Did leaving the gold standard tame the business cycle? Evidence from NBER reference dates and real GNP.
Young, Andrew T. ; Du, Shaoyin
1. Introduction
"Our empirical results are striking [...] a clear rejection of
the null hypothesis of no postwar duration stabilization." This is
how Diebold and Rudebusch (1999, p. 7) summarize the six papers that
constitute the second part of Business Cycles: Durations, Dynamics and
Forecasting. The view that the U.S. economy has been more stable since
World War II is widely held and dates back at least to Arthur
Burns' (1960) presidential address to the American Economic
Association. Furthermore, Baily (1978) can be credited with singling out
1946 as a date of demarcation. He notes that, from 1900-1945, the U.S.
gross national product (GNP) gap was 381% more volatile than it was from
1946-1976. Baily chooses this break point to coincide with the U.S.
Employment Act of 1946, and it is the basis of the Diebold and Rudebusch
(1992; 1999) empirical analyses. (1)
However, there are other plausible dates to consider and an
important paper by Cover and Pecorino (2005) addresses this issue. They
follow Diebold and Rudebusch (1992) in using a rank-sum test to evaluate
potential break points in the length of business cycles. Expansion and
recession lengths are defined primarily in terms of National Bureau of
Economic Research (NBER) reference dates. Unlike Diebold and Rudebusch,
however, Cover and Pecorino (henceforth "CP") evaluate all
potential dates in terms of the associated probability of a structural
break. CP find that March 1933 is the most probable break point when
considering either NBER dates or the Romer (1994) alternative reference
dates. This finding holds whether considering the length of expansions
or the ratio of expansion length to the following recession length. CP
(2005, p. 467) identify March 1933 with the U.S. departure from the gold
standard.
Is the CP claim of a March 1933 break point convincing? Of note, it
is based on a particular and narrow definition of macroeconomic
stability. Specifically, the claim is based on an examination of
business cycles and the durations of their stages. However, a large part
of macroeconomic analysis instead focuses on (i) growth cycles and/or
(ii) the volatility of aggregate time series. The contribution of this
article is to evaluate whether or not 1933 remains the most probable
break point when macroeconomic stability is assessed from a perspective
of (i) and/or (ii).
The issues explored in this article are not only important from the
perspective of economic history. CP's identification of March 1933
with departure from the gold standard leads them to claim (2005, p. 467)
that their findings represent a challenge to real business cycle (RBC)
theory, given that stabilization is then viewed as the product of
discretionary monetary policy. (2) Furthermore, 1933 can be generally
associated with the increased government activism of the Roosevelt
administration. So, did discretionary policy of one type or another
stabilize the U.S. economy? Or, alternatively, what if the break is
actually later--say, 1946, as conventionally assumed? This would
correspond to the Full Employment Act. However, it would also correspond
to the end of World War II and the start of the diffusion of wartime
technologies. Also, returning soldiers and laborers associated with the
domestic war mobilization reentered peacetime production with new human
capital. These changes in real factors could have resulted in a
structural break.
The article is organized as follows. Section 2 elaborates on the
difference between business and growth cycles both in principle and in
practice. Section 3 outlines methodology applied by CP to NBER reference
dates. Section 4 reports the results of applying that methodology to
both NBER reference dates (business cycles) and reference dates defined
using HP-filtered real gross national product (GNP) (growth cycles).
Section 5 then contrasts the existing literature on post-World War II
stabilization (focusing on cycle durations) with the literature on the
"great moderation" of the 1980s (focusing on aggregate time
series volatility). Section 6 outlines two empirical methodologies
related to the later literature, and section 7 reports the results of
applying them to the question of post World War II stabilization.
Section 8 summarizes our conclusions, including (i) the claim of a break
point around 1933 is robust to the consideration of growth rather than
business cycles but (ii) examining the volatility of real GNP suggests a
considerably later break point perhaps as late as the 1950s.
[FIGURE 1 OMITTED]
2. Business Cycles versus Growth Cycles
The difference between the two cycle concepts is semantically
obscured because the term "business cycle" is often used
interchangeably for both types. However, the "growth cycles"
concept arose subsequently to the business cycle concept. Growth cycles
were defined by the NBER in the 1960s as periods of increases and
decreases in economic activity around some defined trend (Mintz 1969,
1974; Moore and Zarnowitz 1986). This can be contrasted to the NBER
concept of business cycles as absolute increases and decreases in
economic activity. (See Figure 1 for a graphical compare and contrast of
the two cycle concepts.) Lucas (1983, 1987) popularized the growth cycle
concept as a focus of macroeconomics and co-opted the "business
cycle" terminology for that purpose. (3) Real business cycle
theorists, such as Kydland and Prescott (1991, 1996), further entrenched
the growth cycle concept as part of accepted macroeconomic methodology.
Thus far, the literature on post World War II stabilization
summarized by Diebold and Rudebusch (1999) is based on the business
cycle concept as stated by the NBER (e.g., "a recession is a
significant decline in economic activity spread across the economy,
lasting more than a few months, normally visible in real gross domestic
product (GDP), real income, employment, industrial production, and
wholesale-retail sales.") (4) NBER reference dates are primarily
monthly and represent months where recessions turn expansionary or
expansions turn recessionary ("troughs" and "peaks,"
respectively).
Growth cycles, on the other hand, are consistent with a
macroeconomics based on some variant of the neoclassical growth model
(Solow 1956, Cass 1965, and Koopmans 1965) where some (constant or
smoothly evolving) growth rate in labor-augmenting technical change
defines a balanced growth path (or trend) for the economy. Shocks can
cause the output of the economy to be temporarily above or below this
trend. One interpretation of such deviations from trend is as periods
when the economy is operating above or below its potential level of
output. Of note, the economy can be above trend during a time when
economic activity is falling (a business cycle recession); likewise, the
economy can be below trend when economic activity is rising (a business
cycle expansion).
The terms expansions and recessions are straightforwardly
descriptive of business cycle stages but they can be awkward in
application to growth cycles. (Better analogous terms might be periods
of general prosperity or depression.) However, expansions and recessions
during growth cycles ostensibly consist of periods' of economic
activity above and below the trend, respectively, and reference dates
would correspond to the turning points. (5)
Also of note, business cycle stages can be analyzed purely in terms
of their durations. However, when applying a growth cycle concept to
actual data, it is almost impossible to abstract entirely from the
magnitude of fluctuations. This is because a trend must be defined and
the definition of the trend is invariably influenced by the volatility
of the relevant data. For example, the popular Hodrick and Prescott (HP)
(1997) filter is a decomposition of a time series into a trend (or
growth) component and a residual (or cyclical) component. This
decomposition arises from the minimization of a function that penalizes
according to the level of the cyclical component and the change in the
trend growth rate. With quadratic penalties for both, all else equal, a
large fluctuation in economic activity will result in a decomposition
assigning a larger change in trend at that point in time. (6)
The differences between a business cycle and growth cycle view of
the macroeconomy can be significant in practice. For example, according
to the NBER reference dates from 1875-1983, the longest recession was
the Great Depression beginning in 1929 (III) and lasting 14 quarters.
However, examining HP-filtered real GNP data covering the same time
period, the U.S. economy was below trend for 19 quarters on two
occasions, the first beginning in 1937 (IV) and the second beginning in
1945 (IV). These long periods below trend are the result of the
relatively high GNP growth periods following the trough of the Great
Depression and during World War II and their (positive) effect on the
HP-filter defined trend.
In other cases the choice of a business cycle or growth cycle
perspective can simply affect how we perceive the timing of events. For
the 1875-1983 time period the NBER reference dates mark 1961 (I) as the
beginning of the longest expansion (35 quarters). Detrended GNP data
suggests the same basic time period as the longest expansion, but it
begins later (1965 [III]) and the duration is shorter (17 quarters).
This discrepancy is due to the time needed for the economy, following
the decrease in economic activity beginning in 1960 (I), to not only
grow but to achieve a level of GNP above trend. (7)
For our purposes, we do not wish to argue for or against either
cycle concept. We note only that the growth cycle concept is at least as
prevalent as the business cycle concept in macroeconomic analyses.
Therefore, if CP's claim of a most probable break point around 1933
is robust to considering growth cycle as well as business cycle
reference dates, this would strengthen that claim considerably.
3. The Diebold and Rudebuseh/Cover and Pecorino Empirical
Methodology
Following the example of Diebold and Rudebusch (1992) and Cover and
Pecorino (2005), we employ a Wilcoxon rank-sum test to evaluate the
likelihood of various potential break points associated with both
business and growth cycles. We use both the business-cycle chronology of
the NBER and expansions and recessions defined from HP-filtered real
GNP. For NBER reference dates, we examine the lengths of expansions
(periods from troughs to peaks), the lengths of recessions (periods from
peaks to troughs), and the ratio of the length of an expansion to the
length of the following recession. Using HP-filtered real GNP the same
measures are constructed, except that the discrete observations dictate
defining expansions in terms of the number of periods above trend and
recessions as the number of periods below trend.
The null hypothesis is that the distributions of the durations of
the U.S. economy before and after a given date are identical. The
alternative hypothesis is that, from that given date onward, the average
expansions are longer (or recessions shorter; or the ratios of
expansions to recessions larger). Following precedent, our prior is that
the U.S. economy either became more stable at some point in time or did
not change, so a one-tail hypothesis test is used.
Denote the n observations, in temporal order, in a sample of
durations as {[X.sub.1], [X.sub.2], ... , [X.sub.n]} and rank them in
descending order. The ranks are then denoted as {[R.sub.1], [R.sub.2].
... , [R.sub.n]} respectively. (8) For example, the 30th expansion in a
given sample ([X.sub.30]) may be the longest in that sample ([R.sub.1].
This would be the case in our sample of expansions based on HP-filtered
quarterly real GNP (Table 1; left side). The 30th expansion in the time
series began in the third quarter of 1965 and lasted for 17
quarter--longer than any other expansion in the sample.
Romer (1994) makes a similar observation concerning the NBER
researcher's focus on detrended data pre-1929. Recall, on a related
note, that Cover and Pecorino (2005) show that the March 1933 break
point is robust to Romer's (1994) alternative reference dates,
which are based on that observation.
The set {[R.sub.1], [R.sub.2], ... , [R.sub.n]} is divided into two
samples: {[R.sub.1], [R.sub.2]. ... , [R.sub.m]} and {[R.sub.m+1,]
[R.su.b.m+2], ... , [R.sub.n]}. The Wilcoxon test statistic is the sum
of the ranks in the second sample:
W = [n.summation over (i=m+1)] [R.sub.i]. (1)
The Wilcoxon test may be interpreted as a distribution-free t test
where we do not need to have normality in the sample distribution. (9)
Intuitively, if the distributions are the same pre and post a potential
break point, the average rank in the earlier sample should equal that of
the later sample.
We consider each observation in a given sample as a potential break
point and compute the corresponding p-value--the marginal significance
of the test. The lowest p-value indicates the most probable structural
break point in the distribution of durations.
In detrending real GNP, the HP-filter is based on defining a given
time series, [y.sub.t], as the sum of a growth component [g.sub.t] and a
cyclical component [c.sub.t]:
[y.sub.t]= [g.sub.1]+[c.sub.t] for t=l, ... , T, (2)
by solving the minimization problem,
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (3)
where the parameter [lambda] is a positive number which penalizes
variability in the growth component series. The larger the value of
[lambda], the smoother is the growth component series defined by the
filter.
From possible detrending methods we choose the HP-filter both
because of its prevalence in macroeconomic applications and because
Canova (1999) has demonstrated that, among a range of possible filters,
it closely reproduces the NBER business cycle dating. We view this as a
virtue because we can ask whether, given that the general view of
macroeconomic performance remains similar, the most probable break point
hinges on the particular cycle concept considered.
We use the quarterly real GNP series provided by Balke and Gordon
(1986) for 18751983. This series is based on conventionally used annual
series for real GNP. (10) The quarterly values are then interpolated
using an algorithm and data described in Gordon and Veitch (1986). (11)
Quarterly observations past 1983 could be readily obtained from the U.S.
National Income and Product Accounts (NIPA). However, given the existing
literature proposing and providing evidence for an important structural
break around 1984, excluding the later time period seems reasonable;
even more so since, in section 4 below, we demonstrate that doing
likewise for the NBER reference dates does not alter the March 1933
result. We HP-filter the real GNP data using [lambda] = 1600. Again, we
only justify this parameter value by noting that it is widely used in
practice and by Canova (1999). (12) Using it creates the type of trend
and deviation time series that are the stuff of most macroeconomic
analyses.
4. Results: NBER Reference Dates versus Detrended GNP
Tables 2-4 summarize the results for monthly NBER reference dates,
1879 (I) to 1980 (III). (13) We follow CP and report only p-values for a
selection of dates. (14) In general, reporting begins with the dates
closest to 1921 and ends with the latest date in the 1960s; this
practice is then applied throughout. (15) The reference date listed in
column 1 represents the beginning of the second sample. For expansion
duration (Table 2) the most probable break point is 1933 (I). For
recession duration (Table 3) the most probable break point is either
1937 (II) or 1945 (1). (16) (1937 [II] represents the first post gold
standard recession, so this is not inconsistent with a 1933 break
point.) However, the 1945 (I) probability still makes the result
ambiguous relative to results obtained when considering expansions. When
we turn to the ratio of expansion length to the following recession
(Table 4), once again 1933 (I) is the most probable break point.
These results are exactly down to every quarter--those reported in
Cover and Pecorino (2005) (see their tables 2, 5, and 6). This is true
despite the fact that CP report results for the longer time period, 1854
(IV) to 2001 (I). This is important because it demonstrates that their
results are robust to considering the shorter time period for which we
analyze quarterly real GNP data below. We can state with confidence the
following: Considering business cycle durations using NBER reference
dates supports the conclusion that the first quarter of 1933 ushered in
longer expansions absolutely and relative to adjacent recessions.
Table 1 presents the lengths and ranks of expansions and recessions
determined from HP--filtered real GNP assuming a value of [lambda] =
1600. Tables 5-7 then present results of the rank sum tests. Though the
results are not as definitive as those using NBER reference dates, it is
hard to argue that they are inconsistent with a 1933 break point.
In the case of expansions (Table 5) 1935 (III) is the most probable
break point. This is only the second expansion subsequent to the
departure from the gold standard with the previous expansion (beginning
in 1934 [II]) lasting only a single quarter. Furthermore, in the case of
recessions (Table 6), 1931 (IV) is the most probable break point. This
is the recession previous to, and encompassing, the U.S. departure from
the gold standard.
Finally, in the case of the expansion to following recession ratio,
while 1950 (III) is the most probable break point, 1933 (I) is second
with a p-value only 0.0006 greater. (Given the range of p-values
reported, 0.0006 is an exceedingly small difference.) But, more
importantly, for either date the marginal significance level is not less
than 20%.
The lack of statistical significance in the tests involving the
expansion to recession ratio is indicative of symmetric changes in
expansion and recession lengths. While the average pre-1935 (III)
expansion is indeed shorter than the average expansion in the later
period (5.2 versus 9 quarters), the average recession length pre-1931
(IV) was 5.2 quarters; the average recession length in the later period
was longer (9.1 quarters). Even if the two 19-quarter recessions
beginning in 1937 (IV) and 1945 (IV) are excluded, the average length of
recessions from 1931 (IV) onward (7.1 quarters) was still longer than
that of the earlier period. (17)
We still view the above as not inconsistent with Cover and
Pecorino's (2005) hypothesis that a break point near 1933 implies a
causal link between the abandonment of the gold standard and relative
macroeconomic stability. In terms of growth cycles, if both expansions
and recessions became longer, this may imply a smoothing of the
evolution of real GNP. Unfortunately, tests involving cycle durations
cannot directly speak to this possibility. In summary, though, we note
that examining HP-filtered GNP and associated growth cycles seems to be
at least weakly supportive of a 1933 break point. The cycle concept
considered does not appear to be critical. (18)
5. Postwar Stabilization versus the "Great Moderation";
Durations versus Volatility
One downfall of the rank-sum test is that it speaks only to
duration--the relative length of periods of decline and increase in
economic activity, or of periods above and below trend. Even in the case
of detrended GNP, where the HP-filter takes into account the volatility
of the time series in defining the trend, the rank-sum test then
considers only relative durations (however they may be defined). Whether
using a simple measure of economic activity, or deviations from a
defined trend for such a measure, it seems desirable to evaluate a
general measure of volatility.
Research on postwar stability considering volatility does exist.
However, it generally focuses on annual data and the comparison of
simple measures of volatility such as sample standard deviations from
earlier and later periods. Examples include Baily (1978), Balke and
Gordon (1989), Romer (1986, 1989), and Watson (1994). However, more
sophisticated tests have been developed and applied in the study of the
"great moderation" of the 1980s.
Kim and Nelson (1999), McConnell and Perez-Quiros (2002), and Stock
and Watson (2002), for example, have explored whether or not the U.S.
economy became more stable during the 1980s and attempting to establish
the most probable break point date associated with that stabilization;
sometime during 1984 appears to be the consensus.
To our knowledge no existing work applies the tools used to date
the "great moderation" of the 1980s to date the earlier break
point associated with post--World War II stability. The available tests
allow us to ask when a structural break in the volatility of real GNP
occurred and, as well, whether the break is associated with the
conditional variance (i.e., the shocks) or conditional mean (i.e., the
persistence of the effects of shocks) of the data generating process.
6. The McConnell and Perez-Quiros and Stock and Watson
Methodologies
We begin by following McConnell and Perez-Quiros (2000),
considering the following system:
[DELTA] ln ([y.sub.t]) = [mu] + [phi] [DELTA] ln (y.sub.t-1]) +
[[epsilon].sub.t]; (4)
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (5)
where y is real GDP, [D.sub.1] and [D.sub.2] are dummy variables
taking values,
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (6)
and T is a potential break point. If there is no break
([[alpha].sub.1] = [[alpha].sub.2]), then [MATHEMATICAL EXPRESSION NOT
REPRODUCIBLE IN ASCII] is an unbiased estimator of the standard
deviation of [[epsilon].sub.t]. In the case of a structural break at T,
[[??].sub.1] and [[??].sub.2] are the estimators of the earlier and
later sub-sample standard deviations, respectively. (19)
Since the nuisance parameter, T, is only present under the
alternative hypothesis, Lagrangian Multiplier, Likelihood Ratio, and
Wald tests of [[alpha].sub.1] = [[alpha].sub.2] do not have standard
asymptotic properties. Andrews (1993), therefore, considers the supremum
of the F statistics associated with a range of potential break points,
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (7)
He demonstrates the asymptotic properties of this statistic and
provides the asymptotic critical values. This statistic allows for the
determination of the most probable break point (i.e., the T that
maximizes Equation 7). Andrews and Ploberger (1994) also propose the
additional test statistics:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (8)
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (9)
McConnell and Perez-Quiros (2000) use the approximation suggested
by Hansen (1997) to compute p-values to these statistics, which speak to
whether or not a break occurred within the range of [T.sub.1] to
[T.sub.2]. These statistics are increasing in the average value of F
statistics across considered [T.sub.s], but they also impose a penalty
for considering a larger range of [T.sub.s].
Following McConnell and Perez-Quiros (2000), we estimate the
system, Equations 4 and 5, for the quarterly real GNP, 1875-1983, and
compute the test statistics, Equations 7, 8, and 9. The estimation
method is generalized method of moments (GMM) with a constant, lagged
[DELTA]ln([y.sub.t-1]), and [D.sub.1t] and [D.sub.2t] as instruments for
period t. This will provide a baseline where the P-filter plays no role
in the results. We then estimate the analogous system using the percent
deviation from HP-trend time series using
[Dev.sub.t] = [phi] [Dev.sub.t-1] + [[epsilon.sub.t], (10)
where no constant is included because it is zero by definition of
the filter. The test statistics are also computed for these cases.
Following McConnell and Perez-Quiros, we begin by using [T.sub.1] = 1891
(III) and [T.sub.2] = 1967 (II), where 15% of the quarterly observations
are truncated at each end of the time series.
We also provide two robustness checks on our results--one regarding
data and one regarding estimation technique. First, we apply the
McConnell and Perez-Quiros (2000) test to annual real GNP time series
(and associated percent deviations from HP-filter trend) that includes,
respectively, the corrected pre-war observations of Romer (1989) and
Balke and Gordon (1989). For each of these annual GNP series we filter
separately, using [lambda] = 100 and = 6.25, producing four separate
histories of growth cycles. The value of 100 is consistent with the
suggestion of Backus and Kehoe (1992) for annual data while the value of
6.25 has been suggested as an alternative by Ravn and Uhlig (2002). (20)
Second, we consider the possibility that the reduced postwar GNP
volatility is based on a break in the conditional mean of the
data-generating process, rather than (or in addition to) the conditional
variance. The conditional variance is determined by the size of the
shocks hitting the economy; the conditional mean is based in part on the
persistence of shock's effects. Stock and Watson (2002) propose a
test based on the specification,
[DELTA]ln([y.sub.t]) = [D.sub.1t] [[micro].sub.1] + [D.sub.2t]
[[alpha].sub.2] + [D.sub.3t] [[beta].sub.1] [DELTA]1n ([y.sub.t]-1) +
[D.sub.4t] [[beta].sub.2] [DELTA]1n ([y.sub.t-1]) + [[epsilon].sub.t],
(11)
where,
[D.sub.1t];[D.sub.3t] = {1 if t [less than or equal to] T 0 if t
> T [D.sub.2t];[D.sub.4t] = {0 if t [less than or equal to] T 1 if t
> T, (12)
and T is a potential break point in the conditional mean of the
series.
In practice, we run an ordinary least squares (OLS) regression for
each T [member of] [[T.sub.1], [T.sub.2]] where [T.sub.1] = 1891 (III)
and [T.sub.2] = 1967 (II) so that we focus on the middle 70% of the
sample. For each regression we test [H.sub.0] : [[micro].sub.l] =
[micro].sub.2] [[beta].sub.1] = [[beta].sub.2]. The T associated with
the largest heteroskedasticity-robust Wald statistic is considered the
most probable break point in the conditional mean.
Using the T as chosen above, we then save the residuals from that
particular regression and consider the additional OLS regression
|[[??].sub.t] (T)| = [[alpha].sub.0] + [[alpha].sub.1] [D.sub.t]+
[v.sub.t], (13)
where
[D.sub.t] = {1 if t [less than or equal to] [tau] 0 if t >
[tau]' (14)
for each [tau] [member of] [1891 (III), 1967 (II)]. The x
associated with the largest Wald statistic for [H.sub.0]:
[[alpha].sub.l] = 0 is considered the most probable break point in the
conditional variance.
The Stock and Watson (2002) test is performed on both the quarterly
real GNP growth rates and the HP-filter percent deviations series.
7. Results: Structural Breaks in the Volatility of Real GNP
Table 8 reports the test statistic values and associated p-values
for a structural break between [T.sub.1] = 1891 (III) and [T.sub.2] =
1967 (II). For real GNP growth rates, as well as the deviations from
HP-filter trend series, the estimated structural break point indicated
by the supremum [F.sub.n] is around the year 1951 (with p-values of
0.000 in each case). For the simple growth rates, supremum [F.sub.n] is
associated with 1950 (III); for the deviation series it is associated
with 1951 (III). The exp [F.sub.n] and ave [F.sub.n] statistics confirm
that a structural break in the 1891 (III) to 1967 (II) range is very
probable.
Furthermore, there is no doubt that the estimated breaks are
associated with decreases in volatility. The standard deviation of the
GNP growth rates pre-1950 (III) is 0.0286; almost three times that
associated with 1950 (III) onward (0.0108). For the percent deviations
from trend series the difference in standard deviations is also
dramatic: 0.0512 for pre-1951 (III) and then 0.0187 from that point
onward.
The year 1951 is closer to the 1946 Full Employment Act than to the
1933 departure from the gold standard. As well, it corresponds very
closely to the Treasury Federal Reserve Accord of (March) 1951. (21) The
Treasury Federal Reserve Accord is associated with a more independent
and flexible monetary policy, but in a different sense than the 1933
departure from the gold standard. The 1951 Accord freed the Fed from an
obligation to support the market of U.S. Treasuries at fixed prices.
This removed a meaningful constraint on the Fed's conduct of
monetary policy.
What may also be meaningful are the [F.sub.n] values associated
with the a priori potential break points. For 1933 (I) the associated
[F.sub.n] is 2.15 (p-value = 0.141) for the simple growth rate series
and 4.97 (p-value = 0.026) for the deviation-from-trend series. For 1946
(I) the corresponding [F.sub.n] values are 65.02 (p-value = 0.000) and
71.80 (p-value = 0.000). If we simply asked whether a break point in
volatility occurred in 1933, we would reject the null with a good level
of confidence; likewise if we asked about 1946. However, when
considering all potential dates, 1946 is more likely, and 1951 is most
probable.
If we consider the two annual data real GNP series incorporating,
respectively, the pre1929 corrections of Romer (1989) and Balke and
Gordon (1989), the implication is that the break point is even later in
the 1950s. Moreover, the similarities between the predictions of the two
corrected GNP series are striking (Table 9). In either case, analyzing
the growth rates of deviations from a HP-filter trend using [lambda] =
6.25, the most probable break point is in 1959. For deviations using
[lambda] = 100, in either case, the most probable break point is
slightly earlier: 1955. (All of the associated test statistics are
significant at better than the I% level.)
Focusing again on the quarterly real GNP series, Table 10 reports
results from the Stock and Watson (2002) test. This test allows
potentially for breaks in both the conditional variance and conditional
mean of the process. For GNP growth rates the most probable break point
is in 1940 (II) and is significant at better than the 5% level. For
deviations from trend the most probable break point is in 1903 (IV), but
is not very probable at all: p-value = 0.313. Based on these conditional
mean break points, the residuals from the resulting regressions for both
series suggest a most probable break point in the conditional variance
sometime in 1947.
These dates are earlier than those implied by the McConnell and
Perez-Quiros (2000) test, but are still later than the 1933 date
suggested by examining durations of reference cycles. A primary
conclusion of this section is that if there was a structural break in
the volatility of real
GNP it was considerably later than the 1933 departure from the gold
standard, and that this conclusion is robust to data corrections,
frequency changes, and detrending using the HP-filter.
8. Conclusions
Cover and Pecorino's (2005) results are remarkable, and their
robustness to the substitution of Romer (1994) reference dates, our
altering of the time period considered, and the substitution of
HP-filter defined growth cycle dates in real GNP is striking. The most
probable structural break appears to be around 1933, coinciding with the
U.S. departure from the gold standard. The particular cycle concept
considered appears not to be critical.
On the other hand, when considering the volatility of quarterly
real GNP growth, or its deviations from an HP-filter trend, the most
probable structural break is in 1947 or 1951. This may or may not weaken
the view that improved monetary policy stabilized the U.S. economy.
While 1947 is not straightforwardly linked to a structural improvement
in monetary policy, the Treasury Federal Reserve Accord of 1951 is
associated with monetary policy less constrained by the debt-finance
priorities of the Treasury. However, if we utilize annual GNP data in
the analysis and incorporate the well-known pre-1929 corrections of
Romer (1989) or Balke and Gordon (1989), the most probable break point
in volatility is even later in the 1950s. If one were to draw a primary
conclusion from this article, then it would seem to be that the choice
of growth cycles or business cycles does not yield dramatically
different answers as to when the U.S. economy stabilized. Rather, it is
the focus on durations or volatility that can make an important
difference.
We should take some space to comment on what types of conclusions
cannot be drawn from this article. First, our results cannot speak, in
and of themselves, as to whether focusing on reference cycle durations
or the volatility of aggregate time series is a more meaningful way of
evaluating macroeconomic performance. Our contribution to this debate is
to note an important question for which the two focuses provide
significantly different answers. Also, a weakness of the present study
involves the ability to deal with the effects of the wartime economy and
the Great Depression. Cover and Pecorino (2005) report that, when
focusing only on peace-time recessions, the break in durations occurred
in either 1937 or 1948 with nearly equal probability. This is an
unenlightening result if one's prior is that the economy changed
structurally in either 1933 or 1946. (May 1937 corresponds to the first
recession to follow the departure from the gold standard; November 1948
corresponds to the first recession to follow the Full Employment Act.)
Moving to an examination of real GNP volatility, removing the WWII
observations for the United States excludes (at least) 1942 through
1945, taking out a large portion of the time between the two potential
break points, and a portion that borders the later potential break
point. Similarly, taking out Great Depression observations actually
excludes 1933 entirely. How to best deal with these problems remains an
important, open question.
Received June 2008; accepted January 2009.
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(1) There may also be other reasonable rationales for a similar
date. Young and Blue (2007) suggest that the Bretton Woods arrangement
(ratified by the United States in 1945 just previously to the Employment
Act) may have, by promoting a long-run, upward trend in prices, led to
more flexible prices and, therefore, more macroeconomic stability.
(2) CPs claim, even conditional on the accuracy of their findings,
is not necessarily reasonable. For example, Chatterjee argues that
ability of RBC models to match key moments of postwar aggregates may
actually be "the legacy of countercyclical policies":
"One possibility is that the success of [RBC] theory reflects
better post-WWII countercyclical policies [that] reduced some of the
instabilities that characterized pre-WWII business cycles" (1999,
p. 26). According to this view, countercyclical policies have succeeded
in making the U.S. economy an approximate one with competitive markets
operating efficiently "and fluctuations in the growth rate of
business-sector productivity ... surfaced as the dominant sources of
business cycles" (1999, p. 26).
(3) Lucas (1983, p. 217) states: "Let me ... review the main
qualitative features of economic time series we call 'the business
cycle." Technically, movements about trend in gross national
product in any country can be well described by a stochastically
disturbed difference equation of very low order."
(4) http://www.nber.org/cycles.html/
(5) A well-known example of growth-cycle-based macroeconomic
analysis is Prescott's (1986) RBC model exercise. Prescott's
model abstracts entirely from trend technological change and then
compares simulated data from that model to detrended U.S. data. Whether
or not economic activity is (in an absolute sense) going up or down is
of second-order importance in practice.
(6) Even in the case of fitting a simple linear trend, periods of
absolute increase and decrease in economic activity are symmetric in
terms of their severity, and volatility will influence the trend.
(7) Table 4 reports the HP-filter trend deviation-defined
expansions and recessions for the Balke and Gordon (1986) data.
(8) When observations tie in terms of rank, we follow Diebold and
Rudebusch (1992) and use the average rank.
(9) See Diebold and Rudebusch (1992, pp. 44-45).
(10) These sources are noted in Balke and Gordon (1986. p. 788).
(11) The quarterly interpolators are a constant, a linear time
trend, and an index of industrial production and trade.
(12) Canova (1999) also considers [lambda] = 4.
(13) These represent the reference dates that most closely
correspond to the beginning and end dates of our real GNP time series.
(14) At the very initial or final NBER reference dates we would
expect p-values to be very high given the lack of observations in one
sample or the other.
(15) In no case does this reporting leave out a p-value lower than
those contained in the tables.
(16) The p-value associated with 1937 (II) is lower but by 0.0002.
Relative to the other reported p-values, this difference is smaller by
an order of magnitude, so noting the (approximate) equivalence in
probability to the 1945 (I) date seems appropriate.
(17) One ad hoc way to deal with the symmetric effects of the
HP-filter on expansion and recession lengths is to define a
more-than-just-below trend definition of recessions. For example. Barro
(2007, p. 176) defines recessions in terms of HP-filtered GDP as,
alternatively, periods either more than 1.5% or more than 3% below
trend. One advantage to such a definition is that it may more
realistically capture what most people think of as recessions (i.e.,
significantly bad economic times, rather than mild slowdowns in growth).
However, such definitions are arbitrary and take us away from the
discipline employed in most macroeconomic analysis. (It should be noted
that Barro's use of these definitions is in the context of a
textbook.) We experimented with defining expansions and recessions from
the filtered GNP using both the 1.5% and 3% rules. Doing so yielded
statistically significant results for expansion lengths but not for
recession lengths. Using the 1.5% rule, the most probable break point
for expansions is in 1942 (Ill); using the 3% rule the most probable
date is 1950 (Ill). These are provocative results in that they are
considerably later than 1933, we but hesitate to stress them here
because of the arbitrariness of the rules.
(18) An anonymous referee pointed out that the growth cycle stages
may be alternatively conceptualized in terms of periods of growth above
and below the trend level of growth (rather than in terms of periods of
GNP levels above and below trend level). This alternative
conceptualization is, taken literally, difficult to bring to GNP data in
a sensible way. This is because quarterly fluctuations are marked,
several "expansions" lasting merely a quarter or two occur
during sustained periods below trend. Such is similar for
"recessions" occurring during periods above trend. However,
the referee's conceptualization is consistent with, and made
operational according to, Moore and Zarnowitz's (1986, p. 772)
statement: "dates mark the approximate time when aggregate economic
activity was farthest from its long-run trend level (peak) or farthest
below its long-run trend level (trough)." We created alternative
growth cycle dates. dating recessions as the largest (absolute value)
percentage deviation from trend during a period of GNP below trend: and
expansions as the largest percentage deviation from trend during an
above trend period. The results are inconsistent across expansion and
recession samples, and inconsistent with the previous literature's
findings. The most likely expansion break point is 1904 (IV): the most
likely recession break point is 1937 (I).
(19) McConnell and Perez-Quiros (2000) also consider possible
structural breaks in the mean of the series, [[mu].sub.1] [not equal to]
[[mu].sub.2]. They find no such statistically significant break with
quarterly GDP data from 1953-1999.
(20) These values for [lambda] are, again, justified only by
convention. However, as we shall see, the estimated most probable break
points are identical regardless of which [lambda] value is used (and,
for that matter, whether the Balke and Gordon 1989 or Romer 1989 series
is used).
(21) This is an event that, to our knowledge, has not been
previously suggested as important in this literature. We are grateful to
an anonymous referee for pointing out the coincidence of the event and
estimated break point.
Andrew T. Young * and Shaoyin Du [dagger]
* Department of Economics, 371 Holman Hall, University of
Mississippi, University, MS 38677, USA: Tel.662915-5829: E-mail
atyoung@olemiss.edu; corresponding author.
[dagger] Department of Economics, University of Mississippi,
University, MS 38677, USA: E-mail sdul@olemiss.edu.
We are indebted to two anonymous referees for their constructive
comments on a previous draft. We thank James Cover and other
participants at the University of Alabama economics seminar series for
helpful discussion; we likewise thank Ron Balvers and other participants
at the West Virginia University economics seminar series and
participants at the San Jose State economics seminar series. We are
especially appreciative toward Paul Pecorino for commenting extensively
on a previous version of this article.
Table 1. Lengths and Ranks of Expansions and Recessions Using
HP-Filtered Quarterly Real GNP
Beginning Expansions
Year and (Quarters
Quarter of above
Expansion Trend) Rank
1875 (I) 3 25
1876 (I) 2 29.5
1879 (IV) 13 3.5
1884 (II) 1 32.5
1886 (II) 7 15
1890 (II) 3 25
1891 (III) 8 13
1895 (I) 4 20
1897 (III) 3 25
1899 (I) 4 20
1901 (I) 5 18
1902 (III) 1 32.5
1903 (I) 3 25
1905 (IV) 8 13
1909 (III) 4 20
1911 (II) 12 5.5
1916 (I) 1 32.5
1917 (IV) 10 8
1922 (IV) 6 16.5
1925 (IIn 8 13
1928 (III) 9 10
1931 (I) 3 25
1934 (II) 1 32.5
1935 (III) 9 10
1942 (III) 13 3.5
1950 (III) 14 2
1955 (I) 11 7
1959 (I) 6 16.5
1962 (I) 3 25
1965 (III) 17 1
1972 (II) 9 10
1977 (II) 12 5.5
1981 (I) 3 25
1983 (III) 2 29.5
Beginning Recessions
Year and (Quarters
Quarter of below
Recession Trend) Rank
1875 (IV) 1 2.5
1876 (III) 13 31
1883 (I) 5 14
1884 (III) 7 21.5
1888 (I) 9 25
1891 (I) 2 5
1893 (III) 6 17.5
1896 (I) 6 17.5
1898 (II) 3 7
1900 (I) 4 10.5
1902 (II) 1 2.5
1902 (IV) 1 2.5
1903 (IV) 8 24
1907 (IV) 7 21.5
1910 (III) 3 7
1914 (II) 7 21.5
1916 (II) 6 17.5
1920 (II) 10 27
1924 (II) 5 14
1927 (III) 4 10.5
1930 (IV) 1 2.5
1931 (IV) 10 27
1934 (III) 4 10.5
1937 (IV) 19 32.5
1945 (IV) 19 32.5
1954 (I) 4 10.5
1957 (IV) 5 14
1960 (III) 6 17.5
1962 (IV) 11 29.5
1969 (IV) 10 27
1974 (III) 11 29.5
1980 (II) 3 7
1981 (IV) 7 21.5
Expansions are ranked longest to shortest, while recessions are
ranked shortest to longest; ties are denoted with the average rank.
The HP-filter is applied with a smoothing parameter value,
[lambda] = 1600.
Table 2. Test for Break in the NBER Sample Using Expansions:
1879 (I)-1980 (III)
Column
1 2 3
Trough Beginning Expansion Wilcoxon Number of
in the Second Sample Statistic Expansions in
Row (and Length in Quarters) First Sample
1 1921 (III) (7) 239 12
2 1924 (III) (9) 229.5 13
3 1927 (IV) (7) 216 14
4 1933 (I) (17) 208.5 15
5 1938 (II) (27) 186.5 16
6 1945 (IV)(12) 162.5 17
7 1949 (IV) (15) 144.5 18
8 1954 (II) (13) 123.5 19
9 1958 (II) (8) 104.5 20
10 1961 (I) (35) 93 21
4 5
Trough Beginning Expansion Number of Exact Marginal
in the Second Sample Expansions in Significance
Row (and Length in Quarters) Second Sample Level
1 1921 (III) (7) 14 0.0043
2 1924 (III) (9) 13 0.0022
3 1927 (IV) (7) 12 0.0021
4 1933 (I) (17) 11 0.0005
5 1938 (II) (27) 10 0.0026
6 1945 (IV)(12) 9 0.0129
7 1949 (IV) (15) 8 0.0211
8 1954 (II) (13) 7 0.0486
9 1958 (II) (8) 6 0.0806
10 1961 (I) (35) 5 0.0511
NBER are primarily monthly and so are durations. Lengths in terms
of quarters are approximated by rounding.
Table 3. Test for Break in the NBER Sample Using Recessions:
1873 (III)-1981 (III)
Column
1 2 3
Peak Beginning Recession in Wilcoxon Number of
the Second Sample Statistic Recessions in
Row (and Length in Quarters) First Sample
1 1923 (II) (5) 130 13
2 1926 (III) (5) 116 14
3 1929 (III) (14) 104.5 15
4 1937 (II) (5) 79.5 16
5 1945 (I) (3) 68 17
6 1948 (IV) (4) 64.5 18
7 1953 (II) (3) 56 19
8 1957 (III) (8) 50 20
9 1960 (II) (3) 46.5 21
10 1969 (IV) (4) 40.5 22
1 4 5
Peak Beginning Recession in Number of Exact Marginal
the Second Sample Recessions in Significance
Row (and Length in Quarters) Second Sample Level
1 1923 (II) (5) 13 0.0090
2 1926 (III) (5) 12 0.0081
3 1929 (III) (14) 11 0.0103
4 1937 (II) (5) 10 0.0011
5 1945 (I) (3) 9 0.0013
6 1948 (IV) (4) 8 0.0068
7 1953 (II) (3) 7 0.0119
8 1957 (III) (8) 6 0.0296
9 1960 (II) (3) 5 0.0914
10 1969 (IV) (4) 4 0.1813
NBER are primarily monthly and so are durations. Lengths in terms of
quarters are approximated by rounding.
Table 4. Test for Break in the Sample in the NBER Sample Using
Expansion to Recession Following Ratio: 1879 (I)-1981 (III)
Column
1 2 3
Trough Beginning Wilcoxon Number of
Expansion Statistic Cycles in
Row in the Second Sample First Sample
1 1921 (III) 208 12
2 1924 (III) 197 13
3 1927 (IV) 184 14
4 1933 (I) 183 15
5 1938 (II) 164 16
6 1945 (IV) 139 17
7 1949 (IV) 121 18
8 1954 (II) 101 19
9 1958 (II) 80 20
10 1961 (I) 65 21
1 4 5
Trough Beginning Number of Cycles Exact Marginal
Expansion in Second Sample Significance
Row in the Second Sample Level
1 1921 (III) 13 0.0173
2 1924 (III) 12 0.0128
3 1927 (IV) 11 0.0123
4 1933 (I) 10 0.0012
5 1938 (II) 9 0.0033
6 1945 (IV) 8 0.0213
7 1949 (IV) 7 0.0369
8 1954 (II) 6 0.0781
9 1958 (II) 5 0.1678
10 1961 (I) 4 0.1843
Table 5. Test for Break in the Real GNP Sample Using Expansions:
1875 (I)-1983 (III)
Column
1 2 3
Trough Beginning First Wilcoxon Number of
Expansion in the Second Statistic Expansions in
Row Sample (and Length in Months) First Sample
1 1922 (IV) (18) 328.0 18
2 1925 (III) (24) 309.5 19
3 1928 (III) (27) 287.5 20
4 1931 (I) (9) 262.5 21
5 1934 (II) (3) 252.5 22
6 1935 (III) (27) 250.0 23
7 1942 (III) (39) 225.0 24
8 1950 (III) (42) 193.5 25
9 1955 (I) (33) 160.5 26
10 1959 (I) (18) 132.5 27
11 1962 (I) (9) 114.0 28
12 1965 (III) (51) 104.0 29
1 4 5
Exact
Trough Beginning First Number of Marginal
Expansion in the Second Expansions in Significance
Row Sample (and Length in Months) Second Sample Level
1 1922 (IV) (18) 16 0.0489
2 1925 (III) (24) I S 0.0517
3 1928 (III) (27) 14 0.0692
4 1931 (I) (9) 13 0.1093
5 1934 (II) (3) 12 0.0635
6 1935 (III) (27) 11 0.0163
7 1942 (III) (39) 10 0.0289
8 1950 (III) (42) 9 0.0816
9 1955 (I) (33) 8 0.2077
10 1959 (I) (18) 7 0.3407
11 1962 (I) (9) 6 0.3485
12 1965 (III) (51) 5 0.2182
The HP-filter is applied with a smoothing parameter value, a = 1600.
Table 6. Test for Break in the Real GNP Sample Using Recessions:
1875 (IV)-1981 (IV)
Column
1 2 3
Trough of First Recession Wilcoxon Number of
in the Second Sample Statistic Expansions in
Row (and Length in Months) First Sample
1 1924 (II) (15) 286.0 18
2 1927 (III) (12) 272.0 19
3 1930 (IV) (3) 261.5 20
4 1931 (IV) (30) 259.0 21
5 1934 (III) (12) 232.0 22
6 1937 (IV) (57) 221.5 23
7 1945 (IV) (57) 189.0 24
8 1954 (I) (12) 156.5 25
9 1957 (IV) (15) 146.0 26
10 1960 (III) (18) 132.0 27
11 1962 (IV) (33) 114.5 28
12 1969 (IV) (30) 85.0 29
1 4 5
Trough of First Recession Number of Exact Marginal
in the Second Sample Expansions in Significance
Row (and Length in Months) Second sample Level
1 1924 (II) (15) IS 0.1340
2 1927 (III) (12) 14 0.1100
3 1930 (IV) (3) 13 0.0689
4 1931 (IV) (30) 12 0.0191
5 1934 (III) (12) 11 0.0430
6 1937 (IV) (57) 10 0.0212
7 1945 (IV) (57) 9 0.0744
8 1954 (I) (12) 8 0.2000
9 1957 (IV) (15) 7 0.1210
10 1960 (III) (18) 6 0.0835
11 1962 (IV) (33) 5 0.0724
12 1969 (IV) (30) 4 0.1827
The HP-filter is applied with a smoothing parameter value, 7v = 1600.
Table 7. Test for Break in the Real GNP Sample Using the Expansion to
Following Recession Ratio: 1875 (I)-1983 (III)
Column
1 2 3
Trough of First Expansion Wilcoxon Number of
in the Second Sample Statistic Expansions in
Row (and Length in Months) First Sample
1 1922 (IV) (18) 263.0 18
2 1925 (III) (24) 243.0 19
3 1928 (III) (27) 217.0 20
4 1931 (I) (9) 184.0 21
5 1934 (II) (3) 178.0 22
6 1935 (III) (27) 174.0 23
7 1942 (III) (39) 165.0 24
8 1950 (III) (42) 154.0 25
9 1955 (I) (33) 124.0 26
10 1959 (I) (18) 97.0 27
11 1962 (I) (9) 81.0 28
12 1965 (III) (51) 76.0 29
1 4 5
Trough of First Expansion Number of Exact Marginal
in the Second Sample Expansions in Significance
Row (and Length in Months) Second Sample Level
1 1922 (IV) (18) 15 0.3908
2 1925 (III) (24) 14 0.4321
3 1928 (III) (27) 13 0.4458
4 1931 (I) (9) 12 0.2326
5 1934 (II) (3) 11 0.3712
6 1935 (III) (27) 10 0.4429
7 1942 (III) (39) 9 0.3205
8 1950 (III) (42) 8 0.2320
9 1955 (I) (33) 7 0.4200
10 1959 (I) (18) 6 0.4161
11 1962 (I) (9) 5 0.4297
12 1965 (III) (51) 4 0.3425
The HP-filter is applied using a smoothing parameter value,
[lambda] = 1600.
Table 8. McConnell & Perez-Quiros (2002) Test for a Break in GNP
Growth Volatility, 1875(I)-1983 (III); [T.sub.1] = 1891 (III) and
[T.sub.2] = 1967 (II)
Column
1 2 3
[DELTA]ln [Dev.sub.t]
Row Statistic ([y.sub.t]) ([lambda]) = 1600)
1 sup [F.sub.n] 79.12 (0.000) 79.81 (0.000)
Most probable 1950 (III) 1951 III)
break point
2 exp [F.sub.n] 35.45 (0.000) 36.82 (0.000)
3 ave [F.sub.n] 24.60 (0.000) 25.61 (0.005)
4 [F.sub.1933] (1) 2.15 (0.141) 4.97 (0.026)
5 [F.sub.1946 (1) 65.02 (0.000) 71.80 (0.000)
The p-values are reported beside the test statistics in parentheses.
The HP-filter is applied using a smoothing parameter value of
7L = 1600.
Table 9. McConnell and Perez-Quiros (2002) Test for a Break in
GNP Growth Volatility Using Romer (1989) and Balke and Gordon
(1989) Corrections: 1875-1983; [T.sub.1] = 1887 and [T.sub.2]
= 1965
Column
1 2 3
[DELTA]ln [Dev.sub.t]
Row Statistic ([y.sub.t]) ([lambda] = 100
1 Romer (1989)
sup [F.sub.n] 19.80 (0.000) 12.84 (0.000)
Most probable 1959 1955
break point
2 Balke and Gordon
(1989)
sup [F.sub.n] 28.42 (0.000) 27.67 (0.000)
Most probable 1959 1955
break point
1 4
[Dev.sub.t]
Row Statistic ([lambda] = 6.25)
1 Romer (1989)
sup [F.sub.n] 14.78 (0.000)
Most probable 1959
break point
2 Balke and Gordon
(1989)
sup [F.sub.n] 30.97 (0.000)
Most probable 1959
break point
Table 10. Stock and Watson (2002) Test for a Break in GNP Growth
Volatility, 1875 (n-1983(III); [T.sub.1] = 1891 (III) and
[T.sub.2] = 1967 (II)
Column
1 2 3
[DELTA]ln [Dev.sub.t]
Row Statistic ([y.sub.t]) ([lambda] = 1600)
1 Conditional mean
Quandt likelihood 7.63 (0.022) 2.33 (0.313)
ratio
Most probable break 1940 (II) 1903 (IV)
point
2 Conditional variance
Wald statistic 48.37 (0.000) 66.94 (0.000)
Most probable break 1947 (I) 1947 (II)
point
The p-values are reported beside the test statistics in parentheses.
The HP-filter is applied using a smoothing parameter value of
[lambda] = 1600.
