold to bank trust departments
(GMAC 1992, p. 13).

3. RISK IN THE COMMERCIAL PAPER MARKET
Ratings
Since 1970, when the Penn Central Transportation Co. defaulted with $82 million of commercial paper outstanding, almost all commercial paper has carried
ratings from one or more rating agency. Currently, the four major rating agencies are Moody’s, Standard & Poor’s, Duff & Phelps, and Fitch. An issuer’s
commercial paper rating is an independent “assessment of the likelihood of
timely payment of [short-term] debt” (Standard & Poor’s 1991, p. iii). Table 3
lists the four rating agencies, the rating scales they publish, and the approximate
number of commercial paper ratings issued at the end of 1990. The ratings are
relative, allowing the investor to compare the risks across issues. For example,
Standard & Poor’s gives an A-1 rating to issues that it believes have a “strong”
degree of safety for timely repayment of debt, an A-2 rating to issues that it
believes have a degree of safety that is “satisfactory,” and an A-3 rating to
issues that it believes have a degree of safety that is “adequate.” Below these

Table 3 Rating Agencies and Commercial Paper Ratings

Higher
A/Prime

Lower
A/Prime

Major
Speculative
Approx. Publication
Below
# of CP Listing
Prime
Defaulted Ratings CP Ratings

P-1

P-2, P-3

NP

NP

2,000

Moody’s Global
Short-Term
Market Record

Standard & A-1+, A-1
Poor’s

A-2, A-3

B, C

D

2,000

S&P
Commercial
Paper Ratings
Guide

Duff &
Phelps

Duff 1+,
Duff 1,
Duff 1-

Duff 2,
Duff 3

Duff 4

Duff 5

175

Short-Term
Ratings and
Research Guide

Fitch

F-1+, F-1

F-2, F-3

F-5

D

125

Fitch Ratings

A, BBB

BB, B,
CCC, CC,
C

Moody’s

AAA, AA,
Range of
A
Likely
S&P LongTerm Bond
Rating

T. K. Hahn: Commercial Paper

55

three categories are the speculative grades in which the capacity for repayment
is small relative to the higher-rated issues. Finally, a D rating indicates the
issuer has defaulted on its commercial paper. Almost all issuers carry one of
the two highest Prime or A ratings.
Issuers hire the rating agencies to rate their short-term debt and pay the
agencies an annual fee ranging from $10,000 to $29,000 per year. For an additional fee the agencies will also rate other liabilities of the issuer, including
their long-term bonds. The ratings are provided to the public, generally by subscription, either through publications, computer databases, or over the phone.
Major announcements by the rating agencies are also reported on news wire
services. Table 3 lists each agency’s major publication in which commercial
paper ratings appear.
Rating agencies rely on a wide variety of information in assessing the default risk of an issuer. The analysis is largely based on the firm’s historical and
projected operating results and its financial structure. Relevant characteristics
include size (both absolute and compared to competitors), profitability (including the level and variation of profits), and leverage. Table 4 shows the means
of selected historical characteristics of a sample of publicly traded nonfinancial
issuers by commercial paper rating category. The table shows that higherrated issuers are on average more profitable than lower-rated issuers and, with
some exceptions, larger. Additionally, higher-rated issuers rely less heavily on
debt financing than lower-rated issuers and have stronger interest-coverage and

Table 4 Characteristics of Industrial Commercial Paper Issuers by
Rating, Three-Year Averages
Standard &
Poor’s
Commercial Number of Assets
Interest
Debt
Paper Rating Companies (millions) Coverage Coverage Leverage Profitability
A-1+
A-1
A-2
A-3

91
102
97
9

$4,547
$2,924
$1,866
$5,252

8x
5x
4x
2x

.7x
.5x
.4x
.2x

27%
35%
36%
52%

18%
16%
14%
10%

Notes: Sample consists of nonfinancial commercial paper issuers required to file with the SEC.
Interest coverage is defined as the ratio of income available for interest to interest expense. Income
available for interest is defined as pre-tax income less special income plus interest expense.
Debt coverage is defined as the ratio of cash flow to short- and long-term debt. Cash flow is
income plus preferred dividends plus deferred taxes.
Leverage is defined as the ratio of total debt to invested capital. Invested capital is the sum of
short- and long-term debt, minority interest, preferred and common equity, and deferred taxes.
Profitability is defined as the ratio of income available for interest to invested capital.
Source: Standard & Poor’s Compustat Services.

56

Federal Reserve Bank of Richmond Economic Quarterly

debt-coverage ratios.8 In addition to evaluating the firm’s operating results and
financial structure, rating agencies also evaluate more subjective criteria like
quality of management and industry characteristics. The same factors influence
the issuer’s short-term and long-term debt rating so there is generally a close
correspondence between the commercial paper rating and the bond rating.
Ratings are crucially important in the commercial paper market. Ratings
are useful as an independent evaluation of credit risk that summarizes available
public information and reduces the duplication of analysis in a market with
many investors (Wakeman 1981). Ratings are also used to guide investments
in commercial paper. Some investors, either by regulation or choice, restrict
their holdings to high-quality paper and the measure of quality used for these
investment decisions is the rating. For example, regulations of MMFs limit
their holdings of commercial paper rated less than A1-P1. Other market participants, including dealers and clearing agencies, also generally require issuers
to maintain a certain quality. Again, credit quality is measured by the rating.
Backup Liquidity
Commercial paper issuers maintain access to funds that can be used to pay
off all or some of their maturing commercial paper and other short-term debt.
These funds are either in the form of their own cash reserves or bank lines
of credit. Rating agencies require evidence of short-term liquidity and will not
issue a commercial paper rating without it. The highest-rated issuers can maintain liquidity backup of as little as 50 percent of commercial paper outstanding,
but firms with less than a high A1-P1 rating generally have to maintain 100
percent backup.
Most commercial paper issuers maintain backup liquidity through bank
lines of credit available in a variety of forms. Standard credit lines allow borrowing under a 90-day note. Swing lines provide funds on a day-to-day basis,
allowing issuers to cover a shortfall in proceeds from paper issuance on a
particular day. Increasingly, backup lines of credit are being structured as more
secure multi-year revolver agreements in which a bank or syndicate of banks
commit to loan funds to a firm on demand at a floating base rate that is tied
to the prime rate, LIBOR rate, or Certificate of Deposit rate. The spread over
the base rate is negotiated at the time the agreement is made and can either
be fixed or dependent on the bond rating of the borrower at the time the loan
is drawn down. The length of the revolver commitment varies, but the trend
in revolvers has been towards shorter terms, typically around three years. As
compensation for the revolver commitment, the firm pays various fees to the
bank. The facility fee is a percentage of the credit line and is paid whether or
8 Because

ratings depend on historical operating results, researchers have had some success
in predicting ratings based on accounting data. See, for example, Peavy and Edgar (1983).

T. K. Hahn: Commercial Paper

57

not the line is activated. The commitment fee is a percentage of the unused
credit line. This type of fee has become less common in recent years. A usage
fee is sometimes charged if the credit line is heavily used.
Backup lines of credit are intended to provide funds to retire maturing
commercial paper when an event prevents an issuer from rolling over the paper. Such an event may be specific to an issuer: an industrial accident, sudden
liability exposure, or other adverse business conditions that investors perceive
as significantly weakening the credit strength of the issuer. Or the event may
be a general development affecting the commercial paper market. For instance,
a major issuer might default, as Penn Central did in 1970, and make it prohibitively expensive for some issuers to roll over new paper, or a natural disaster
such as a hurricane may interrupt the normal function of the market.
Backup lines of credit will generally not be useful for a firm whose operating and financial condition has deteriorated to the point where it is about
to default on its short-term liabilities. Credit agreements frequently contain
“material adverse change” clauses which allow banks to cancel credit lines
if the financial condition of a firm significantly changes. Indeed, the recent
history of commercial paper defaults has shown that as an issuer’s financial
condition deteriorates and its commercial paper cannot be rolled over, backup
lines of credit are usually canceled before they can be used to pay off maturing
commercial paper.
General factors affecting the commercial paper market may also result in
the disruption of backup lines of credit. Standard & Poor’s has emphasized
this point in an evaluation of the benefits to investors of backup credit lines:
“A general disruption of commercial paper markets would be a highly volatile
scenario, under which most bank lines would represent unreliable claims on
whatever cash would be made available through the banking system to support
the market” (Samson and Bachmann 1990, p. 23). Part of the risk assumed by
commercial paper investors is the possibility of this highly volatile scenario.
Credit Enhancements
While backup lines of credit are needed to obtain a commercial paper rating,
they will not raise the rating above the underlying creditworthiness of the issuer.
Issuers can significantly increase the rating of their paper, however, by using
one of a variety of credit enhancements which lower default risk by arranging
for an alternative party to retire the commercial paper if the issuer cannot. These
credit enhancements differ from backup lines of credit in that they provide a
guarantee of support which cannot be withdrawn. Some smaller and riskier
firms, which normally would find the commercial paper market unreceptive,
access the commercial paper market using these enhancements.
Some large firms with strong credit ratings raise the ratings of smaller
and less creditworthy subsidiaries by supporting their commercial paper with

58

Federal Reserve Bank of Richmond Economic Quarterly

outright guarantees or with less secure “keepwell” agreements which describe
the commitment the parent makes to assist the subsidiary to maintain a certain
creditworthiness (Moody’s, July 1992). Since parent companies may have incentives to prevent default by their subsidiaries, the affiliation of a subsidiary
with a strong parent can raise the credit rating of the subsidiary issuer.
Firms also raise their credit ratings by purchasing indemnity bonds from
insurance companies or standby letters of credit sold by commercial banks.
Both of these enhancements provide assurance that the supporting entity will
retire maturing commercial paper if the issuer cannot. With a letter of credit,
for example, the issuer pays a fee to the bank, attaches the letter of credit to
the commercial paper and effectively rents the bank’s rating. The attention of
the rating agency and investors shift from the issuer to the supporting bank.
The issue will generally receive the same rating as the bank’s own commercial
paper and offer an interest rate close to the bank’s paper. Since relatively few
U.S. banks have A1-P1 ratings, highly rated foreign banks are the primary
sellers of commercial paper letters of credit. At the end of the first quarter
of 1992, approximately 6 percent of commercial paper was fully backed by
a credit enhancement, primarily bank letters of credit, issued by a third party
unaffiliated with the issuer (Federal Reserve Bank of New York 1992).
Slovin et al. (1988) show that the announcement of a commercial paper program with a credit enhancement9 has been associated with a significant increase
in the value of the issuer’s equity, but the announcement of a commercial paper
program with no credit enhancement has no impact on firm value. This evidence
suggests that by issuing a letter of credit and certifying the creditworthiness
of the issuer, the commercial bank provides new information to the capital
markets. These results provide support for the hypothesis that banks generate
information relevant for assessing credit risk that the securities markets do not
have. Banks supply this information to the capital market through commercial
paper programs supported by letters of credit.
Default History and Yields
Commercial paper pays a market-determined interest rate that is closely related
to other market interest rates like the rate on large certificates of deposit. Because commercial paper has default risk, its yield is higher than the yield on
Treasury bills. From 1967 through 1991, the spread of the one-month commercial paper rate over the one-month Treasury bill rate averaged 117 basis points.
Default risk also creates a differential between the rates on different quality
grades of commercial paper. Figure 4 shows the spread between the yield on
commercial paper rated A1-P1 and the yield on paper rated A2-P2. This spread
9 The

credit enhancements examined were standby letters of credit and, for programs outside
the United States, note issuance facilities.

T. K. Hahn: Commercial Paper

59

Basis Points

Figure 4 Spread Between the Rates on Prime- and Medium-Grade Commercial Paper

Source: Board of Governors of the Federal Reserve System.

averaged 52 basis points from 1974 through 1991. Default risk as measured
by the quality spread shows some variation over time, rising during recessions
and falling during expansions.
Historically, the commercial paper market has been remarkably free of
default. As shown in Table 5, in the 20-year period from 1969 through 1988
there were only two major defaults. The low default rates in the commercial
paper market largely reflect the tastes of commercial paper investors. As shown
in Table 4, investors typically prefer commercial paper issued by large firms
with long track records, conservative financing strategies, and stable profitability. Most investors will not buy paper from small, unknown, highly leveraged
issuers unless the paper has credit enhancements attached. Moreover, rating
services will not assign a prime rating to these issues and most dealers will not
distribute the paper.
Even a major issuer can find the commercial paper market unreceptive
if its financial condition is perceived by the market to have weakened. Fons
and Kimball (1992) estimate that issuers who defaulted on long-term debt
withdrew from the commercial paper market an average of almost three years
prior to default. As ratings declined, these issuers significantly decreased their
commercial paper borrowings. Fons and Kimball (1992) take this “orderly exit”

60

Federal Reserve Bank of Richmond Economic Quarterly

Table 5 Major Defaults in the U.S. Commercial Paper Market

Issuer

Date of
Default

Amount
Outstanding
at Default
($ millions)

Penn Central
Manville Corp.
Integrated Resources
Colorado Ute Electric
Equitable Lomas Leasing
Mortgage & Realty Trust
Washington Bancorp
Stotler Group
Columbia Gas

6/21/70
8/26/82
6/15/89
8/17/89
9/12/89
3/15/90
5/11/90
7/25/90
6/12/91

82.0
15.2
213.0
19.0
53.0
166.9
36.7
0.75
268.0

Original Rating
of Longest
Outstanding
Defaulting CP
Moody’s
S&P
NR
P-2
NR
P-1
P-3
NR
NR
NR
P-2

NR
A-2
A-2
A-1
A-3
A-2
NR
NR
A-2

Source: Fons and Kimball (1992), Wall Street Journal, Dow Jones News Wire, Business Week,
Standard & Poor’s.

mechanism as evidence that investors in the commercial paper market are “unreceptive to lower-quality paper.” Crabbe and Post (January 1992) document
the orderly exit mechanism using a sample of bank holding company issuers
during 1986 to 1990. For issuers which experienced Moody’s commercial paper
rating downgrades, commercial paper outstanding declined on average by 12.2
percent in the ten weeks prior to the rating change and 15.7 percent in the first
four weeks after the change.
The number of commercial paper defaults rose to seven in 1989 to 1991,
but even in this period the default rate was low. Fons and Kimball (1992)
estimate the dollar amount of defaults over this period as a percentage of the
total volume issued.10 They find that the default rate for the United States was
only 0.0040 percent in 1989–91, which means that “an investor purchasing
U.S.-issued commercial paper˙ throughout the 1989–1991 period experienced,
..
on average, interruption in promised payments of roughly [40/100] of a penny
for every $100 invested” (p. 13).
The rise in defaults in the 1989 to 1990 period may have partially reflected
an increased tolerance for riskier paper in the later part of the 1980s. Unrated
commercial paper grew significantly in the late 1980s to $5 billion in January
1990. Over the same period, the spread between the yields on A1-P1 paper and
A2-P2 paper was unusually low (averaging less than 30 basis points). These
10 Fons and Kimball (1992) estimate the total volume of commercial paper issuance as average outstanding commercial paper times (365/average maturity). Average maturity is estimated
at 30 days.

T. K. Hahn: Commercial Paper

61

developments were reversed in the early 1990s following the rise in commercial
paper defaults, the deterioration in economic conditions, and the bankruptcy of
Drexel Burnham, a major dealer and promoter of unrated commercial paper.
By early 1991, unrated paper outstanding had fallen to below $1 billion and the
A1-A2 spread had risen to almost 50 basis points, its highest level since 1982.
The commercial paper defaults in 1989 and 1990 had a significant impact
on the demand for lower-rated paper by money market mutual funds. Several
MMFs were major holders of defaulted paper of Integrated Resources and
Mortgage & Realty Trust.11 Following these defaults, some MMFs began to
voluntarily restrict their commercial paper holdings to A1-P1 issues. Then in
June 1991, SEC regulations became effective that limited MMFs to investing
no more than one percent of their assets in any single A2-P2 issuer and no
more than 5 percent of assets in A2-P2 paper. Previously, there had been no
restriction on MMF total holding of A2-P2 paper, and MMFs had held approximately 10 percent of their assets in A2-P2 paper at the end of 1990. Crabbe
and Post (May 1992) find that by the end of 1991, MMFs had reduced their
holdings of A2-P2 commercial paper to almost zero. Along with the 1989 and
1990 defaults, they point to the June 1991 regulations as an important factor
influencing MMF investment choices.

4. INNOVATIONS
Asset-Backed Commercial Paper
A relatively new innovation in the commercial paper market is the backing
of commercial paper with assets. The risk of most commercial paper depends
on the entire firm’s operating and financial risk. With asset-backed paper, the
paper’s risk is instead tied directly to the creditworthiness of specific financial
assets, usually some form of receivable. Asset-backed paper is one way smaller,
riskier firms can access the commercial paper market. The advantages of assetbacked securities have led large, lower-risk commercial paper issuers to also
participate in asset-backed commercial paper programs. Asset-backed programs
have grown rapidly since the first program in 1983. Standard & Poor’s has
rated more than 60 asset-backed issues (Kavanagh et al. 1992, p. 109) with an
estimated $40 billion outstanding.
Asset-backed commercial paper is issued by a company, called a special
purpose entity, which purchases receivables from one firm or a group of firms
and finances the purchase with funds raised in the commercial paper market.
The sole business activity of the special company is the purchase and finance of
11 Value Line’s MMF, for example, held 3.5 percent of its portfolio in $22.6 million of
Integrated’s paper. Value Line protected the fund’s investors, absorbing the loss at an after-tax
cost of $7.5 million.

62

Federal Reserve Bank of Richmond Economic Quarterly

the receivables so the risk of the company and the commercial paper it issues
is isolated from the risk of the firm or firms which originated the receivables.
The trade receivables and credit card receivables that are typically used
in asset-backed programs have a predictable cash flow and default rate so the
risk of the assets can be estimated. Asset-backed paper programs are structured
so that the amount of receivables exceeds the outstanding paper. In addition
to this over-collaterization, credit enhancements are used, including guarantees
by the firm selling the receivables, bank letters of credit, or surety bonds. As
with all commercial paper issues, rating agencies require backup liquidity.
The combining of similar receivables from a group of companies into a pool
large enough to justify a commercial paper program allows small firms to participate in asset-backed programs and serves to diversify some of the receivables’
default risk. Typically, the financing firm which pools the receivables is managed by a commercial bank which purchases assets from its corporate clients.
Swaps
A factor in the growth of the commercial paper market during the 1980s
has been the rapid growth in the market for interest rate swaps. Interest rate
swaps are one of a variety of relatively new instruments that have significantly
increased the financing options of commercial paper issuers. Swaps provide
issuers with flexibility to rapidly restructure their liabilities, to raise funds at
reduced costs, and to hedge risks arising from short-term financing programs.
Interest rate swaps are agreements between two parties to exchange interest
rate payments over some specified time period on a certain amount of unexchanged principle. To appreciate the role of swaps it is necessary to understand
that there are two interest rate risks associated with commercial paper borrowing. First, the firm faces market interest rate risk: the risk that the rate it pays on
commercial paper will rise because the level of market interest rates increases.
A change in the risk-free rate, such as the Treasury bill rate, will cause a
corresponding change in all commercial paper and borrowing rates. Second,
the firm faces idiosyncratic interest rate risk: the risk that commercial paper
investors will demand a higher rate because they perceive the firm’s credit risk
to have increased. With idiosyncratic risk, the rate on its commercial paper can
rise without an increase in the risk-free rate or in other commercial paper rates.
A commercial paper issuer can eliminate market interest rate risk by entering into a swap and agreeing to exchange a fixed interest rate payment for
a variable interest rate. For example, in the swap the firm may pay a fixed
interest rate that is some spread over the multi-year Treasury bond rate and
receive the floating six-month LIBOR rate. If the commercial paper rate rises
because of a general rise in the market interest rate, the firm’s increased interest
payment on its commercial paper is offset by the increased payment it receives
from the swap. This swap allows the firm to transform its short-term, variablerate commercial paper financing into a fixed-rate liability that hedges market

T. K. Hahn: Commercial Paper

63

interest rate risks in the same manner as long-term fixed-rate, noncallable debt.
Note that the firm still bears the risk of idiosyncratic changes in its commercial
paper rate. If its own commercial paper rate rises while other rates, including
the LIBOR rate, do not rise, the cost of borrowing in the commercial paper
market will rise without a corresponding increase in the payment from the swap.
Alternatively, the firm can fix the cost of its idiosyncratic risk by borrowing
in the long-term market at a fixed rate and entering into a swap in which it
pays a floating rate and receives a fixed rate. The swap effectively converts
the long-term fixed-rate liability into a floating-rate liability that is similar to
commercial paper. The firm now faces the risk of a general change in the level
on interest rates, just like a financing strategy of issuing commercial paper, but
has fixed the cost of its idiosyncratic risk by borrowing long-term in the bond
market at a fixed-rate.
One important and unresolved issue is what the advantage of swaps are
relative to alternative financing strategies. For example, why would a firm
issue short-term debt and swap the flexible rate into a long-term rate instead of
issuing long-term debt? Researchers have advanced a variety of hypotheses to
explain the rapid growth of the interest rate swap market, but no real consensus
has been reached. Many explanations view swaps as a way for firms to exploit
differences in the premium for credit risk at different maturities and in different
markets. For example, one firm may find it can issue commercial paper at a
rate close to the average for similarly rated issuers but pays a significantly
higher spread in the long-term fixed-rate market. If the firm prefers fixed-rate
financing, a commercial paper program combined with a swap may provide
cheaper financing than issuing fixed-rate debt. But it is uncertain what causes
these borrowing differentials.12
The two interest rate swaps discussed above are the most basic examples
of a wide variety of available swaps. The examples are constructed to highlight
some important aspects of interest rate swaps, but it is not known how many
of these swaps are currently being used in conjunction with commercial paper
programs.13 Some commercial paper programs involve international debt issues
in conjunction with both interest rate and currency swaps.
Foreign Commercial Paper Markets
While the U.S. market is by far the largest, a variety of foreign commercial
paper markets began operating in the 1980s and early 1990s. Table 6 lists the
international markets and shows estimates of paper outstanding at the end of
1990. Even though the U.S. commercial paper market continued to grow in
12 Some

suggested reasons include market inefficiencies and differences in agency costs and
bankruptcy costs across various forms of debt. Wall and Pringle (1988) provide a review of the
uses and motivations for interest rate swaps.
13 Einzig & Lange (1990) discuss some examples of interest rates swaps used in practice.

64

Federal Reserve Bank of Richmond Economic Quarterly

Table 6 International Commercial Paper Markets
Amounts Outstanding, End of 1990
Billions of U.S. dollars
United States
Japan
France
Canada
Sweden
Spain
Australia
United Kingdom
Finland
Norway
Netherlands
Euro-CP

557.8
117.3
31.0
26.8
22.3
20.0*
10.9
9.1
8.3
2.6
2.0
70.4

Total

878.5

*Estimate
Source: Bank for International Settlements.

the later 1980s, its share of the worldwide commercial paper market fell from
almost 90 percent in 1986 to less than 65 percent in 1990. The Japanese market,
which began in 1987, is the largest commercial paper market outside the United
States. In Europe, the French, Spanish, and Swedish commercial paper markets
are well established and the German market has shown rapid growth since it
began in 1991.14
Some U.S. firms simultaneously maintain a commercial paper program in
the United States and issue dollar-denominated commercial paper abroad in the
Euro commercial paper market. The Euro commercial paper market developed
from note issuance and revolving underwriting facilities of the late 1970s in
which firms issued tradable notes with the characteristics of commercial paper
in conjunction with a loan agreement in which a bank or bank syndicate agreed
to purchase the notes if the issuer was unable to place them with investors. In
the early 1980s, higher-quality issuers began issuing notes without the backup
facilities. The Euro commercial paper market grew rapidly from 1985 to 1990.
By the middle of 1992, outstanding Euro commercial paper totaled $87 billion. U.S. financial and industrial firms are important issuers, either directly or
through their foreign subsidiaries. Approximately 75 percent of Euro commercial paper is denominated in U.S. dollars while the remainder is denominated
in European currency units, Italian liras, and Japanese yen. Issuers commonly
issue Euro commercial paper in dollars and use swaps or foreign exchange
transactions to convert their borrowings to another currency. The foreign mar14 Bank of International Settlements (1991) reviews the international commercial paper markets. Also see Euromoney (1992) for a review of the European money markets.

T. K. Hahn: Commercial Paper

65

kets, including the Euro commercial paper market, provide issuers flexibility
in raising short-term funds, allowing them to diversify their investor base, to
establish presence in the international credit markets, and to obtain the lowest
cost of funds.
While the Euro commercial paper market has similarities to the U.S. market, there are some important differences. The maturity of Euro commercial
paper has been longer than in the United States, typically between 60 to 180
days, and, partly reflecting the longer maturities, there is an active secondary
market. There is some evidence that the credit quality of the typical issuer in
the Euro commercial paper market is not as high as in the U.S. market. Both
Standard & Poor’s and Moody’s rate Euro commercial paper programs, but
ratings have not been as crucial in the Euro market as they have been in the
U.S. market. U.S. firms with less than A1-P1 ratings have found that the Euro
market has been more receptive than the domestic market to commercial paper
issues with no credit enhancements attached. Higher default rates abroad reflect
the less stringent credit standards. Fons and Kimball (1992) estimate that the
amount of defaults as a percent of the total volume of commercial paper issued
in the non-U.S. markets (including the Euro commercial paper market) in 1989
to 1991 was 0.0242 percent, which was significantly greater than the 0.0040
percent in the U.S. market. In 1989, the four Euro commercial paper defaults
affected almost 1 percent of the market.
The Growing Importance of Commercial Paper
The rapid growth of commercial paper shown in Figure 1 reflects the advantages
of financing and investing using the capital markets rather than the banking
system. To a significant extent, the advantage of commercial paper issuance is
cost: high-quality issuers have generally found borrowing in the commercial
paper to be cheaper than bank loans. The cost of commercial paper programs,
including the cost of distribution, agent fees, rating fees, and fees for backup
credit lines, are small, amounting to perhaps 15 basis points in a large program.
A highly rated bank borrows at a cost of funds comparable to other commercial
paper issuers, and it must add a spread when lending to cover the expenses and
capital cost of its operations and to cover any reserve requirements. Riskier
firms are willing to pay this spread because the bank adds value by generating
information about the creditworthiness of the borrower which enables it to lend
at less cost than the commercial paper market. A large creditworthy issuer will
generally find it cheaper to bypass the bank and raise funds directly in the
credit market.
The growth of the commercial paper market can be viewed as part of
a wider trend towards corporate financing using securities rather than bank
loans. Other aspects of this trend, commonly referred to as asset securitization,
include the rapid growth of the bond and junk bond markets and the market for
asset-backed securities. The pace of asset securitization increased sharply in the

66

Federal Reserve Bank of Richmond Economic Quarterly

1980s. New security technology, including the development of risk management
tools like swaps and interest rate caps, became widespread. At the same time,
established markets expanded to include new issuers. Smaller, riskier firms
increased their issuance of long-term bonds and entered the commercial paper
market with asset-backed paper and letter of credit programs. Commercial paper
is likely to remain a significant source of financing for domestic and foreign
firms and a relatively safe short-term security for investors.

REFERENCES
Bank for International Settlements. International Banking and Financial
Market Developments. Basle, Switzerland, August 1991.
Board of Governors of the Federal Reserve System. Flow of Funds Accounts,
Financial Assets and Liabilities, First Quarter 1992. Washington: Board
of Governors, 1992.
Crabbe, Leland, and Mitchell A. Post. “The Effect of a Rating Change on
Commercial Paper Outstandings.” Washington: Board of Governors of the
Federal Reserve System, January 1992.
. “The Effect of SEC Amendments to Rule 2A-7 on the Commercial
Paper Market.” Washington: Board of Governors of the Federal Reserve
System, May 1992.
The Depository Trust Company. Final Plan for a Commercial Paper Program.
Memorandum, April 1990.
Einzig, Robert, and Bruce Lange. “Swaps at TransAmerica: Analysis and
Applications,” Journal of Applied Corporate Finance, vol. 2 (Winter
1990), pp. 48–58.
“1992 Guide to European Domestic Money Markets,” published with Euromoney, September 1992.
Federal Reserve Bank of New York. Press Release No. 1932, Market Reports
Division, May 13, 1992.
Felix, Richard, ed. Commercial Paper. London: Euromoney Publications,
1987.
Fons, Jerome S., and Andrew E. Kimball. “Defaults and Orderly Exits of
Commercial Paper Issuers,” Moody’s Special Report, Moody’s Investor
Service, February 1992.
General Motors Acceptance Corporation. 1991 Annual Report. Detroit,
Michigan: 1992.

T. K. Hahn: Commercial Paper

67

Kakutani, Masaru, M. Douglas Watson, Jr., and Donald E. Noe. “Analytical
Framework Involving the Rating of Debt Instruments Supported by
‘Keepwell’ Agreements,” Moody’s Special Comment, Moody’s Investors
Service, July 1992.
Kavanagh, Barbara, Thomas R. Boemio, and Gerald A. Edwards, Jr. “AssetBacked Commercial Paper Programs,” Federal Reserve Bulletin, vol. 78
(February 1992), pp. 107–16.
Peavy, John W., and S. Michael Edgar. “A Multiple Discriminant Analysis of
BHC Commercial Paper Ratings,” Journal of Banking and Finance, vol.
7 (1983), pp. 161–73.
Samson, Solomon B. and Mark Bachmann. “Paper Backup Policies Revisited,”
Standard & Poor’s Creditweek, September 10, 1990, pp. 23–24.
Slovin, Myron B., Marie E. Sushka, and Carl D. Hudson. “Corporate Commercial Paper, Note Issuance Facilities, and Shareholder Wealth,” Journal
of International Money and Finance, vol. 7 (1988), pp. 289–302.
Standard & Poor’s Corporation. Commercial Paper Ratings Guide. April 1991.
Stigum, Marcia. The Money Market. Homewood, Ill.: Dow Jones-Irwin, 1990.
Wakeman, L. Macdonald. “The Real Function of Bond Rating Agencies,”
Chase Financial Quarterly, vol. 1 (Fall 1981), pp. 19–25.
Wall, Larry D., and John J. Pringle. “Interest Rate Swaps: A Review
of the Issues,” Federal Reserve Bank of Atlanta Economic Review,
November/December 1988, pp. 22–40.

Personal Saving Behavior
and Real Economic Activity
Roy H. Webb

M

any analysts view personal saving behavior, summarized by statistics
such as the personal saving rate or household debt acquisition, as a
key determinant of real economic activity. Some blame the recent
sluggishness of output and employment growth on low personal saving in recent
years.
The low rate of personal saving leaves consumers unprepared for their customary role of pulling the economy out of recession, according to Lacy Hunt,
chief economist for the Hong Kong Bank Group in the United States.1
The biggest problem in America’s economy˙ is debt. It is not so much cor..
porate debt,˙ but consumer debt˙ [I]ndividuals are in no position to spend
..
...
the economy out of recession˙ no room to raise borrowing, no savings to run
..
down.2
The past three years have not been a normal postwar recession, but a depression˙ [T]he current episode of strength will soon peter out in a triple dip,
...
followed by a deeper stage of depression˙ Debt has grown too large to be
...
sustained out of cash flow. As soon as the balance sheet is depleted, a deeper
crisis of asset liquidation will catch the world by surprise.3
The author gratefully acknowledges helpful comments from Dan Bechter, Gary Burtless,
Mary Finn, Marvin Goodfriend, and Thomas M. Humphrey. Max Reid provided valuable
research assistance. The views and opinions expressed in this article are solely those of the
author and should not be attributed to the Federal Reserve Bank of Richmond or the Federal
Reserve System.
1 American

Banker 1992, p. 11.
Economist 1992, pp. 13–14.
3 Davidson 1993, p. A15. While the author is also looking at saving by other sectors in the
United States as well as saving in other leading economies, the saving behavior of U.S. households
plays an important role in his analysis.
2 The

68

R. H. Webb: Personal Saving Behavior

69

Others take a longer-term view and see low personal saving lowering capital
formation, thereby leading to lower growth in real output, productivity, and
future standards of living.
Mr. Hunt said savings as a percentage of disposable income are lower than
at the end of any of the five previous recessions. This will have adverse
long-term ramifications for investment in plant and equipment and for U.S.
competitiveness in world markets˙ With the U.S. saving rate consistently less
...
than one-half those in Japan and Germany, “it would appear that the nation is
ill-prepared˙ to compete effectively.” 4
..
The United States has long had one of the lowest saving rates in the world˙
...
The low rate of saving means that the United States has a lower level of
income and possibly a substantially lower rate of income growth than would
otherwise be possible.5
[L]ow national saving is the most serious problem facing the U.S. economy.
Low saving accounted for˙ the slow growth in standards of living that con..
tinued throughout the 1980s˙ [T]he low saving rate is increasingly the result
...
of insufficient personal saving by U.S. households.6

In contrast to these views, this paper argues that personal saving data alone
reveal little about the current or future state of the economy. Consider first the
assertion that low saving, as it is conventionally measured, is to blame for the
recent sluggishness of real economic activity. Most economists would agree
that a proposition is valid if (1) it accords with a generally accepted, internally
consistent theoretical framework, (2) measurements implied by the theory are
consistent with its predictions, and (3) alternative theories are not consistent
with some of the measurements. The assertion that recent economic sluggishness is tied to low saving is questionable on several grounds. Proponents of that
view have failed to present a well-articulated theory; the view is not consistent
with data on household wealth; and the basic data on personal saving rates can
be explained in a way that does not imply a linkage of low saving rates and
recent economic sluggishness.
Next, the assertion that current low saving will result in lower long-term
growth does follow from an influential theoretical framework, unlike the asserted linkage between personal saving and current economic activity. That
long-run relation, however, is more complex than suggested by simple theory.
Determining the adequacy of the nation’s prospects for real growth will require
much more data than simple saving rates.
A by-product of this inquiry is an exposition and explanation of several
statistics that help describe the saving behavior of households. The most commonly cited statistic is not consistent with standard consumer theory, and may
4 American

Banker 1992, p. 11.
1989. While the author is referring to national saving, household saving is an
important part of his analysis.
6 Summers 1990, p. 153.
5 Feldstein

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Federal Reserve Bank of Richmond Economic Quarterly

also be subject to substantial measurement error. All told, one should not view
household saving or debt rates as conclusive indicators of real economic vitality;
at best they may suggest that a look at more relevant data is in order.

1. WEALTH AND SAVING
This section tackles the assertion that recent economic sluggishness is due
to recent rates of household saving and debt acquisition. The first step is to
question the relevance of the most widely cited statistic, which was not derived
from the most widely used consumer theory. A measure that is more relevant
to consumer spending is then discussed.
Measuring Saving
Analysts who view recent personal saving with alarm often focus on a particular
statistic published in the National Income and Product Accounts (NIPAs). That
statistic, which is often referred to as the saving rate, is simply the ratio of saving to disposable personal income. As shown in Figure 1, it declined from 9 percent to 4 percent in the 1980s and remains well below levels of the 1950s,1960s,
and 1970s. To understand the significance of that decline, note first that personal saving is defined as unspent income. The definition suggests the indirect approach actually used to estimate saving, which is to subtract estimated

Percent

Figure 1 Personal Saving Rate

Note: Ratio of personal savings to disposable personal income.
Source: National Income and Product Accounts

R. H. Webb: Personal Saving Behavior

71

outlays (mostly consumer spending for goods and services) from estimated
income. Saving, however, is much smaller than either income or spending;
therefore any error in estimating either item will cause a much larger error in
estimating saving. For example, in 1991 personal income was $4.8 trillion and
personal saving was $0.2 trillion; thus a 1 percent error in estimating personal
income would result in a 24 percent error in estimating personal saving. Since
neither income nor spending is measured precisely, personal saving is probably
estimated with a large error. That fact alone should make any user of saving
data especially cautious.7
Even if NIPA income and consumption were both measured precisely,
one might question the relevance of the particular definitions employed. Two
examples illustrate this point.
(1) NIPA income is defined as income from current production. By definition
asset revaluations are not part of NIPA income. A country could therefore
boost its NIPA income by depleting its exhaustible mineral reserves without
having to account for the reduced land values that would result. Similarly,
NIPA personal income is not affected when the market value of assets
owned by individuals changes. Accordingly, the bull market in residential
real estate in the 1970s and bull markets in stocks and bonds in the 1980s
did not directly affect NIPA measures of income and saving. As will be
discussed below, asset appreciation, whether or not officially measured, can
substitute for saving in that both provide the means for future consumption.
(2) Another definitional problem is dividing private spending between consumption and investment. NIPA investment is defined as the purchase of
physical assets. If a person acquires productive capabilities through additional schooling, any payments for tuition, textbooks, and related items are
defined as consumption. Many economists, however, see a strong analogy
between physical capital, the tangible assets that can be used for future
production, and human capital, the skills and abilities that people can use
for future production. Since future production can be boosted by either
physical or human capital formation, and since the purchase of either human or physical capital involves a trade-off of consumption today for future
productive capacity, it is somewhat arbitrary to label spending for one as
investment while labeling spending for the other as consumption.8

7 There is even more reason to be suspicious of early estimates of saving rates, which are
based on incomplete data. Months or even years after the first estimates, revised values based on
more complete information can substantially change the reported saving rates. At times the first
reports have had significant bias. For example, from 1980 to 1987 initial releases underestimated
saving rates by an average of 2 full percentage points (200 basis points). It is certainly conceivable
that current reports of low saving will be revised upward at some future date.
8 Estimates of the size of the stock of human capital suggest it is no minor matter. Jorgenson
and Fraumeni (1989), for example, estimated the value of the stock of human capital to be $194
trillion in 1984, versus $16 trillion for tangible physical capital.

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Federal Reserve Bank of Richmond Economic Quarterly

Two Nobel Laureates, Sir John Hicks and Milton Friedman, have separately
noted that the NIPA definition of income (income from current production) was
not derived from mainstream economic theory. “[A]ny one who seeks to make
a statistical calculation of social income is confronted with a dilemma. The
income he can calculate is not the true income he seeks; the income he seeks
cannot be calculated.”9 “I do not believe that [terms such as Income and Saving] are suitable tools for any analysis which aims at logical precision.”10 “The
designation of current receipts as ‘income’ in statistical studies is an expedient
enforced by limitations of data.”11
A concern of both Hicks and Friedman was that while national income
accountants were developing a system that could display an abundance of consistent information at any particular point in time, the information would not
be consistent over time.12 Because the relative price of capital changes over
time, the evolution of the market value of the capital stock cannot be measured
by NIPA investment and depreciation. Accordingly, the time profile of personal
wealth cannot be constructed from initial wealth holdings and NIPA saving data.
Wealth
One could approach the NIPAs with a fresh eye and reconstruct aggregates
such as income and saving that are based more firmly on economic theory.
Since that task is beyond the scope of a single paper, an interested reader is
referred to a good book on the subject such as Eisner (1989). The more modest
aim of this section is to suggest that aggregate wealth figures are relevant for
analysis of consumer spending and real economic activity.13
In order to appreciate the linkage of consumption and wealth, consider the
following problem. An individual wishes to consume at a constant rate over
his lifetime. His salary, however, will rise over time but then cease during
retirement. What constant level of consumption can be maintained?
The answer is illustrated in Figure 2, which illustrates a simple version of
the life-cycle theory of consumption. Early in life when earnings are low he
9 Hicks

1939, p. 179.
p. 171.
11 Friedman 1957, p. 10.
12 The choice of words is deliberate; consider “Since we have shown in the preceding
chapters what determines the volume of employment at any time, it follows, if we are right, that
our theory must be capable of explaining the phenomena of the Trade Cycle” (Keynes 1936).
The textbook IS-LM presentation of Keynesian theory continues the point-in-time focus, thereby
leading to shortcomings such as (1) investment not affecting the capital stock and (2) expectations
taken as given rather than explained. In contrast, more recent dynamic equilibrium models such
as those surveyed in Sargent (1987) or Barro (1989) explicitly model the evolution of the capital
stock, expectations, and other variables over time. These newer models highlight the shortcomings of the NIPA definition of income, whereas models of the IS-LM type fit well with the NIPA
definition.
13 A more detailed look at saving, wealth, and economic activity is taken by Bradford (1990).
10 Ibid.,

R. H. Webb: Personal Saving Behavior

73

Thousands of Dollars

Figure 2 An Individual’s Optimal Pattern of Wealth

Thousands of Dollars

Wealth

Age

Note: The horizontal axis represents time, divided between a working life of 40 years and retirement of 25 years. The vertical axis represents dollars of constant purchasing power. Given the
path for income, consumption is the largest constant value consistent with a real interest rate of 3
percent and zero initial and final wealth, and the path for wealth is then calculated. The general
shape of the income line, including the ratio of peak to initial income and the age of peak income,
was taken from Graham and Webb (1979), and was calculated from cross-sectional estimates of
lifetime earnings of men with college degrees.

74

Federal Reserve Bank of Richmond Economic Quarterly

would like to borrow to raise consumption; as earnings rise he would repay
the accumulated debt and then build wealth that could be consumed during
retirement.14 While this simple example abstracts from uncertainty and other
complexities of the real world, it serves to present the intuition of the basic
economic theory of consumption.15 A few key points should be noted. (1) Optimal saving varies substantially over an individual’s life, swinging from negative
to positive to negative. (2) A single observation of income and consumption
describes just what the individual is doing at a single point in time. (3) An
observation of wealth adds the additional information on the results of all past
saving. (4) The ability to borrow and save allows the individual to enjoy a
stable consumption stream despite a variable income stream. (5) The ability to
borrow presupposes that someone else has already accumulated wealth and is
willing to lend; in this example, an older individual with positive wealth might
wish to lend to a younger one wishing to borrow.
To measure wealth one must track over time the prices and quantities of
commodities that are not immediately consumed. For the whole economy, land,
residential structures, and business plant and equipment are important items that
can be productively employed for substantial lengths of time. Individuals, however, often do not own such assets directly but instead own financial assets—the
paper claims to the physical assets or the income streams resulting from their
use.
When people acquire physical and financial assets in order to smooth consumption over time, one can track their ability to pay for future consumption.
A balance sheet for the household sector presents the assets and liabilities held
by persons (rather than firms or government agencies).16 One can look at the
detailed information or use a simple summary statistic, such as households’
net financial assets (or financial net worth), which is defined as financial assets
such as cash, bank accounts, stocks, bonds, mutual fund shares and pension
fund reserves, minus financial liabilities such as mortgages, revolving credit,
and installment loans. This magnitude does measure the capacity of households
to spend, whereas any period’s saving rate does not.
Although the NIPAs do not contain comprehensive statements of wealth,
estimates are contained in the Flow of Funds Accounts (FFAs) published by the

14 An implication of this model is that saving should anticipate changes in labor income to
the extent that such changes can be predicted. Campbell (1987) has found some evidence for this
even with a NIPA saving measure.
15 The extent to which a model of this type has been consistent with actual consumption
behavior was examined by Fuhrer (1992), who found that while the model predicts long-run
behavior well, it did not predict the downturn in auto sales in the 1990–91 recession.
16 The NIPA definition of personal saving includes saving from families and single persons
plus saving by unincorporated businesses, nonprofit institutions serving persons, and private welfare funds and private trust funds. Included under this definition are certain investment returns from
private, but not public, pension funds. The reasoning underlying this definition of the household
sector is discussed by Holloway (1989).

R. H. Webb: Personal Saving Behavior

75

Table 1 Assets and Liabilities of Households, 1991
Billions of dollars
Assets

24,292
Tangible
Owner-occupied housing
Land
Consumer durables
Tangible assets of nonprofit institutions

9,102
3,712
2,624
2,099
677

Financial
Deposits
Government securities
Bonds and other credit market instruments
Mutual fund shares
Corporate equity
Equity in noncorporate business
Pension fund reserves
Other
Liabilities

15,190
3,376
838
1,156
734
2,334
2,568
3,473
711
4,190

Home mortgages
Installment consumer credit
Other
Net Worth
Financial Net Worth

2,854
744
592
20,102
11,000

Note: Data represent year-end values and are taken from the Federal Reserve Board’s “Balance
Sheets for the U.S. Economy 1960–91,” (Release C.9) March 1992.

Board of Governors of the Federal Reserve System.17 The FFAs contain detailed
balance sheets for financial intermediaries, other businesses, households, and
the federal government. A simplified balance sheet for the household sector is
presented in Table 1 that includes major categories of assets and liabilities. A
word of warning: many items on the household balance sheet are estimated as
residuals, just as NIPA saving is a residual. Accordingly, measurement errors
for many items can affect estimates of household net worth. Also, the FFAs take
NIPA values as starting points for many estimates, and thus measurement errors
in items such as income will be present in both sets of accounts. Moreover,
some items in the FFAs are inherently difficult to estimate with precision. Also,
while in principle each item should be measured at market value, in practice
market values are not calculated for debt instruments such as mortgages and
corporate, federal government, and municipal bonds. Corporate equity holdings,
however, are presented at market value. For these reasons net worth is a statistic
that is best used with caution.

17 An

introduction to the FFAs is given by Ritter (1974).

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Federal Reserve Bank of Richmond Economic Quarterly

Figure 3 Financial Net Worth

340
320

Percent

300
280
260
240
220

Note: Ratio of net financial assets, household sector (end-of-year) to disposable personal income
(annual average).
Source: Flow of Funds Accounts and National Income and Product Accounts.

Since asset holdings grow over time due to real economic growth and inflation, it is useful to scale them by considering the ratio of net financial assets
to disposable personal income.18 As Figure 3 illustrates, the asset-income ratio
has fluctuated between 2.2 and 3.3 times income over the past 40 years. The
most dramatic change was the decline from 3.2 in 1968 to 2.25 in 1974. During
the 1980s the ratio was reasonably stable, rising slightly over the decade. There
is nothing in this figure to suggest that consumers have saved so little that
18 Why

not net assets, rather than the less comprehensive net financial assets? The two differ
by the amount of real assets owned by households, that is, durable goods, land, and housing. Adequate treatment of the reliability of estimated market values of land and housing would require
a good bit of additional discussion that would be tangential to this paper’s topic. At a later date
an article is planned for this Quarterly that will address land and housing values. One piece of
evidence is that survey estimates of residential housing values often report much higher values
than are given in the FFAs, with analysts such as Curtin, Juster, and Morgan (1989) judging the
surveys to be more accurate.
For what they are worth, the FFA housing figures show a decline in household housing and
land values of $160 billion in 1990, but with gains of $402 billion in 1989 and $397 billion in 1991.
Other figures, such as constant quality price indexes for existing homes do not show a downward
movement in 1990 or other years. Thus despite anecdotes of house prices falling these figures do
not reveal an aggregate sustained fall in housing values that would affect the conclusion of this
section that household wealth rose more rapidly than income over the 1980s and early 1990s.

R. H. Webb: Personal Saving Behavior

77

Figure 4 Net Financial Wealth of Household Sector Ratio to Disposable
Personal Income

Percent

United States

Japan

they cannot now afford to purchase goods and services. If current saving looks
low to some observers, that may simply reflect households having accumulated
a level of wealth they consider satisfactory. That interpretation is consistent
with the decline in the personal saving rate in the 1980s being accompanied
by rising household wealth.
How does household wealth in the United States compare with similar
statistics in foreign countries? Although the saving rate of U.S. households is
below that rate in other countries, Figure 4 illustrates that U.S. households are
wealthier. Households in countries holding less wealth often save more in order
to accumulate wealth, as exemplified by Japan.
Possible Objections
One might acknowledge the potential usefulness of data on household wealth
while raising objections to its current validity. This portion of the paper attempts
to address some of the most important concerns.
Concentration of Wealth
Aggregate net wealth would not be a good measure for the majority of
households if most wealth were held by relatively few households. While wealth

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Federal Reserve Bank of Richmond Economic Quarterly

Figure 4 (continued)

350
300
United States
Percent

250
200

Germany

150
100
France
50
1980

81

82

83

84

85

86

87

88

89

90

91

89

90

91

350
300
United States
Percent

250
United Kingdom

200
150

Canada

100
50
1980

81

82

83

84

85

86

87

88

Note: Ratio of net financial assets, household sector (end-of-year) to disposable personal income
(annual average).
Source: United States, Flow of Funds Accounts and National Income and Product Accounts; other
countries, OECD Economic Outlook, December 1991: Organisation for Economic Co-operation
and Development, Paris, p. 21.

R. H. Webb: Personal Saving Behavior

79

in the United States is more concentrated than income, it does not appear
so concentrated as to render data on wealth irrelevant. The 1989 Survey of
Consumer Finances19 reported that families with incomes below $10,000 had
a median net worth of $2,300. It is certainly likely that these families in the
lowest quintile of the income distribution would be unable to draw on savings to
finance additional consumption. Families in the next quintile, earning between
$10,000 and $20,000, had a median net worth of over $27,000, and higherincome groups also had median net worth well over annual income. Another
way of describing the survey data is that the median family of a subset of
the population that accounts for 80 percent of household income and a greater
percentage of aggregate consumption had accumulated a significant amount of
wealth. The data therefore do not appear to support the view that wealth is too
narrowly distributed to be a useful indicator of potential aggregate consumption.
Debt
Another objection addresses the role of debt. If people are highly indebted
and many of their assets are illiquid, then the burden of debt repayment might
restrict their consumption even if the value of their assets is relatively large.
As Figure 5a indicates, household debt is indeed high, relative to the recent
past; in 1991 it was almost equal to a full year’s disposable personal income,
whereas in the mid-1950s debt was less than half a year’s income.20 As the
figure indicates, the debt-income ratio grew about 2 percentage points per year
from 1952 to the mid-1960s, grew fairly slowly until the early 1980s, and has
since grown by 3 percentage points per year. Interestingly, corporate debt shows
somewhat similar behavior in Figure 5b, namely, an initial period of growth
that was interrupted in the 1970s and resumed in the 1980s.21 Is that simply a
coincidence?
What follows is one possible explanation of the data. The behavior of debt,
income, and wealth can be reconciled by noting that a revolution in financial
intermediation has occurred over the past 40 years, as a few examples indicate.
Credit cards serve two functions: allowing routine transactions to be made
without currency and supplying widespread unsecured lines of credit. Mutual
funds allow individuals, even those who have fairly small amounts to invest, to
benefit from broadly diversified and professionally managed equity and bond
portfolios. Home equity lines of credit allow easy, tax-advantaged access to equity in owner-occupied housing. Corporate lending has also been transformed,
as many firms that would have borrowed from banks in the 1950s now have
access to security markets. In short, the efficiency of financial intermediation
19 Data

are taken from Kennickell and Shack-Marquez (1992).
figure is similar to Figure 2 in Altig, Byrne, and Samolyk (1992).
21 This figure is similar to Figure 1 in Paulus (1991).
20 This

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Federal Reserve Bank of Richmond Economic Quarterly

Figure 5a Household Debt to Income Ratio

104
96
88
Percent

80
72
64
56
48
40
32

Notes: Ratio of household liabilities (end-of-year) to disposable personal income (annual average).
The trend line from 1952 to 1966 represents annual growth of 2.5 percentage points per year, the
trend line from 1966 to 1982 represents growth of 0.40 percentage points per year, and the trend
line from 1982 to 1991 represents growth of 3.1 percentage points per year.
Source: Flow of Funds Accounts and National Income and Product Accounts.

has improved, in the sense that individuals can better smooth consumption over
time and many producers can more readily finance investments yielding high
returns.
The trend toward more efficient financial intermediation was interrupted
from 1967 to 1981. In a different context Webb (1992) argued that this period
had an inflation-tolerant monetary policy. Inflation averaged 1.5 percent from
1952 to 1966, 7.3 percent from 1966 to 1982, 3.9 percent from 1982 to 1991,
and 3.0 percent in 1992. Rising inflation in the late 1960s and early 1970s
and high, variable inflation in the remainder of the decade played havoc with
investing in financial instruments that had traditionally been denominated in
nominal terms. During this period Regulation Q restricted the nominal interest
rates payable on many deposits, and taxes were levied on nominal rather than
real returns. The always difficult process of channeling savings to their most
productive uses became even more difficult as financial intermediation was
thereby strained and distorted. Debt-income ratios stagnated during this period
despite the benefit debtors received from unanticipated inflation and the bias in
the tax laws at the time that favored financing by debt rather than by equity.

R. H. Webb: Personal Saving Behavior

81

Figure 5b Corporate Debt to Income Ratio

120
110

Percent

100
90
80
70
60

Notes: Ratio of nonfinancial corporate liabilities (end-of-year) to national income originating in
private nonfinancial business. The trend line from 1952 to 1966 represents annual growth of 1.5
percentage points, the trend line from 1966 to 1982 represents a 0.1 percentage point rate of
decline, and the trend line from 1982 to 1991 represents growth of 2.6 percentage points per year.
Source: Flow of Funds Accounts and National Income and Product Accounts.

The idea that the rise in private debt in the 1980s reflected increasing
efficiency of financial intermediation is not consistent with the quotations at
the beginning of this paper. The alternative view of the authors quoted seems to
be that the rise in debt backed an unsustainable consumption binge. Proponents
of that alternative have not, to the author’s knowledge, recognized that wealth
rose relative to income in the 1980s even though saving rates declined. Since
higher levels of wealth allow higher levels of future consumption, consumption
levels of the 1980s appear to be sustainable. Moreover, it appears that the rate
of return on invested assets was relatively high in the 1980s.22 A high rate of
return is symptomatic of savings being put to highly productive uses, which in
turn is symptomatic of efficient financial intermediation.
22 The

change in financial wealth can be stated as the saving from labor income and transfer
payments plus the return on assets; in symbols, dW = Y − C + rW ≡ S + R. The change in
the wealth-income ratio is by definition d W = Y dW−W dY ; substituting from the previous
Y
Y2
S
expression and rearranging terms, an increasing wealth-income ratio means that R > W g − Y ,
Y
Y
where g is the growth rate of real income. Thus with a wealth-income ratio of 2.5, a real growth
rate of 3.5 percent, and a saving rate of 4.5 percent, the real rate of return on net financial wealth
must exceed 4.25 percent.

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Federal Reserve Bank of Richmond Economic Quarterly

If one still wished to argue that (1) financial asset holdings are irrelevant
due to imperfect markets and (2) household debt levels are nonoptimal in the
sense of being higher than fully informed borrowers and lenders would choose,
then there are further problems. Why would large numbers of borrowers and
lenders make the same mistake in the 1980s? Did they believe there would
never be a recession? Unless some such widespread error occurred, what is the
basis of the assertion that debt levels are too high? The author is unaware of
such questions being seriously addressed; as a result, assertions of debt being
too high do not appear to be based on an economic theory involving rational
people with stable preferences. When economic theory is used to study imperfect markets, the usual result is that some people are able to borrow too little,
not too much.23
Measurement of Wealth
Another objection concerns the relevance of the FFAs. Questions of definition can arise over items included in household financial assets such as (1)
nonprofit institutions as part of the household sector, (2) substantial assets and
liabilities recorded at historical values rather than market values, (3) government bonds recorded without excluding a liability for the future taxes that will
be levied to pay interest on the bonds, and (4) pension fund reserves that are far
removed from household control. These are valid concerns which demonstrate
that these statistics from the FFAs, like every other macroeconomic statistic,
are not estimated in the exact form that many users would prefer.
Addressing the objections in order, (1) nonprofit institutions account for a
small fraction of the household sector’s economic activity; note in Table 1 that
tangible assets of nonprofit institutions are less than 8 percent of the household
sector total. (2) Marking debt instruments to market would strengthen the argument that household wealth is not unusually low, because the increase in bond
prices as interest rates fell over the last ten years is excluded from the figures
presented in this paper. (3) Excluding government bonds from these figures
would not alter any conclusions, since they account for less that 6 percent of
household financial assets. Also, economists are divided on the extent to which
one should offset government bonds with anticipated future tax liabilities. (4)
Wealth held in pension funds can affect household behavior. Households with
a large amount of pension wealth can consume more today precisely because
they do not have to save as much from current cash flows in order to provide
for retirement.
The conceptual and measurement problems with the FFAs suggest that
the accounts should be used with caution. Analysts who keep the accounts’
23 For example, Bernanke and Gertler (1989) present a model in which potential borrowers
with low net worth are unable to finance productive investment projects. Whited (1992) presents
empirical evidence consistent with the view that financial constraints can reduce investment.

R. H. Webb: Personal Saving Behavior

83

weaknesses in mind will find the data useful. The alternative is to ignore relevant balance sheet data.
Evaluation
Figure 1 illustrates that saving from current income is relatively low, and Figure 5a illustrates that the household debt to income ratio is relatively high.
These phenomena can be explained without asserting that something has been
so seriously wrong with consumer finances as to explain the past recession
and the subpar expansion that followed. The explanation instead notes that the
relatively large net worth of households contradicts the notion that consumers
are currently unable to finance optimal spending plans.
Authors who have linked saving behavior with recent economic weakness
have several obstacles to overcome to establish their point. First, they need to
detail the theoretical model of consumer spending that they use to define recent
saving rates as too low or recent debt levels as too high. The widely used lifecycle model discussed above is apparently not the basis for such assertions, due
to rising wealth levels in recent years.24 A possible alternative could be models
with imperfect loan markets, although these usually imply that debt levels are
too low. And when a theoretical model is used to show that savings are too low,
or debt too high, the authors then need to explain why consumers saved too
little or borrowed too much, and why lenders willingly lent too much. Finally,
it would help if the authors explained why they believe the conventional saving
rate is measured with sufficient accuracy to allow confident assertions to be
made.
The case has not been made that personal saving behavior has much to do
with the recent subpar economic performance. While an unproven case might
still be valid, there are plausible alternative explanations of the basic data. For
example, if weak consumer spending was an important factor in explaining the
slow recovery in 1991, that weakness could reflect the uncertainty caused by
the large number of permanent job losses in the last few years and the prospect
of more losses ahead due to job reductions announced but not implemented by
many large organizations.25

2. LONG-RUN GROWTH
The previous section found only a questionable theoretical link between saving measures from the recent past and current spending. In contrast, standard
economic theory posits a firm link between saving and the long-run level of
24 An

exception is the analysis of Bernheim and Scholz (1992), who present evidence that
they interpret as showing that people without college educations do not save enough to maintain
their standard of living in retirement.
25 See, for example, Carroll (1992).

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Federal Reserve Bank of Richmond Economic Quarterly

real output; in addition, there are theoretical frameworks in which saving can
also affect the rate of growth. The linkage is that saving allows investment to
raise the stock of productive capital. Many analysts are concerned about growth
because recent growth rates in the United States appear low, relative to either
growth in the United States in the 1950s and 1960s, or to growth rates in many
other countries.
This section first reviews some data on economic growth in the United
States, and possible interpretations of that experience. Next, the potential role
of saving in a widely used theoretical model is examined. Some recent advances
in growth theory that affect the interpretation of saving are next discussed. Unlike the first section of this paper, this section finds that a properly measured
saving rate would be a useful statistic to the extent that it is a valid indicator
of capital formation and thereby also an indicator of future growth prospects.
Some empirical evidence on the correlation of saving and investment rates
concludes this section.
Recent Experience
Figure 6 and Table 2 contain some basic data on Gross Domestic Product (GDP)
per capita for over a century.26 Figure 6 illustrates that the growth rate of per
capita GDP has fluctuated around a trend of 1.7 percent, which means that it has
doubled approximately every 40 years. The two largest departures from trend
are the Great Depression and World War II. Table 2 allows one to calculate
growth rates for shorter periods. Of particular interest is the most recent experience, in which growth declined from 2.1 percent between 1950 and 1973 to 1.6
percent between 1973 and 1989. Despite the fact that growth in the latter period
is close to its long-run trend, some observers believe that the decline in growth
indicates that the United States is failing to realize its economic potential.
Table 2 also indicates that while the level of output per capita is higher in
the United States than in other major countries, several other countries have
grown more rapidly in recent years. Most spectacular is Japan, where output per
capita grew by 7.7 percent from 1950 to 1973, and by 3.1 percent from 1973
to 1989. Simply extrapolating the latest growth rates puts several countries
ahead of the United States early in the next century. That too leads some to
26 GDP is used to facilitate comparisons over time and across countries. It is not and was
not designed to be a measure of economic welfare. There are also better measures of product one
could devise; many investigators, however, believe that the correlation between GDP and a better
measure is sufficiently high to warrant the use of GDP statistics.
It should also be noted that the accuracy of almost every economic statistic declines as one
goes farther back in time. Analysts who produce the NIPAs today have much more raw data to use
to construct aggregate statistics than did their counterparts 40 years ago, who in turn had much
more raw data than did the individuals who have constructed estimates for GDP before 1929.

R. H. Webb: Personal Saving Behavior

85

Figure 6 Output per Capita with Trend

10.00
9.75
9.50

In Y/N

9.25
9.00
8.75
8.50
8.25
8.00
7.75
1869

1889

1909

1929

1949

1969

1989

Notes: Gross domestic product divided by population, annual data, logarithmic scale. Trend line
represents annual growth at a 1.7 percent rate and is based on estimates from 1869 to 1929 and
extrapolated for 1930 to 1991.
Source: GDP, National Income and Product Accounts, 1929–91, and Balke and Gordon (1989),
1869–1928; population, United States Census, 1950 to 1991, and Historical Statistics of the United
States: Colonial Times to 1970, U.S. Government Printing Office, Washington, 1975: Series A7.

Table 2 Gross Domestic Product per Capita, 1985 Dollars,
United States Prices
1870
United States
Canada
France
Germany
Japan
United Kingdom

1913

1950

1973

1989

2,247
1,347
1,571
1,300
618
2,610

4,854
3,560
2,734
2,606
1,114
4,024

8,611
6,113
4,149
3,339
1,563
5,651

14,103
11,866
10,323
10,110
9,237
10,063

18,317
17,576
13,837
13,989
15,101
13,468

Note: These figures are taken from Maddison (1991), Table 1.1. They represent per capita GDP,
expressed in constant dollars to remove the effects of inflation, and adjusted for differing purchasing power of currencies.

86

Federal Reserve Bank of Richmond Economic Quarterly

believe that the United States is growing too slowly, and to view low saving
as a possible cause.
The Solow Growth Model
The name of Nobel Laureate Robert Solow is linked with a straightforward
and influential theoretical model of economic growth.27 Consider a specific
production function, which states with symbols that national product depends
on the amounts of capital and labor employed, as well as the state of knowledge:
Yt = Ktα (At Lt )1−α ,

(1)

where Y is the quantity of output, K is the stock of capital, L is the labor force,
A can be interpreted as the state of knowledge about producing output, t indexes
time, and α is a parameter between zero and one, the value of which can be
statistically estimated. If one assumes (1) that the labor force and knowledge
grow at given exponential rates of n and g, respectively, (2) that a constant
fraction s of output is saved and invested,28 and (3) that capital depreciates at
an exponential rate d, it then follows that
ln

α
α
Yt
= gt +
ln(s) −
ln(n + g + d) + ln A0
Lt
1−α
1−α

(2)

for a country experiencing steady-state growth, that is, a country for which the
capital stock is consistent with the model’s parameters and initial conditions.
Note in equation 2 that the growth rate of output per capita is determined solely
by the exogenous parameter g, the growth rate of knowledge. Other parameters
in the bracketed term, including the saving rate, only affect the level of output
per capita.
Differences in Growth Rates Across Countries
For a country like the United States in which output per capita does not depart too much from a constant trend over a long interval of time, the assumption
of steady-state growth appears reasonable. An opposite case would be a country
like Japan immediately after World War II where much of the capital stock had
been destroyed. The Solow framework can be used to determine how fast a
country off its steady-state growth path would converge to that path. Assuming
that the speed of convergence is proportional to the difference (in logarithms)
between the steady-state and the actual levels of output per capita, then
θ = (n + g + d)(1 − α),
27 A

(3)

good exposition is Solow (1969).
the growth literature, the saving rate almost always refers to the national saving rate,
which is the personal saving rate plus saving by firms and by the government.
28 In

R. H. Webb: Personal Saving Behavior

87

where the parameter θ denotes the speed of convergence to the steady-state
path. Note that the speed of convergence does not depend on the saving rate.29
For example, if population growth n is 1 percent per year, the steady-state
growth rate g is 2 percent, the depreciation rate d is 4 percent, and α is 0.3,
then the speed of convergence would be about 5 percent. In other words, about
5 percent of the percentage gap between actual and steady-state output per
capita would be eliminated each year, or half the gap would be closed in about
eight years.
The idea of convergence has been used to interpret differential growth
rates among different areas or countries. Mankiw, Romer, and Weil (1992),
for example, augment the basic Solow model by adding a third factor of production, human capital, to physical capital and labor. Looking at a group of
98 countries and two smaller groups, they found that poorer countries in 1960
tended to grow faster from 1960 to 1985 than did richer countries; the estimated
speed of convergence was about 2 percent. Barro and Sala-i-Martin (1992) also
found evidence for convergence, both among states in the United States from
1880 to 1988 and in the set of 98 countries over a shorter interval; interestingly,
they also estimate speeds of convergence of about 2 percent.
If convergence in the level of per capita output accounted for all the differences in growth, then one would not be concerned that countries with lower
output were growing more rapidly than the United States. That faster growth
would be a temporary phenomenon and would slow as a country’s level of
output per capita approached that of the United States. Evidently, however,
more than just convergence is needed to account for all the variation in output growth. In Table 2, note that output per capita was higher in the United
Kingdom than in the United States in 1870; by 1913 the countries’ standings
reversed. What accounts for the reversal? Between 1870 and 1913 the United
States, Canada, and Germany grew faster than Japan, the poorest country. What
accounts for this divergence? What accounts for the experience in the United
States from 1950 to 1973 when growth was above the previous trend? And why
have many countries remained poor over the last 40 years without showing any
tendency toward rapid growth?
Endogenous Growth
These questions illustrate why some economists believe that while convergence
is probably an important factor in many cases, other explanations of differential growth rates should also be examined. They have accordingly constructed
models that depart in an important way from the basic Solow model. Instead of
assuming that the economy’s steady-state growth rate is a given value g based
29 A

change in the saving rate can change the steady-state capital stock, however, and thus
influence the growth rate off the steady-state path.

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Federal Reserve Bank of Richmond Economic Quarterly

on the automatic growth of knowledge, they emphasize the individual decisions
that result in growth. This is now an especially rich area of macroeconomic
research, and there will be no attempt to mention all the important models. Two
examples of such endogenous growth models that are relevant for this paper
are Lucas (1988) and Greenwood and Jovanovic (1990).
The Lucas model is of interest in that it provides a reason why growth
might be too low, and points to the types of public policies that would raise
the rate of growth. The model contains human capital, as do many in the
endogenous growth literature, but notably makes an individual’s productivity
depend on both the individual’s level of human capital and the community’s
average level of human capital. In other words, there is a positive externality
to human capital accumulation: an individual’s decision to acquire additional
human capital would balance his own costs and benefits without taking into
account that raising one’s own stock of human capital also raises the community’s stock and thereby raises the productivity of other members of the
community. Human capital accumulation is the basic engine of growth in this
model, analogous to the exogenous value g in the Solow model. Due to the
positive externality, public policies such as subsidies to education can raise the
growth rate and aggregate economic welfare.
An implication of the Lucas model is that saving is relevant, in that it
coincides with the capital formation that affects the level and rate of growth
of output. The measure of saving implied by his model includes both saving
as conventionally measured plus investment in human capital. A generally
acceptable measure of the latter would require an ambitious research undertaking. Individual researchers have proposed strategies for estimating investment
in human capital, but different strategies have led to vastly different results.
Measurement of some of the resources that are used for investment in human capital, such as teachers’ salaries, buildings, and textbooks is straightforward. A more difficult question is valuing a student’s time in school. How
are differences in the quality of education to be estimated? When a person
develops skills through experience, how is that measured? A professional consensus has not emerged on these and other difficult questions. But any saving
statistic that fails to confront human capital measurement is omitting a very
important part.
Financial institutions play a key role in the model of Greenwood and Jovanovic, in which the extent of financial intermediation and the degree of
development are linked. Financial intermediation allows a given amount of
saving to finance a greater amount of investment than could occur without
intermediation. And mature economies can have relatively low saving rates
with high growth due to well-developed financial intermediation. Therefore,
simply comparing saving rates in different countries would not provide useful
information on the adequacy of investment or on future growth prospects.
The theoretical linkage of financial intermediation and growth is supported
by empirical evidence. King and Levine (1993) studied real growth and several

R. H. Webb: Personal Saving Behavior

89

measures related to financial intermediation in 80 countries from 1960 to 1989.
They found a robust correlation between the extent of financial development
and contemporaneous growth, and also that financial development predicts
future growth.
The Correlation of National Saving and Investment
The intuition linking saving and growth is highlighted by the formal models
examined. In the basic Solow model the long-run growth rate is exogenous and
is therefore unaffected by saving. Over shorter time spans, however, growth can
be affected by saving. Once the growth rate is made endogenous, interpreting
saving data can become even more difficult. If the Lucas assumption of externalities in human capital accumulation is important, then we should be focusing
on a better understanding and measurement of human capital. And to the extent
that more highly developed financial intermediation raises the return to saving,
the meaning of a given rate of saving changes as an economy matures.
Despite these difficulties, researchers have presented empirical evidence
that suggests a strong linkage between a country’s saving and investment. One
of the most influential studies, by Feldstein and Horioka (1980), found a strong
correlation between rates of saving and investment for 21 countries. Figure 7
presents national saving and gross investment data, relative to GDP, for the
postwar United States. The two series clearly move together over the 1960–
74 interval studied by Feldstein and Horioka, although for much of the 1980s
investment outpaced saving as foreign investment in the United States was relatively large. In 1991 both saving and investment hit postwar lows, reinforcing
the concerns of many over inadequate investment due to inadequate saving.
Simple correlations such as this are always difficult to interpret. Two variables can be correlated, even if movements in one do not cause movements
in the other, if both are responding to movements of a third variable. There
are many possible factors that might explain movements in both saving and
investment. For example, both are low at business cycle troughs and rise during cyclical expansions. Interest rates are another factor affecting saving and
investment.
A quick look confirms the possibility that the correlation might vanish after
allowing for other factors. Table 3 contains empirical results based on:
4

αt−i

Vt = c +
i=1

It−i
+
Yt−i

4

βt−i
i=1

St−i
+
Yt−i

4

4

γt−i Rt−i +
i=1

δt−1 Ut−i + et , (4)
i=1

where V is the dependent variable, either the gross investment to GDP ratio
or the national saving to GDP ratio, I is investment, Y is GDP, S is saving,
R is the interest rate on 90-day Treasury bills, U is the capacity utilization
rate in manufacturing, e is an error term, t indexes time, and the remaining
symbols are coefficients that can be estimated by ordinary least squares. The

90

Federal Reserve Bank of Richmond Economic Quarterly

Figure 7 Gross Saving and Investment Relative to GDP

20
19
Saving

18
Percent

17
16
15
Investment

14
13
12
1948

52

56

60

64

68

72

76

80

84

88

Note: Gross private domestic investment, divided by gross domestic product, and gross national
saving, divided by gross domestic product.
Source: National Income and Product Accounts.

two equations can be used to examine the extent to which either investment
or saving is correlated with previous values of those two series and also with
previous values of an interest rate and the capacity utilization rate (which can
be interpreted as an indication of the stage of the business cycle). Especially
notable results from the investment equation are (1) the lagged variables are
associated with a large portion of the movement of the investment-GDP ratio,
and (2) the coefficients on lagged saving are not significantly different from
zero, unlike coefficients on all the other variables.
If taken at face value, these results suggest that savings in the recent past do
not directly affect investment; however, the results in Table 3 are suggestive
rather than definitive. Most importantly, there was no experimentation with
other measures of saving, investment, and output,30 and there was no analysis
of contemporaneous correlations of saving, investment, output, interest rates,
and possibly other variables. The results do show, however, that the empirical
correlation of investment and saving is not easy to interpret since it could well
reflect the business cycle and possibly other influences.
30 Cullison (1991) studied the relation of several measures of saving to quarterly GDP growth.

R. H. Webb: Personal Saving Behavior

91

Table 3 Regression Results for Investment and Saving Rates

(1)

It
=c+
Yt

4

αt−i
i=1

It−i
+
Yt−i

4

βt−i
i=1

St−i
+
Yt−i

4

4

γt−i Rt−i +
i=1

δt−1 Ut−i
i=1
2

R = .84

Time bounds: 1952 Q2 to 1992 Q2
Variable

F-Statistic

Significance Level

I/Y
S/Y
R
U

54.06
0.80
5.09
3.61

.00
.53
.00
.01

(2)

St
=c+
Yt

4

αt−i
i=1

It−1
+
Yt−i

4

βt−i
i=1

St−i
+
Yt−i

Time bounds: 1952 Q2 to 1992 Q2

4

4

γt−i Rt−i +
i=1

δt−1 Ut−i
i=1
2

R = .87

Variable

F-Statistic

Significance Level

S/Y
I/Y
R
U

101.45
1.64
6.07
2.26

.00
.17
.00
.07

Note: I is gross private domestic investment, Y is GDP, S is gross national saving, R is the 90-day
Treasury bill rate, and U is the capacity utilization rate in manufacturing.

3. CONCLUSION
Although many analysts cite the personal saving rate as a key indicator of the
current and prospective strength of the economy, the saving rate alone actually reveals little about current and future conditions. Difficulties in defining,
measuring, and interpreting saving should be kept in mind by prospective users.
Current saving data reveal little about prospective consumer spending. Basic economic theory instead indicates that household wealth measures resources
accumulated for future spending. In addition, it would be a mistake to focus
simply on one part of the household balance sheet, debt, without first determining its optimal level. Since debt has the positive roles of allowing individuals
to smooth consumption over time as income varies and of financing productive
investment, it should not be simply assumed that current debt levels are too
high.
In contrast to the weak link between recent saving and current consumer

92

Federal Reserve Bank of Richmond Economic Quarterly

spending, there is a well-established theoretical link between saving and

R. H. Webb: Personal Saving Behavior

93

investment, and therefore between saving and economic growth. Even here the
message given by saving data can be difficult to interpret, since low national
saving can occur while investment is buoyed by inflows of foreign funds; in
addition, human capital formation is omitted from the usual saving measure. To
determine whether national investment is adequate it could be more productive
to look directly at detailed investment data. If profitable investments were not
being made, one might wish to search for underlying causes such as taxes,
regulation, externalities, or inadequate financing. A focus on conventionally
measured saving may well divert attention from these important fundamentals.

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