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Working Paper 9605
ENDOGENOUS MONEY SUPPLY AND
THE BUSINESS CYCLE
by William T. Gavin and Finn E. Kydland
William T. Gavin is vice president and research
coordinator at the Federal Reserve Bank of St. Louis,
and Finn E. K ydland is a professor of economics in
the Graduate School of Industrial Administration at
Carnegie-Mellon University and a research associate
at the Federal Reserve Bank of Cleveland. For helpful
comments and suggestions, the authors thank David
Altig, Mike Bryan, Mike Dotsey, Milton Friedman,
Kevin Lansing, Mike Pakko, Joe Ritter, Ben Russo,
and seminar participants at the University of Texas,
Cornell University, Brigham Young University, and
the Federal Reserve Banks of Dallas, Richmond, and
St. Louis.
Working papers of the Federal Reserve Bank of Cleveland
are preliminary materials circulated to stimulate discussion
and critical comment. The views stated herein are those
of the authors and not necessarily those of the Federal
Reserve Banks of Cleveland or St. Louis, or of the Board
of Governors of the Federal Reserve System.
Working papers are now available electronically through
the Cleveland Fed's home page on the World Wide Web:
http://www.clev.frb.org.
July 1996
Abstract
This paper documents changes in the cyclical behavior of nominal data series that appear
after 1979:IIIQ, when the Federal Reserve implemented a policy to end the acceleration of
inflation. Such changes were not apparent in real variables. A business cycle model with
impulses to technology and a role for money is used to show how alternativ.e money
supply rules ·are expected to affect observed business cycle facts. In this model, changes in
the money supply rules have almost no effect on the cyclical behavior of real variables, yet
have a significant impact on the cyclical nature of nominal variables. Computational
experiments V{ith alternative policy rules suggest that the change in monetary policy in
1979 may account for the sort of instability observed in the U.S. data.
Introduction
One of the main ideas to come out of real business cycle theory is that a significant
share of the variation in the real economy can be accounted for in a simple economic model
of production and consumption that abstracts from money. The credibility of this finding is,
in some way, associated with the relative stability of the covariance structure of real
aggregate
dat~ across
time and countries, as documented by Backus and Kehoe (1992). The
relative constancy of the business cycle facts guides model development.
Unfortunately, attempts to include money and inflation do not have this advantage.
When money and prices are added to the data series, the covariance structure becomes
unstable and the search for a monetary structure becomes more complicated. Backus and
Kehoe present evidence contrasting the stability of the covariance structure of real data series
with the instability in the cyclical behavior of money and prices. They use annual data to
compare the correlations measured across three periods: before World War I, the interwar
period, and post-World War II. Further evidence on the instability of the output-price
correlations can be found in Cooley and Ohanian (1991), Smith (1992), and Wolf (1991). In
this paper, we use postwar quarterly data to document the changes in the nominal data series
that are apparent after October 1979, and to show how a shift in the money supply rule may
account for such instability. 1
The first part of the paper describes the business cycle facts. There appears to be an
important break in the covariance structure in 1979:IIIQ, when the Federal Reserve
implemented a policy to end the acceleration of inflation. 2 We present Wald statistics
suggesting that the changes in cyclical behavior are significant. Because there is some doubt
about whether the distributional assumptions underlying the W ald tests are valid, we also use
2
Monte Carlo methods to construct small-sample test statistics, which provide strong evidence
of a break in the cyclical behavior of money and prices about the time of the Fed's policy
change.
The
~econd
part of the paper experiments with alternative money supply rules in a
business cycle model with impulses to technology. In this model, the cyclical nature of the
nominal
varia~les
is highly sensitive to small changes in the decision rule governing the
money supply. However, such changes have almost no impact on the cyclical behavior of the
real variables. Finally, we present the results of experiments which suggest that attempting to
increase control over the money supply may account for the sort of changes we document.
The Facts
We begin by updating some of the business cycle facts presented in Kydland and
Prescott (1990). The Hodrick-Prescott filter was used to define the business cycle
components of the data series. The first column of statistics in table 1 reports the percentage
standard deviation of each variable, and the other columns report the cross-correlations with
real GDP. The statistics reported in Kydland and Prescott use data for a different sample than
is used here. For GNP components and price data, their sample period begins in 1954:1Q and
ends in 1989:IVQ. Their sample for the monetary data begins in 1959:IQ. We use a sample
of data from 1959:IQ through 1994:1VQ. Instead of GNP, we follow current government
practice and switch to GDP data. Despite these differences in data and time periods, our
reported correlation coefficients are, in most cases, virtually identical to those reported by
Kydland and Prescott. The components of consumption and investment are highly
procyclical. Consumption of nondurables and services is less variable than output, while
3
expenditures on durables and all the components of investment are much more variable than
output, in percentage terms.
Like the real variables, the statistics reported for the price level and money supply
measures in ~able 2 also appear to have nearly the same variability and cross-correlation with
real output growth as reported by Kydland and Prescott. In the case of both the GDP deflator
and the CPI, tile business cycle regularities over the full sample show that prices move
countercyclically. The monetary base varies procyclically and ·contemporaneously with
output, while M 1 and M2 move procyclically and lead output by a quarter or two. Measures
of velocity also move procyclically. Base velocity tends to move coincidentally, while the
velocity of Ml and M2 lag the cycle in real GDP.
Taken as a whole, the statistics show little change with the addition of five years.
However, if we break the sample after 1979:illQ, we see a significant change in some of the
facts. The real variables are apparently unaffected, but the correlation between real output
and the nominal variables is altered dramatically. We should note that orle real variable,
velocity, also appears to behave differently across the two periods. In general, we include
velocity with the monetary variables because the demand for real balances may depend on the
money supply rule.
Table 3 reports the results for the real variables when we treat 1979:illQ as a
breakpoint in the data. It was at the end of this quarter that the Federal Reserve announced a
major change in operating procedures and a new commitment to reducing the inflation rate
through controlling the money supply. Apparently, this policy change had almost no
measurable effect on the cyclical behavior of hours worked or on the components of
consumption and investment.
4
In contrast to the results for the real variables shown in table 3, the business cycle
facts for prices and money shown in table 4 are different in the two periods. The variability
of the price measures is similar across periods. However, the negative cross-correlations
between the ?eflator and real GDP become much larger in absolute value for leads of three to
five quarters. The absolute value of the contemporaneous and leading correlations falls. The
differences ac£oss periods for the GDP deflator are similar to differences observed in the CPl.
Substantial changes occur in the variability of the monetary aggregates around trend.
The narrow monetary aggregates-- the monetary base and Ml --are less variable before
1979:illQ than afterward, while the broad monetary aggregate, M2, becomes less variable
after 1979:illQ. All of the aggregates appear to be less procyclical in the second period than
in the first. The contemporaneous correlation of the monetary base with real GDP falls about
one-fourth, from 0.46 to 0.34. The contemporaneous correlations ofM1 and M2 drop
dramatically, from 0.71 to 0.18 and from 0.64 to -0.04, respectively.
To test whether changes in the correlation coefficients are statistiCally significant, we
construct a Wald test to compare the null hypothesis that the correlation coefficient in the
latter period is equal to the correlation coefficient in the earlier period against the alternative
that they are not equal. 3 If one assumes that the two variables are a random sample drawn
from a bivariate normal distribution, then the Wald statistic is distributed as a Chi-square
with one degree of freedom. The 10 percent critical value is 2.71.
Table 5 reports the Chi-square statistics for the real variables, including the results of
testing 77 cross-correlations between real GDP and the other real variables across the two
periods. Only in two cases (highlighted in the table) do the calculated statistics exceed the 10
percent critical value. In contrast, the top panel of table 6 reports the results for 55 cross-
5
correlations calculated between real GDP and the nominal variables. Here, 33 of the 55 are
above the 10 percent critical value. For every nominal variable, at least part of the crosscorrelation structure is significantly different after 1979:illQ. The bottom panel of table 6
includes results for the velocity variables. Here, 20 of 33 statistics exceed the 10 percent
critical value of 2. 71. Of course, we cannot be sure how much the actual data differ from the
maintained as·~:~umptions of the Wald test. However, our main point is simply to emphasize
the difference between the nominal and real cases.
We provide some check on the reliability of the Wald test by constructing simulated
critical values from 1,000 repetitions of the following experiment. Using actual data from
1959:1Q to 1979:illQ (not deviations from trend), we estimate a bivariate vector
autoregression that includes real GDP and one of each of the other variables. In every case,
we recover estimates of autoregressive parameters and the covariance matrix, which are then
used with a random number generator to create 1,000 artificial series for each pair. These
series are then detrended, the sample split at 1979:illQ, and the cross-correlations calculated.
For each artificial series, the Wald test is constructed to determine stability across the two
periods. The 1,000 tests are sorted by size, and the one-hundredth largest is reported in
parentheses in tables 5 and 6.
Use of the simulated critical value makes the two rejections for the real data no longer
significant (see table 5). In the case of the nominal variables and velocity shown in table 6,
the number of significant changes drops from 33 to 20 out of 55. For the velocity measures,
we find that 12 of the 33 tests reject the null hypothesis. Even though there is a reduction in
the number of rejections using the Monte Carlo method, an overwhelming difference in the
cyclical stability of real versus nominal variables remains.
6
A Model of Aggregate Fluctuations with Monetary Policy
The model used here-- a modification of a monetary model developed by Kydland
( 1991) to ex~mine the role of money in business cycles -- is based on a neoclassical growth
model with technology shocks. It includes a time-to-build technology for producing
consumer dur~bles, which affect the ability and willingness of households to substitute
intertemporally. In each period, the consumer decides how to allocate time between work
and leisure. Larger money balances increase the amount of time that can be allocated to these
two activities. Money enters the economy as a government transfer. In Kydland, the money
supply is treated as an exogenous univariate process. In this paper, the money supply
function also depends on last period's output. This extension allows us to investigate the
implications of a central bank's decision about whether to focus more sharply on nominal or
real variables.
The Economy
The model economy is inhabited by many households that are all alike. Their
available time, T, is spent in three basic activities: input in market production, leisure, and
transaction-related activities such as trips to the bank, shopping, and so on. The role of
money is to make the third activity less time consuming. By holding larger money balances,
households have more time for work and/or leisure. Assume that the time spent on
transactions-related activities in period tis given by the expression
7
where w0 > 0, w1 > 0, 0 < w2 < 1, II\ is the nominal money stock, and p1 is the price of money
relative to that of physical goods. Thus, the amount of time saved increases as a function of
real money holdings, but at a decreasing rate. 4 Leisure in period t, then, is
where n1 is time spent in market production. Without loss of generality, we choose units so
that T -w0 equals one.
Each household maximizes
E
L
t =
Wu(ctA,Qt),
0
where c is consumption, d is the stock of durables (the services of which are proportional to
the stock), and 0 <
~
< 1 is a discount factor. The functional form of the current-period
utility function is
where J..l, 8, and y are positive parameters, with J..l + 8 < 1. This special case of the CES
function, with unitary substitution elasticities among the goods, was chosen for two reasons.
First, within this class, it is consistent with long-run hours worked per person being roughly
constant (as in postwar U.S. data), despite the large increase in real hourly compensation.
Second, unitary elasticity between consumer durables and nondurables is evidenced by the
fact that the long-run share of nominal expenditures on durables has remained essentially
8
constant in the postwar period, in the face of a sizable decline in their relative price.
The time-to-build specification of Kydland and Prescott (1982) is applied to
consumer durables. Stocks of finished and unfinished consumer durables are governed by the
laws of motion,
sj,t+I
= sj+I,t• j = 1, ... , 1 - 1,
where 0 < o< 1 is the depreciation rate and s11 is the addition to the stock of durables initiated
in period t - J + 1. Suppose additions to durables planned in period t do not start producing
services until period t + J, as expressed by the two relations above. The expenditures,
however, are distributed with a fraction <l>j in the jth stage from the last for all j. Formally,
then, total expenditures on durables in period t are
J
where
L <j>.
. I
J;
J
1.
The budget constraint for the typical individual is c1 + x1 + p1mt+ 1 =w1n1 + p1m1 + p1v1,
where v, is a nominal lump-sum transfer from the government.
Aggregate output, Y1 , is given by the product of the labor input and aggregate
productivity: Y1 =~ N1• In equilibrium, the real wage rate, w1, will equal the level of
productivity, which changes over time according to
~+I
= p~
+ .A't+ 1, where 0 < p < 1.
The innovations are assumed to be normally distributed with positive mean and variance
ai .
Laws of motion analogous to those of individual variables govern the aggregate
quantities of durables and the addition to the stock of durables initiated in each period. The
9
distinction between individual and aggregate variables, represented here by lower- and
upper-case letters, respectively, plays a role when computing the equilibrium of models in
which the equilibrium is not simply the solution to a stand-in planner's problem. In
particular, this is true in models with government policy. The details are available in
Kydland (1989).
Steady State and Calibration
We use a priori knowledge to quantify most parameters, such as capital depreciation
rates, capital-output ratios, weights on lags in durable expenditures, steady-state time
allocation, and so on. Such restrictions are easily imposed within this framework and, in
principle, leave no free parameters, although accurate measurements are not necessarily
available for all of them at this point.
To obtain the steady state, we first substitute for c1 from the budget constraint into the
utility function. Omitting time subscripts for steady states, we have (because x = s)
c = wn- x.
We also have X =od.
If there is no lag in the production of durables, that is, J = 1, then the implicit
steady-state rental price q of durables in terms of nondurables is r + o, where r is given by
1/(1 +r) =
~-
If, on the other hand, it takes time to produce durables, then this price becomes
q
To determine relations between the steady-state values of c, d, and n on the one hand,
10
and values of the parameters 11 and
e on the other, suppose first that the sum of services from
nondurables and durables is c + qd. Then, from the condition MU/MUc
(1 -11 - 8)/Q
Using
=w, one obtains
(!l + 8)w/( c + qd).
this condition can be rewritten as
Q
c+qd
The values of 11 and
~
e
e now follow from the condition
c
qd
Finally, the first-order condition with respect to money can be solved for steady-state
pm in terms of the given parameters. Steady-state p, then, is implied by the assumed steadystate nominal money stock, m.
The model is calibrated as follows. The discount factor
0-P)IP =
Pis chosen such that
r = 0.01, corresponding to a 4 percent annual real rate of interest. The
depreciation rate of durables is set to 0.05. The value of y is two, which means more
curvature on the utility function than that corresponding to logarithmic utility. This value is
consistent with the empirical findings of Neely, Roy, and Whiteman (1995).
Steady-state n is set equal to 0.3. This value is the household's share of the timeT -w0
allocated to market activity. Although we do not have any independent measurements of w0 ,
it is probably small in relation to total timeT. The value for n, then, is in line with the
measurements of Ghez and Becker (1975).
11
The share of output going to investment in durables is 0.3, corresponding roughly to
the fraction spent on producer and consumer durables in the United States. From these
values, it follows that~= 0.20 and 8 = 0.10. Average Z (and therefore w) is chosen so that
steady-state output is one. The value of J, the time needed to build durables, is set equal to
three, and the values of <j> 1, <j> 2, and <1> 3 are one-third. Consistent with the evidence that
changes in the.technology level are long-lived (see, for example, Prescott [1986]), the
autocorrelation parameter pis set equal to 0.95.
The values assumed for w1 and w2 are 0.0065 and 0.50, respectively. These
magnitudes can be understood through a marginal evaluation around the average. If the real
money stock, pm, is increased 1 percent relative to its steady state, then a household's
resulting weekly time saving is less than a minute. The implied steady-state velocity is 5.3,
which corresponds to average M1 velocity since 1959. Without loss of generality, steadystate nominal money stock is chosen to equal one, and the price level, p, is then determined
accordingly.
The model economy we use in our computational experiments is a quadratic
approximation around the steady state. The resulting structure fits into the general
framework outlined in Kydland (1989), and the dynamic competitive equilibrium is
computed as described there.
Monetary Policy
We modify the basic model to include a monetary policy function that changes the
money supply growth rate in response to last period's level of output and the money supply.
The alternatives we examine are all specific instances of the following general rule:
12
where v 1 is the proportional response to last period's output level, v2 is the response to the
money stock, and
E 1 is
the money supply shock in period t. If both v 1 and v2 are 0, the money
supply is a random walk. One way to judge the magnitude of the vi's is to note that the
steady-state values of Y and M are both one. We do not estimate or calibrate the policy
function in this paper. Recent work by Salemi ( 1995) suggests that, in future research, we
may be able to calibrate the various policy rules that were in effect in the United States in the
postwar period. In this paper, we merely show that the quantitative implications of
alternative policy rules on the nominal-to-nominal and nominal-to-real correlations can be
large.
Table 7 includes cyclical statistics calculated from the model economy with a fixed
money stock; that is, with the vi's and the variance of E equal to 0. Like the U.S. economy,
our model generates components of consumption and investment that are highly procyclical.
In percentage terms, consumption of nondurables and services is less variable, and
expenditures on durables are much more variable, than output. The price level
(conventionally measured) is countercyclical. The cyclical standard deviation of the price
level is 0.67, a little lower than the average standard deviation of the GDP deflator in the U.S.
data (0.87 for the full sample [see table 2]). Without the lag in the production of durables,
the price fluctuation is somewhat smaller. Velocity in the model moves procyclically.
With no money-stock variability, the price fluctuation in this model is below that
observed in U.S. data. Still, the benchmark of a constant money stock (interpreted as a
constant growth rate) produces variability in the price level that is more than half of output
13
variability. The first row of table 8 repeats statistics from the benchmark cao;;e. When the
benchmark assumptions are changed by increasing the variance of the money supply shock,
the cyclical standard deviation of the price level increases. Row four shows that when the
standard deviation of the money supply shock is increased from 0 to 0.60 percent, the
standard deviation of the price level rises to 1.11 percent, that of velocity increases from 0.58
to 0.85 percent, and the contemporaneous correlation coefficient between the conventional
price level and output becomes -0.57, close to that in U.S. data.
Table 8 also reports selected statistics from experiments involving alternative policy
rules. One might think of the money supply error as a policy control error. Even if this error
is set to 0, allowing money growth to be correlated with output induced realistic levels of
variability in the nominal variables. This can be seen in the second row (cao;;e II). Compared
to the benchmark case in row one, the variance of the price level increases and the behavior
of the price level switches from highly countercyclical to highly procyclical. The variance of
the money stock is driven by the variance in output. As can be seen in both cases II and VI,
allowing money growth to depend on output this way causes velocity to be highly variable
and strongly procyclical.
In case ill, the money supply error variance is set to 0 and v 1 is set to 0.10, as in case
II, but v2 is lowered to -0.05, so that the money stock is stationary. This change reduces price
variability by about half, causes the price level and inflation to become countercyclical, and
induces a switch in the sign of the correlation between money growth and inflation.
In the fifth row, we report the results of the experiment when money supply growth
responds to the level of the money stock but not to output. The most important effect is the
reduction of the contemporaneous correlation between inflation and money growth that was
14
induced by the introduction of uncertainty into the money supply process (0.77 in case IV).
In the last two experiments, we leave the variance of the money shock at 0.6 percent
and set v 1 to 0.1. We set v2 equal to 0 in case VI and to -0.05 in case Vll. Adding variance to
the money shock when money growth is tied to past output increases the variability of both
money and the price level. Adding this variance also induces a strong positive correlation
between
infla~on
and money growth. As shown in row seven, moving away from a unit root
in the money supply process also makes a substantial difference in the results. Most
noticeable are the reduction in the standard deviation of the price level from 1.22 to 0.48, and
the switch in the sign of the correlation between output and the price level from 0.73 to -0.90.
Setting v2 equal to -0.05 also changes the sign on the correlation between inflation and output
and reduces the correlation of money growth and inflation.
To summarize the main results in table 8, we find that changes in the money supply
process could have significant effects on both the variability of the price level and the size
and sign of the correlation between the price level and output. The size and sign of the
inflation/output correlations and the inflation/money growth correlations depend on the size
of the policy parameters. The variability of velocity is also quite sensitive to alternative
policy specifications.
Next, we look more closely at price-output, inflation-output, and inflation-money
growth correlations. Figure 1 shows the effect of varying the response to output, v 1, from 0 to
0.2 while holding the response to the money supply, v2 , at -0.02. Setting v 1 to 0 results in a
strong negative correlation between the price level and output (op.y). As v 1 is rai.;;ed to 0.15,
the correlation coefficient rises toward 0, and with v 1 at 0.2, op.y becomes greater than onehalf. The inflation-output correlation (odp,y) follows the same general pattern as op.y· Figure 1
15
also shows how the contemporaneous correlation between inflation and money growth
( adm,dp)
changes as the policy response to output is varied. Here,
adm, dp
is small and positive
when v 1 equals 0, rises to a peak when v 1 is around 0.15, and declines as v 1 is increased
further.
Figure 2 shows how the correlations change when we vary the policy response to the
money stock,
¥2, while holding the response to output, v 1, at 0.1.
The negative correlation
between output and the price level rises toward 0 as v2 is raised from -0.05 toward 0. Most of
the change in the correlation occurs after v 2 is raised above -0.02. The same pattern emerges
in the correlation between inflation and output. The contemporaneous correlation between
inflation and money growth rises to a peak as v2 is raised from -0.05 to about -0.0 1. It then
declines as v2 is increased to 0.
These dramatic changes in the covariance structure of the nominal series occur in a
model in which the monetary rule has almost no impact on the real variables. Of all the real
variables, hours worked is the most affected by the alternative monetary regimes. Even so,
the results are not shown here because the differences are not apparent at two significant
digits. We also experimented with alternative specifications of the business cycle model,
including versions with a shorter time-to-build for durable goods. In all cases, the results are
basically the same as for the specification presented in this paper: Changes in the monetary
policy rule have large effects on the correlations among nominal variables and on the crosscorrelation structure between nominal and real series, without having any noticeable impact
on the real variables.
16
Conclusion
The behavior of money and prices over the business cycle defies simple classification
in empirical regularities. We document the relative instability of the behavior of nominal
variables vis-a-vis the behavior of real variables. Looking at the stability of crosscorrelations between real GDP and each of seven real variables -- personal consumption
expenditures, expenditures on nondurables and services, expenditures on consumer durables,
private domestic investment, fixed investment, hours worked, and productivity -- we found
that only in two of 77 cases did the
x2 statistic reject the null hypothesis of stability at the 10
percent critical level. When we constructed Monte Carlo estimates of the statistic's
distribution, even those two rejections were overturned. The result for the nominal variables
--the GDP deflator, CPI, monetary base, Ml, and M2 --was much different. In this case, we
were able to reject stability in 33 of 55 cases using the 10 percent critical region of the
asymptotic distribution. When we used the simulated critical values, the number of
rejections dropped to 20.
In the second part of the paper, we explore the possibility that the instability in the
cyclical behavior of the nominal data is caused by instability in the money supply function.
We modify a real business cycle model with time-to-build consumer durables and a laborleisure trade-off by adding a time-saving role for money balances. We also include a
monetary policy function that could react to both real output and the money supply. In a
variety of experiments testing the sensitivity of the model to the policy function parameters,
we find that the cross-correlations of nominal variables with real GDP, and the crosscorrelations of inflation with lagged money growth, are sensitive to the specification of the
policy rule. Whether the price level is procyclical or countercyclical depends importantly on
17
whether the money stock is allowed to react to real factors and to the amount of persistence
that the authorities induce in money supply shocks. These findings are obtained in a model in
which the specification of the monetary rule has almost no impact on the cyclical behavior of
real variables.
18
Endnotes
1. Bryan and Gavin (1994) show how the change in the money supply rule in 1979:IDQ might
explain the change in the cross-correlation between inflation and monetary base growth that
occurred about that time.
2. , Rolnick and Weber ( 1994) show that the covariance structure of money, output, and prices
seems to depend'on whether a country is on a fiat or commodity money standard. Within a fiat
money regime, Friedman and Kuttner (1992) use results from vector autoregressions to argue that
a deterioration in nominal-real relationships followed the Federal Reserve's policy change in
1979:IDQ.
3. See Ostle (1963), pp. 225-227, for a detailed description of the test statistic used.
4. One could also let the trade-off be a function of expenditures. Since hours and consumption
have a fairly high correlation, that modification would increase the amplitude of the price level.
Thus, abstracting from it gives a conservative estimate of the amount of velocity and price-level
volatility accounted for. Finally, one could let transactions require the use of physical resources
rather than time, as is done in Sims ( 1989). While that is not unreasonable, the view here is that
time is the main resource expended in the act of carrying out the transactions involved in this
environment.
19
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,:
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Control Theory to Interpret the Policy Equation of a Vector Autoregression,"
Journal of Economic and Business Statistics, vol. 13, no. 4 (October 19.95),
pp. 419-33.
Sims, Christopher A. "Models and Their Uses," American Journal of Agricultural
Econoft:ics, vol. 71, no. 2 (May 1989), pp. 489-94.
Smith, R. Todd. "The Cyclical Behavior of Prices," Journal of Money, Credit, and
Banking, vol. 24, no. 4 (November 1992), pp. 413-30.
Wolf, Holger C. "Procyclical Prices: A Demi-Myth?" Federal Reserve Bank of
Minneapolis, Quarterly Review, vol. 15 (Spring 1991), pp. 25-28
Table 1
Cyclical Behavior of U.S. Quarterly Data / Real Variables
(Deviations from Trend)
Std.
Dev.
x(t-5)
x(t-4)
x(t-3)
GDP in 1987 Dollars
(RGDP)
Consumption
1.62
0.05
0.25
0.46
0.68
0.86
1.00
0.86
0.68
1.23
0.27
0.45
0.62
0.77
0.87
0.88
0.73
Durables
5.00
0.34
0.48
0.59
0.71
0.78
0.80
Nondurables and
Services
Private Domestic
Investment
Fixed Investment
0.83
0.18
0.38
0.57
0.73
0.84
7.72
0.14
0.29
0.46
0.63
5.63
0.15
0.32
0.50
Hours Worked
(Estab.)
Productivity
1.54
-.19
-.01
0.80
0.47
0.54
Variable x
(RGDP/Hours
Worked)
Source: Authors calculations.
Correlations with RGDP from 1959:IQ to 1994:IVQ
x(t-2)
x(t-1)
x(t)
x(t+1)
x(t+2)
x(t+3)
x(t+4)
x(t+5)
0.46
0.25
0.05
0.54
0.33
0.10
-.09
0.61
0.40
0.18
-.04
-.22
0.86
0.74
0.59
0.40
0.19
0.01
0.79
0.91
0.76
0.55
0.31
0.08
-.15
0.68
0.83
0.90
0.81
0.63
0.42
0.19
-.03
0.19
0.42
0.67
0.88
0.92
0.86
0.73
0.56
0.37
0.55
0.56
0.47
0.35
-.01
-.26
-.48
-.58
-.59
Table 2
Cyclical Behavior of U.S. Quarterly Data / Nominal Variables and Velocity
(Deviations from Trend)
Variable x
Std.
Dev.
Correlations with RGDP from 1959:IQ to 1994:IVQ
x(t-5)
x(t-4)
x(t-3)
x(t-2)
x(t-1)
x(t)
x(t+1)
x(t+2)
x(t+3)
x(t+4)
x(t+5)
GDP Deflator
0.87
-.57
-.65
-.71
-.72
-.67
-.58
-.46
-.33
-.18
-.04
0.10
CPI
1.42
-.60
-.71
-.76
-.77
-.71
-.59
-.42
-.26
-.07
0.11
0.27
Monetary Base
0.88
0.11
0.20
0.26
0.32
0.37
0.38
0.34
0.29
0.22
0.14
0.09
M1
1.94
0.24
0.30
0.35
0.39
0.38
0.31
0.20
0.10
0.01
-.05
-.07
M2
1.38
0.40
0.51
0.59
0.62
0.58
0.45
0.26
0.08
-.09
-.25
-.37
Base Velocity
1.40
-.35
-.24
-.08
0.13
0.34
0.55
0.50
0.39
0.28
0.18
0.07
M1 Velocity
2.29
-.38
0.32
-.25
-.13
0.03
0.22
0.26
0.26
0.24
0.20
0.14
M2 Velocity
1.71
-.56
-.51
-.41
-.23
0.01
0.29
0.37
0.40
0.41
0.42
0.40
Source: Authors calculations.
Table 3
Cyclical Behavior of Real Variables in Subperiods
Variable x
Std.
Dev.
Correlations with RGDP from 1959:IQ to 1979:IIIQ
x(t-5)
x(t-4)
x(t-3)
x(t-2)
x(t-1)
x(t)
x(t+1)
x(t+2)
x(t+3)
x(t+4)
x(t+5)
Real GDP
1.67
0.03
0.24
0.46
0.69
0.86
1.00
0.86
0.68
0.45
0.22
-.01
Consumption
1.26
0.19
0.40
0.59
0.78
0.87
0.89
0.74
0.54
0.30
0.02
-.21
Durables
5.18
0.29
0.46
0.58
0.72
0.80
0.83
0.67
0.45
0.20
-.07
-.28
Nondur. & Serv.
0.86
0.10
0.31
0.53
0.73
0.83
0.84
0.73
0.56
0.35
0.09
-.14
Pvt. Dom. Invest.
7.78
0.14
0.29
0.46
0.64
0.78
0.91
0.76
0.57
0.34
0.11
-.15
Fixed Investment
5.87
0.13
0.31
0.50
0.70
0.83
0.89
0.79
0.62
0.41
0.17
-.07
Hours
1.58
-.23
-.06
0.16
0.39
0.63
0.85
0.92
0.86
0.74
0.56
0.34
0.89
0.45
0.54
0.57
0.60
0.51
0.38
0.00
-.24
-.48
-.59
-.61
(Estab.)
Productivity
Std.
Dev.
Correlations with RGDP from 1979:IVQ to 1994:IVQ
x(t-5)
x(t-4)
x(t-3)
x(t-2)
x(t-1)
x(t)
x(t+1)
x(t+2)
x(t+3)
x(t+4)
x(t+5)
Real GDP
1.56
0.07
0.26
0.45
0.64
0.87
1.00
0.87
0.67
0.47
0.30
0.14
Consumption
1.18
0.38
0.53
0.64
0.74
0.86
0.87
0.71
0.54
0.37
0.22
0.07
Durables
4.72
0.41
0.52
0.60
0.67
0.74
0.74
0.52
0.34
0.14
0.00
-.14
Nondur. & Serv.
0.80
0.31
0.49
0.61
0.71
0.85
0.88
0.77
0.62
0.48
0.34
0.21
Pvt. Dom. Invest.
7.63
0.12
0.26
0.43
0.60
0.80
0.91
0.77
0.50
0.26
0.04
-.16
Fixed Investment
5.22
0.18
0.34
0.48
0.65
0.84
0.93
0.83
0.65
0.43
0.23
0.02
Hours
1.54
-.14
0.05
0.24
0.46
0.73
0.91
0.93
0.85
0.72
0.57
0.40
0.66
0.52
0.53
0.51
0.46
0.39
0.29
-.06
-.33
-.51
-.58
-.59
(Estab.)
Productivity
Source: Authors calculations.
Table 4
Cyclical Behavior of Nominal Variables and Velocity in Subperiods
Variable x
Std.
Dev.
Correlations with RGDP from 1959:IQ to 1979:IIIQ
x(t-5)
x(t-4)
x(t-3)
x(t-2)
x(t-1)
x(t)
x(t+1)
x(t+2)
x(t+3)
x(t+4)
x(t+5)
GDP Deflator
0.78
-.41
-.52
-.66
-.74
-.72
-.65
-.55
-.42
-.23
-.04
0.18
CPI
1.38
-.49
-.67
-.81
-.86
-.83
-.74
-.57
-.38
-.16
0.09
0.30
Monetary Base
0.69
-.21
-.12
0.00
0.15
0.32
0.46
0.54
0.58
0.53
0.44
0.35
M1
0.94
-.16
0.03
0.28
0.52
0.65
0.71
0.67
0.56
0.41
0.27
0.11
M2
1.63
0.45
0.61
0.73
0.78
0.76
0.64
0.45
0.20
-.04
-.28
-.46
Base Velocity
1.07
-.10
0.07
0.24
0.44
0.61
0.79
0.60
0.40
0.23
0.09
-.07
M1 Velocity
0.96
-.11
-.04
-.01
0.09
0.27
0.51
0.39
0.29
0.20
0.11
0.03
M2 Velocity
1.59
-.62
-.63
-.59
-.44
-.23
0.07
0.17
0.29
0.39
0.49
0.55
Variable x
Std.
Dev.
x(t-5)
x(t-4)
x(t-3)
x(t+4)
x(t+5)
GDP Deflator
0.97
-.78
-.84
-.81
-.72
-.63
-.50
-.36
-.24
-.13
-.04
.02
CPI
1.43
-.78
-.78
-.71
-.64
-.55
-.38
-.21
-.08
0.04
0.14
0.22
Monetary Base
1.10
0.44
0.54
0.55
0.51
0.46
0.34
0.19
0.09
0.02
-.04
-.06
M1
2.82
0.51
0.51
0.47
0.42
0.33
0.18
0.02
-.09
-.15
-.18
-.16
M2
0.94
0.28
0.28
0.25
0.22
0.14
-.04
-.18
-.21
-.21
-.23
-.23
Base Velocity
1.82
-.62
-.55
-.38
-.15
0.13
0.40
0.45
0.40
0.33
0.26
0.17
M1 Velocity
3.40
-.61
-.55
-.42
-.26
-.06
0.17
0.28
0.31
0.31
0.27
0.20
M2 Velocity
1.90
-.48
-.35
-.17
0.05
0.33
0.60
0.63
0.54
0.44
0.34
0.24
Source: Authors calculations.
Correlations with RGDP from 1979:IVQ 1994:IVQ
x(t-2)
x(t-1)
x(t)
x(t+1)
x(t+2)
x(t+3)
T able 5. T ests for Stability of R eal V ariables
C hi-square testfor equality of correlations across sam ple periods (break in 1979:IIIQ )
V ariable x
C onsum ption
x(t-5)
x(t-4)
x(t-3)
x(t-2)
x(t-1)
x(t)
x(t+1)
x(t+2)
x(t+3)
x(t+4)
1.30
0.99
0.23
0.20
0.11
0.16
0.13
0.00
0.19
1.29
(6.12)
(5.77)
(5.59)
(6.52)
(8.36)
(9.05)
(6.04)
(5.31)
(5.40)
(6.16)
0.64 (5.91) 0.23 (5.96) 0.01 (6.67) 0.29 (7.64) 0.69 (8.37) 1.94 (7.44) 1.70 (5.01) 0.52 (4.41) 0.10 (4.78) 0.15 (5.10)
x(t+5)
2.55
(6.80)
D urables
0.62
(5.51)
N ondurs.&
1.63
1.44
0.40
0.07
0.13
0.56
0.31
0.29
0.87
2.40
4.10
Services
(5.68)
(5.32)
(4.96)
(5.87)
(7.57)
(10.15)
(7.96)
(7.64)
(7.44)
(7.87)
(8.07)
Investm ent
0.01
0.03
0.06
0.14
0.11
0.01
0.01
0.32
0.24
0.15
0.01
(5.82)
(6.10)
(5.76)
(6.10)
(6.95)
(9.25)
(4.82)
(3.07)
(3.00)
(3.21)
(3.62)
Fixed Investm ent
0.08
0.03
0.01
0.26
0.09
1.93
0.45
0.08
0.04
0.13
0.26
(6.86)
(6.68)
(7.47)
(7.71)
(9.45)
(12.71)
(7.95)
(5.47)
(4.65)
(4.56)
(5.32)
Hours (Estab.)
0.23
0.39
0.23
0.24
1.07
2.98
0.51
0.07
0.10
0.00
0.18
(6.22)
(6.18)
(5.80)
(5.22)
(4.51)
(5.61)
(9.07)
(9.49)
(7.88)
(6.99)
(6.67)
Productivity
0.25
0.01
0.26
1.20
0.77
0.35
0.12
0.31
0.06
0.00
0.05
(9.69)
(8.40)
(6.80)
(5.31)
(4.87)
(4.85)
(3.76)
(4.21)
(5.77)
(6.63)
(7.07)
N ote:Shading indicates thatthe Wald statistic rejects stability assum ing the asym totic 10% criticalvalue, 2.71. Sim ulated 10% criticalvalues are show n in parentheses.
Source:A uthors calculations.
Table 6. Tests for Stability of Nominal Variables
Chi-square test for equality of correlations across sample periods (break in 1979:IIIQ)
Variable x
x(t-5)
x(t-4)
x(t-3)
x(t-2)
x(t-1)
x(t)
x(t+1)
x(t+2)
x(t+3)
x(t+4)
x(t+5)
GDP
Deflator
CPI
12.14
(9.59)
8.61
(7.08)
15.17
(7.39)
16.64
(6.93)
1.22
(8.75)
13.84
(10.33)
1.87
(7.37)
16.84
(6.72)
9.39
6.13)
5.51
(8.76)
3.58
(10.76)
1.84
(9.70)
12.64
(6.38)
1.69
(5.92)
14.85
(10.17)
0.03
(11.10)
8.97
(12.46)
5.70
(7.03)
0.51
(6.89)
23.08
(11.60)
1.05
(11.94)
10.65
(10.89)
0.97
(7.24)
6.04
(7.75)
24.05
(10.12)
1.74
(11.87)
9.76
(8.67)
0.69
(8.02)
17.08
(7.60)
21.68
(7.84)
1.88
(10.39)
6.28
(6.56)
5.62
(7.83)
21.06
(7.46)
14.60
(6.74)
1.25
(9.04)
3.47
(5.83)
10.74
(8.65)
17.21
(8.02)
5.95
(6.86)
0.41
(8.06)
1.31
(6.05)
10.80
(9.28)
11.68
(9.15)
0.94
(7.85)
0.00
(7.64)
0.08
(6.66)
8.62
(9.56)
6.65
(9.19)
0.08
(9.50)
0.80
(7.42)
0.26
(7.06)
6.06
(10.43)
2.40
(8.81)
2.29
(10.48)
Monetary
Base
M1
M2
Tests for Stability of Velocity
Chi-square test for equality of correlations across sample periods (break in 1979:IIIQ)
Variable x
x(t-5)
x(t-4)
x(t-3)
x(t-2)
x(t-1)
x(t)
x(t+1)
x(t+2)
x(t+3)
x(t+4)
x(t+5)
Base
Velocity
M1 Velocity
12.57
(7.85)
11.46
(7.16)
1.35
(10.28)
15.21
(7.92)
10.57
(6.68)
4.27
(10.29)
13.61
(7.55)
6.17
(7.67)
8.25
(9.17)
12.91
(6.69)
4.40
(6.90)
9.10
(8.02)
11.07
(6.48)
3.81
(6.06)
10.
(7.19)
13.79
(8.67)
5.03
(7.80)
12.95
(8.67)
1.46
(4.91)
0.47
(6.71)
10.94
(8.78)
0.00
(4.46)
0.02
(5.67)
3.23
(8.24)
0.43
(5.05)
0.50
(6.08)
0.10
(9.53)
1.
(4.98)
0.96
(5.92)
1.01
(10.20)
1.87
(4.54)
1.00
(5.84)
4.48
(10.89)
M2 Velocity
Note: Shading indicates that the Wald statistic rejects stability assuming the asymtotic 10% critical value, 2.71. Simulated 10% critical values are shown in
parentheses.
Light shading indicates that stability is not rejected using the simulated critical values.
Source: Authors’ calculations.
T able 7. C yclicalB ehavior of Econom y w ith Fixed M oney Stocka
C ross-C orrelation of Outputw ith
Std.
D ev.
x(t-5)
x(t-4)
x(t-3)
x(t-2)
x(t-1)
x(t)
x(t+1)
x(t+2)
x(t+3)
x(t+4)
x(t+5)
Output
1.15
(.11)
-.11
(.11)
.01
(.11)
.17
(.10)
.42
(.08)
.69
(.05)
1.00
(.00)
.69
(.05)
.42
(.08)
.17
(.10)
.01
(.11)
-.11
(.11)
N ondurables
C onsum ption
.59
(.05)
-.17
(.09)
-.05
(.09)
.09
(.09)
.36
(.07)
.65
(.05)
.97
(.00)
.69
(.05)
.47
(.08)
.31
(.10)
.13
(.12)
.01
(.12)
D urables Expenditures
2.57
(.23)
-.06
(.11)
.06
(.11)
.21
(.10)
.44
(.08)
.70
(.05)
.99
(.00)
.67
(.04)
.38
(.07)
.10
(.09)
-.03
(.10)
-.15
(.10)
Hours
.43
(.04)
-.03
(.12)
.09
(.11)
.24
(.10)
.45
(.08)
.69
(.05)
.98
(.00)
.66
(.04)
.35
(.07)
.03
(.09)
-.08
(.09)
-.19
(.09)
Price Level
.67
(.07)
.21
(.08)
.10
(.08)
-.03
(.08)
-.31
(.06)
-.61
(.04)
-.93
(.01)
-.68
(.05)
-.50
(.08)
-.38
(.10)
-.20
(.12)
-.07
(.12)
V elocity
.59
(.05)
.04
(.13)
.16
(.12)
.30
(.10)
.47
(.08)
.67
(.05)
.92
(.01)
.59
(.04)
.26
(.05)
-.10
(.07)
-.18
(.07)
-.28
(.07)
V ariables x
a T hese are the m eans of 50 m odelhistories, each of w hich w as 144 periods long. T he num bers in parentheses are standard deviations.
Source:A uthors calculations.
Table 8. Cyclical Behavior under Alternative Specifications of the Money Supply Rule
a.
VI
v2
(Jp
(Jpy
om
Omy
Ovel
Ovel,y
at.p,y
Ot.m,t.p
I
0
0
0
.67
-.93
0
0
.59
.92
-.39
0
II
0
.10
0
.94
.96
.38
-.1.5
2.18
1.00
.48
-.29
III
0
.10
-.05
.47
-.92
.37
.00
.95
.84
-.36
.25
IV
.6
0
0
1.11
-.57
.72
-.02
.85
.61
-.26
.77
v
.6
0
-.05
.67
-.93
.73
-.02
.89
.60
-.39
.11
VI
.6
.10
0
1.22
.73
.82
-.08
2.28
.96
.36
.58
VII
.6
.10
-.05
.48
-.90
.81
-.01
1.15
.69
-.36
.19
Case
Source: Authors' calculations.
Figure 1: Model Correlations Under Alternative
Policy Responses to Output a
1
~------------------------------~
0.8
(j
dm,dp
0.6
..... - .... -.-
--
.. -
0.4
0.2
-0.2
-0.4
-0.6
-0.8
-1
~--~--~--~--~--~--~--~--~
0
0.05
0.1
0.15
0.2
a In these experiments, the response to the money
stock, 1> 2 , was held constant at -0.02.
Source: Authors' calculations.
Figure 2: Model Correlations Under Alternative
Policy Responses to the Money Stock a
1
~---------------------------------~
0.8
.'
'.
0.6
,·
()
'.
'.
'.
'.
,·
dm,dp
0.4
...............................
_
0.2
0
-0.2
~----------------------~+-------~
----------------~~-------------~--·--·///
-0.4
-0.6
-0.8
-1
~----~------~----~----~------~
-0.05
-0.04
-0.03
-0.02
-0.01
0
a In these experiments, the response to output, U 1
was held constant at 0.1.
Source: Authors' calculations.
,
@FedFRASER