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T h e P o s t - W a r U .S . P h i l l i p s C u r v e :
A R e v is io n is t E c o n o m e tr ic H is to r y

Robert G. King and Mark W. Watson

Working Papers Series
Macroeconomic Issues
Research Department
Federal Reserve Bank of Chicago
September (W P-94-14)

FEDERAL R£SERVE B A N K
O F C H IC A G O

T h e
A

P o s t - W a r U .S . P h illip s

C u rv e :

R e v is io n is t E c o n o m e tric H is to r y

Robert G. King*
University of Virginia and
Federal Reserve Bank of Richmond
Mark W. Watson
Northwestern University and
Federal Reserve Bank of Chicago
November 1993 , Revised March 1994

A bstract
In 1958, A.W. Phillips discovered a strong negative correlation between
inflation and unemployment in U.K. data. Continuing controversy surrounds
the long-run trade-off suggested by a curve he drew through these observations.
We conduct a wide-ranging investigation of the post-war U.S. Phillips cor­
relations and Phillips curve. Many economists view the Phillips correlations as
chimerical, given the rise in both inflation and unemployment during the 1970s,
and the Phillips curve as plagued by subtle identification difficulties raised by
Lucas and Sargent. Yet, a strikingly stable negative correlation exists over the
business cycle and recent theory indicates the Lucas-Sargent critique may not
be empirically relevant. When we estimate the long-run trade-off as Gordon
and Solow did, we find it is roughly one-for-one. This traditional Keynesian
identification also makes business cycles entirely due to demand shocks. How­
ever, in U.S. data, there is close to a Granger-causal ordering of unemployment
and inflation: the Gordon-Solow model is thus not the only one that fits the
data well. Alternative identifications lead to much more modest effects of de­
mand on business cycles and essentially negligible long-run trade-offs.
Keywords: Phillips curve, business cycles, long-run neutrality econometrics.
JEL Classification: E3, C5
*P rep ared for p resen tatio n a t the C arnegie-R ochester Conference on Public Policy, C arnegieMellon U niversity, N ovem ber, 1993. We have received m any constructive com m ents on this paper:
we p articu larly th a n k C harles Evans, R obert J. G ordon, B ennett M cC allum , and C harles Plosser.
S u p p o rt was provided by the N ational Science Foundation via g ra n t NSF-91-22463.




1

1

In tr o d u c tio n

The relationship between inflation and unemployment has been among the most con­
troversial macroeconometric topics of the post-war period. Early work by Phillips
[1958] for the United Kingdom documented a pronounced negative correlation be­
tween these series over 1861-1957. This P h illip s c o rre la tio n was subsequently inves­
tigated for other countries and other periods. Notably, Samuelson and Solow [1960]
suggested that a similar negative relationship held for the United States over roughly
the same time period as Phillips had studied.
Phillips and Samuelson-Solow drew curves through the inflation and unemploy­
ment data; they used these as structural relations to discuss a long-run P h illip s c u r v e
tr a d e - o f f between inflation and unemployment. Subsequent macroeconometric re­
search built structural models of inflation and unemployment designed to add more
detailed theoretical underpinnings to the Phillips curve; it also uncovered quantita­
tively important dynamic interactions between these variables (e.g., in Gordon [1970])
so that short-run as well as long-run trade-offs could be explored.
During the 1960s and 1970s, economists of widely varying perspectives focused
their research on the Phillips correlation and the Phillips trade-off. There was also
substantial exchange of views on the origins and significance of these relationships.
For example, the classic Eckstein [1972] volume on the econometrics of price deter­
mination includes contributions on the testing of the natural rate hypothesis by a
neoclassical economist (Lucas), on the effect of money on prices and output by mon­
etarist economists from the St. Louis Federal Reserve Bank (Anderson and Carlson),
on models of price setting by a theoretically oriented Keynesian (Nordhaus), on the
wage-price sectors of large econometric models by academics (Hymans and Klein) and
Federal Reserve researchers (de Menil and Enzler), on the construction of wage and
price statistics by an NBER business cycle researcher (Moore) and on the typical spec­
tral shape of price series by a time series econometrician (Nerlove). Through roughly
1980, the nature and stability of the linkages between inflation and unemployment
was the central topic for macroeconometric research.

1.1

T h e Great Divide

In the last decade, however, research on this topic has fallen into a period of quies­
cence. Curiously, this relative lack of research activity does not reflect the emergence
of a general consensus, but rather the division of macroeconomists into two groups
with widely different perspectives on the structure and stability of the linkages be­
tween inflation and unemployment.
N e o c la ssic a l a n d M o n e ta r is t E c o n o m ists : On one side of the street, the Phillips
curve and the Phillips correlation essentially disappeared as research topics as a result




2

of three related factors.
First, new empirical evidence suggested a striking change in the behavior of in­
flation and unemployment after 1970. Notably, the pronounced negative correlation
of Phillips apparently disappeared from the U.S. data after 1970: since 1970, there
have been length}' time periods in which inflation and unemployment were positively
rather than negatively associated. Thus, it became possible to view the Phillips corre­
lation as effectively dead in the post-1970 period, relegating it to the list of facts that
held for some periods but not for others. To some, this indicated that the Phillips
correlation was an empirical feature of secondary interest for business cycle theory
and forecasting.
The second factor was new theory: more than two decades ago, Lucas [1972] and
Sargent [1971] argued that studies of the links between inflation and unemployment
were subject to a subtle identification problem. Adopting the then-prevailing view
that the real effects of nominal disturbances depended on whether these were antic­
ipated or unanticipated, Lucas and Sargent showed that it could be impossible to
estimate the long-run Phillips trade-off using then-standard econometric methods.
In particular, if there was no permanent variation in inflation over the sample pe­
riod, then the effect of a change in trend inflation could not be determined without
a fully articulated behavioral model. Even more strikingly, Lucas and Sargent con­
structed examples of “natural rate models”-settings without any effect of sustained
inflation on unemployment-that displayed an apparent long-run trade-off. To many
economists, the increase in U.S. inflation during the 1970s corresponded to the “grand
experiment” of permanently increasing the growth rate of nominal aggregate demand
as envisioned earlier by Samuelson and Solow [I960]. Thus, the simultaneous rise in
the average levels of inflation and unemployment during the 1970s provided strik­
ing evidence against any long-run trade-off, consistent with predictions by Friedman
[1968] and Phelps [1968], and suggested that earlier apparent trade-offs were due to
the identification problem stressed by Lucas and Sargent. Overall, in the eyes of
Neoclassical and Monetarist economists the result was that the Keynesian macroeconometric models displayed “econometric failure on a grand scale,” in the phrase
of Lucas and Sargent [1979], due to mainly the structural specifications of wage and
price adjustment underlying the Phillips curve trade-off in these models.
The third factor leading to disappearance of research on the Phillips curve was
the necessity of developing new methods to execute the program advocated by Lucas
and Sargent. On the one hand, to construct the fully articulated dynamic models
that Lucas and Sargent advocated, many neoclassical economists spent the bulk of
their energy working on real theories of aggregate fluctuations. While these models
are arguably a natural starting point for macroeconomic analysis, they are ones in
which Phillips trade-offs are essentially absent, and the implications of these models
for the Phillips correlation have typically not been explored. On the other hand, the
solution of the identification problem uncovered by Lucas and Sargent involved a new
style of econometrics and associated technical problems.




3

One the other side of the street, many Keynesian macroe­
conomists were surprised by the strong reaction of neoclassical and monetarist economists
to the new theory and new evidence. That is, particularly for those Keynesian macroe­
conomists engaged in forecasting, the remarkable feature of the Phillips curve in the
post-war period was its sta b ility . To be sure, there was the embarrassing failure to
predict the post-1970 increase in average levels of unemployment and inflation; that
difficulty could be fixed, however, by requiring that there was no long-run trade-off
implied by the appropriate structural specifications of Keynesian macroeconometric
models and by incorporating exogenous variables to capture the effects of “supply
shocks”. But, with these modifications, the standard structural identification of
Phillips [1958], Solow [1969], and Gordon [1970], continued to be a powerful tool
for organizing the dynamics of unemployment and inflation. For the short term, it
provided a reasonable forecasting tool, even after 1970. In the longer term, the world
was a more difficult place to forecast after 1970 and the conventional equations did
as well as anything else. The Keynesian macroeconometricians argued that one could
continue to use the structural Phillips curve for considering the effects of monetary
policy acceleration or deceleration: they computed the dynamic effects of these poli­
cies shifts and evaluated their benefits and costs using methods that were essentially
unchanged by the arguments of Lucas and Sargent.1
Thus, during the 1980s, business cycle research was basically conducted by two
groups. The first did not study the Phillips correlation or the Phillips curve because
the former was viewed as chimerical and the latter as subject to deep identification
problems. The second viewed the Phillips curve as an essentially intact structural
relation: most research activity sought to add variables to represent supply shocks
and to build in the a zero long-run trade-off. But even without these modifications,
conventional Phillips curves continued to be a much used tool for medium term fore­
casting and policy analysis.
K e y n e s ia n E c o n o m is ts :

1.2

O u r Revisionist History

In this paper, we reexamine the post-war U.S. unemployment and inflation experience
using some new theoretical results and two complementary time series econometric
methodologies. Our history of the Phillips curve and the Phillips correlation is revi­
sionist because it challenges important aspects of the views of each of the prevailing
schools.
T h e n e o c la s s ic a l/m o n e ta r is t p o sitio n . We provide challenges that are theoretical
and empirical. On the theoretical side, we find that the Lucas-Sargent identification
problem may not be as devastating for the long-run estimates of Solow-Gordon as
originally supposed. (In this regard, we detail arguments made earlier in Fisher and
Seater [1993] and King and Watson [1992]). Notably, we show that if inflation contains
important low-frequency variation, as captured by a “unit root” stochastic process,
1For exam ple, see G ordon an d S. King [1982].




4

then one can estimate long-run trade-offs using procedures like those of Gordon and
Solovv. Further, these types of estimates can be large even after 1970, as shown in
King and Watson [1992],
On the empirical side, when we reexamine the nature of the “stylized facts,” we
find evidence that the Phillips correlation is not dead. To do this, we decompose the
post-war inflation and unemployment time series into three parts, which may usefully
be labelled as “trend”, “business cycle” and “irregular components.” We find that
there is a pronounced, negative relationship between the business cycle components
of inflation and unemployment. That is, for the post-war U.S. data, the Phillips
correlation is alive and well, once one recognizes that it lives at the business cycle
frequencies. After 1970, simultaneous increases and decreases in trend inflation and
unemployment obscure these business cycle comovements. We also document that
there is a changing cyclical pattei'n of inflation after 1970: as inflation became more
volatile there was a corresponding increase in its covariance with unemployment, so
that the overall correlation remained roughly over the entire postwar period.
T h e K e y n e s ia n P o s itio n : Our documentation of the post-war Phillips correlation
at business cycle frequencies would seem to be good news for Keynesian macroeco­
nomics. But challenges also appear for the traditional Keynesian position when we
estimate structural models of the Phillips curve. The traditional Keynesian identifi­
cation of the structural Phillips curve is not the only one which fits the post-war data
well and, on many dimensions, it appears to be an extreme one.
S tr u c tu r a l M o d elin g : When we begin the process of structural modeling, we un­
cover an additional key feature of the dynamic interactions of inflation and unem­
ployment: there a near-causal ordering, in the sense of Granger [1969], of inflation
and unemployment. More specifically, in a reduced form vector autoregression, past
unemployment is important for predicting current inflation but past inflation contains
little information about current unemployment.
This finding has important implications for structural modeling of inflation and
unemployment. As in any simultaneous equations setting, we must make some iden­
tifying assumptions to build a structural Phillips curve and to explore Phillips trade­
offs. When we consider alternative identifying assumptions about the short-run effect
of inflation on unemployment, we find that these have dramatic effects on the dynamic
structure as well. For example, there is a ready real business cycle interpretation of
the data: if we assume that there is little short-run effect of inflation on unemploy­
ment, then there is also little effect at any horizon. This outcome, which results from
the near Granger-causal structure, then implies that most of the negative Phillips cor­
relation at business cycle frequencies arises from the negative effect of unemployment
on inflation.
Traditional Keynesian estimates of the Phillips curve by Solow [1969], Gordon
[1970] and others were based on the assumption that unemployment is dominated by
aggregate demand disturbances, sufficiently so that it may be used as a regressor in
wage and price equations. While this identification is one that many macroeconomists




5

would now question, it was standard practice in Keynesian macroeconomics before
1970: we find that it leads to a very traditional Keynesian interpretation of business
cycles. That is, when we assume that there is a large short-run effect of inflation on
unemployment, then the near Granger-causal structure has the reverse implication:
post-war fluctuations in macroeconomic activity are entirely driven by shocks to de­
mand which manifest themselves mainly in unemployment in the short-run and with
little short-run effect on inflation. Further, there are also major costs of disinflation.
Notably, under the Gordon-Solow identification, we find that there is a large long-run
Phillips curve slope in both the pre-1970 and post-1970 data. We also find large
“sacrifice ratios,” defined as the unemployment cost of disinflation over a five year
period as in Okun [1978], which are in line with the traditional Keynesian estimates
surveyed by Okun.
An intermediate interpretation of the time series results from an identification that
has its origins in the rational expectations monetarist (REM) studies of Sargent [1976]
and Barro and Rush [1980]. Under this identification, there is a Phillips curve with a
small long-run slope. Business cycles turn out to be about half a result of disturbances
to demand and those to aggregate supply. There is also a much smaller sacrifice ratio,
which is broadly in line with recent estimates by Ball [1993] and Mankiw [1990].
All of these structural models fit the data equally well. Yet, they have substan­
tially different implications for the sources of business cycles, for the trade-off be­
tween inflation and unemployment, and for the interpretation of particular historical
episodes.

1.3

I m p l i c a t i o n s for t h e L o n g - R u n t r a d e - o f f

To preview our results, it is useful to consider the problem of estimating the long-run
trade-off between inflation and unemployment. Looking across various subsamples of
the post-war period in King and Watson [1992], we found clear evidence of structural
change in the behavior of post-war U.S. inflation and unemployment that occurs
around 1970. Further, as predicted by Lucas and Sargent, higher average values of
inflation and increased persistence of inflation are associated with a decline in the
estimate of the long-run trade-off between unemployment and inflation constructed
from our analogues of the methods of Gordon [1970] and Solow [1969].
This decline in the long-run trade-off is quantitatively important, as illustrated in
the first column of Table 1. (These estimates are based on King and Watson [1992]
and explained in greater detail in sections 3 and 4 below). In the sample period
th at corresponds to Gordon’s [1970] study of the Phillips curve, 1954-1969, we find
th at our variant of his methods suggests that a permanent one percent increase in
inflation—arising from an increased growth rate of aggregate demand—is associated
with a 1.3 percentage point decline in the unemployment rate. Strikingly, this es­
timate is close to the unit value which Solow [1970] extracts from Gordon’s [1970]
study; the unit value is also suggested by a graph in the 1969 Annual Report of




6

the President representing the relevant trade-off for the U.S. In the la tte r sample
period, 1970-1992, the estim ate is cut by roughly one-half to -0.57.2 Thus, there is
clear evidence of the im portance of the Lucas-Sargent critique for the estim ation of
stru ctu ral Phillips curves, at least as it bears on the estim ated extent of long-run
trade-offs between inflation and unemployment. However, the extent of the long-run
inflation and unem ploym ent trade-off remains quantitatively im p o rtan t for the full
sam ple period. One view is th a t this is because inflation is an 1(0) process, as in
the models of Lucas and Sargent, but results of unit root tests suggest considerable
persistence, consistent w ith an 1(1) inflation process. Indeed, as we will show below
unit root tests are consistent with the presence of perm anent com ponents in inflation
even in the 1954-69 sample period.
T he traditional Keynesian (TI<) estim ates of the Phillips curve by Solow [1969],
G ordon [1970] and others were based on the assum ption th a t unem ploym ent is dom ­
inated by aggregate dem and disturbances, sufficiently so th a t it m ay be used as a
regressor in wage and price equations. When we use an alternative identification
derived from the “rational expectations m onetarist” (REM ) studies of Sargent [1976]
and Barro and Rush [1980], we find a very different estim ate of the long-run trade-off
between inflation and unemployment. O ur estim ate is given in column 2 of Table 1:
it is -.47 for the pre-1970 sample period and -.23 for the later sample period. Further,
when we im plem ent a real business cycle (RBC) identification, which is th a t there
is no short-run link between inflation and unemployment, we find th a t there is an
essentially zero trade-off in both periods.
By looking down the two columns of Table 1, one gets a sense of how sam ple period
affects the long-run trade-off between inflation and unem ploym ent. By looking across
the rows, one gets a sense of how short-run identifications affect the long-run trade-off
between inflation and unemployment. One reaction to this table is th a t the shortrun identifications are quantitatively a t least as im portant as the sam ple period for
the long-run trade-off between inflation and unemployment. In the rem ainder of the
paper, we will see th a t this reaction is consistently appropriate as we consider a range
of evidence on the dynam ic interaction of inflation and unem ploj'm ent.

1.4

P l a n of t h e P a p e r

T he organization of the remainder of the paper is as follows. We begin in section 2
by reporting the d a ta th a t we study in the paper, both in its original form and using
moving averages designed to highlight “trend” and “cyclical” com ponents of the data.
While the basic tim e series display little evident correlation, this section docum ents
throughout this paper we measure the Phillips curve tradeoff by the ratio of the change in the
unemployment rate to the change in the inflation rate, i.e., d u /d x in the notation used below. This
is the inverse of the traditional Phillips curve slope. From a testing standpoint, it is useful that for
the measure d u /d i r, neutrality corresponds to a value of zero, instead of —oo in the usual Phillips
curve slope.




7

a rem arkably stable negative correlation between unem ploym ent and inflation over
business cycle frequencies, which we refer to as the “Phillips correlation” through­
o ut the paper. Section 3 begins our discussion of the “Phillips trade-off,” defined
as the relative effects of aggregate dem and on unem ploym ent and inflation w ithin a
particular stru ctu ral model. It begins with the theoretical background to our study,
considering the types of models th a t Keynesian and m onetarist econom ists have ty p ­
ically used to give stru ctu re to the Phillips correlation. This section then considers
the identification problem s raised by Lucas [1972] and Sargent [1971], and discusses
how these problems are affected by unit roots in the inflation process. In section
4, we develop a bivariate dynam ic structural model of inflation and unem ploym ent.
W orking w ith the three alternative short-run identifications discussed above, we in­
vestigate the m odel’s im plications for (i) the dynam ic response of unem ploym ent and
inflation to dem and disturbances; (ii) the contribution of “dem and” and “supply”
shocks to post-w ar U.S. economic fluctuations suggested by this model; (iii) th e con­
tributio n of dem and disturbances to specific historical episodes and (iv) th e long-run
trade-off between unem ploym ent. In section 5, we consider issues of th e econom etric
stability of the post-w ar inflation and unemployment processes, seeking to assess the
im portance of changing structure for both forecasting and stru c tu ra l estim ates of the
Phillips trade-off. In section 6, we conduct a sensitivity analysis of our m ain em piri­
cal results to various assum ptions made elsewhere in the paper, including evaluating
the im portance of u nit roots, d a ta frequency, measures of inflation, and inclusion of
exogenous supply shocks. Section 7 is a sum m ary and conclusions.

2

T h e P h illip s C o r r e la tio n in P o s t- W a r U .S . D a t a

W e begin w ith a brief review of the post-w ar U.S. inflation and unem ploym ent expe­
rience; this also serves to introduce the d a ta th a t we will study in the rem ainder of
the paper. Panel A of Figure 1 plots the m onthly inflation ra te series, wt , which is
the annualized percentage rate of change in the consumer price index.3 Because the
m onthly inflation series is very choppy, we also graph the annual average inflation
rate, which is the bold solid line in the figure.4 The vertical lines in th e panels of
Figure 1 indicate the sam ple period th a t we use to estim ate to estim ate our “early”
Phillips curve: it is chosen to m atch the effective sam ple period of G ordon [1971],
who excluded the earlier observations to elim inate the inflation of th e K orean W ar
and some large outliers im m ediately following the lifting of W orld W ar II price con3We use the seasonally adjusted index for all urban consumers (Citibase series PUNEW). The
annual inflation rate is ir, = 1200 * log(cpj(/cpit-i), where cpit is the value of the index at time t.
4The choppiness in the raw data reflects rounding error in the CPI, which is reported to one
decimal place (with a base of 100 in 1982-84). The annual average inflation rate shown in the figure
is the centered moving average rrf = (Yli=~6 7rt—>)/13.




8

trols. Panel B of Figure 1 plots the unemployment ra te .5 Some sum m ary features of
these d a ta are presented in Table 2, which presents means and stan d ard deviations
for various subintervals of the post-war (1950-1992) period.
T here are three distinct features of the tim e series plotted in Figures 1. First,
there is large high frequency variation in inflation. Second, bo th series show signif­
icant variation over periodicities associated with U.S. business cycles. Finally, both
series show slowly varying average levels or trend behavior; for exam ple, the average
inflation ra te increased from 2.5% in the 1960’s to 7.1% in th e 1970’s and then fell to
4.7% in the 1980’s.
These features of the tim e series are highlighted in Figure 2, which shows figure
shows the results from passing the d ata through sym m etric two-sided filters designed
to highlight the contribution of various periodicities. Panel A displays low frequency
variation (com ponents with periodicities longer than eight years), panel B displays
business cycle variation (components with periodicities between eighteen m onths and
eight years), and panel C displays high frequency variation (com ponents w ith peri­
odicities less th a n eighteen m onths).6
T he series plotted in panel A show the long-run movem ents in unem ploym ent
and inflation over the post-w ar period obtained from th e low-pass filter (isolating
periodicities greater than 8 years) filter.7 Inflation was low in the late 1950’s and
early 1960’s w ith an average level of approxim ately 1.5%; this was followed by a
rising tren d in inflation th a t peaked at nearly 10% in 1980, followed by a decrease to
4% by 1990. Similarly, the trend unemployment rate drifted up from approxim ately
4% in the late 1960’s to 8% in the early 1980’s, before falling to 5% in the late 19S0’s.
T he figure also shows an apparent change in the correlation betw een the long-run
movem ents in unem ploym ent and inflation. During 1954-1969 (shown by vertical
lines on the graph) there is a strong negative correlation (-.62); from 1970-1987 there
is no consistent relation (the sample correlation is .03), and over the en tire period
there is a positive correlation (.50).8
5This is the unemployment rate for all workers 16 years and over, in percent and seasonally
adjusted (Citibase series LHUR).
6Baxter and King [1993] discuss the construction of optimal approximate band-pass filters: some
approximation is necessary because exact band-pass filters are infinite two-sided moving averages.
Their definition of optimal is a standard one in the frequency domain literature,*.e., the filters
are designed to minimize the integrated square losses over all frequencies subject to constraints on
specific points. The low-pass filter that produces figure 2, panel A, is constrained to place unit
weight at the zero frequency and the band-pass filter that produces Figure 2, panels B and C, is
constrained to place zero weight at the zero frequency. The quality of approximation depends on
the length of the moving average: here we choose relatively long moving averages that use data from
t —K to t -f K , with K — 60 months.
7The trend components of inflation and umeployment are very close to the series that results
from the familiar procedure of applying a five year centered moving average-with equal weights-to
inflation and unemployment.
8 We use the sample correlation as a summary measure of association over the two sample periods.
Of course, if the series are 1( 1 ), as we assume below, these sample correlations are poor estimates of




9

Panel B shows the analogous “business-cycle” com ponents of th e series, th a t is the
results of applying a band-pass filter th at isolates periodic com ponents of betw een 18
m onths and 8 years in duration. Before and after 1970, these series vary as Phillips
would have expected, with the unemployment rate rising and th e inflation ra te falling
during N B E R -dated recessions: in this sense, there is a rem arkable stab ility of the
business cycle regularities th a t is masked by the trend and irregular com ponents in
Figure l . *9 B ut ou r plot provides also evidence of a change in th e inflation process: the
inflation process is more volatile post-1970 than it is before 1970, w ith th e stan d ard
deviation increasing from 0.93 to 2.04. Despite this changing variability, th ere is a
strong and stable Phillips correlation: the sample correlation of th e filtered series is
-.69 for 1954-69, -.67 from 1970-1987 and -0.66 for the full sam ple.10
Finally, panel C shows th a t inflation has much larger high frequency variation
th a n unem ploym ent. These components have a small negative correlation over the
sam ple period.
O verall, Figures 1 and 2 display two im portant features of th e post-w ar U.S.
d a ta. F irst, low frequency components of inflation and unem ploym ent becam e more
im p o rtan t after 1970 and these did not display the original, negative Phillips [1958]
correlation. Second, and by contrast, the Phillips correlation has been rem arkably
stable over business cycle frequencies.

3

T h e o re tic a l B a c k g ro u n d

In this section, we review the theoretical background to our research. T he presenta­
tion is designed to highlight the identification problems th a t are crucial to th e study
of unem ploym ent and inflation.

3.1

T h e Traditional K e y n e s i a n M a c r o e c o n o m e t r i c M o d e l

T he IS-LM m odel of Hicks [1937] and Modigliani [1944] provided th e m ain point of
d ep artu re for th e Keynesian macroeconometric model-building program of th e 1950s
the correlation between the stochastic trends in the series.
9One concern about exploration of filtered data such as these is that one is uncovering “spurious
relations” that arise from the filtering rather than from the original series. For example, it is wellknown that spurious periodic characteristics can be induced by filtering (as discussed in Sargent
[1979, chapter XI], for example). It is also well understood that shifts in timing can be introduced
by filtering. However, the features that we stress are unlikely to be spurious. We are not concerned
with the periodic nature of the univariate series, which is an artifact of the filtering. Rather, we
are interested in the comovements of the two series, and their behavior relative to the NBER peak
and trough dates. These comovements will be summarized by estimated correlations and associated
standard errors that account for serial correlation in the filtered data. Note also that we have applied
the same symmetric linear filter to each series, so that no phase shifts have been induced.
10Standard errors (computed using an AR(1*2) spectral estimator) for the estimated correlations
are .17, .19 and .18, respectively.




10

and 1960s. Given the behavior of nominal wages and prices, the m odel could de­
term ine em ploym ent, national income and its components, and the ra te of interest.
B ut, in this form, the IS-LM model was incomplete for m acroeconom etric purposes:
a specification of the dynam ic adjustm ent of wages and prices had to be added.
The impressive evidence of Phillips [1958] regarding the relationship betw een un­
em ploym ent and wage inflation offered macroeconometric m odel-builders a way to
com plete their system . T here were two steps in this process. F irst, th e Phillips curve
was treated as a stru ctu ral relation for wage determ ination. Second, th e Phillips
curve was combined w ith a “price equation” , as in Eckstein and From m [1968], th a t
determ ined prices as a function of wages and other economic variables.
For expositional convenience, we will conduct our initial discussion w ithout being
explicit about dynam ics and focus on the contemporaneous interaction of inflation
( 7rt) and unem ploym ent (u t). (Thus, for now we make no distinction betw een
and
the logarithm of the price level.) Later, we will use these results to discuss short-run
identification restrictions in dynamic models, treating the variables th a t we consider
now as the unpredictable components of inflation and unem ploym ent.
Our Keynesian system is given by the two structural equations (1) an d (2). T he
first of these two equations is a “price equation.” This specification describes how the
inflation rate responds to the unemployment rate, which is an indicator of aggregate
dem and conditions in the model. The param eter “a” indicates the e x ten t of price
adjustm ent to dem and: rapid adjustm ent of inflation to dem and conditions arises for
large absolute values of “a” , correspondingly prices are essentially unresponsive to
dem and w ith “a ” close to zero. In addition, there is a price shock term , p t , th a t is
the residual in th e price equation.
7rt

= a u t + pt

(1)

More generally, th e price equation was part of the wage-price block in Keynesian
m acroeconom etric models. But, since many Keynesian modelers viewed prices as a
relatively fixed m arkup over wages, we use the simpler specification (1).
T he second equation in our Keynesian model determines the unem ploym ent ra te
as a function of inflation irt and a demand shift variable d t . This equation captures
the Hicksian (IS-LM) determ ination of real variables as functions of wages and prices.
u t — h 7rt + dt

(2)

T he param eter h governs the extent of the short-run Hicksian influence of inflation on
dem and. D ating from the work of Klein [1950], the conventional Keynesian m acroe­
conom etric view was th a t the short-run dependence of real variables on th e price level
was minor, suggesting small values of h in equation (2), and th a t dem and variations
were dom inated by exogenous shocks ( d t). Econometrically, this last observation sug­
gested th a t the ex ten t of short-run price adjustm ent in (1) could be estim ated via
ordinary least squares procedures, as in Solow [1969] and Gordon [1970].




11

3.2

M o n e t a r i s t M o d e l s o f Inflation a n d U n e m p l o y m e n t

M onetarist models of inflation and unemployment typically specified an altern ativ e
behavioral stru c tu re (as, for example, in Anderson and Carlson [1972]). W orking in
the same static term s as above, they posited an aggregate supply curve, equation (3)
and an aggregate dem and curve, equation (4), frequently deriving the la tte r from a
simple qu an tity equation. T he aggregate supply specification took th e form,
ut = f *t + S t

(3)

where large absolute values of / imply large effects of inflation on real activ ity and
s t is a shock to aggregate supply. Comparably, the dem and side took th e form:
irt = q u t + m t

(4)

where q indicates the sensitivity of inflation to real activity (perhaps com bining the
income elasticity of money dem and with an O kun’s law relation betw een real income
grow th and unem ploym ent) and m t is a shock to the inflation rate, typically viewed
as originating in changes in the money growth rate.

3.3

Observational Equivalence of the T w o F r a m e w o r k s

Generally, th e two models described above are observationally equivalent: there is a
simple translation from the shocks and param eters in one model into the shocks and
param eters of the other. For example, the price equation of th e Keynesian model,
7rt = a u t -f p t , can be rew ritten as the aggregate supply equation of th e m onetarist
model, u t = / 7rt + s*, w ith the change of variables / = (£) and s t = —(^)p t. T h a t is,
in Figure 3, the price shock is the vertical displacement in the supply schedule/price
equation and the supply shock is the horizontal displacement. Similarly, th e reduced
form of the IS-LM m odel, u t = h x t + dt , can be rew ritten as 7rt = q u t + m t w ith a
change of variables q = (^ ) and m t = —(j^)dt .
W hile these system s are observationally equivalent, choice betw een th em likely
affects the identification strategies used for estim ation and inference. Indeed, in our
em pirical sections below, we will see precisely how im portant these choices can be for
one’s views of the long-run and short-run trade-off between inflation and unem ploy­
m ent as well as for the one’s views about the dom inant sources of macroeconom ic
fluctuations.

3.4

D y n a m i c Phillips C u r v e Specific a t i o n s

The dynam ic generalization of the Phillips curve specification (1) is:




tt< =

a u t + p„u(L )u t-1 -I- &„(£)*-<_! -f p t

12

(5)

where /3wu( L ) u t- i perm its aggregate demand to have an effect on inflation th a t is
distributed over tim e and
permits price shocks to have rich dynam ic effects
on the inflation rate. Keynesian macroeconometricians like Eckstein and Fromm[1968]
and Gordon [1970, 1971] found th a t specifications like (5) were necessary to fit the
post-w ar d a ta well.
In this context, there are two “slopes” to the Phillips curve th a t are of interest.
F irst, the short-run slope of the Phillips curve is given by
dirt/ d u t = a .

(6)

T he long-run slope is obtained by contem plating sustained changes in inflation and
unem ploym ent - i.e ., by setting u t = u and irt = ir for all t before taking the p artial
derivative - so th at:
d n / d u = [a + p vu{ l ) \ / [ l -

(7)

where /?xu(l) denotes the sum of lag coefficients in f3vu(L ) and /?U7r(l) is defined
analogously. The derivatives in (6) and (7) are the reciprocals of our measure of the
unem ploym ent-inflation trade-off.
C om putation of short-run and long-run trade-offs as in (6) and (7) were standard
practice in traditional Keynesian macroeconometrics, including results of sim ulating
com plete models and studying the properties of the wage-price block, i.e., of stru ctu ral
wage and price specifications. Typically, these studies also traced out a full set of
dynam ic m ultipliers. O ur structural Phillips curve investigation in section 4 below
will follow this path.

3.5

Testing the Natural R a t e Hypothesis

T he n atural rate hypothesis of Friedm an [1968] and Phelps [1968] suggested no longrun trade-off between inflation and unem ploym ent, i.e., a very large value of d n / d u
in (7). Gordon [1970] and Solow [1969] sought to test this hypothesis by making
two modifications to the Phillips curve. They began w ith a stru ctu ral equation of
the general form of (1) augm ented to introduce the effects of expected inflation,
7T* : Trt = a u t + b 7r* + p t . They then proxied expected inflation using a distributed
lag m ethod. In the sim plest version,
was treated as the “adaptive” expectation
irf — 7rt*_j =
this specification had the im plication th a t if there were
a perm anent increase in inflation, expectations would ultim ately capture it in the
long run, i.e ., d x '/ d i r = 1 for such changes. More com plicated schemes allowed for
richer dynam ic patterns of expectation adjustm ent, 7rt* = v ( L ) n t =
hut
continued to impose the requirem ent th a t d i r '/ d x = 1 or equivalently the requirem ent
th a t
= 1- Hence, the Gordon [1970] and Solow [1969] procedures fit naturally
into the dynam ic Phillips curve specification (5) w ith a v„ (L ) = b v { L ). -If the n atural
rate hypothesis was invalid, then it was also possible to estim ate the extent of the




13

long-run trade-off in an “expectations adjusted” Phillips curve. And, indeed, Gordon
and Solow found substantial long-run trade-offs in U.S. and U.K. d ata. T he unit value
of the d ir /d u trade-off estim ates th a t Solow [1970] extracts from Gordon [1970], for
exam ple, is not very different from the reciprocal of the value of d u jd i r in Table 1:
our estim ate of d i r / d u is .8 for the same sample period.

3.6

T h e Lucas-Sargent Critique

T he Gordon-Solow tests were criticized by Lucas [1972] and Sargent [1971] in a pair of
papers th a t set the stage for a revolution in macroeconometrics. O ur presentation will
be a blend of the Lucas and Sargent examples, dealing explicitly w ith th e “m o netarist”
specification of the Phillips curve as suggested by Lucas’ analysis and using a general
autoregressive specification of the inflation process as in Sargent [1971].
T he stru ctu ral framework contains two equations. F irst, the aggregate supply
specification makes u t simply a function of unexpected inflation: it is an expectationsaugm ented version of (3).
u t = f irt - g ir’ + s t .

(8)

T he n atu ral ra te hypothesis is then th a t / = g. Inflation is generated by th e autore­
gressive process,
=

P i* t-1

+

...p

+ rnt .

n * t- n

(9)

where m t is an unpredictable shock. The rational expectations assum ption is:
7Tt
* =

E t - I ^ i

=

p lT T t-l

+

...p n K t-n -

(10)

T hen, the reduced form unem ploym ent and inflation relation is:
n
u t = f* t - Y ld

p i* t- i

+ St .

(11)

1=1

Hence, if a m acroeconom etrician com puted our long-run trade-off on th e d a ta from
this economy, he would find th a t d u /d ir = ( f —g ]T)"=i Pi)- Even if th e long-run system
is neutral ( / = g ), the assum ption th a t inflation is a stationary stochastic process
implies th a t d u /d i r = /( 1 —£ ”=1 pi) is not zero. T h a t is, Lucas and Sargent pointed
o u t th a t there would be an apparent long-run trade-off when none was implied by
the stru ctu ral specification (8). Lucas [1972], Sargent [1971], and Lucas and Sargent
[1979] elaborated on the macroeconometric implications of this example: proper tests
of models w ith rational expectations would necessarily involve cross-equation tests.
In particular, they argued th a t it was necessary to provide a detailed stru ctu ral de­
scription of the inflation process in order to test the n atu ral ra te hypothesis.
Economists were persuaded by the Lucas-Sargent argum ent for three reasons.
F irst, it was so clearly correct in its analytics. Second, rational expectations offered a




14

way to avoid treating expectations as a source of “free param eters” in em pirical work.
T hird, their argum ent provided a coherent explanation of the breakdown of empirical
Phillips curves. Notably, it suggested th a t as inflation became more persistent, in the
sense th a t Yl?=i Pi became closer to unity, then there should be smaller estim ates of
the long-run trade-ofF.

3.7

T h e Lucas-Sargent E x a m p l e O n c e A g a i n

The stru c tu ra l model (8) w ith f = g has a very strong n atu ral rate property: inflation
affects d a te t real activity only if it is unexpected as of d ate t — 1. N atu ral rate
models of the class developed by Fischer [1977], Gray [1976] and Phelps and Taylor
[1977] perm it inflation forecasting errors of a longer duration to affect real activity,
suggesting the value of studying specifications like (12).
<7
u t = f * t - Y s d iE t- i V t + s t

(12)

:= 1
In this model, the n atu ral rate property is th a t simultaneous changes in x t and E t- iX t
by the sam e am ount have no affect on unem ploym ent, i.e ., th a t / — J2i=i 9i — 0As above, we assume th a t inflation is generated by an autoregressive process,
7rt = p i x t_ i + ... fin ^ t-n + m t, which we write as
p {L ) 7rt = m t ,

(13)

w ith p ( L ) = 1 — p i L — ... — pnL n, where L is the lag operator. T hroughout, we
require th a t the change in inflation, Ax* = x t —7rt_ !, is a stationary random variable
w ith moving average representation A x t = g (-L )m t , where p ( z ) = ^ y . We explore
two cases: (i) the Lucas-Sargent case in which inflation is stationary, so th a t p (L ) has
all of its roots outside the unit circle, p (l) ^ 0 and p ( 1) = 0; and (ii) an alternative
in which there is a single unit root in p ( L ) , so th a t p (L ) = (1 — L)<f>(L) w ith <t>(L)
having all of its roots outside the unit circle.
W ith a unit root in the inflation process, we can derive two results (the details are
given in A ppendix A). F irst, we find th a t a unit root in the inflation process implies
th a t the sum of coefficients restriction tested by Solow and Gordon is equivalent to
the long-run neutrality restriction. Second, we find th a t th e presence or absence
of a unit root is critical to whether the tim e series d a ta are inform ative about the
consequences of sustained inflation, as variously argued by Sargent [1971] and Fisher
and Seater [1993].
The first result is th a t the reduced form of (12) and (13) is:14




u t = Pu * ( L ) x t + s t

15

(14)

where f3uir(L) is a (<7 + n)th order polynomial in L. Further, under the unit root
assumption, it follows that:
Axjr(l) = / —2 ^</i

(15)

1=1
T h a t is, if there is a unit root in the inflation process, then the sum of coefficient is
inform ative about the slope of the long-run Phillips curve, as suggested by Solow and
G ordon.
To develop th e second result, let itt denote the Beveridge-Nelson [1981] m easure
of trend inflation, and let M t = M t - i + m t = £ * =1 rrij + M 0 denote th e sum of the
(dem and) shocks in the inflation equation (13). Then, fit = f i ( l ) M t , and (14) can be
rearranged as:
ut = [ / -

+ xj}{L)mt + s t ,

(16)

1=1

w here i{)(L )int is a stationary component of unem ploym ent arising from th e dem and
shifter m t. In (16) the long-run param eter, [ / —
appears as th e coefficient
on trend inflation,
= f t - W hen inflationary is stationary, /x( 1) = 0, trend
inflation is identically zero, and the neutrality param eter [ / —Y%=i <7«] is not identified
in (16). T hus, as stressed by Lucas and Sargent, the relevant ex p erim ent-perm anent
changes in the ra te of inflation-are absent from the inflation d a ta and so th e long-run
Phillips trade-off could not be estim ated from (16). In the u n it root case, by contrast,
it follows th a t /z(l) =
=£ 0, so th a t the relevant experim ents are present in the
d ata: variation in Ttt allows the long-run slope to be determ ined.

4

E s tim a tin g

a

S tr u c tu r a l P h illip s

C u rv e

In this section we investigate the structural Phillips Curve and im plied trade-offs
betw een inflation and unemployment. For this purpose, we use a bivariate VAR of
th e form:
p

p

A tlf = A A7T( - f ^ ' <f>u -n'i&TTt— i "b ) ]

~

& & U t

t=l

1=1

p

p

*b ^

i

1=1

*b ) ]

*b ^st

(1 7 )

"b £d t

(18)

i=l

We will in terp ret equation (17) as the Phillips Curve. In term s of the Keynesian
m odel discussed in section 2, equation (17) is the “price” or “m ark-up” equation
(1) rearranged so th a t n t appears the right hand side. Thus, the param eter A in
(17) corresponds to A in (1), and est is proportional to the shock in th e “price”
equation. In term s of the m onetarist model, equation (17) is the “supply” equation
(3), so th a t A in (17) corresponds to / in (3) and csf is the “supply” shock. In either




16

model, tdt in (IS) corresponds to the demand shock, and our interest here focuses
on the dynam ic effects of this shock on both u t and -Kt . Equations (17) and (18) are
w ritten in first difference form, so th a t both u t and irt are assum ed to be 1(1) and not
cointegrated. T he specification (17)-(IS) thus perm its us to estim ate the “long run”
effects of the disturbances tdt and est in ways similar to those used by Solow [1969] and
Gordon [1970]. However, rather th an computing d u jd 7 r, we will be concerned with
limjt_oo{[<9ut+fc/d e d ,]l[d ^t+ k l $Q,]} and thus focus on the relative effects of dem and
shocks on unem ploym ent and inflation.
T he first difference form of this specification is consistent w ith the stochastic
trends evident in the series as displayed in section 2. More formal statistical tests
do not reject the unit root restriction built into (17) and (18): for example, as re­
ported in Table 3, the 95% confidence intervals for the largest autoregressive root are
(0.968,1.007) for the unemployment rate and (0.960, 1.006) for inflation over the full
sam ple period. Table 3 provides these largest root estim ates and also com parable
inform ation on the estim ates for the sub periods 1954-1969 and 1970-1992. In section
6 we consider the robustness of our primary results to the unit root specification and
present results for the model estim ated in levels.
Evidently, equations (17) and (18) are a set of two dynam ic sim ultaneous equa­
tions. S tandard results imply th a t two a p rio ri assum ptions are required to econometrically identify the param eters and shocks in the equations. Here we consider three
different sets of identifying assumptions th at are in tu rn suggested by three in ter­
pretations of (17)-(18): (i) the traditional Keynesian interpretation; (ii) the rational
expectations m onetarist interpretation; and (iii) a real business cycle interpretation.
Each interp retatio n leads to different identifying assum ptions, which in tu rn lead to
different estim ates of the equations and shocks. These differences are quantitatively
very large and imply very different estimates of the inflation-unem ploym ent trad e­
off and the corresponding “costs” of disinflation. They also lead to very different
historical interpretations of postwar U.S. business cycles.
In all of the interpretations of (17)-(1S) we will assume th a t the disturbances t st
and tdt are m utually uncorrelated. Conceptually, this allows us to think of each shock
as arising from distinct and independent sources, and means th a t any contem pora­
neous correlation between u t and 7tt arises from non-zero values of the param eters A
and 8. Only one additional assum ption is necessary to econom etrically identify the
param eters and shocks in (17)-(18).

4.1

T h r e e S h o r t - R u n Identifications

The three identifications th a t we consider differ from one an o th er in their assumed
correlation between tdt and u t. The first identification is suggested by economet­
ric im plem entations of the traditional Keynesian model (l)-(2 ) which allowed little
contem poraneous feedback between the wage-price block (sum m arized b y (l)) and the
IS-LM block (sum m arized by (2)). This structure implies th a t one-step ahead forecast




17

errors in the unem ploym ent rate are dom inated by aggregate dem and disturbances.
A t the other extrem e, real business cycle models postulate th a t m ovem ents in real
variables such as n t are perfectly correlated with aggregate supply shocks. There
is a large middle ground between these two extrem e views; we use an identification
suggested by the rational expectation m onetarist models of Sargent [1976] and Barro
and Rush [1980] which, as we show below, yields results midway betw een the two
extrem e views.
T h e T ra d itio n a l K e y n e s ia n ( T K ) Id en tific a tio n : As discussed Section 3, in tra d i­
tional Keynesian models, changes in prices arising from realizations of est have little
contem poraneous effect on u t : in th e extrem e, est and u t are contem poraneously un­
correlated. This m eans th a t in addition to lagged variables, th e contem poraneous
value of u t can be used as an instrum ent to estim ate equation (17); im plicitly this
defines A in equation (17) as A = v a r ( u t) /c o v ( u t , 7ct ), where * denotes an unfore­
castable com ponent. Equivalently, equation (17) can be estim ated by OLS using th e
reverse regression of 7rt onto u t and relevant lags. In this form, we recognize th e “price
equation” estim ation strategy used by Gordon [1970] and other researchers in th e Key­
nesian tra d itio n .11 Using our d ata, this leads to an estim ate of A = —1.56; throughout
we will use this value of A to represent the traditional Keynesian specification.12
T h e R a tio n a l E x p e c ta tio n s M o n e ta r ist (R E M ) Id e n tific a tio n : In rational expec­
tatio n s m onetarist models, researchers also looked for an additional in stru m en t th a t
would allow them to estim ate (17). In the “supply” equation in terp retatio n of (17),
this instrum ent is required to be correlated with th e unforecastable com ponent of
inflation and uncorrelated w ith the supply disturbance. W hile em pirical researchers
in this tradition did not settle on a consensus instrum ent (or set of instrum ents)
th ey obtained sim ilar estim ates of A and the resulting Phillips C urve trade-off. For
exam ple, Sargent [1976] estim ated an equation like (17) as p a rt of his larger clas­
sical m acroeconom etric model. In addition to lags, he used money, population and
governm ent spending variables as instrum ents. Barro and Rush [1980] estim ated the
effects of “unanticipated money grow th” on unem ploym ent and th e price level, re­
11This is a stylized characterization of the empirical Phillips curve literature of the 1960s and
early 1970s. These researchers often included additional shift variables to account for particular
events and transformed the data in a variety of ways to model nonlinearities in the Phillips Curve.
But, in estimation procedures and in policy evaluations, they treated unemployment as exogenous in
wage and price equations. More recent econometric analysis of the Phillips Curve (notably, Gordon
[1982,1990b]) allows for correlation between IT, and c,( and uses identification procedures like those
used in the rational expectations monetarist models.
12This estimate of A is quite imprecise with an estimated standard error of 1.61. To see the source
of this imprecision recall (from the usual IV formula) that the estimated standard error for A is given
by T[C
---^0«.(u,,Jr,)p
-1 “'■) .. In the data, the one-step ahead forecast errors for unemployment and inflation are
very weakly correlated, leading to a small estimated value of [cou(2 (, ?;)] and a corresponding large
standard error for A. Interestingly, this is what would be expected from a model with in which prices
move very little on impact in response to a change in aggregate demand. In any event, Section 6
summarizes results for a large range of values of A.




18

suiting in an im plicit instrum ental variables estim ator of the p aram eter A in (17).13
The im plicit estim ate of A from Sargent’s analysis is -0.07, while th e Barro and Rush
estim ates ranged from -0.17 to -0.07. In our analysis, we will use -0.07 as the value
of A for the rational expectations m onetarist model. As the results will make clear,
this seems to be a reasonable interm ediate value between the trad itio n al Keynesian
and real business cycle model extrem es.14
T h e R e a l B u s in e s s C ycle (R B C ) Id en tifica tio n : In real business cycle models, the
unem ploym ent ra te is unaffected by nominal shocks. Thus, inflation does not en ter
(17), i.e ., A = 4>U* {L ) = 0 in (17). We will use the assum ption th a t A = 0 as the
additional identifying assum ption in this interpretation of (17). W hile this is an
a rb itra ry interp retatio n of the identifying assumptions in this model (since we could
have set A or any value of <f>u-r,i equal to zero to achieve identification), this restriction
does leads to an em pirical model w ith clear RBC characteristics.

4.2

I m p l i c a t i o n s o f t h e Identifications

A sum m ary of the results for each of these specifications is given in Figure 4 and
Table 4. These results were obtained by estim ating (17) using A = —1.56 (the TK
identification), A = —0.07 (the REM identification) and A = 0.0 (th e RBC identi­
fication). T he models were estim ated using d a ta from 1954:1-1992:12 and included
twelve lags and a constant term . The figure shows the estim ated im pulse responses
from th e dem and shock (panel A); the fraction of the fc-step ahead variance of u and tt
a ttrib u te d to the dem and shock (panel B); and the inflation-unem ploym ent trade-off
a t different horizons (panel C). This trade-off is [dut+ k/d ed t]/[d n t+ k/d td t], and thus
shows the relative effect of a dem and shock on unemployment and inflation. (This
slope formed as the ratio of the two impulse response functions in panel A.)
It is convenient to begin the discussion with the RBC identifying restriction (A =
0.0); the results for this specification are summarized in the first column of panels in
Figure 4. In this specification, est corresponds to the one-step-ahead forecast error
in u t, and e^t is the portion of the forecast in 7rt th a t is orthogonal to the forecast
error in u t. T he im pulse response function and variance decom position show th a t
u t is essentially G ranger causally prior to u<; th a t is lagged values of 7r< (and the
associated lags of e jt), explain a tiny fraction of future values of u t. (T he F -sta tistic
13The implicit instrumental variables estimator from Barro and Rush [1980] is constructed as fol­
lows: let bum be the ordinary least squares estimate of the effect of (unanticipated) money on unem­
ployment and let bpm be the corresponding ols estimate of the effect of (unanticipated) money on the
price level (or inflation). Then, the implicit IV estimator is bum/bpm, i.e., it is cov(u,m )/cov(p,m ),
which is the conventional IV formula. See Appendix B for some additional discussion of how we
derive estimates of A from the studies of Sargent [1976] and Barro and Rush [1980].
14R.J. Gordon has suggested to us that “mainstream” is a better label for this identification, since
it produces results in which both supply and demand disturbances play a major role in the business
cycle, a result accepted by all mainstream economists irrespective of “Keynesian” or “Monetarist”
perspectives.




19

for the null hypothesis th a t x t does not Granger-cause u t is 1.25 w ith a p -value of
.26.) A t lag zero the unemployment-inflation trade-off is zero by assum ption for this
specification, since [d u t+k/d(-dt\ — 0 for k = 0. For other values of k , the trade-off is
em pirically determ ined, and panel C shows th a t it is positive, but very small. In this
sense, the identification yields a picture of the business cycle th a t is essentially real.
T he next colum n of panels in Figure 3 shows the results for th e REM identifying
restriction A = —0.07. Here, tdt explains roughly 40-50% of th e variability of the
unem ploym ent ra te a t all horizons. This shock explains 52% of inflation on im pact;
84% after 4 years, and over 95% of the long run variance. T he shock has a large
im pact effect on inflation and a m oderate im pact effect on th e unem ploym ent rate:
hence, th ere is only a small value of d u f d i t on im pact. After one year, th ere is a much
larger effect on unem ploym ent and inflation; the trade-off increases to d u / d i r = —.32
and then falls to —.29 after 4 years. (The standard errors range from .07 a t a year
to .05 a t four years.) The estim ated long-run trade-off is —.29 (se = .05), which is
no t fully consistent w ith the natural rate hypothesis, but is a small value relative to
the 1-for-l trade-offs reported in the early empirical. Overall, th e identification leads
to a very m onetarist picture of business cycles, in th a t dem and disturbances are of
substan tial im portance for economic fluctuations-roughly 40% -and explain nearly all
of the variation in inflation.15
T he last colum n of panels shows the results for the T K identifying restriction
A = —1.56. Recall th a t this model identifies tdt as the one-step ahead forecast error
in u t . Since irt does not Granger-cause u t , the one-step ahead forecast error in u t
explains essentially 100% of the variance of u t a t all horizons. T hus, th e identifying
restriction im posed in the traditional Keynesian interpretation of (17) implies th a t
th e unem ploym ent ra te is essentially a perfect indicator of dem and. In co n trast, the
dem and shock explains little of the short-run variability in 7r* (th e p oint estim ate at
lag 0 is 0.00% and 15% a t lag 12) and approxim ately 40% of th e long-run variance of
inflation. This interpretation of (17) leads to a trade-off of d u /d i r o f -1.56 on im pact,
which falls to —.71 (se = .12).

4.3

W h y t h e S h o r t - R u n Identification (A) M a t t e r s S o M u c h

A key feature of the em pirical results discussed in the prior section is th a t th e assumed
short-run effect of inflation on unem ploym ent (A) substantially affects all of the other
features of the dynam ic system. Notably, A dictates the level of the long-run m ultiplier
15Another implementation of a monetarist identification is that long-run inflation is always and
everywhere a monetary (demand) phenomenon, i.e., that inflation is unaffected by e}t in the long
run. These sorts of long-run identifications are variously explored in Fisher and Seater [1993], King
and Watson [1992] and Roberts [1993]; the latter two papers explicitly consider the trade-off between
inflation and unemployment under this identification. For our full sample period, this identification
leads to an estimated short-run tradeoff of —0.05, and is thus intermediate to our REM and RBC
identifications.




20

(d u /d 7 r); the sources of business cycles as revealed by estim ated decom positions of
variance; the shape of the impulse responses, etc.
To gain some intuition for these results, consider the reduced form of the dynam ic
system (17) and (IS):

A u t = a ( L ) A u t- i + b {L )A ir t- y -f- eut

(19)

A n t = c ( L ) A u t- i + d{L)A-K t- \ + e*t,

(20)

where all of the lag polynomials contain only positive powers of L (so th a t only lagged
values appear on the left hand side of (19) and (20)). In this reduced form system , the
forecasting errors e ut and eTt are linear combinations of the stru c tu ra l disturbances
est and tdt ;specifically since eut = D {\e.dt + £st) and e„t = D (edt + d e st), where
D = (1 — A<$)-1 .Larger values of A thus imply th a t there is a larger short-run effect
of dem and shocks on unem ploym ent. Indeed, in the lim iting case w ith A —*• oo, it
follows th a t shocks to dem and and shocks to unemployment are identical.
Sum m ary statistics for the estim ated reduced form are given in Table 5. We
now consider two aspects of the reduced form which are approxim ately, although not
exactly true for our estim ates. These are: (i) th a t the sum of th e b coefficients, which
we denote 6(1), is essentially zero; and (ii) th a t the individual 6,- coefficients are close
to zero. C onsideration of these two features of the reduced form helps us understand
why the selection of A is so critical to the empirical results discussed in th e previous
section.
F irst, when 6(1) = 0, the long-run Phillips trade-off is m onotonically increasing in
A. To see this, solve (19)-(20) for the long-run trends in unem ploym ent an d inflation:
t u1 = a ( l ) r ut + 6(l)7vt + eu( and Tvt = c ( l) r ut + d(l)r,* + efft, and recognize th a t
lim ^ o o d u t+ k/d ed t = dTut/d e d t and limjt-oo dirt+ k/dtdt = d r ^ /d e d t- T hen, by direct
calculation:

i:

dut+k/dtdt

[(1 - d(l))A + 6(1)]

d rt+ k /d e d t

[(1 - «(1)) + A c ( l) ] ‘

W

W ith the condition 6(1) = 0 imposed and using the facts th a t d (l) < 1 and a ( l) < 1,
(21) provides a simple characterization of the relationship betw een A an d th e longrun Phillips trade-off. First, a t A = 0, the long-run slope is zero (which confirms
our finding w ith the RBC interpretation). Second, d u / d n is increasing in A : a
larger short-run negative slopes implies a larger long-run negative slope.16 Hence, if
one assumes th a t inflation has a m ajor short-run effect on unem ploym ent (which is
our version of the traditional TK identification) then one also finds th a t there is a
m ajor long-run effect of inflation on unemployment. By contrast, if one assumes th a t
inflation has a small short-run effect, then one also finds little long-run effect.
16The point estimates reported in Table 5 suggest that c(l) < 0, which implies that d u /d t r does
not have any discontinuities for values of A < 0.




21

W hen all of the 6,’s= 0, (19) becomes:
A u t = a ( L ) A u t- i + { ^ \ $ edt

i _

}>

where we have w ritten eut in term s of th e stru ctu ral errors. Two im plication follow
directly. First, when A = 0 (as in th e RBC identification), then the dem and shock
has no effect on unem ploym ent a t any horizon. This finding accords w ith th e findings
in panel C of Table 4, w ith m inor discrepancies th a t are associated w ith th e fact
the b (L ) is only approxim ately rath er th a n exactly zero. Second, increases in A lead
to larger effects of dem and shocks on unem ploym ent a t all horizons as we move
to consideration of the impulse responses under the REM and TK identifications.
F urther, th e fraction of fc—step-ahead forecast error variance a ttrib u ta b le to dem and
shocks is roughly constant across horizons and is increasing in A. T he large value of A
used in the TK identification, for exam ple, essentially makes the dem and shock equal
to the unem ploym ent forecast error (as occurs exactly when A —+ oo in the form ula
above).
Thus, the near G ranger-causal relationship between Trt and u t means th a t selection
of the short-run identification dictates th e relative of dem and and supply shocks in
economic fluctuations.

4.4

M e a s u r i n g t h e C o s t s o f Disinflation.

These different models suggest dram atically different costs of disinflation. Table 6
shows the estim ated responses of unem ploym ent and inflation to a dem and shock th a t
eventually leads to a 1% perm anent reduction in inflation. In addition, the table shows
the “Sacrifice R atio” defined as the cum ulative annual percentage point changes in
unem ploym ent required to produce this perm anent reduction in inflation. E stim ates
predicated on the T K identification suggest th a t the unem ploym ent ra te rises by 0.9%
after 1 year, is still 0.7% higher after 5 years, and th a t the five year sacrifice ratio is
3.7. T h a t is, over five years, the cost of a 1% perm anent reduction in inflation is a
cum ulative 3.7% annual percentage points increase in unem ploym ent. By contrast,
the REM identification yields a much smaller change in th e unem ploym ent rate and
a correspondingly smaller value of the 60-m onth sacrifice ratio of 1.52. This value is
sim ilar to results found by Gordon and King [1982], Mankiw [1990] and Ball [1993]
using different identifying assum ptions.17 In the RBC identification, unem ploym ent
17Mankiw [1990] estimates a sacrifice ratio of 1.4 for the Volker disinflation over 1981-85 by
assuming that aggregate demand was responsible for the entire decrease in inflation and the increase
in unemployment over a 6 % natural rate. Ball [1993] estimated average output sacrfice ratios for the
U.S. of 2.4 by assuming the movements in trend inflation between “inflation peaks” and “inflation
troughs” was attributed to aggregate demand. Dividing his estimate by an Okun’s law coefficient
of 2 yields an unemployment sacrifice ratio of 1.2. Gordon and King [1982] estimate a 48 month
output/inflation sacrifice ratio of 3.0, which again corresponds to an unemployment/inflation sacrifice
ratio of approximately 1.5. Their estimates are constructed from a model that determines real and




22

is essentially exogenous, so th a t the reduction in inflation has no unem ploym ent cost.
All of these estim ates can be contrasted to sim ulation results reported in Eckstein
[1981] for the DRI model. The DRI m odel’s cost of disinflation is very large (the
sacrifice ratio is 8), more than twice as large as the sacrifice ratio of the Keynesian
identification in the bivariate VAR.

4.5

Interpretations of Episodes

These different identifications also lead to dram atically different interpretations of the
postw ar business cycle history in th e U nited States. Figures 5-7 show the 24-month
ahead forecast errors in the unemployment rate, the rate of inflation and the price
level. T he price level forecast error is the percentage error; since the horizon is 24
m onths, this means th a t the average inflation error over th e forecast period can be
determ ined by dividing the price forecast error by 2. T he figures also show the com­
ponent of the forecast error associated w ith realizations of the dem and disturbance.
Table 7 summarizes the total and dem and shock com ponents of the forecast error
for the N B ER dated business cycle peaks and troughs. It is instructive to focus
on two episodes on which one may bring some prior knowledge to bear, namely
(i) the recession th a t began in 73:11 and ended in 75:3; and (ii) the recession th a t
began in 81:7 and ended in 82:11. M any macroeconomists would argue th a t the
former recession was dom inated by a “supply shock,” in the form of energy price
increases, and the latter was dom inated by a “dem and shock” originating in m onetary
policy. As expected from the results sum m arized in Figure 3, the RBC identification
associates essentially all movements in u t to supply shocks in both of these episodes.
In contrast, the TK identification attrib u tes essentially all movements in u t to dem and
disturbances in both episodes. Further, under this identification, the dem and shock
explains 25% of the variance in inflation over the entire period. B ut, in the two
episodes of interest, this dem and-based theory predicts too much disinflation in 1974
and too little in 1982.
T he REM identification yields an interpretation of the U.S. postw ar business cycle
between these two extrem es. The dem and shock accounts for a negligible p a rt of the
unem ploym ent th a t occurred during the 1974 recessions, b u t the bulk of unem ploy­
m ent during the 1982 recession. T h a t is, the to tal 24-m onth-ahead forecast error for
unem ploym ent in 1975:3 represents the “surprise” in unem ploym ent as of 1973:3: it
was 3.37% and the m onetarist model indicates th a t only .20% of this increase was
attrib u ta b le to dem and. Comparably, the forecast error for unem ploym ent in 19S2:11
is the surprise in unem ploym ent as of 1980:11: it is 3.64 % and the m onetarist model
indicates th a t 2.84% of this was demand-induced. This model also indicates th a t
the bulk of the surprise disinflation of the 19S2 recession was due to dem and factors
and th a t there was an im portant effect of supply shocks on inflation and real activity
during the 1974 recession.
nominal output, given exogenous movements in the money supply.




23

4.6

S u m m a r y of Findings

In sum m ary, this section has dem onstrated th a t different ways of interpreting the
dynam ic correlations between unemployment and inflation lead to radically differ­
e n t estim ates of the unemployment-inflation (Phillips Curve) trade-off, the costs of
disinflation and the interpretation of the U.S. postw ar business cycle. Of course,
since our versions of these different models are “ju st identified” in a econom etric
sense, they each fit the d a ta on unem ploym ent and inflation equally well. A dditional
inform ation-econom ic theory, or knowledge of the source of changes in unem ploy­
m ent or inflation in specific episodes-is needed to discrim inate betw een the models.
W e think th a t m ost macroeconomists are likely to find the REM identification m ost
compelling: its long-run predictions square b e tte r w ith th e n atu ral ra te theory, it
provides a balanced decomposition of the influence of supply and dem and shocks on
economic fluctuations, and it performs b e tte r in explaining episodes in which prior
knowledge can plausibly be applied.

5

S ta b ility

o f th e

P h illip s

C u rv e

In this section we investigate the stability of the bivariate relation betw een unem ploy­
m ent and inflation. We do this is three ways. F irst, we exam ine th e stability of the
reduced form VAR using a variety of tests for tim e varying coefficients. Second, we
exam ine th e stability of forecasting equations and forecast perform ance. Finally, we
com pare estim ates of the structural models and their implied Phillips Curve trade-off
over the 1954-69 and 1970-92 periods.

5.1

Stability o f t h e R e d u c e d F o r m

T able 8 sum m arizes results from a variety of tim e varying coefficient tests. Panels A
and B contain results from split-sample Chow tests, using a break d a ta of 1970:1. In
panel A we present tests for each of the two equations in the unem ploym ent-inflation
VAR and for the system as a whole. T he null hypothesis of stab ility is rejected,
and more instability is evident in the inflation equation th a n in the unem ploym ent
equation. Panel B presents tests for stability of univariate autoregressions for unem ­
ploym ent and inflation. Stability is strongly rejected for the inflation process, by not
for the unem ploym ent process.
O ur choice of 1970 as a break d ate is predicated in p a rt on literatu re from the early
1970’s docum enting shifts in the Phillips C urve, and so statistical inference in panels
A and B suffers from pre-testing problems. These problems are remedied in panel C
which sum m arizes results from a variety of statistical tests th a t are not predicated on
a specific break date. The first three tests, labeled Nyblom, PK1 and PK 2 are OLS
versions of tests developed for stochastically varying regression coefficients (e.g., the
CUSUM and CUSUM-squared tests of Brown, D urbin and Evans [1975]), T he final




24

tests, labeled Q, A P and A PI are modifications of the Wald (Chow) split-sam ple test
for the case of an unknown break date. The first is the Q uandt (1960) likelihood ratio
test, which is formed as the maximum of the split-sample W ald tests over all possible
break dates. (Here, the maximum is chosen over all possible dates in the middle
70% of the sam ple.) The A PI and AP2 tests are the A ndrew s-Ploberger average and
average exponential Wald tests over the same possible break dates. (See Andrews,
Lee and Ploberger [1992].) Since all of these tests have different non-standard null
distributions, we do not report the value of the statistics. Instead, th e table lists the
statistics th a t are significant a t the 1%, 5% and 10% levels.
These statistics tell much the same story as the split-sam ple Chow tests in panels A
and B. F irst, there is significant evidence of a shift in th e inflation process. Moreover,
it appears as if this shift occurred in the early 1970’s. T here is also evidence of
in stability in th e unemployment equation in the VAR. For this equation, th e Q uandt
te st finds a m axim um of the Wald statistic in 1959:3; yet th e value of th e statistic
in the early 1970’s is nearly as large as the 1959:3 value. T hus, these tests suggest
a shift in the VAR occurring around 1970. Finally, there is some lim ited evidence of
in stability in the univariate autoregression of unemployment.

5.2

S t a bility o f F o r e c a s t i n g M o d e l s a n d P e r f o r m a n c e

Table 9 and Figure 8 examine the stability of forecasting perform ance over th e sample
period. In Table 9, the root mean square forecasting error (RM SE) is shown for three
forecasting models, over three periods, and for four forecasting horizons. For example,
panel A shows the results for one-step ahead forecasts. The first row of the panel shows
results for a VAR w ith coefficients estim ated over 1954-69; th e next row shows results
from a VAR estim ated over 1970-92, and the final row shows results over 1954-92. The
first two columns show the forecasting performance over 1954-69 for unem ploym ent
and inflation respectively; the next two columns show th a t forecasting perform ance
over 1970-92; and the last two columns summarize the forecasting perform ance over
the entire 1954-92 period.
Two m ajor conclusions follow from this table. First, th e 1954-69 model forecasts
the 1970-92 period nearly as well as the 1970-92 model, and th e 1970-92 m odel fore­
casts the 1954-69 period nearly as will as the 1954-69 model. For exam ple, looking
a t the one-step ahead forecasts over 1970-92, the RM SE’s for th e unem ploym ent rate
are 0.21 for the 1954-69 model versus 0.17 for the 1970-92 model; th e corresponding
R M SE’s for inflation are 3.18 and 2.56. While the differences in R M SE’s are statis­
tically significantly different from one another, they do not signal an overwhelming
failure of the 1954-69 model relative to the 1970-92 model for this period. This con­
clusion obtains for both periods and all forecasting horizons considered in the table.
This relative stability of the forecasting models is evident in Figure 8 which plots the
24-m onth ahead forecast error for both the 1954-69 and the 1970-92 models. While
some differences standout (notably the unemployment forecasts in 1956 and 1960),




25

the forecasts errors for the two model are remarkably similar.
T h e second m ain conclusion from Table 9 is th a t forecasts for horizons 12 m onths
and longer were significantly less accurate in the 1970-92 period th a n in th e 1954-69
period. This result obtains regardless of the VAR model used for forecasting. For
exam ple, using th e full sample VAR, the 24-month ahead RM SE was 2.71 overl95469, and nearly doubled to 4.59 over the 1970-92 period. This forecast deterioration
is also evident for th e unem ploym ent rate a t the 24-month horizon. For horizons less
th a n twelve m onths, there is little apparent deterioration in th e forecasts for either
series.
These forecasting results suggest two broad conclusions ab o u t changes in th e
im pulse-propagation mechanism characterizing the unem ploym ent-inflation VAR. F irst,
since th ere is no deterioration in th e short-run forecasts, there appears to have been
little change in th e variance of shocks across the two periods, a t least when shocks
are lim ited the bivariate process examined here. Second, the deterioration in m edium
to longer-run forecasts in the second period suggests more p ersistent effects of shocks
in th e la tte r period. (By an increase in persistence we mean an increase in th e size
of m oving average coefficients a t long lags. This increase in the m ag n itu d e of moving
average coefficients leads directly to an increase in medium to longer-run forecast
error variances.)
In spite of these changes in th e post-1969 period, the 1954-69 VAR forecasts
perform nearly as well as the 1970-92 VAR, even a t the 24-m onth horizon. This
m eans th a t the intrinsic forecast error in the model dom inates th e erro r arising from
m odel m isspecification. This is shown in Table 10 which shows p o p u latio n R M SE’s
for th e b o th the 1954-69 and 1970-92 forecasting models, assuming first th a t th e d a ta
are generated by th e 1965-69 model and then by the 1970-92 m odel. T h e conclusions
from these population R M SE’s are the same as the sample R M SE’s in T able 9: the
1954-69 m odel forecasts d a ta generated by the 1970-92 model nearly as well as the
optim al forecasting model.

5.3

St a b i l i t y o f S t r u c t u r a l M o d e l s

T he change in the VA R’s propagation mechanism uncovered by th e forecasting com­
parison suggest potential instability in the Phillips Curve trade-off. T his possibility
is exam ined in Table 11 for the three identifying restrictions discussed in section 4.
Panel A presents results for the TI< identification. Consistent w ith th e forecasting
com parisons, there is little change in the very short-run properties of th e m odel. T he
point estim ates of the impulse responses suggest an increase in th e persistence of
dem and disturbances: a t the 48-month horizon the impulse results for unem ploym ent
increases by 50% in th e latter period, and the impulse response for inflation increases
by a factor of 4. This change in th e relative persistence across unem ploym ent and
inflation reduces the estim ated long-run Phillips trade-off in the 1970-92 period. T he
trade-off falls from -1.3 in the early period to -0.6 in the la tte r period. S tan d ard errors




26

are large however, and the t-statistic for this change is only -l.S. T he m odel’s supply
shocks have more persistence effects on the second period, and this is particularly true
for their effect on unem ploym ent. Yet, they still explain only a small fraction of un­
em ploym ent forecast errors: 6% at the 48-month horizon. Panel B shows the results
for the REM identification. In this model, the response of unem ploym ent to dem and
shocks is rem arkably stable across the two periods for all horizons. T he increased
persistence in the inflation rate is accounted for almost entirely by dem and shocks.
Again, the change in the relative persistence of demand shocks across unem ploym ent
and inflation lead to a change in the estim ated Phillips trade-off; in this identification
it falls for -.47 in th e early period to -.23 in the latter period. Finally, panel C shows
the results for the RBC identification; in both periods this m odel behaves like the
TK model w ith th e interpretation of the shocks reversed.
Taken together these results point to a decline in the effect of dem and shocks
on unem ploym ent relative to their effect on inflation. In bo th th e TK and REM
identifications, the point estim ates suggests this relative trade-off has decreased by
approxim ately 50% in the second p art of the sample. As usual in work w ith VAR’s,
these results are tem pered by large standard errors and a resulting lack of statistical
precision.

6

R o b u s tn e s s

o f R e s u lts

In the previous section we provided a detailed exam ination of th e effect of sample
period on estim ates of the Phillips trade-off. In this section we consider the effects
of other changes in our basic specification. We begin by considering u n certainty in
the value of A, and present results for a wide range of values of A. We then consider
the robustness of the m ain findings to: (i) changes in the lag length in th e VAR,
(ii) relaxation of the unit root constraint, (iii) increasing th e sam pling interval from
m onthly to quarterly, (iv) changes in the measure of the aggregate price level, and
(v) incorporating additional indicators of aggregate supply disturbances directly in
the model.
In the previous sections we have discussed structural VAR estim ates conditioned
on three values of A th a t served to identify the VAR. Yet, as discussed in Section 3,
there is some uncertainty in the precise value of A most indicative of th e T I\ and REM
models. Specifically, the standard error associated with the estim ate of A constructed
from the TI< identification is large (see footnote 12), and the point estim ates or A from
the studies of B arro and Rush [1980] and Sargent [1976] ranged from -.07 to -.17, and
were constructed using quarterly rather than m onthly d a ta (see A ppendix B). We now
discuss how uncertainty about this param eter affects the conclusions reached in the
previous sections. Table 12 summarizes of results for values of A ranging from 0.0 to 3.0, using bo th m onthly and quarterly data. Panel A of the tab le shows th e estim ated
Phillips trade-off a t im pact and for the 1-year and 3-year horizon. Panel B shows the
resulting estim ates of the fraction of the forecast errors a ttrib u ta b le to th e identified




27

dem and shock. Looking first a t the results for the m onthly d a ta, the results change
little as A varies from -0.5 to -3.0. For example, as A increases from -3.0 to -0.5, the
estim ated 3-year trade-off increases from -.77 to -.66 and the identified dem and shock
continues to be nearly perfectly correlated with unem ploym ent. On th e o th er hand,
the results change dram atically as A varies from -.15 to -0.03, w ith estim ated 3-year
Phillips trade-offs changing from -.46 to -.15 and correlation betw een th e identified
dem and shock and the unem ploym ent forecast error falling from .85 to .16. Table
12 puts our choice of A in perspective: the TK identification (A = —1.56) equates
edt w ith the forecast error in unemployment; the RBC identification (A = 0.0) equates
est w ith the forecast error in unemployment; and the REM identification (A = —0.07)
a ttrib u te s 50% of the variance in unemployment forecast errors w ith e* an d 50% with
est. Table 11 also includes results for quarterly d a ta for th e range of point estim ates
of A constructed from Barro and Rush [1980]. The quarterly results w ith A = —.07
correspond roughly to the m onthly results w ith A = —.03 and th e q u arterly results
w ith A = —.17 correspond roughly to the m onthly results w ith A = —.07. T hus, our
choice of A = —.07 corresponds to the upper range of the point estim ates from Barro
and R ush [1980].
Table 13 and 14 sum m arize results for eight different specifications of em pirical
model; Table 13 shows the estim ated Phillips trade-off and Table 14 shows th e fore­
cast error variance decomposition. The first row of each panel shows th e baseline
specification used in Sections 4 and 5. The other seven rows show results from m odi­
fications to this baseline specification. Specification 2 relaxes th e u n it root constraint,
and presents results for the VAR estim ated using the levels of inflation and the unem ­
ploym ent rate. W hile this specification makes it impossible to calculate th e long-run
Phillips trade-off; the im pact and m edium-run trade-offs can be calculated. T he only
notable difference between the results for this specification and th e baseline specifi­
cation is the decrease in precision of estim ates a t the 3 year horizon when A = —1.56.
Specification 3 modifies the baseline model by increasing the num ber of lags in the
VAR from 12 to 18. The results are robust to this change.
T he high frequency variability in the inflation rate evident in Figure 1 suggests th a t
th e baseline estim ates m ight be contam inated by m easurem ent error in th e index of
the price level. T he next three specifications investigate this possibility. Specifications
4 and 5 use quarterly averages of the price index and unem ploym ent ra te to help
a tte n u a te any m easurem ent errors in the levels of these series. (Specification 4 uses
4 quarterly lags in the VAR and specification 5 uses 6 lags.) Specification 6 replaces
the quarterly consum er price index with the quarterly gross dom estic pro d u ct price
deflator. T he results from these three specifications are very sim ilar to one another,
and to the baseline m onthly results when A = —1.56 or A = 0.0. T hey differ from
the baseline m onthly results when A = —0.07, and as discussed above are sim ilar the
results for a m onthly model w ith A = —0.03.
Finally, specifications 7 and 8 add an additional supply indicator to th e quarterly
and m onthly specifications. Specifically, following Gordon (19S2, 1990b) we add a




28

m easure of the relative price of food and energy. Letting 7rfe denote the inflation
ra te for food and energy, the VAR is now specified with(7rfe — 7r), A u t and A t * ,
and is identified w ith the additional assum ption th a t (7rfe —7T^) is contem poraneously
exogenous (or equivalently, ordered first in a Wold causal chain). 18 As shown in the
table, the baseline results are robust to this modification.

7

S u m m a ry

a n d

C o n c lu s io n s

In this paper, we study the post-w ar U.S. Phillips correlations and Phillips curve.
T h a t is, we consider the joint (bivariate) time series behavior of U.S. inflation and
unem ploym ent. We use m onthly d a ta over the post-war period, focusing on two
subperiods (1954-1969 and 1970-present) as well as the full period. T he results of
this econom etric investigation can usefully be broken into two parts: tim e series
interactions of inflation and unemployment; and results from bivariate stru ctu ral
models.
We use two econom etric m ethods to determ ine some central features of the joint
behavior of inflation and unemployment. In section 2 of the paper, we explore how
th e links betw een inflation and unemployment depend on w hether we look a t low
frequencies (trend behavior), interm ediate frequencies (business cycle behavior) or
high frequencies (irregular behavior). In sections 4,5, and 6 of th e paper, we use
linear tim e series m ethods to stud}' the reduced form interaction of inflation and
unem ploym ent as well as the stru ctu ral Phillips curve.
We begin by docum enting th a t there is a pronounced, negative correlation of in­
flation and unem ploym ent a t business cycle frequencies, which is rem arkably stable
over the post-w ar period. Lower frequency comovements of inflation and unem ploy­
m ent, however, display links th a t are very unstable across tim e. W hen we tu rn to
a more detailed tim e series characterization of the bivariate process, there are three
notable results. F irst, there is evidence of 1(1) behavior in inflation and unem ploy­
m ent, but no evidence of cointegration. This corresponds to th e idea th a t there are
“stochastic trends” in inflation and unemployment; it sets the stage for stru ctu ral
estim ates relating these trends. Second, there is close to a one-way G ranger causal
structure. T h a t is, in the dynam ic reduced form (forecasting VAR), unem ploym ent
depends mainly on its own one-step-ahead forecast errors while inflation depends on
errors to both inflation and unemployment. Third, there is im p o rtan t evidence of
econom etric instability over subsamples. We begin by using a b attery of tests to doc­
um ent general evidence of changing structure. We then provide a characterization of
how the stru ctu re changes through time, focusing on differences betw een th e pre-1970
18The food and energy price index is formed as a weighted average of the food and energy compo­
nents of the crude material producer price index (PPI). The weights are the relative importance of
these indexes in the December 1992 PPI. (Specifically, we used Citibase series PW1100 and PW1300
with weights 0.66 and 0.34, respectively.)




29

and later sam ple periods. In term s of short-term forecasting, vve find th a t there is lit­
tle difference betw een subperiods: the standard deviation of one-step ahead forecast
error is essentially the same over subperiods, and there are only small differences in
forecast perform ance out to a horizon of twelve m onths. By contrast, there are m ajor
changes th a t affect th e ability to forecast inflation and unem ploym ent in th e longer
term . In particular, the standard deviation of long horizon forecast error (tw o years
and beyond) is much larger in the later period, m ost strikingly for inflation. This is an
indication of increased persistence of th e effects of shocks. It is this increased persis­
tence, not more volatile shocks, th a t makes the post-1970 interval intrinsically more
difficult to forecast. Moreover, m edium to long-term forecasts are affected by p aram ­
e ter instability, b u t this instability - which would suggest th e value of re-estim ating
earlier Phillips curve models over th e 1970 to 1990 period - is swam ped by th e general
increase in th e difficulty of forecasting in the post-1970 period.
In term s of results from stru ctu ral models of inflation and unem ploym ent, we
find some results th a t are surprising. We work in the style of researchers like G or­
don and Solow, who interpreted the Phillips curve structurally, b u t we do this using
stru ctu ral VAR techniques. These procedures require th a t we specify how to m ap
from the forecast errors of the VAR into economically interpretable shocks, i.e ., th a t
we undertake an identification of the Phillips curves system. A lternative identifying
assum ptions have im p o rtan t im plications for the m agnitude of long-run m ultipliers;
for the sources of business cycle fluctuations; for the in terp retatio n of episodes; and
for sacrifice ratios, defined as th e unem ploym ent cost of moving to a perm anently
lower ra te of inflation. We com pute long-run trade-offs between inflation and unem ­
ploym ent, despite the argum ents of Lucas [1972] and Sargent [1971]. As discussed
in Fisher and Seater [1993] and King and W atson [1992], when inflation is an 1(1)
process this is a valid exercise; we provide evidence th a t the d a ta are consistent w ith
the 1(1) restriction for all of the sam ple periods th a t we study.
A traditional Keynesian identification yields: (i) large estim ated long-run tra d e ­
offs between inflation and unem ploym ent, although these fall by 50% in la tte r sam ple
period; (ii) 2 year ahead forecast errors (one measure of business cycle fluctuations)
in which dem and shocks explain essentially all of unemployment and only 25% of in­
flation; (iii) long-run variability in inflation w ith a source th a t is approxim ately 50%
dem and shocks and 50% other (price, supply) shocks. Further, under this identifica­
tion, every m ajo r post-w ar recession is fully explained by dem and shocks (even the
oil price interval) and m ost recession intervals involve a decline in inflation. Finally,
sacrifice ratios - specified as the cum ulative loss in unem ploym ent over a five year
period - of a perm anent disinflation (induced by dem and changes) are large (3.7),
b u t not as large as those in the DRI model (8.0).
By contrast, a real business cycle identification yields very small estim ated trad e­
offs between inflation and unem ploym ent a t all horizons, and 2 year ahead forecast
errors in unem ploym ent th a t are dom inated by identified disturbances. In addition,
all post-w ar recessions are explained by supply shocks (even th e 1981-82 recession).




30

T hus, both the traditional Keynesian and RBC models provide coherent - although
very different - explanations of the postw ar data.
An alternative identified assum ption - suggested by the work of Sargent [1976]
and Barro and Rush [1980] - yields a very different picture of economic fluctuations
in the short and long term : (i) there are much smaller estim ated long-run trad e­
offs between inflation and unemployment th a n in the trad itio n al Keynesian model;
(ii) dem and shocks explain 43% of the two-year forecast error in unem ploym ent and
75% of th a t in inflation; (iii) the long-run variability of inflation is nearly entirely
due to dem and shocks; and (iv) supply shocks have little long-run effect on inflation
bu t have im p o rtan t effects on real activity in both the short and long run. Further,
m ajor post-w ar recessions appear to be a result of a mix of supply and dem and shocks
(even the oil price interval); most recessions continue to involve declines in inflation.
Finally, sacrifice ratios a t the five year horizon are much smaller (1.52) th a n in the
traditional Keynesian model (3.71). Arguably, this identification yields a m ainstream
interpretation of the post-w ar U.S. data.
O ur results reinforce some beliefs of th e neoclassical/m onetarist and Keynesian
schools, but they provide m any more challenges. We highlight three of these results.
F irst, there is there is evidence for the Lucas-Sargent hypothesis: increased persis­
tence of inflation reduces the long-run Phillips curve slope. However, the inflationunem ploym ent trade-off slope is also affected by short-run identifications in a way
th a t is a t least as im portant quantitatively. Second, the tim e series evidence indi­
cates why Keynesian macroeconometricians have seen little reason to change their
practices, except for potentially “patching up” the long-run slope of the Phillips
curve. T h a t is, they have seen relatively little evidence of instability over horizons of
interest (forecasts of up to a year). W hile the quality of longer-run forecasts of both
inflation and unem ploym ent have deteriorated in the post-1970 period, the deteriora­
tion reflects an increase in the intrinsic uncertainty surrounding longer-run forecasts
of these series. Little improvement is achieved by updating th e forecasting equations
estim ated through 1969. T hird, the Phillips curve at every horizon is more unstable
across identifications than it is across time: a t shorter horizons, the identification is
essentially all th a t m atters.
Thus, as a result of our investigation, it is hard for a neoclassical m onetarist
economist to argue th a t the Phillips correlations are absent from the U.S. d a ta or
th a t a stru ctu ral Phillips curve is unstable in the short run. W hile traditional Key­
nesian macroeconom etricians may take comfort in the stability of the short-term
Phillips curve, we think th a t few other macroeconomists will find th a t their short-run
identifications generate a plausible description of post-war U.S. business cycles.




31

R e fe re n c e s
[1] A nderson, L.C. and K.M. Carlson (1972), “An Econom etric Analysis of the Re­
lation of M onetary Variables to the Behavior of Prices and U nem ploym ent,” in
T h e E c o n o m e tr ic s o f P rice D e te r m in a tio n , (ed.) 0 . Eckstein.. W ashington, D.C.:
B oard of Governors of the Federal Reserve System.
[2] Andrews, D .W .K ., I. Lee and W. Ploberger (1992), “O ptim al C hangepoint Tests
for Norm al Linear Regression,” Cowles Foundation working p aper no. 1016, Yale
University.
[3] Ball, L. (1993), “W hat Determines the Sacrifice R atio?” , m anuscript, Princeton
University.
[4] B arro, R .J. and M .Rush (1980), “U nanticipated Money and Economic A ctivity,”
in R a tio n a l E x p e c ta tio n s a n d E c o n o m ic P o licy, (ed.) S. Fischer, Chicago, IL:
U niversity of Chicago Press.
[5] B axter, M., and R.G. King (1993), “M easuring Business Cycles: A pproxim ate
B and-Pass Filters for Economic Tim e Series,” m anuscript, U niversity of Virginia.
[6] Beveridge, S. and C.R. Nelson (1981), “A New Approach to th e Decomposition of
Tim e Series in Perm anent and Transitory C om ponents w ith P articu lar A ttention
to the M easurem ent of the Business Cycle,” J o u r n a l o f M o n e ta r y E c o n o m ic s, 7:
151-74.
[7] Brown, R.L., J. D urbin and J.M . Evans (1975), “Techniques for Testing the Con­
stancy of Regression Relationships Over T im e,” Journal of th e Royal Statistical
Society, Series B , 37: 149-63.
[8] Eckstein, 0 . (1972), The E c o n o m e tric s o f P ric e D e te r m in a tio n , W ashington,
D.C.: B oard of Governors of the Federal Reserve System.
[9] Eckstein, O. (1981), C ore In fla tio n , Englewood Cliffs, N .J.: Prentice-H all.
[10] Eckstein, O. and G. Fromm (1968), “The Price E quation,” A m e r ic a n E c o n o m ic
R ev iew , 58: 1159-1183.
[11] Fischer, S.(1977),“Long-term C ontracts, R ational E xpectations, and the O ptim al
Money Supply Rule,” J o u r n a l o f P o litica l E c o n o m y , 85: 191-205.
[12] Fisher, M., and J. Seater (1993), “Long-Run N eutrality and S uperneutrality in
an ARIMA framework,” A m e r ic a n E c o n o m ic R eview , 83: 402:415.13
[13] Friedm an, M. (1968), “The Role of M onetary Policy,” A m e r ic a n E c o n o m ic R e ­
view , 58: 1-17.




32

[14] G ordon, R .J. (1970), “The Recent Acceleration of Inflation and Its Lessons for
the F uture,” B ro o k in g s P apers on E co n o m ic A c tiv ity , 1: 8-41.
[15] G ordon, R .J. (1971), “Prices in 1970: The Horizontal Phillips C urve,” iBrookings
P a p e rs on E c o n o m ic A c tiv ity , 3: 449-58.
[16] G ordon, R obert J. (1982), “Price Inertia and Ineffectiveness in th e United States,
1890-1980,” J o u r n a l o f P olitical E co n o m y, 90: 1087-1117.
[17] G ordon, R obert J. (1990a), “Comments: The Phillips Curve Now and T hen,” in
G r o w th /P r o d u c tiv ity /U n e m p lo y m e n t, (ed.) P. Diamond Cam bridge, MA: MIT
Press.
[18] G ordon, R obert J. (1990b), “W hat is New-Keynesian Economics?” J o u r n a l o f
E c o n o m ic L ite ra tu re , 28: 1115-1171.
[19] G ordon, R .J. and S. King (1982), “The O utput Cost of Disinflation in T raditional
and Vector Autoregressive Models,” B rookings P a p ers on E c o n o m ic A c tiv ity , 1:
205-44.
[20] G ranger, C. (1969), “Investigating Causal Relations by Econom etric models and
C ross-spectral M ethods,” E co n o m e tric a , 34:150-161.
[21] Gray, J. (1976), “Wage Indexation: A Macroeconomic A pproach,” J o u r n a l o f
M o n e ta r y E c o n o m ic s, 2: 221-235.
[22] Hansen, B.E. (1991), “Tests for Param eter Instability in Regressions with 1(1)
Processes,” J o u r n a l o f B u sin e ss an d E co n o m ic S ta tis tic s, 10: 321-36.
[23] H ansen, L.P. and T .J. Sargent (1980), “Formulating and E stim ating Dynamic
Linear R ational Expectations Models,” J o u rn a l o f E c o n o m ic D y n a m ic s a n d C o n ­
trol, 2: 7-46.
[24] Hicks, J. (1937), “Mr. Keynes and the Classics,” E c o n o m e tr ic a , 5:147-159.
[25] King, R.G ., and M.W. W atson (1992), “Testing Long Run N eutrality,” N ational
B ureau of Economic Research working paper no. 4156.
[26] Klein, L. (1950), E co n o m ic F lu ctu a tio n s in the U nited S ta te s , New York: John
W iley and Sons.
[27] Lucas, R.E., Jr. (1972), “Econometric Testing of the N atural R ate H ypothesis,”
in T h e E c o n o m e tric s o f P rice D e te rm in a tio n , (ed.) 0 . Eckstein.. W ashington,
D.C.: Board of Governors of the Federal Reserve System. 28
[28] Lucas, R.E., Jr. and T .J. Sargent (1979), “After Keynesian M acroeconom etrics,”
in A f te r the P h illip s C urve: P ersiste n ce o f H igh In fla tio n a n d U n e m p lo y m e n t,
Federal Reserve Bank of Boston, Conference Series No. 19.




33

[29] M ankiw , N. G. (1990), “A Quick Refresher Course in M acroeconom ics,” J o u r n a l
o f E c o n o m ic L ite ra tu re , 28: 1645-60.
[30] M odigliani,F. (1944) “Liquidity Preference and the Theory of In terest and
M oney,” E c o n o m e tric a , 12: 45-88.
[31] Nyblom, J. (1989), “Testing for the Constancy of Param eters O ver T im e,” J o u r ­
n a l o f th e A m e r ic a n S ta tis tic a l A sso c ia tio n , 84:223-30.
[32] Ploberger, W . and W. Kram er (1991), “A Trend-R esistant Test of S tru ctu ral
C hange Based on OLS-Residuals,” m anuscript, Yale U niversity and U niversity
of D ortm und (G erm any).
[33] Phelps, E..(1967), “Phillips Curves, Expectations of Inflation, and O ptim al In­
flation O ver Tim e,” E conom ica, NS 34: 254-281.
[34] Phelps, E. and J. B. Taylor (1977), “Stabilization Powers of M oneatry Policy
Under R ational Expectations,” J o u r n a l o f P olitical E c o n o m y , 85: 163-90.
[35] Phillips, A.W .H. (1958), “The Relation Between U nemployment and th e R ate
of C hange of Money Wages in the United Kingdom, 1861-1957,” E c o n o m ic a , NS
25: 283-299.
[36] R oberts, J., (1993), “The Sources of Business Cycles: A M onetarist In te rp reta ­
tion ” , I n te r n a tio n a l E c o n o m ic R eview , 34: 923-934.
[37] Q u an d t, R.E. (1960), “Tests of the Hypothesis th a t a Linear Regression System
Obeys Tw o Separate Regimes,” J o u r n a l o f the A m e r ic a n S ta tis tic a l A s s o c ia tio n ,
55: 324-330.
[38] Sam uelson, P aul A. and Robert M. Solow (1960), “A nalytical A spects of AntiInflation Policy,” A m e r ic a n E c o n o m ic R eview , P apers a n d P roceedings, 50:177194.
[39] Sargent, T .J . (1971), “A Note on the Accelerationist Controversy,” J o u r n a l o f
M o n e y , C red it a n d B anking, 3: 50-60.
[40] Sargent, T .J. (1976), “A Classical Macroeconometric Model for th e U nited
S tates,” J o u r n a l o f P o litica l E c o n o m y, 84: 207-37.
[41] Sargent, T .J . (1979), M acroeconom ic T heory, Orlando, FL: Academic Press.
[42] Solow, R.M. (1969), P rice E xp e cta tio n s an d the P h illip s C urve, M anchester, UK:
M anchester University Press.43
[43] Solow, R.M. (1970), “Discussion of R .J. G ordon’s The R ecent A cceleration of
Inflation and Its Lessons for the Future,” B rookings P a p ers on E c o n o m ic A c tiv ity ,
1 : 42-6.




34

[44] Stock, J.H . (1991), “Confidence Intervals of the Largest Autoregressive Root in
U.S. M acroeconomic Tim e Series,” J o u rn a l o f M o n e ta r y E c o n o m ic s, 28: 435460.




35

A

D e riv a tio n

o f T h e o re tic a l R e s u lts

In this appendix we provide some background for results stated in section 3 of the
m ain test. In th a t section, we considered the structural model:
(22)

Ut = f Xt -'% 2 g iE t-i'X t + s t ,

X—1
7Tt =

p 1 7rt _ 1 +

. . . . / > n 7Tt _ n +

(23)

m *,

where s t and m t are ii d zero-mean random variables. The model has a rational ex­
pectations reduced form
<?+n
== ^ ^ PuTT^t-i “t“ $t =
t=l

4" Sti

( 2 ^)

and our first goal is to show th a t /?UJr(l) = J2f=i Pu*,i = / —Ylt= i 9> if th ere is a single
unit root in th e inflation generating process.
To begin, w rite (23) as p(L)-7Tt = m t , and assume th a t p ( z ) has one u n it root and
all other roots outside the unite circle. Define by <j>(z) by p { z ) — (1 —z)<f>(z), so th a t
A n t = 7t£—7rt_i is stationary with moving average representation A tt£ = <j>(L)~l m t =
p ( L ) m t . T hen,

Et-jAirt = pjint-j+ p.j+imt-j+i-f ....
=
=

[L~j p (L )] + m t
[ L -i p ( L ) ) +<f>(L) A x t

where [-]+ m eans "ignore negative powers of V
Further,

(25)

as in Hansen and Sargent [1980].

+ A - ,_ J+1 + ....Ar,}
=

{1 + S . , [ £ - V

=

K j{L )ir t-j,

( £ ) ] + (1

-£)}*«-,•■

(26)

where *,-(1) = lf o r all j. Thus, in(24):
/?utt(L )ict =
=
=

f 7Tt - Y ,U 1 QiEt-i-Kt
f * t - I l L \ 9 i* i(L )K t- i

{/-Ei=i5.«.(r)T‘}7rt

So th a t 0 un( z ) = { / - E i= i 9 iKi{z ) z '} and P u*{l) = { / - E L iP i} as required.
In section 3, we also wrote (24) as




36

(27)

Q
u t = { / - ^ 2 g i } f i ( l ) M t + tp (L )m t -f s t

(28)

:'=1
where M t = M t - i +
is a m a r t i n g a l e , i s a stationary com ponent of un­
em ploym ent arising from dem and shocks, and where A irt = /j,(L )m t is the moving
average representation for A ir t. We will derive (28) under the assum ption th a t fi{ L )
is 1-summable; thus (28) is valid when n t is 1(1), so th a t fi(L ) = 4>{L)~l as above, or
when 7rt is 1(0), so th a t f.i{L) = (1 — Z-)/j(L)-1.
To derive (28), let
denote th e perm anent component inflation as in Beveridge
and Nelson [1981]: if* = limjt—oo
*. Since wt+j =
+ { A ir t -f A7rt+i -f ...

Etnt+

=

xt-i+lim^ooELo^^^+i
**-i + lim^oo T
,l=0[L~jv(L)]+mt

—

if t- i + ^ ( l ) m (

7rt =

^ 9)

= /*(l)A/f,
from the 1-sum m ability of fi(L ) and the definitions of ift and M t . Notice th a t if
inflation is 1(0), then /x(l)
= 0 and there is no variation in trend inflation. By
contrast, if inflation contains a unit root, then there is tim e series variation in 7ft
since //(l) =
is non-zero.. ■
Now, w rite (22) as:
9

9

ut = { / -

+ ( X ! 9i{*t ~ E t - i n t )} + s t .
1= 1

*= 1

(30)

Decompose Ttt =
+ /r*(L)m<, where pt*{z) =
W hen f.t{L) is 1sum m able, fi*( 1) = 0, so th a t pLm{ L ) m t can be interpreted as a ’’tem porary com­
p onent” . Com bining these expressions, we can write:
9

u t = { / ~ Y ^ 9 i } ^ t + ip (L )m t + St.

(31)

;=i
where ip ( L ) m t = {£?=i g ^ t - £ t_t-7rt)} + { / - £ ? _ 1g i}g .* {L )m t. E quation (2S) follows
from (29) and (31).




37

B

R E M

E s tim a te s o f th e S h o rt-R u n P h illip s C u rv e

As our value of the short-run Phillips curve slope from the rational expectations
m onetarist (R EM ) literature, we use A = —.07. In this appendix, we show how
estim ates in this range m ay be derived from the REM studies of Sargent [1976] and
B arro and Rush [1980].

B.l

S a r g e n t ’s S h o r t - R u n Phillips C u r v e

T he short-run Phillips curve estim ated by Sargent [1976, Table 9] takes th e form:
u t = —0.287(Pt — E t- \ P t ) + predeterm ined variables -f et

T h a t is, unem ploym ent innovations are attrib u tab le to a price level forecast error
and a shock term . (In this expression, P t denotes the logarithm of th e price level
a t d a te t, represented empirically by th e GNP deflator.) The predeterm ined p a rt of
unem ploym ent,
is explained by its own lags as well as by a constant plus
determ inistic trend. Since his model suggested th a t u t and P t — E t~ \P t would be
jointly determ ined, Sargent estim ated this specification by in stru m en tal variables.
He estim ated his m odel on quarterly, U.S. d a ta from 1947 to 1978.
To relate S argent’s specification to ours, we simply note th a t the annualized in­
flation rate, 7r* = A (P t — P t - i). Further, forecasting errors for the price level and
inflation ra te coincide (up to a scaling factor) if P t- i is an elem ent of th e inform a­
tion set on which E t~ iP t is based, as it is in Sargents analysis and outs. T hus,
7T( — E t - i ^ t = 4 ( jPt — E t- \ P t ). Hence, Sargent’s estim ator of A is —.287/4 = —.07.

B.2

T h e Barro a n d R u s h Slope Estimate

One can derive an im plicit instrum ental variables estim ator of A from th e work of
Barro and Rush [1980] on the effects of unanticipated money growth on unem ploym ent
and the price level.
These au th o rs’ estim ates may be interpreted as pertaining to th e unem ploym ent
rate and the price level, as in:
u t = AuAf(Mt — E t- i M t ) + predeterm ined variables + Cut

Pt = ^ P M ^ t +

— E t - i M t ) + predeterm ined variables + t p t

T he price level is positively affected by the level of the money stock (ApA/ = 1)
and negatively by unanticipated money when th a t raises o u tp u t. T he overall price




38

level effect of a money shock is X pm = (ApA/ -f ApA/) > 0. Thus, we can form an
implicit instrumental variables estimator of our A parameter as:
\

—

"4A P M -

That is, the Barro-Rush estimator determines the short-run slope as the effect
of monetary induced price changes on unemployment. As in the Sargent analysis,
we must scale price level surprises by 4 to convert them into surprises in our annual
inflation rate.
A complication arises from the fact that the Barro-Rush unemployment equation
is actually estimated using a dependent variable of the form x t = log(ut/ ( l —u*)).
Hence, we must scale estimates of Axm by ^ = u(l —u) ~ .05.
There are a battery of estimates in Barro and Rush [1980], which are differentiated
by various assumptions about whether the constraint that APM = 1 is imposed, serial
correlation correction, lag length, etc. The largest magnitude of the short-run slope
comes about when Arm = —4.0 and \ p m — AlPM -f \ 2PM = .30 : these are the point
estimates in the final columns of Tables 2.1 and 2.2.
d u Xxm
dx

_

—4.0
4(.30)

4Ap m

-.17.

This Aestimate involves the smallest estimated short-run effect of money on prices.
Using another estimate of Ap m = \ lPM + A2PM = .63 provides a value of A that is
less than one-half as large in magnitude and, hence, is very close to that of Sargent.
Perhaps this coincidence is not surprising since one of Sargent’s instrumental variables
was the unexpected component of money.




39

Figure 1

P e r c e n t (A n n u a l R a t e )

A. Inflation

Date

Percent

B. U n e m p lo y m e n t R a t e

Notes: Panel A:
(thick line).



Raw Data (thin line), Centered 13-Month Moving Average

Figure 2

Percent

A.TrendComponents

Percent

8.BusinessCycleComponents

Percent

C.HighFrequencyComponents

Notes:




Unemployment (solid line), Inflation (dashed line).

Figure 3:
The Price Equation/Supply Curve

in fla tio n

Note:




The price equation interpretation of this figure is that 7 r = a u + p,
so that the slope is "a" and the vertical shift is the price shock
"p". The supply curve interpretation is that u = f 7T + s, so the
slope is (1/f) and the horizontal displacement is "s". These models
are observationally equivalent with f = (1/a) and s = — (1/a) p.

Figure 4
RBC Modal(X-0.00)
RatponsaToDamond Shock

REM Modal(X--0.07)
Response ToOamond Shock

12
24
36
FroclionofVorioncafromOemond Shock

Notes:




Panels A and B: Unemployment (solid line), Inflation (dashed line).
Panel C: Point Estimate (solid line), ± 2 Standard Errors (dotted line)

TK Modal (X--I.6C)
Ratponsa ToDamond Shock

Figure 5. 24-Month Ahead Forecast Errors
RBC Identification (A—0.00)

Unemployment

Prices(7.Error)

Notes:



Total Error (thick line), Demand Shock Component (thin line)

Figure 6. 24-Month Ahead Forecast Errors
REM Identification (A--0.07)

Unemployment

Inflotion(7.AnnuotRote)

Prices (7. Error)

Notes:



Total Error (thick line), Demand Shock Component (thin line)

Figure 7. 24-Month Ahead Forecast Errors
TK Identification (A--1.56)

Unemployment

Inflation(XAnnua!Rata)

Prices(7.Error)

Notes:



Total Error (thick line), Demand Shock Component (thin line)

Figure 8.

24-Month Ahead Forecast Errors

Unem ploym ent

Inflation

Notes:




1954-69 VAR (thick line), 1970-72 VAR (thin line)

Table 1
Estimated Long-Run Phillips Curve Trade-offs

--Sample Period

Identifying Restriction ---

Keynesian

Monetarist

1954-69

-1.30

-0.47

1970-92

-0.57

-0.23

1954-92

-0.71

-0.29

Notes: The long-run trade-off is defined as l^mic-^cot^ut + k ^ ed t ^ ^ 7rt+k/^£dt
where




denotes a "demand" shock, defined formally in Sections 3 and 4.

Table 2
Summary Statistics

Unemployment Rate
Sample Period

X

s

Inflation
X

S

1950-53

3.61

1.08

3.27

5.27

1954-92

5.98

1.54

4.27

3.98

1954-59

5.11

1.03

1.48

3.28

1960-69

4.77

1.07

2.48

2.66

1970-79

6.22

1.16

7.12

3.81

1980-92

7.11

1.38

4.73

3.71

Notes:

X denotes the sample mean and S denotes the sample standard

deviation.




Table 3
Unit Root Statistics

Series

Sample Period

Larg. AR Root

tn

95% Conf. Interv;

Unemp.

1954-92

0.97

-2.05

(.97

1.01)

Unemp.

1954-69

0.97

-1.15

(.97

1.02)

Unemp.

1970-92

0.94

-3.12

(.89

1.00)

Infl.

1954-92

0.98

-2.34

(.96

1.01)

Infl.

1954-69

0.97

-1.04

(.97

1.02)

Infl.

1970-92

0.96

-2.09

(.94

1.01)

Note:

These results are based on a univariate VAR(12) including a constant
A

term.

denotes the t-tstatistic testing that the sum of AR coefficients is

equal to 1.

The 95% confidence intervals are constructed from

procedure developed in Stock (1991).




using the

Table 4
Summary of Results From Structral Models, 1954:1-1992:12

A. Traditional Keynesian Model (\~-l.56)

Lae
1
12
24
36
48
CO

Demand IRF
Unemp.
Inf 1.
-0.19
0.12
(0.23)
(0.37)
0.61
-0.37
(0.73)
(1.19)
0.36
-0.24
(0.48)
(0.71)
0.37
-0.27
(0.73)
(0.55)
0.38
-0.27
(0.75)
(0.54)
0.38
-0.27
(0.74)
(0.53)

Demand Var.. Dec.
Inf 1.
Unemp.
0.00
1.00
(0.00)
(0.01)
0.99
0.15
(0.12)
(0.30)
0.99
0.25
(0.12)
(0.70)
0.99
0.27
(0.12)
(0.82)
0.29
0.99
(0.93)
(0.11)
0.99
0.37
(1.36)
(0.11)

PC Trade-off
-1.56
(0.00)
-0.63
(0.16)
-0.66
(0.11)
-0.74
(0.13)
-0.70
(0.13)
-0.71
(0.12)

B . Rational Expectations Monetarist Model (X*=-0.07)

Lag
1
12
24
36
48
CO

Demand IRF
Infl.
Unemp.
1.91
-0.13
(0.07)
(0.01)
0.84
-0.24
(0.14)
(0.04)
0.56
-0.15
(0.08)
(0.04)
-0.18
0.60
(0.08)
(0.03)
0.61
-0.18
(0.08)
(0.03)
0.60
-0.18
(0.08)
(0.03)

Demand Var. Dec.
Unemp.
Infl.
0.52
0.52
(0.04)
(0.04)
0.68
0.43
(0.04)
(0.09)
0.42
0.77
(0.04)
(0.10)
0.81
0.42
(0.04)
(0.10)
0.84
0.42
(0.04)
(0.11)
0.42
0.96
(0.03)
(0.11)

PC Trade-off
-0.07
(0.00)
-0.32
(0.07)
-0.27
(0.05)
-0.30
(0.05)
-0.29
(0.05)
-0.29
(0.05)

c. Real Business Cycle Model ( \ ~ 0 . 0 0 )
Lag
1
12
24
36
48
CO

Demand IRF
Infl.
Unemp.
0.00
2.64
(0.14)
(0.00)
0.03
0.58
(0.04)
(0.13)
0.02
0.43
(0.03)
(0.07)
0.48
0.03
(0.03)
(0.07)
0.03
0.48
(0.03)
(0.07)
0.03
0.48
(0.03)
(0.07)

Demand Var. Dec.
Unemp.
Infl.
0.00
1.00
(0.00)
(0.00)
0.85
0.01
(0.04)
(0.02)
0.01
0.75
(0.02)
(0.07)
0.01
0.73
(0.02)
(0.08)
0.01
0.71
(0.02)
(0.09)
0.01
0.62
(0.02)
(0.11)

Note: Estimated standard errors are shown in parentheses.




PC Trade-off
0.00
(0.00)
0.09
(0.11)
0.05
(0.06)
0.06
(0.07)
0.06
(0.07)
0.06
(0.07)

Table 5
Summary of the Reduced Form VAR

Aut -

a(L)Aut

^ + b(L)A7rt + e u t

A7Tt -

c ( L ) A u t ^ + d(L)A7rt + e ^ t

Sums of Coefficients:
Parameter
a(l)
b(l)
c(l)
d(l)

Estimate (SE)
.36 (.10)
.04 (.04)
-6.83 (1.41)
-4.16 (.59)

Residual Covariance Matrix:
sd(e ) - .190
sd(ejr) - 2.717
cor(eu ,ejr)=- .05

Granger-Causality Test Statistics:
Hypothesis

b(L)=0
d(L)=0

F-Statistic (p-values)
1.23 (0.26)
3.42 (0.00)

Notes: The estimates are constructed from a VAR(12), including a constant,
estimated over 1954:1-1992:12.




Table 6
Sacrifice Ratios For Permanent Reductions in Inflation
A . R e s u l t s f o r t h e B i v a r i a t e VAR
Horizon
(Months)
0
12
24
36
48
60

u
0..49
(0..10)
0..90
(0.•16)
0..64
(0. 12)
0,.73
(0..13)
0..71
(0. 13)
0..71
(0. 12)

-- 1rK -7r
-0..31
(0..07)
-1..42
(0. 24)
-0..96
(0..08)
-0..98
(0..04)
-1..01
(0..03)
-1..00
(0..01)

SR
0..04
(0. 01)
0. 87
(0. 17)
1. 60
(0. 28)
2.,28
(0..40)
3. 01
(0.,53)
3. 71
(0. 65)

u
0,.22
(0..03)
0..36
(0..06)
0..26
(0..05)
0..30
(0..04)
0..29
(0. 05)
0..29
(0..05)

R E M ................. RBC
n
SR
u
7T
0.00
-3.17
0.02
-5.55
(0.40) (0.00)
(0.00) (0.77)
0.36
-1.12
-0.08
-0.88
(0.16) (0.04)
(0.09) (0.22)
-0.96
0.66
-0.05
-0.96
(0.05) (0.09)
(0.06) (0.05)
0.94
-0.99
-0.06
-1.00
(0.02) (0.14)
(0.07) (0.02)
-1.01
1.23
-0.06
-1.00
(0.01) (0.18)
(0.07) (0.01)
-1.00
1.52
-0.06
-1.00
(0.00) (0.23)
(0.07) (0.00)

SR
0.00
(0.00)
-0.07
(0.06)
-0.12
(0.13)
-0.18
(0.20)
-0.23
(0.26)
-0.29
(0.33)

B. Simulations from the DRI Model
Horizon
(Years)
0
1
2
3
4
5

u
0.2
0.9
1.4
1.6
1.8
2.1

Core Inflation
0.0
-0.1
-0.3
-0.6
-0.9
-1.0

SR
0.2
1.1
2.5
4.1
5.9
8.0

Notes: TK denotes the model A=-1.56, REM the model with A=-0.07 and RBC the
model with A=0.

The results in Panel A are calculated from the impulse

responses summarized in Figure 3.

They show the estimated responses for

unemployment (u) and the inflation rate (tt) corresponding to an impulse in
that eventually lowers inflation by 1%. The sacrifice ratio (SR) is the
accumulated number of annual unemployment percentage points attributed to this
shock.

Estimated standard errors are shown in parentheses.

Panel B are taken from Eckstein (1981, Table 6.2, page 46).




The results in

Table 7
Twenty-four Month Ahead Forecast Errors and Demand Shock Component
NBER Cyclical Turning Points

A . Cyclical Peaks
--- Unemployment ■
Total

--- Demand

Inflation

—

Total

—

Demand

Price Level
Total

—

Demand

Date

TK

57:8

-0.62 -0.77 -1.08

60:4

-2.07 -1.96

69:12

-0.32 -0.39 -0.46

0.07

1.82

0.38

0.73

73:11

-1.24 -1.46 -1.70

0.22

5.75

2.33

4.74

80:1

-0.37 -0.63 -1.76

0.26

8.55

1.10

5.99

7.45

7.69

0.77 *-0.09

-1.12

-2.07

-1.95

0.95

-1.59

2.51

0.72

0.38

1.78

0.10

0.63

81:7
90:7

1.28

1.37

—

TK

REM

RBC

TK

REM

RBC

0.15

2.02

1.11

2.31

0.91

5.45

1.52

5.00

3.93

0.64 -0.31

0.78

3.61

-0.02 -2.83

0.54

4.56

2.70 -4.02

1.44

1.38

0.57

1.35

0.81

3.41

3.94

1.70

3.71

2.23

1.63

6.45

6.05

-2.55

-2.43

1.19

REM

-0.25 -0.28 -0.03

RBC

0.03

0.36 -0.53

B. Cyclical Troughs
iniiation

unemployment
Total
Date

—

Demand

—

TK

REM

RBC

Total

—
TK__

Price Level "

Demand ----

Total

—

REM

RBC

0.05

4.88

5.52

-0.70

-0.38

0.53

TK__

Demand

—

REM

RBC

2.81

6.21

58:4

3.18

3.00

0.51

0.18

1.84

-3.04

61:2

0.87

0.88

0.64 -0.02

-1.75

-0.60

-1.65 -1.15

70:11

2.38

2.30

0.70

0.09

0.65

-2.14

-2.10

2.80

0.57

-1.44

-0.96

75:3

3.37

3.06

0.20

0.32

-1.11

-3.46

-0.22

2.35

6.20

-0.80

3.55

7.00

80:7

1.18

0.85 -0.56

0.34

-1.54

-1.08

0.63 -0.47

6.16

1.44

5.01

4.71

82:11

3.64

3.74

2.84 •-0.09

-10.99

91:4

1.19

1.20

0.58 ■-0.01

-3.67

-0.49 -0.90

2.00

-4.63 -10.94 -6.36

-8.25

-3.59

-8.81 -4.66

-1.08

-2.19

-0.66

-2.33 -1.53

-3.54 -2.59

Notes: TK denotes the model with A=-1.56, REM denotes the model with A*-.07,
and RBC denotes the model with A=0.09. Inflation is average of forecast errors
(% AR) with ±1 month of trough. Price level is in percentage points




Table 8
Stability Tests for the Autoregressions

A.

Chow Tests for A Single break in 1970 -- VAR
Wald Statistic (df)
41.3 (25)
47.9 (25)
88.7 (50)

Equation:
Unemploment Equation
Inflation Equation
Both Equations

B.

P-Value
.021
.004
.001

Chow Tests for a Single break in 1970 -- Univariate Autoregress
Wald Statistic (df)
16.3 (13)
28.4 (13)

Eauation:
Unemploment Equation
Inflation Equation

P-Value
.231
.008

C . Alternative Tests for instability in autoregress ions

Specification
Unem. (Univ.)
Unem. (Biv.)
Infl. (Univ.)
Infl. (Biv.)

.. .............Stability T e s t ...............
Nyblom
PK2
API
PK1
AP2
Q
**
:k
**
***
•kick
kkk
-

-

-

kkk
***

kkk
***

:kkk
kkk

Qdate
59:3
59:3
74:8
74:8

Notes: All regressions contained a constant terra and twelve lags. The Wald
statistics in Panels A and B allowed difference error covariance matrices in
the two sub-samples. The entries in Panel C represent: not significant at the
10% level (-), and signficant at the 10% level (*), 5% level (**), and 1% level
(***)# Nyblom denotes Nyblom's (1989) test, robustified as in Hansen (1991);
PK1 and PK2 are the CUSUM and CUSUM^ tests from Ploberger and Kramer (1991). Q
is the Quandt (1960) likelihood ratio test for discrete change in coefficients
at an unknown time, calculated as the maximum of the standard Wald test
statistic calculated over all dates in the middle 70% of the sample. API and
AP2 are the mean Wald and mean exponential Wald tests over all possible break
dates in the middle 70% of the sample period. (See Andrews, Lee and Ploberger
[1992].) Qdate is the date corresponding to the maximum for the Quandt
statistic.




Table 9
Root Mean Squared Error for Models Estimated
Over Different Sample Periods

A. 1-Step Ahead Forecast Error RMSE

Estimation Period
1954:1-1969:12
1970:1-1992:12
1954:1-1992:12

1954:1-1969:12
Unemp.
Infl.
0.182
2.459
0.214
3.002
0.192
2.643

Forecasting Period
1970:1-1992:12
Unemp
Infl.
0.208
3.177
0.174
2.560
0.180
2.643

1954:1-1992:12
Unemp.
Infl.
0.198
2.904
0.192
2.750
0.185
2.750

B. 6-Step Ahead Forecast Error RMSE

Estimation Period
1954:1-1969:12
1970:1-1992:12
1954:1-1992:12

1954:1-1969:12
Unemp.
Infl.
0.560
2.515
0.700
2.666
0.605
2.557

Forecasting Period
1970:1-1992:12
Unemp
Infl.
0.748
3.203
0.609
3.125
0.639
3.150

1954:1-1992:12
Unemp.
Infl.
0.677
2.940
0.648
2.945
0.625
2.945

C. 12-Step Ahead Forecast Error RMSE

Estimation Period
1954:1-1969:12
1970:1-1992:12
1954:1-1992:12

---------------1954:1-1969:12
Unemp
Infl.
0.905
2.625
3.033
1.182
2.730
0.977

Forecasting Period
1970:1-1992:12
Unemp
Infl.
3.804
1.344
1.104
3.527
1.178
3.597

1954:1-1992:12
Unemp.
Infl.
1.184
3.371
1.137
3.333
1.100
3.333

D. 24-Step Ahead Forecast Error RMSE

Estimation Period
1954:1-1969:12
1970:1-1992:12
1954:1-1992:12

1954:1-1969:12
Unemp.
Infl,
1.050
2.680
1.277
2.881
1.101
2.708

Forecasting Period
1970:1-1992:12
Unemp.
Infl.
1.851
4.747
1.680
4.482
1.751
4.592

1954:1-1992:12
Unemp.
Infl,
1.573
4.029
1.528
3.906
1.519
3.906

Notes: The entries in the table refer to the root mean square forecast error
for unemployment and inflation for the forecasting period shown. For example,
the forecast error dated 1954:1 is the forecast error for 1954:1 using
forecasts computed in earlier periods. The forecasts were formed using VAR(12)
models (including a constant) estimated over the periods given in the first
column of the table.




Table 10
Population Standard Errors for Forecasts from
Estimated Sub-Sample Models

A . Unemployment Rate

Forecast
Horizon
i
6
12
24

DGP: 54-69 Model
Forecast Model
70-92
54-69
0.18
0.21
0.58
0.69
0.94
1.14
1.12
1.21

DGP: 70-92 Model
Forecast Model
54-69
70-92
0.21
0.17
0.61
0.73
1.28
1.11
1.77
1.72

B. Inflation Rate

Forecast
Horizon
i
6
12
24

DGP: 54-69 Model
Forecast Model
54-69
70-92
2.98
2.46
2.55
2.65
2.77
3.02
3.05
3.18

DGP: 70-92 Model
Forecast Model
54-69
70-92
3.17
2.56
3.19
3.12
3.79
3.61
4.61
4.53

Notes: Each entry in the table is the population standard error of the
forecast constructed from models estimated over either 1954-69 or 1970-92.
The first two columns of entries assume that the data are generated by the 54
69 model (so that the 54-69 model is the optimal forecasting model and the 70
92 model is sub-optimal); the last two columns assume that the data are
generated by the 70-92 model (so that the 70-92 model is the optimal
forecasting model and the 54-69 model is sub-optimal)




Table 11
Sub-Sample Stability of Phillips Curve Models
A.

Traditional Keynesian Model (A--1.56)
A.2 Unemployment

Lag
1
12
24
36
48
00

Demand Shock
Impulse Response
54-69
70-92
-0.18
-0.17
(0.31)
(0.61)
-0.41
-0.28
(1.44)
(0.47)
-0.16
-0.33
(0.27)
(1.17)
-0.32
-0.22
(0.37)
(1.12)
-0.19
-0.33
(0.32)
(1.15)
-0.20
-0.32
(0.34)
(1.15)

...... Forecast Error RMSE's
Demand Shock
Supply Shock
54-69
70-72
54-69
70-72
0.18
0.01
0.17
0.01
(0.31)
(0.61)
(0.01)
(0.01)
0.93
1.09
0.07
0.22
(3.86)
(0.41)
(1.57)
(0.20)
1.12
1.67
0.09
0.41
(1.89)
(5.92)
(0.37)
(0.27)
1.32
1.99
0.10
0.51
(2.24)
(7.06)
(0.38)
(0.33)
1.49
2.29
0.11
0.59
(2.52)
(8.10)
(0.38)
(0.39)

A.2 Inflation

Lag
1
12
24
36
48
oo

Demand Shock
Impulse Response
54-69
70-92
0.12
0.11
(0.20)
(0.39)
0.80
0.25
(2.74)
(0.46)
0.63
0.09
(2.23)
(0.17)
0.18
0.54
(0.30)
(1.90)
0.14
0.57
(0.25)
(1.93)
0.15
0.57
(1.98)
(0.27)

------ Forecast Error RMSE's ■
Demand Shock
Supply Shock
54-69
70-72
54-69
70-72
0.12
0.11
2.46
2.56
(0.20)
(0.39)
(0.13)
(0.21)
0.75
1.78
3.14
2.67
(1.26)
(6.15)
(0.20)
(0.36)
0.95
2.90
2.87
3.51
(1.60)
(9.93)
(0.64)
(0.27)
1.08
3.10
3.86
3.47
(1.83)
(12.04)
(0.31)
(0.82)
3.30
1.21
3.99
4.20
(2.06)
(13.80)
(0.35)
(0.95)

A.3 Phillips Curve Trade-off
Sample Period
Lag
0
12
24
36
48
60
72
OO

Note:




1954-69
-1.56 (0.00)
-1.15 (0.94)
-1.26 (0.55)
-1.31 (0.45)
-1.29 (0.39)
-1.30 (0.40)
-1.29 (0.39)
-1.30 (0.39)

1970-92
-1.56 (0.00)
-0.54 (0.14)
-0.54 (0.14)
-0.58 (0.21)
-0.57 (0.15)
-0.56 (0.15)
-0.57 (0.12)
-0.57 (0.13)

Estimated standard errors are shown in parentheses.

Table 11 (Continued)
Sub-Sample Stability of Phillips Curve Models
B.

Rational Expectations Monetarist Model (A=-0.07)

B .1 Unemployment

Lag
1
12
24
36
48
00

Demandl Shock
Impulse Response
70-92
54-69
-0.13
-0.12
(0.01)
(0.01)
-0.23
-0.21
(0.05)
(0.06)
-0.12
-0.17
(0.03)
(0.07)
-0.17
-0.17
(0.04)
(0.05)
-0.15
-0.17
(0.04)
(0.05)
-0.15
-0.17
(0.06)
(0.03)

Forecast Error RMSE's •
Demand Shock
Supply Shock
54-69
54-69
70-72
70-72
0.12
0.13
0.13
0.12
(0.01)
(0.01)
(0.01)
(0.01)
0.64
0.61
0.71
0.91
(0.12)
(0.12)
(0.12)
(0.16)
0.86
0.92
0.72
1.45
(0.23)
(0.17)
(0.17)
(0.32)
1.09
0.85
1.02
1.75
(0.19)
(0.30)
(0.19)
(0.40)
1.24
1.15
0.95
2.01
(0.23)
(0.35)
(0.22)
(0.47)

B.2 Inflation

Lag
1
12
24
36
48
00

Demand Shock
Impulse Response
54-69
70-92
1.75
1.86
(0.08)
(0.10)
1.04
0.31
(0.18)
(0.19)
0.30
0.75
(0.15)
(0.07)
0.34
0.71
(0.06)
(0.13)
0.74
0.33
(0.06)
(0.13)
0.33
0.74
(0.06)
(0.13)

------ Forecast Error RMSE's
Demand Shock
Supply Shock
54-69
70-72
54-69
70-72
1.75
1.86
1.72
1.76
(0.08)
(0.10)
(0.17)
(0.24)
2.13
3.09
1.77
1.87
(0.14)
(0.18)
(0.32)
(0.22)
2.43
4.10
1.83
1.94
(0.21)
(0.53)
(0.21)
(0.23)
2.68
4.81
1.89
1.95
(0.68)
(0.24)
(0.26)
(0.26)
1.94
2.92
5.45
1.96
(0.28)
(0.32)
(0.81)
(0.29)

B.3 Phillips Curve Trade-off

Lag
0
12
24
36
48
60
72
00

Note:




Sample Period
1954-69
1970-92
-0.07 (0.00)
-0.07 (0.00)
-0.24 (0.07)
-0.62 (0.35)
-0.40 (0.10)
-0.24 (0.07)
-0.50 (0.10)
-0.23 (0.06)
-0.45 (0.09)
-0.23 (0.06)
-0.47 (0.09)
-0.23 (0.06)
-0.46 (0.09)
-0.23 (0.06)
-0.47 (0.09)
-0.23 (0.06)

Estimated standard errors are shown in parentheses.

Table 11 (Continued)
Sub-Sample Stability of Phillips Curve Models
C.

Real Business Cycle Model (A-0.00)

C.l Unemployment

Lag
1
12
24
36
48
oo

Demand Shock
Impulse Response
54-69
70-92
0.00
0.00
(0.00)
(0.00)
-0.04
0.11
(0.06)
(0.05)
-0.02
0.11
(0.02)
(0.06)
0.10
-0.03
(0.03)
(0.05)
0.10
-0.03
(0.05)
(0.03)
-0.03
0.10
(0.03)
(0.05)

...... Forecast Error RMSE's
Demand Shock
Supply Shock
54-69
70-72
54-69
70-72
0.00
0.00
0.18
0.17
(0.00)
(0.01)
(0.00)
(0.01)
0.12
0.26
0.93
1.08
(0.12)
(0.12)
(0.12)
(0.15)
0.48
0.17
1.11
1.65
(0.25)
(0.17)
(0.17)
(0.30)
0.19
0.59
1.31
1.97
(0.20)
(0.31)
(0.19)
(0.40)
0.22
0.68
1.48
2.26
(0.23)
(0.35)
(0.23)
(0.46)

C.2 Inflation

Lag
1
12
24
36
48
CO

Demand Shock
Impulse Response
54-69
70-92
2.46
2.55
(0.13)
(0.21)
0.21
0.64
(0.18)
(0.19)
0.40
0.35
(0.08)
(0.13)
0.44
0.33
(0.06)
(0.12)
0.33
0.46
(0.06)
(0.12)
0.33
0.45
(0.06)
(0.12)

Forecast Error RMSE's •
Demand Shock
Supply Shock
54-69
70-72
54-69
70-72
2.46
2.55
0.08
0.22
(0.13)
(0.21)
(0.15)
(0.17)
2.69
3.10
0.68
1.85
(0.16)
(0.30)
(0.34)
(0.17)
2.93
2.96
3.43
0.83
(0.21)
(0.41)
(0.24)
(0.63)
3.15
3.75
0.93
3.59
(0.26)
(0.82)
(0.53)
(0.29)
1.04
3.35
4.12
4.07
(0.64)
(0.31)
(0.35)
(0.96)

C.3 Phillips Curve Trade-off
Sample Period
Lag
0
12
24
36
48
60
72
CO

Note:




1954-69
0.00 (0.00)
-0.17 (0.21)
-0.06 (0.07)
-0.10 (0.10)
-0.08 (0.08)
-0.09 (0.09)
-0.09 (0.09)
-0.09 (0.09)

1970-92
0.00 (0.00)
0.25 (0.18)
0.28 (0.23)
0.21 (0.15)
0.22 (0.16)
0.23 (0.16)
0.22 (0.16)
0.22 (0.16)

Estimated standard errors are shown in parentheses.

Table 12
Sensitivity of Results to Changes in Impact Phillips Trade-off (A)

A. Phillips Trade-off
Horizon
3 Year

1 Year

A
Monthly Data
-3.00
-1.56
-0.75
-0.50
-0.25
-0.15
-0.07
-0.03
0.00

-0.64
-0.63
-0.61
-0.58
-0.52
-0.45
-0.32
-0.17
0.09

-0.17
-0.07

-0.29 (.06)
-0.13 (.11)

-0.77
-0.74
-0.70
-0.66
-0.56
-0.46
-0.30
-0.15
0.06

(.17)
(.16)
(.15)
(.14)
(.11)
(.09)
(.07)
(.07)
(.11)

(.41)
(.13)
(.12)
(.11)
(.08)
(.06)
(.05)
(.05)
(.07)

Quarterly Data
-0.27 (.05)
-0.12 (.12

B. Contribution of Demand Shock to Forecast Error in u and 7r
(Variance Decomposition in Percent)
Horizon
1 year

A
u
Monthly Data
-3. 00
1. 00 ( .33)
-1. 56
1. 00 (■.01)
-0. 75
1. 00 (•.00)
-0. 50
0. 99 (•.01)
-0. 25
0. 95 ( .02)
-0. 15
0. 85 ( .03)
-0. 07
0. 52 ( .04)
-0. 03
0. 16 ( .02)
0. 00
0. 00 ( .00)
Quarterly Data
-0. 17
0. 40 ( .06)
-0.,07
0. 10 ( .02)

____7T
0..00
0..00
0..01
0..02
0..07
0..19
0..52
0..87
1,.00

( .00)
( .00)
( .00)
( .00)
( .01)
( .02)
( .04)
( .03)
( .00)

0..60 ( .06)
0..90 ( .05)

u____
0. 99
0. 99
0. 98
0. 96
0. 90
0. 77
0. 43
0. 10
0. 01

(1.6)
( -12)
( .03)
( .03)
( .05)
( .07)
( .09)
( .05)
( .02)

0. 34 ( .08)
0. 07 ( .04)

3 year
7T

0..15
0.,15
0.,17
0.,20
0.,28
0.,40
0.,68
0.,88
0.,85
00
u>

Impact

(31.8)
(. 30)
(• 05)
(. 05)
(• 05)
(. 05)
(• 04)
(• 03)
(• 04)

0.
(• 04)
0..89 (C1.04)

u____
0..99
0..99
0,.98
0,.96
0..89
0,.77
0..42
0..09
0,.01

(1.5)
( •12)
( .03)
( .04)
( .06)
( .09)
( .10)
(.06)
( .02)

0..30 (.11)
0,,05 ( .04)

7T

0..26
0..27
0,.30
0..34
0..44
0..57
0..81
0..89
0,.73

(10.)
( .82)
( .10)
( .09)
(.09)
( .08)
( .04)
( .04)
(.08)

0..92 ( .03)
0..80 ( .10)

Notes: The quarterly results are constructed from a VAR(4) using quarterly averages
of the monthly CPI and unemployment rate data. Standard errors are shown in
parentheses,




Table 13
Sensitivity of Estimated Phillips Trade-off to Changes in Specification

Impact
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00

A-0.00
Phillips Trade-off for Horizon:
1 year
3 year
0.09 (.11)
0.06 (.07)
0.18 (.11)
0.84 (.49)
0.21 (.18)
0.18 (.14)
0.10 (.12)
0.08 (.09)
0.16 (.14)
0.22 (.19)
-0.09 (.10)
0.02 (.13)
0.20 (.17)
0.11 (.09)
0.22 (.20)
0.22 (.21)

1
o
o
VO

CM
r—1 o
o o
1 1

Specification
1. Baseline Model
2. Levels
3. 18 Monthly Lags
4. 4 Quarterly Lags
5. 6 Quarterly Lags
6. GDP Deflator
7. irfe (Monthly)
8
(Quarterly)

Impact
-0.07
-0.07
-0.07
-0.07
-0.07
-0.07
-0.07
-0.07

A— 0.07
Phillips Trade-off for Horizon:
1 year
3 year
-0.32 (.07)
-0.30 (.05)
0.54 (.35)
(.07)
-0.31 (.08)
-0.27 (.06)
-0.13 (.07)
(.06)
(.08)
(.10)
-0.35 (.11)
-0.26 (.12)
(.09)
-0.32 (.05)
-0.11 (.11)
(.11)
CM
CM
O
i

1
o
H*
O

Specification
1. Baseline Model
2. Levels
3. 18 Monthly Lags
4. 4 Quarterly Lags
5. 6 Quarterly Lags
6. GDP Deflator
7. 7r^e (Monthly)
8 7r^e (Quarterly)

Impact
-1.56
-1.56
-1.56
-1.56
-1.56
-1.56
-1.56
-1.56

1
o
w

Specification
1. Baseline Model
2. Levels
3. 18 Monthly Lags
4. 4 Quarterly Lags
5. 6 Quarterly Lags
6. GDP Deflator
7. JTfe (Monthly)
8 »r^e (Quarterly)

A— 1.56
Phillips Trade-off for Horizon:
1 year
3 year
-0.63 (.16)
-0.74 (.13)
-0.59 (.16)
0.22 (36.)
-0.64 (.16)
-0.64 (-12)
-0.62 (.10)
-0.61 (.09)
-0.57 (.09)
-0.55 (.10)
-2.67 (1.6)
-1.91 (.82)
-0.69 (.19)
-0.82 (.18)
-0.68 (.13)
-0.64 (.14)

Description of Specifications:
1. The VAR(12) used Section 4
2. VAR(12) with levels used in place of first differences
3. VAR(18)
4. Quarterly VAR(4) using quarterly averages of the CPI and unemployment rate
5. Quarterly VAR(6) using quarterly averages of the CPI and unemployment rate
6. Quarterly VAR(6) using the GDP deflator instead of the CPI
7. VAR(12) with the relative price of food and energy included.
8. Quarterly VAR(6) with the relative price of food and energy included.




Table 14
Sensitivity of Estimated Variance Decompositions to Changes in Specification
Contribution of Demand Shock to Forecast Error
(Variance Decomposition in Percent)

A=-l.56
... .......................H o r i z o n ...........................
Impact
1 year
3 year
u
71r
7T
u
u
71
Spec.
0.99 (.12) 0.27 (.82)
0.99 (.12) 0.15 (.30)
1.00 (.01) 0.00 (.00)
1
0.73 (3.0) 0.24 (.72)
0.99 (.80) 0.16 (.32)
1.00 (.01) 0.00 (.00)
2
0.98 (.24) 0.17 (.37)
0.95 (.55) 0.39 (1.5)
1.00 (.01) 0.00 (.00)
3
0.95 (.06) 0.54 (.13)
0.96 (.04) 0.30 (.08)
4
0.98 (.03) 0.02 (.00)
0.89 (.10) 0.62 (.13)
0.96 (.04) 0.31 (.08)
5
0.99 (.02) 0.02 (.00)
0.99 (.02) 0.13 (.09)
1.00 (.00) 0.07 (.04)
6
1.00 (.01) 0.02 (.00)
0.91 (1.0) 0.20 (.40)
0.95 (.53) 0.13 (.19)
7
1.00 (.01) 0.00 (.00)
0.85 (.10) 0.42 (.14)
0.89 (.06) 0.22 (.07)
8
0.94 (.04) 0.02 (.00)

A— 0.07
-........ ..............H o r i z o n ......................... .....
Impact
1 year
3 year
Spec.
1
2
3
4
5

6
7

8

7T

U

0..52
0..53
0..52
0..10
0..10
0..12
0..50
0..09

( .04)
( .04)
( .04)
( .02)
(•.02)
( .02)
(..04)
( .02)

0..52
0..52
0..52
0..90
0..91
0.,92
0..52
0.,86

( .04)
( .04)
( .04)
( .05)
( .05)
( .05)
( .04)
( .05)

7T

U

0..43
0..41
0..38
0..07
0..06
0..16
0..35
0..05

( .09)
( .08)
( .09)
( .04)
( .03)
( .07)
( .08)
( .03)

0..68
0..67
0..67
0..89
0..88
0..94
0..57
0..70

( .04)
( .04)
( .04)
( .04)
( .05)
(•.03)
( .07)
(•.08)

7T

U

0..42
0..36
0..32
0..05
0..02
0..12
0.,32
0..02

( .10)
( .08)
(.11)
( .04)
( .02)
( .09)
( .09)
( .03)

0..81
0,.75
0..80
0..80
0..72
0..97
0..55
0..45

( .04)
( .05)
( .04)
( .10)
( .13)
( .02)
( •14)
( .13)

A=0.00
............ -.... -.....Horizon ............................
Impact
1 year
3 year
7T
7T
U
7T
u
U
Spec.
0..01 ( .02) 0..73 ( .08)
1
0..00 ( .00) 1..00 ( .00)
0..01 ( .02) 0.,85 ( .04)
2
0..00 ( .00) 1..00 ( .00)
0..01 ( .02) 0..84 ( .05)
0..27 ( •10) 0..76 ( .08)
3
0..00 ( .00) 1..00 ( .00)
0..04 ( .05) 0..61 ( .10)
0..02 ( .02) 0..83 ( .05)
4
0..00 ( .00) 1..00 ( .00)
0..01 ( .02) 0..57 ( •13)
0..00 ( .01) 0..78 ( .08)
5
0..00 ( .00) 1,.00 ( .00)
0..01 ( •01) 0..77 ( .09)
0..05 ( .06) 0..47 ( •14)
6
0..00 ( .00) 1..00 ( .01)
0..01 ( .01) 0..95 ( .05)
0..01 ( •01) 0..91 (•.09)
7
0..00 ( .00) 0..99 ( .01)
0..02 ( .02) 0..76 ( .07)
0..02 ( .03) 0..52 ( .14)
8
0 .00 ( .00) 0..99 ( .02)
0..01 ( .01) 0..66 ( .09)
0..03 ( .04) 0..31 ( .11)

Description of Specifications:
1. The VAR(12) used Section 4
2. VAR(12) with levels used in place of first differences
3. VAR(18)
4. Quarterly VAR(4) using quarterly averages of the CPI and unemployment rate
5. Quarterly VAR(6) using quarterly averages of the CPI and unemployment rate
6. Quarterly VAR(6) using the GDP deflator instead of the CPI
7. VAR(12) with the relative price of food and energy included.
8. Quarterly VAR(6) with the relative price of food and energy included.




Working Paper Series
A series of research studies on regional economic issues relating to the Seventh Federal
Reserve District, and on financial and economic topics.

REGIONAL ECONOMIC ISSUES
Estimating Monthly Regional Value Added by Combining Regional Input
With National Production Data

WP-92-8

Philip R . Israilevich and Kenneth N. Kuttner

Local Impact of Foreign Trade Zone

WP-92-9

D avid D . Weiss

Trends and Prospects for Rural Manufacturing

WP-92-12

William A . Testa

State and Local Government Spending-The Balance
Between Investment and Consumption

WP-92-14

Richard H. Mattoon

Forecasting with Regional Input-Output Tables

WP-92-20

P.R. Israilevich, R . M ahidhara, and G J D . Hewings

A Primer on Global Auto Markets

WP-93-1

P aul D. Ballew and Robert H. Schnorbus

Industry Approaches to Environmental Policy
in the Great Lakes Region

WP-93-8

D avid R. Allardice, Richard H. M attoon and William A. Testa

The Midwest Stock Price Index-Leading Indicator
of Regional Economic Activity

WP-93-9

William A . Strauss

Lean Manufacturing and the Decision to Vertically Integrate
Some Empirical Evidence From the U .S. Automobile Industry

WP-94-1

Thomas H. K lier

Domestic Consumption Patterns and the Midwest Economy

WP-94-4

Robert Schnorbus and Paul Ballew




l

W orking paper series continued

To Trade or Not to Trade: Who Participates in R EC LA IM ?

WP.94.11

Thomas H. K lier and Richard Mattoon

Restructuring & Worker Displacement in the Midwest

W P-94-18

Paul D. Ballew and Robert H. Schnorbus

ISSUES IN FINANCIAL REGULATION
Incentive Conflict in Deposit-Institution Regulation: Evidence from Australia

WP-92-5

Edw ard J. Kane and George G. Kaufman

Capital Adequacy and the Growth of U.S. Banks

WP-92-11

H erbert Baer and John M cElravey

Bank Contagion: Theory and Evidence

WP-92-13

George G. Kaufman

Trading Activity, Progarm Trading and the Volatility of Stock Returns

WP-92-16

Jam es T. M oser

Preferred Sources of Market Discipline: Depositors vs.
Subordinated Debt Holders

WP-92-21

D ouglas D. E vanoff

An Investigation of Returns Conditional
on Trading Performance

WP-92-24

Jam es T. M oser and Jacky C. So

The Effect of Capital on Portfolio Risk at Life Insurance Companies

WP-92-29

Elijah Brewer III, Thomas H. Mondschean, and Philip E. Strahan

A Framework for Estimating the Value and
Interest Rate Risk of Retail Bank Deposits

WP-92-30

D avid E. Hutchison, George G. Pennacchi

Capital Shocks and Bank Growth-1973 to 1991

WP-92-31

Herbert L. Baer and John N. McElravey

The Impact of S& L Failures and Regulatory Changes
on the C D Market 1987-1991

WP-92-33

Elijah Brewer and Thomas H. Mondschean




2

W orking paper series continued

Junk Bond Holdings, Premium Tax Offsets, and Risk
Exposure at Life Insurance Companies
Elijah Brewer III and Thomas H . Mondschean

WP-93-3

Stock Margins and the Conditional Probability of Price Reversals

WP-93-5

Paul Kofman and Jam es T. M oser

Is There Lif(f)e After D TB ?
Competitive Aspects of Cross Listed Futures
Contracts on Synchronous Markets
Paul Kofm an , Tony Bouwman and James T. Moser

WP-93-11

Opportunity Cost and Prudentiality: A RepresentativeAgent Model of Futures Clearinghouse Behavior
Herbert L . B aer , Virginia G. France and James T. Moser

WP-93-18

The Ownership Structure of Japanese Financial Institutions

WP-93-19

H esna Genay

Origins of the Modem Exchange Clearinghouse: A History of Early
Clearing and Settlement Methods at Futures Exchanges

WP-94-3

Jam es T. M oser

The Effect of Bank-Held Derivatives on Credit Accessibility

WP-94-5

Elijah Brewer III , Bernadette A. M inton and James T. Moser

Small Business Investment Companies:
Financial Characteristics and Investments

WP-94-10

Elijah Brewer III and Hesna Genay

MACROECONOMIC ISSUES
An Examination of Change in Energy Dependence and Efficiency
in the Six Largest Energy Using Countries-1970-1988

WP-92-2

Ja c k L .H e rv e y

Does the Federal Reserve Affect Asset Prices?

W P-92-3

Vefa Tarhan

Investment and Market Imperfections in the U .S. Manufacturing Sector

WP-92-4

Paula R. Worthington




3

W orking paper series continued

Business Cycle Durations and Postwar Stabilization of the U.S. Economy

WP-92-6

M ark W. Watson

A Procedure for Predicting Recessions with Leading Indicators: Econometric Issues
and Recent Performance

WP-92-7

Jam es H. Stock and M ark W. Watson

Production and Inventory Control at the General Motors Corporation
During the 1920s and 1930s

WP-92-10

A nil K. Kashyap and D avid W. Wilcox

Liquidity Effects, Monetary Policy and the Business Cycle

WP-92-15

Lawrence J. Christiano and Martin Eichenbaum

Monetary Policy and External Finance: Interpreting the
Behavior of Financial Hows and Interest Rate Spreads

WP-92-17

Kenneth N. Kuttner

Testing Long Run Neutrality

WP-92-18

Robert G. King and M ark W. Watson
A Policymaker's Guide to Indicators of Economic Activity
Charles Evans, Steven Strongin, and Francesca Eugeni

WP-92-19

Barriers to Trade and Union Wage Dynamics

WP-92-22

Ellen R. Rissman

Wage Growth and Sectoral Shifts: Phillips Curve Redux

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Ellen R. Rissman

Excess Volatility and The Smoothing of Interest Rates:
An Application Using Money Announcements

W P-92-25

Steven Strongin

Market Structure, Technology and the Cyclicality of Output

WP-92-26

Bruce Petersen and Steven Strongin

The Identification of Monetary Policy Disturbances:
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W P-92-27

Steven Strongin




4

W orking paper series continued

Earnings Losses and Displaced Workers

WP-92-28

Louis S. Jacobson, Robert J. LaLonde, and D aniel G. Sullivan

Some Empirical Evidence of the Effects on Monetary Policy
Shocks on Exchange Rates

WP-92-32

M artin Eichenbaum and Charles Evans

An Unobserved-Components Model of
Constant-Inflation Potential Output

WP-93-2

Kenneth N. Kuttner

Investment, Cash Flow, and Sunk Costs

WP-93-4

Paula R. Worthington

Lessons from the Japanese Main Bank System
for Financial System Reform in Poland

WP-93-6

Takeo Hoshi, A nil Kashyap, and Gary Loveman

Credit Conditions and the Cyclical Behavior of Inventories

WP-93-7

A nil K. Kashyap, Owen A. Lam ont and Jeremy C. Stein

Labor Productivity During the Great Depression

WP-93-10

M ichael D . Bordo and Charles L. Evans

Monetary Policy Shocks and Productivity Measures
in the G -7 Countries

WP-93-12

Charles L. Evans and Fernando Santos

Consumer Confidence and Economic Fluctuations

WP-93-13

John G. M atsusaka and Argia M. Sbordone

Vector Autoregressions and Cointegration

WP-93-14

M ark W. Watson

Testing for Cointegration When Some of the
Cointegrating Vectors Are Known

WP-93-15

M ichael T. K. Horvath and M ark W. Watson

Technical Change, Diffusion, and Productivity

WP-93-16

Jeffrey R. Campbell




5

W orking paper series continued

Economic Activity and the Short-Term Credit Markets:
An Analysis of Prices and Quantities

W P-93-17

Benjamin M. Friedman and Kenneth N. Kuttner
Cyclical Productivity in a Model of Labor Hoarding

WP-93-20

Argia M. Sbordone
The Effects of Monetary Policy Shocks: Evidence from the Flow of Funds

WP-94-2

Lawrence J. Christiano, Martin Eichenbaum and Charles Evans
Algorithms for Solving Dynamic Models with Occasionally Binding Constraints

WP-94-6

Lawrence /. Christiano and Jonas D.M. Fisher
Identification and the Effects of Monetary Policy Shocks

WP-94-7

Lawrence J . Christiano, Martin Eichenbaum and Charles L. Evans
Small Sample Bias in GM M Estimation of Covariance Structures

WP-94-8

Joseph G. Altonji and Lewis M. Segal
Interpreting the Procyclical Productivity of Manufacturing Sectors:
External Effects of Labor Hoarding?

WP-94-9

Argia M . Sbordone
Evidence on Structural Instability in Macroeconomic Time Series Relations

WP-94-13

James H. Stock and Mark W. Watson
The Post-War U.S. Phillips Curve: A Revisionist Econometric History

WP-94-14

Robert G. King and Mark W. Watson
The Post-War U.S. Phillips Curve: A Comment

WP-94-15

Charles L . Evans
Identification of Inflation-Unemployment

W P-94-16

Bennett T. McCallum
The Post-War U.S. Phillips Curve: A Revisionist Econometric History
Response to Evans and McCallum

WP-94-17

Robert G. King and Mark W. Watson




6