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Productivity Shocks and
Real Business Cycles
Charles L. Evans
Working Papers Series
issues in Macroeconomics
Research Department
Federal Reserve Bank of Chicago
December 1991 (WP-91 -22)
FEDERAL RESERVE BANK
OF CHICAGO
Productivity Shocks and Real Business Cycles
1*
Charles L. Evans
Federal Reserve Bank of Chicago
May 1989
Revised
November 1991
Abstract
Productivity shocks play a central role in real business cycles as an
exogenous impulse to macroeconomic activity. However, measured Solow/Prescott
residuals do not behave as an exogenous impulse. Rather, econometric evidence
provided in this paper indicates that (1) money, interest rates, and
government spending Granger-cause these impulses;
and (2) a substantial
component of the variance of these impulses (between one quarter and one half)
is attributable to variations in aggregate demand.
These results are robust
to a number of econometric issues, including measurement errors, specification
of the production function, and certain forms of omitted real variables.
Address:
Charles L. Evans
Research Department
Federal Reserve Bank of Chicago
P.0. Box 834
Chicago, IL 60690-0834
(312) 322-5812
This paper has evolved from Chapter 2 of my Carnegie Mellon Ph.D.
dissertation.
I thank my committee members, Bennett McCallum (chairman),
Martin Eichenbaum, Albert Marcet;
also Toni Braun, Robert Clower, Finn
Kydland, the editors of this Journal and an anonymous referee for helpful
comments. I alone am responsible for any errors. The views expressed in this
paper are solely those of the author and do not necessarily represent those
of the Federal Reserve Bank of Chicago or the Federal Reserve System.
1
1.
Introduction
Productivity shocks play a central role in Real Business Cycle theories
as an impulse to macroeconomic activity (as in Kydland and Prescott (1982),
Hansen
(1985),
example).
and
then
Altug
(1985),
and
King,
Plosser,
and
Rebelo
(1988),
for
In characterizing the business cycle properties of these models,
comparing
them with
the
cyclical
properties
of
the
data,
these
researchers assume that productivity shocks are exogenous and uninfluenced by
other economic factors.
And yet no evidence currently exists to support this
standard Real Business Cycle assumption.
Many
critics
of
Real
Business
Cycle
(RBC)
exogeneity of procyclical productivity shocks;
these
shocks
to be
endogenous.
For
theories
question
the
indeed, many theories predict
example,
Summers
(1986)
argues
that
empirical measures of the change in total factor productivity are contaminated
by labor hoarding phenomena;
consequently, aggregate demand impulses can give
rise to a procyclical productivity measure.
Mankiw (1989) argues that the
large growth in total factor productivity from 1939-1944 is interpreted most
plausibly as a demand-driven response to the military buildup of World War II.
Hall (1988) finds evidence in annual data that cost-based measures of Solow
residuals covary with exogenous instruments:
to
noncompetitive
forces.
Murphy,
he attributes this endogeneity
Shleifer,
and
competitive theories with external increasing returns;
Vishny
(1989)
survey
these theories predict
that changes in total factor productivity are endogenous and demand-driven.
Caballero and Lyons (1990) find evidence in annual data of external increasing
returns
in
manufacturing.
According
to
these
criticisms,
measures
of
productivity shocks which are based upon changes in total factor productivity
will not be strictly exogenous.
This paper investigates several quarterly measures of the impulse to an
aggregate productivity shock and asks if these measured Solow residuals can
2
survive
simple
exogeneity
tests.
The
evidence
is
inconsistent
hypothesis that the impulse to an aggregate productivity
consequently, the productivity shock is not exogenous.
with
the
shock is exogenous;
Initially, in Section
2, the analysis employs Prescott's (1986) measure of the impulse to aggregate
productivity.
Money,
nominal
interest
rates,
and
government
consistently provide significant predictive power for this
results are economically significant:
spending
impulse.
These
about one-quarter of the variance of
the productivity impulse can be attributed to aggregate demand shocks.^*
The
analysis of Sections 3-5 demonstrates that these conclusions are robust to a
number of econometric issues.
Section 3 considers the possibility of random
measurement error in the productivity data:
in this case, about one-half of
the variance of the productivity impulse can be attributed to aggregate demand
shocks.
Section 4 considers the possibility of specification errors in the
production
function;
twelve
measures
of
the
productivity
considered and the exogeneity test results are unchanged.
impulse
are
Section 5 considers
the possibility that these results are due to omitted real shocks, along the
lines considered by King and Plosser (1984) and Litterman and Weiss
(1985).
However, the finding that money and nominal interest rates provide predictive
power a year in advance of the productivity impulse realization makes this an
unlikely
explanation.
For
each
possibility,
the
evidence
favors
the
conclusion that measured aggregate productivity impulses do not behave as a
strictly exogenous stochastic process.
These
findings
indicate
that
the
role
of
productivity
shocks
in
generating economic fluctuations has been overstated in the RBC literature.
Further research aimed at identifying and understanding "productivity shocks”
may be an important element in the debate between RBC theorists and their
critics.
3
2.
Are Productivity Shocks Exogenous?
Prescott (1986) measures the impulse to the aggregate productivity shock
as
the
change
in
total
factor
productivity.
Assuming
an
aggregate
Cobb-Douglas production function,
[]
i
the productivity shock z _ can be measured using data on output
^
hours
(Y) , labor
(N), and the capital stock (K) for a given labor share parameter 0.
Assuming that
contains a unit root in logarithms leads to:
zt =
£t
where c
zt l exp ( / + et )
i
“
[2]
^ (L) £t-l + W t
is a stationary random variable,
/?(L) is a polynomial
in the lag
operator L, and w^ is a mean zero, serially uncorrelated random variable.
Prescott's
study,
€
is
the
measure
of
technological
change.
The
In
Real
Business Cycle literature has not taken a firm stand on the stochastic process
for
e^.
Braun
Prescott
(1989)
(1986),
assume
that
Altug
(1985),
e
white
is
Christiano-Eichenbaum
noise;
while
(1991),
Christiano
and
(1988),
King-Plosser-Rebelo (1988), and Eichenbaum-Singleton (1986) allow objects like
to be serially correlated.
2
A critical assumption that these papers share is that z^ is an exogenous
random variable.
policy variables
models
like
These models assume that changes
in monetary and fiscal
do not alter the distribution of z^;
these
can usefully
"provide
a
evaluating the importance of other factors
...
consequently,
well-defined benchmark
(e.g., monetary disturbances)
actual business-cycle episodes [Long-Plosser(1983, p.68)]."
z^
is
endogenously-determined,
as
real
Summers
(1986)
and
for
in
Alternatively, if
the
models
of
Murphy-Shleifer-Vishny (1989) imply, then the omission of fiscal and monetary
variables distorts the benchmark assessment.
[2],
the exogeneity of z . requires
^
4
that
In the context of specification
be
exogenous.
Thus,
the RBC
literature relies upon the exogeneity of
but it may be either white noise
or a serially correlated random variable.
Using
[1] and [2], e
€t -
A
can be measured as follows:
6 A log Nt - (1-0) A log Kt -
log Yt -
/
x
and e will hereafter be referred to as the productivity impulse.
[3]
3
To measure
e, Prescott (1986) uses GNP data, an efficiency labor hours series as computed
by Hansen
(1984),
and a capital stock measure which includes
the stock of
residential housing but excludes the stock of durable consumption goods.
calibration purposes,
This
particular
Prescott states that a value of 0=.75 is appropriate.
choice
requires
Prescott uses the value
output
during
the
elaboration.
In
the
postwar
period
when
output
is
defined
Since GNP understates the theoretical
but labor's compensation is unaffected,
postwar period.
model,
to
include
the
His empirical analysis, however, uses
measureof output, and GNP does not include the
consumption goods.
theoretical
64 since this is the average of labor's share in
services of durable consumption goods.
GNP as the
For
services of durable
measure of output,
labor's share rises to
.75 for the
This reasoning underlies the value of 0«.75 and Prescott's
measure of the productivity impulse e .
Given
a measure
exogeneity
of
assumption
furthermore,
the
of
aggregate productivity
RBC
models
a
c, a standard
refutable
assumption;
standard exogeneity testing remains valid even if measures
other real shocks are not available.
models in which there are two real,
that r
becomes
impulse
For example,
of
consider a class of RBC
driving variables,
and r^.
Suppose
follows
log Tt
-
p log Tt_1 +
Vt
where v^ is a mean zero, random variable.
|P|<1
The innovations
assumed to constitute a vector white noise process,
contemporaneously correlated.
and
and
are
and i ^ may be
/
According to specification [2], past values of
5
v should not help predict e
beyond the own past history of e.
the productivity impulse e
is unpredictable based upon the past values of
real variables,
context,
the
of
to more
than
generalization
or the omitted real
representations for r
e can
two
shock u:
be
nominal variables,
exogeneity
measuring
refuted
without
driving variables
should be clear.
omission of lagged shocks
Consequently,
and
in this
v.
alternative
The
linear
The critical assumption in [2] is the
e (namely,
other than
, s>l):
all
of the
previously cited RBC papers share this assumption.
One way to investigate the exogeneity issue is to conduct a standard,
multivariate
variables.
time
series
analysis
of
e and
other
potential
explanatory
The following specification is investigated:^
£t =
^ (L) et-i +
where /?(L), and a(L)
specification
a(L) xt-i +
are polynomials
[u]
wt
in the Lag operator L.
According to
[2], x should not provide predictive power for c.
A finding
that a(L)?*0 in [4] is sufficient to refute the assumption that e is strictly
exogenous (for example, see Geweke (1984)).^
The list of variables included in the vector x is:
money
(Ml),
90-day Treasury Bill
rates
(TBILL), the
the Ml measure of
Consumer
Price
(CPI), real government expenditures (GOVT), and Crude Oil prices (OIL).
variables
were
selected
since,
in
an RBC
model,
reflect the influence of any omitted variables:
typically omitted.
productivity
index
These
shocks
may
all of these variables are
The data is quarterly and seasonally adjusted.
Four lags
of all variables are included in the autoregression [4] .
The interest rate
variable is measured as the change in Treasury Bill rates;
money, government
expenditures,
the consumer price index,
and the crude oil price
measured as growth rates (that is, log first-differences).^
periods studied are 1957:11-1983:11 and 1957:11-1978:IV.
The two sample
The 1983:11 sample
period is dictated largely by the availability of Prescott's
6
index are
series
for €
which begins in 1954:IV.
sensitivity of the
The 1978:IV sample period was chosen to gauge the
results
to an alternative
sample period which
did not
include the "Volcker experiment" years, 1979-1982.
Table 1 reports that Ml, TBILL, CPI, and GOVT individually Granger-cause
6 over the 1983:11 sample period.
the
statistical
significant.
always
significance
7 8
of
2
The R
these
for this regression is .47, so
results
is
also
quantitatively
For both periods, government spending, money and inflation are
significant
significant
at
at
levels
conventional
below
the
levels.
2%
level.
This
Oil
suggests
prices
that
are
not
identifying
productivity shocks with past oil price increases may be misleading.
9
The
significance of interest rates in the 1983:11 period does not hold for the
shorter 1978:IV period.
McCallum (1983) has argued in a similar context that
both Ml and TBILL may reflect monetary policy in an equation such as this.
Therefore,
a
specification
which
includes
both
TBILL
and
Ml
appreciably better than one with simply TBILL (or simply Ml).
this possibility,
significant
not
be
To investigate
notice that Ml and TBILL are jointly significant at less
than the 1% level in both periods.
only TBILL
may
(and not Ml)
(at the
2.5%
Further, when only Ml (and not TBILL) or
are included in the x-vector,
level).
Thus,
these variables are
money and nominal
jointly provide significant explanatory power for c.
interest rates
The results in Table 1
provide evidence against the hypothesis that this measure of the productivity
impulse
e is
exogenous;
consequently,
the
productivity
shock
z
is
not
exogenous.
The
quantitative
significance
of
these
nonexogeneity
investigated by a decomposition of variance analysis.
Ml, TBILL,
OIL and GOVT,
Table 2 reports
results
can
be
For a VAR containing c,
the percentage of the 16-quarter
ahead forecast error variance of e attributable to these variables.
Since the
own e-innovations account for 70.8% and 68.5% of the variance in e in the
7
1983:11 and 1978:IV samples, the Ml, TBILL, OIL and GOVT innovations jointly
account for 29.2% and 31.5% of the variance in e.
The lower bound of the 95%
confidence interval is 16.6%,^ so the nonexogeneity of e is quantitatively
significant.
OIL,
Taken singly, the lower bounds of the intervals for Ml, TBILL,
and GOVT are near zero;
innovations
are
some uncertainty remains about exactly which
quantitatively
significant.
However,
following
McCallum
(1983) in interpreting monetary policy as Ml and TBILL innovations jointly,
monetary policy is quantitatively significant for the full sample period.
To
conclude
Prescott's
aggregate
this
measure
demand,
of
section,
evidence
productivity
reflected
in Ml,
has
been
shocks
is
TBILL,
and
presented
not
to
exogenous.
GOVT,
show
that
Changes
influence
statistically as well as economically significant way.
11 12
e
in
in
a
These results alone,
however, are insufficient to refute the exogeneity hypothesis.
In principle,
these results could represent erroneous rejections if certain econometric and
theoretical objections are quantitatively important.
Sections 3, 4, and 5
tackle the issues of measurement error bias, specification error bias, and a
special form of omitted shock bias.
In fact,
the essential conclusions of
this section are unchanged by these considerations.3
3.
Measurement Error Analysis
The failure of e to pass simple exogeneity tests in Section 2 could be
due to measurement errors in the data.
Ordinary
Least
Squares
estimator
of
If e is measured with error, then the
/?(L)
in
estimated standard errors are not consistent,
are uninterpretable.
exogeneity
tests,
To assess
consider
the
[4]
is
not
consistent,
the
and the previous test results
the influence of measurement error on the
following
statistical
model
of
the
true
productivity impulse (now referred to as e ), the other variables (x), and two
error-ridden measures of the productivity impulse (e^ and
8
H0 : A 12(L)-0
‘t - A U (L) ‘t-l + A 12(L) xt-l + V
[5]
k
x t " A 21(L) et-l + A 22(L> xt-l + "t
[6]
‘it - et
+
B1 <L) vlt
[7]
e2t “ 't
+
B2 (L) v2t
[8]
where A^. (L) and B^(L) are polynomials in the lag operator L, and
are
the
innovations
to
k
€
and
x^.
Economic
agents
observe
and
the
k
productivity impulse e , but the econometrician can only observe
true
and e^.
The random variables v^ and V 2 are mean zero, serially independent measurement
errors generated by the data reporting agencies.
random measurement errors,
independent
of
k
e .
When
Since this is a model of
each of the errors v^ and V 2 is assumed to be
the
two
productivity
measures
and
are
constructed with data reported by independent agencies, the errors v^ and V 2
are
assumed
measurement
to
be
error
mutually
similar
to
independent
this
as
well.
one have been
Models
of
investigated
classical
recently by
Sargent (1989), Prescott (1986), and Christiano-Eichenbaum (1991).
To complete the measurement error model, the relationship between x,
and
€2
must be clarified.
without error:
I assume that the test variables x are measured
x, v^, and V 2 are jointly independent at all leads and lags.
Allowing for measurement errors in x, as well as
and
data
merit.
series
symmetrically,
an
analysis
with
much
would treat all
Unfortunately,
insufficient data on x is available to implement the instrumental variables
estimator described below.
errors,
therefore,
To make some progress on the issue of measurement
I follow Prescott (1986) and Christiano-Eichenbaum (1991)
in treating the data series asymmetrically.
Testing the exogeneity hypothesis
in this
context requires
estimation of A^( L ) and its covariance matrix estimator;
consistent estimation of A^(L) as well.
k
If either
consistent
the latter requires
or c^ is used in place
of the unobserved e , and OLS is applied to equation [5], the A^( L ) estimator
9
Using e^ as an instrument for e^ in equation [5] ,
will not be consistent.
however, results in consistent estimation and a valid exogeneity test can be
conducted.
This
estimation procedure
estimates of B^(L) are not necessary;
is semiparametric
in the
sense
that
consequently, misspecification of the
order of B.(L) is not an issue.
l
A decomposition of variance analysis of the VAR system [5] and [6] is
possible
if
a
consistent
estimator
innovation vector, is available.
of
Q,
the
covariance
matrix
In fact, for each innovation
for
and
the
two
error-ridden observations are available given estimates of A^. (L) and the two
error-ridden series
are
orthogonal,
Since the measurement errors in e ^ and e ^
and ^t*
the
error-ridden residual
Construction of a consistent covariance
these residual series.
series will
estimator
also be
orthogonal.
is straightforward given
13
Implementing this econometric procedure requires two measures of e
measurement
errors
are
arguably
independent.
Prescott
assumes
whose
that
the
measurement errors in the growth rates of GNP and the capital stock measure
are negligible.
He focuses on measurement errors in the labor input, where
two independent series are available for total labor hours:
efficiency hours
(constructed
from
the
Household
Survey
Gary Hansen's
data), and
nonagricultural hours from the Survey of Business Establishments.
The data
for these series are collected by two separate government agencies,
measurement
errors
errors
are
arguably
independent.
I also
in output by employing the Federal Reserve's
Production as a proxy for GNP.
total
so the
consider measurement
series
for Industrial
If the one-sector theoretical economy exhibits
balanced growth, then the data's actual sectoral outputs should aggregate to
the one-sector aggregate output series.
Thus, the growth rates of GNP and IP
should be measuring the same theoretical growth rate in output:
to the extent
that these growth rates differ, this is interpreted as being due to (serially
10
correlated)
measurement
errors.
Finally,
the
tables below
do not
report
results which allow for measurement errors in the capital stock variable:
I
am unable to find an independent measure of the capital stock which is highly
correlated with the primary measure used in this study.
14
Table 3 presents the Instrumental Variable (IV) exogeneity test results.
The results are presented for two cases:
(1) assuming that only the growth
rate of hours is measured with error (Hours only);^
and (2) assuming that
only
measured
the
growth
rates
of
hours
and
output
are
with
error
•
f
f
(Hours/Output).
For the Hours only case, €
continues to fail the exogeneity
•ff
CPI and GOVT Granger-cause e
test, but the patterns of failure differ.
both periods;
in
TBILL does in only the 1983:11 period; and Ml does in only the
•ff
1978:IV period.
periods;
Included
However,
Ml
and TBILL jointly
Granger-cause
and when only TBILL (and not Ml) or only Ml
in the
system,
these variables
are
e
in both
(and not TBILL) are
significant
in both periods.
Interpreting both Ml and TBILL as instruments of monetary policy sustains the
conclusion
that
monetary
policy
has
influenced
the
evolution
of
the
*
productivity impulse c .
•ff
For the case of Hours/Output, the evidence of predictability in e
weaker.
Ml, TBILL and CPI are jointly significant in the 1983:11 period, but
not in the 1978:IV period.
be
due
is
to
a
change
in
This lack of stability across sample periods could
monetary
policy
over
the
period
1979-82.
GOVT
•ff
Granger-causes
e
in both periods.
For this case,
there is some evidence
•ff
against
the
exogeneity
of
€ ,
but
the
Granger-causality
evidence
is
substantially weaker than in Table 1.
A
A
Given IV estimates of A^. (L) and 0,
Table 4 reports decomposition of
•ff
variance
results
includes
Ml,
e , the
for
TBILL,
OIL,
true
and GOVT.
productivity
For
each
impulse,
case
in
a VAR
which
in both periods,
the
•jjf
percentage
of variance
in e
which
11
is attributable
to own
innovations
is
Apparently, in Table 2 the measurement error in e is
smaller than in Table 2.
being attributed more to the productivity impulse innovations than the other
innovations.
The confidence intervals tend to be wider when measurement error
is accommodated.
Nevertheless, aggregate
demand variables
k
contribute between 34-60% of the variance of e ;
confidence interval are between 10-43%.
and oil prices
the lower bounds on the 95%
The nonexogeneity evidence here is
stronger than in Table 2.
Based upon the evidence presented in Tables 3 and 4,
the failure of
measured productivity impulses to pass simple exogeneity tests is not likely
to be due to the presence of classical measurement errors in the productivity
data.
4.
Specification Error Analysis
Another potential criticism of the exogeneity tests
measure of the aggregate productivity impulse c.
Section 2 might be specific to:
capacity
technology;
utilization.
or
This
In principle, the results in
(1) the choice of labor input data;
value of the constant labor share parameter 0;
the aggregate
is the particular
(4)
the
section
(3)
(2)
the
the functional form for
assumption of a constant rate
briefly
discusses
the
results
of
of
a
sensitivity analysis. The principal finding is that the results of Section 2
are
robust:
the
strict
exogeneity
of
c
is
refuted
for
the
12
measures
considered.
First,
Prescott's
measure
of
e uses Hansen's
series as the measure of labor hours.
(1984)
efficiency hours
In principle, the predictability of e
could be an artifact of this constructed series.
Two alternative aggregate
labor hours series, however, are available: the Household Survey measure
and
the Survey of Business Establishments. Accordingly, alternative measures of e
have been computed using the Household and Establishment Survey hours data to
12
address this possibility.
Second,
function,
under
the
assumption
of
an
aggregate
Cobb-Douglas
measuring e requires an estimate of labor's share in output
The previous measure assumes that 0=.75, just as Prescott did.
the
three
production
labor
measures,
0 can be
however,
aggregate Cobb-Douglas production function.
estimated
(0).
For each of
directly
from
the
Since theory predicts that labor
hours will respond to productivity shocks, consistent estimation requires the
use of an instrumental variables estimator.
uncorrelated, however,
labor
hours,
If the true impulse is serially
a valid set of instruments includes lagged values of
capital,
and
output.
Given
consistent
estimates
of
0,
appropriate measures of e can be constructed.
A
third
problem
production function.
may
be
the
assumption
an
aggregate
Cobb-Douglas
This criticism can be addressed by computing a standard
Solow measure of total factor productivity,
weights.
of
which uses
time-varying factor
This measure is consistent with any constant-returns-to-scale (CRS)
aggregate technology if markets are competitive.
Since Real Business Cycle
theories typically assume a competitive environment, the Solow residual is an
appropriate measure of the productivity impulse for any CRS technology.
As
Hall (1988) has noted, however, in noncompetitive environments this measure of
productivity impulses will not be exogenous.
In this case, an exogeneity test
failure would be consistent with Hall's findings.^
Finally, using the entire aggregate capital stock as a measure of the
capital input to production implicitly assumes that capacity utilization is
constant over the business cycle.
Relaxing this assumption is difficult since
existing measures of capacity utilization are inappropriate for computing a
utilized capital series (see Shapiro (1989) for example).
I follow Prescott
(1986) in allowing for variable capital utilization through the variations in
labor input.
Specifically, utilized capital services in production is u^k^,
13
u
is the utilization rate,
and u^n^.
Prescott used a value
of a=0.40;
selecting a variety of a values left the test results qualitatively unchanged.
The Granger-causality and variance decomposition results are similar to
the results of Section 2, and so are not reported here to conserve space.
four-variable VAR containing £, Ml, TBILL, and GOVT was estimated.
A
In each of
the 12 specifications,^ either Ml, TBILL, or both Granger-causes e at very low
significance levels (less than 2.5%);
GOVT Granger-causes e in each of the 12
cases also at low significance levels.
The predictability of the productivity
impulse e is a remarkably robust result.
The
variance
decomposition
Granger-causality test results.
results
mimic
the
robustness
Innovations in Ml, TBILL,
of
the
and GOVT account
for between 26-33% of the variance in the 16-quarter ahead forecast error of
£.
The lower bounds
of the
95%
confidence
intervals
are between 12-21%.
Thus, the quantitative significance of these variables is also robust across
the alternative measures of e .
5
5.
Signalling and the Omitted Real Shock Hypothesis
The predictability of e can be interpreted plausibly in one of two ways:
either (1)
changes in money, interest rates, and government spending lead to
changes in measured productivity e, or (2) changes in these variables reflect
changes
in
other
interpretation,
real
the
shocks
omitted
findings above are spurious,
which
real
lead
to
changes
shock hypothesis,
is
in
c.
that
The
the
latter
empirical
and a more complete specification of the real
shocks in the economy would overturn the results.
As I discussed in Section
2, specification [2] rules out many omitted shock hypotheses;
however,
the
RBC literature has featured one important alternative which has not been ruled
out so far.
King and Plosser (1984) consider an RBC model in which endogenous
money can respond to real shocks before output can respond.
14
Specifically,
some productivity shocks which occur in period t+1 are revealed in period t;
endogenous money and other financial variables respond to this information in
period t.
Similarly,
Litterman and Weiss
(1985) describe an economy where
economic agents have more information about future aggregate supply shocks
than does the econometrician;
since financial and monetary variables convey
information about
these unobserved shocks,
real
After
variables.
controlling
for
nominal variables
the
unobserved
Granger-cause
shocks,
however,
Litterman-Weiss find that real variables are block exogenous with respect to
nominal variables.
Litterman-Weiss
Thus, the apparent importance of nominal variables in the
economy
is
spurious.
These
examples
suggest
that
the
importance of nominal variables for predicting productivity shocks may simply
reflect
the
influence
of omitted
real
shocks, even
in
the
context
of
specification [2].
To see this in a simple context, suppose that the productivity shock z _
^
follows the stochastic process:
log zt =
e^
where
and
log zt_1 + M + elt + «2 ,t-l
€2 t 1 are
assumec* to ke mean zero, serially uncorrelated,
stationary random variables
impulse
is
both impulses,
the
spirit
of
[9]
and
E
[
€^t c2
^ 1
^ ^ 0 is permitted.
revealed in period t, whereas
^ is revealed in period t-1;
however, are realized in period
King-Plosser
(1984):
The
t. This
economic
agents
specification is in
can
anticipate
some
productivity shocks prior to their realization, while others are completely
unanticipated.
Define
+ 62 t 1 an<*
note
is t^ measured
le
productivity impulse from equation [3].
In
a monetary
economy with
this
aggregate
technology,
inside
money,
outside money, stock prices, and nominal interest rates can respond in period
t to an impulse (c2t^
period
t+l„
In
this
signalled in period t but not realized until
sense,
a
finding
15
that
time
t
nominal
variables
Granger-cause e c o u l d be spurious;
that is, e could fail Granger-causality
tests but be strictly exogenous.
In the context of
[9] , 6t+} should not be
.
correlated with money and
interest rates which are sufficiently distant in time:
growth rate
of money
and nominal
18
uncorrelated with
periods
in
advance
of
interest
More generally,
their
rates
in this example, the
in period
specification
[4]
realization,
can be
possible signalling factors:
et “
^ (L) et-i +
should be
some impulses may be revealed p
but
information
available in period t-p should be uncorrelated with
of p,
t-1
appropriately
which
becomes
For a given choice
altered
to
control
for
the
19
a(L) xt-P-i +
wt
[4']
Thus, the exogeneity hypothesis now implies that a(L)=0 in [4'].
No a priori information is available to suggest one, unique value for p.
Litterman-Weiss (1985) and King-Plosser (1984) each select a model which would
set p equal
to one period.
Since
the sample
interval
for
this
study is
quarterly, and the King-Plosser model could easily refer to yearly decisions,
Table 5 reports signalling test results for p= 1, 2, 3, and 4 quarters.
In Table 5, the vector of explanatory variables includes Ml, TBILL, and
GOVT.
First, government spending is not significant at any reasonable level
for any choice of p>l.
Second, TBILL provides explanatory power as early as
four quarters ahead (p=3), and Ml provides explanatory power at seven quarters
ahead (p=6, unreported).
p=6,
unreported).
Jointly, Ml and TBILL are always significant (up to
Third,
when
e is computed using
0=.75 and either the
Establishment or Household Survey hours, the corresponding results for Table 5
are not appreciably different (again, unreported).
If
the
signalling
hypothesis
is
the
20
correct
explanation
for
the
explanatory power of money and interest rates, then productivity impulses must
be anticipated 7 quarters ahead:
this feature is at variance with every RBC
16
model which has been studied to date.
Consequently,
the evidence favors an
e in a fundamental
interpretation in which the nominal variables influence
way, not an omitted variable channel such as specification [9],
6.
21
Conclusions
The results above demonstrate that productivity shocks as measured by
Solow/Prescott
processes.
methods
Money,
do
not
nominal
behave
as
interest
strictly
rates,
exogenous
and
stochastic
government
spending
individually and jointly Granger-cause various measures of the impulses
these shocks.
hypothesis
These results are not due to Classical measurement errors. The
that
investigated,
and
this
result
is
no
evidence
due
has
to
been
omitted
found
to
real
economically
significant:
their
factors
support
Furthermore, the influence of money, interest rates, and
is
to
innovations
the
has
been
hypothesis.
government spending
account
for
between
one-quarter and one-half of the forecast error variance in e at the 16-quarter
forecast horizon.
The
lower
one-quarter value
orthogonalization of the innovations
is
computed under
an RBC
in the absence of measurement errors;
the upper one-half value, after accounting for measurement errors.
As a whole,
these results cast a shadow over the current generation of
RBC models which assume strictly exogenous productivity shocks and exclude any
interesting role for aggregate demand shocks or other supply shocks.
At a
minimum, these results imply that the RBC literature to date has overstated
the importance of productivity shocks for economic fluctuations.
which
may
be
consistent
with
the
evidence
presented
here
Two theories
are
the
labor
hoarding model of Burnside, Eichenbaum, and Rebelo (1990) and the productive
externality model
of
Baxter
and King
(1990).
According
to both models,
conventionally measured Solow/Prescott residuals are not exogenous.
17
In these
models prices are perfectly flexible, so the empirical finding that money and
interest rates Granger-cause productivity shocks would presumably be explained
as reverse causation as in King and Plosser (1984).
Alternatively, if prices
were assumed to be sticky in these types of economies, these Granger-causality
findings would be explained as direct causality.
To discriminate among these
various theories as well as further assess the role of productivity shocks,
researchers should investigate economic structures which jointly predict the
stylized facts of business cycles and endogenous Solow residuals.
Data Appendix
Many of the data series used in this study are directly available from
the CITIBASE data base (their CITIBASE labels are in []):
price
index
expenditures
GNP,
less
shelter
[GGE82];
OIL,
[PUXHS];
[GNP82];
Establishment survey
and the Capital Stock [KRH72, KN72].
(1984).
(federal)
government
IP,
Industrial Production
[LPMHU], Household Survey
[IP];
[LHOURS];
The Efficiency hours data is from Hansen
The Ml (money) and TBILL (90-day Treasury Bill rates) data are the
same as in Eichenbaum-Singleton (1986).
real
the producer price index for crude oil [PW561];
real gross national product
Labor hours data:
GOVT,
CPI, the consumer
18
Table 1:
The Predictability of Prescott1s Productivity Impulse0
£t =
[4]
^ (L) et-i + q(l) xt-i + wt
Marginal Significance Levels for Testing Hq :
_ b
X- vector
a.
1957:11 - 1983:11
a(l
1957:11 - 1978:IV
Ml
TBILL
CPI
GOVT
OIL
.0033
.0183
.0003
.0005
.8895
.0172
.1628
.0193
.0019
.1455
Ml, TBILL
Ml, TBILL, CPI
.0000
.0000
.0001
.0001
b.
Ml alone*
.0003+
.0002
c.
TBILL alone*
.0048
.0209+
a
Four lagged values of c and X are used in the autoregression.
The marginal
significance levels can be interpreted in the following manner: for Ml in the
period 1957:11-1978:IV, the marginal level .0172 indicates that the Null
Hypothesis of a(L)«0 (with respect to the Ml components of X) would be
rejected at significance levels of 1.72% and higher.
^The vector autoregression includes Ml, TBILL, CPI, GOVT, and OIL as
components of the X-vector.
The line "Ml, TBILL" reports marginal
significance levels for testing the joint hypotheses that the Ml and TBILL
coefficients are a block zero vector. Similarly for "Ml, TBILL, CPI."
* Other elements in the X-vector are: GOVT, OIL, and CPI.
+ OIL is significant at the 5% significance level.
19
Table 2:
Decomposition of Variance Results
a
Percentage of Variance in Prescott's Productivity Impulse e
Explained by Innovations in Vector Autoregression [4]:
Point Estimates and 95% Confidence Intervals
Components of X-vector
1957:11 ^ 1978:IV
70.8
(58.2, 83.4)
8.2
( 2.5, 14.0)
7.7
( 0.4, 15.1)
2.4
( 0.0, 5.6)
10.8
( 0.0, 21.9)
e
Ml
TBILL
OIL
GOVT
Ml, TBILL*3
u
OIL, GOVT
1957:11 - 1983:11
68.5
(55.0, 82.1)
6.5
( 0.9, 12.1)
9.0
( 0.0, 18.4)
4.2
( 1.1, 7.2)
11.8
( 0.0, 25.4)
15.9
( 6.5, 25.3)
13.2
( 1.9, 24.5)
15.5
( 3.9, 27.0)
16.0
( 2.9, 29.1)
The order of orthogonalization is in the order of the variables listed.
forecast horizon is 16 quarters.
The
^The line "Ml, TBILL" reports the percentage of variance jointly explained by
Ml and TBILL innovations.
The point estimate is the simple sum of the
individual Ml and TBILL percentages;
however, the 95% confidence interval
requires more extensive calculations (see footnote #11 in the text).
Similarly for "OIL, GOVT."
20
Table 3:
The Predictability of Prescott 's Productivity Impulse5
in the Presence of Classical Measurement Errors
et _
An (L) V l
[5]
+ A12(L) Xt-1 + W t
Marginal Significance Levels for Testing: H :
1957:11 - 1983:11
_ b
X- vector
a.
0
Hours Only
Hours/Output
= l
1957:11 - 1978:IV
0
Hours Only
Hours /Output
Ml
TBILL
CPI
GOVT
OIL
.0699
.0004
.0000
.0369
.7428
.7455
.2286
.0338
.0145
.7518
.0092
.2533
.0005
.0327
.0780
.8240
.7554
.3136
.0137
.0405
Ml, TBILL
Ml, TBILL, CPI
.0000
.0000
.1210
.0004
.0000
.0000
.5305
.3160
b.
Ml alone*
.0191
.5404
.0056
.4493
c.
TBILL alone*
.0015
.0840
.0458
.4137
Four lagged values of c and X are used in [5] , and 8 lags are used in
computing
the
Newey-West heteroskedasticity-autocorrelation
consistent
covariance matrix estimator.
^See footnote b in Table 1.
q
"Hours Only":
IV estimation assumes that only the Hours series contains
measurement error;
"Hours/Output": IV estimation assumes that the Hours and
Output series contain measurement error.
*Other elements in the X-vector are:
21
GOVT, OIL, CPI.
Table 4:
Decomposition of Variance Results in the Presence ofc
Classical Measurement Errors
Percentage of Variance in Prescott's Productivity Impulse
Explained by Innovations in the Vector Autoregression [5]:
Point Estimates and 95% Confidence Intervals
1957:11 - 1983:11
Components of
X-vector
*
6
Ml
TBILL
OIL
GOVT
Ml, TBILLd
OIL, GOVT
1957:11
-
1978:IV
Hours Only
Hours/Output
Hours Onlv
Hours /Output
47.5
(30.1, 65.0)
16.1
( 8.0, 24.2)
13.7
( 1.2, 26.2)
4.8
( 0.0, 10.7)
17.9
( 0.0, 41.3)
66.0
(42.8, 89.3)
9.5
( 0.0, 20.8)
5.9
( 0.0, 12.0)
3.2
( 0.0, 9.7)
15.5
( 0.0, 36.7)
39.8
(23.5, 56.1)
13.8
( 3.5, 24.0)
15.1
( 0.0, 31.2)
8.4
( 0.0, 17.2)
22.9
( 0.0, 49.5)
50.8
(22.4, 79.2)
8.0
( 0.0, 23.0)
7.1
( 0.0, 21.7)
4.8
( 0.0, 11.3)
29.2
( 0.0, 58.5)
29.8
(14.9, 44.7)
22.7
( 0.0, 46.7)
15.4
3.4, 27.4)
(
18.7
( 0.0, 39.6)
28.9
( 9.5, 48.3)
31.3
( 7.2, 55.4)
15.1
( 0.0, 38.7)
34.0
( 6.7, 61.3)
c
l
The order of orthogonalization is in the order of the variables listed.
forecast horizon is 16 quarters.
b c
’ See the corresponding footnotes in Table 3.
^See footnote b in Table 2.
22
T
1
Table 5:
. a
Testing the Signalling Hypothesis
£t
“ <L) V p - i + wt
[4']
Marginal Significance Levels for Testing H q :
X-vector^
d
~ 1
0
= 2
o = 3
a(L)~0
o = 4
Ml
.1536
.0311
.0294
.0013
TBILL
.0278
.0008
.0008
.1497
GOVT
.8907
.6924
.7703
.9462
Ml, TBILLC
.0000
.0000
.0000
.0000
aThe productivity impulse e is Prescott's measure, the sample
1957:11 - 1983:11, and four lags are used in the estimation.
period
The elements of the X-vector are Ml, TBILL, and GOVT.
The Null hypothesis is that the block of coefficients associated with Ml and
TBILL are jointly zero.
23
References
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empirical analysis, manuscript, University of Minnesota.
Baxter, M. and R. King, 1990, Productive externalities and cyclical
volatility, Rochester Center for Economic Research,
working paper no. 245.
Boschen, J. and L. Mills, 1988, Tests of the relation between money
and output in the real business cycle model, Journal of
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Braun, R . , 1989, Taxes and postwar U.S. business cycles,
manuscript, University of Virginia.
Burnside, C., M. Eichenbaum, and S. Rebelo, 1990, Labor hoarding and
the business cycle, manuscript, Northwestern University.
Caballero, R . , and R. Lyons, 1990, The role of external economies in
U.S. manufacturing, manuscript, Columbia University.
Christiano, L., 1988, Why does inventory investment fluctuate so much?
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Christiano, L. and M. Eichenbaum, 1991, Current real business cycle
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the American Economic Review.
Costello, D., 1989, A cross-country, cross-industry comparison
of the behavior of Solow residuals, manuscript,
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Econometrica 51, 277-304.
Geweke, J., 1984, Inference and causality in economic time series
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Hall, R . , 1988, The relationship between price and marginal cost in
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Hansen, G., 1984, Fluctuations in total hours worked: a study using
efficiency units, manuscript, University of Minnesota.
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Monetary Economics 16, 309-327.
Hansen, G. and T. Sargent, 1988, Straight time and overtime in
equilibrium, Journal of Monetary Economics 21, 281-308.
Hansen, L., 1982, Large sample properties of generalized method of moments
estimators, Econometrica 50, 1029-1054.
24
King, R. and C. Plosser, 1984, Money, credit, and prices in a real business
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King, R . , C. Plosser, and S. Rebelo, 1988, Production, growth, and
business cycles, Journal of Monetary Economics 21, 309-342.
Kydland, F. and E. Prescott, 1982, Time to build and aggregate
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Litterman, R. and L. Weiss, 1985, Money, real interest rates, and output:
a reinterpretation of postwar U.S. data, Econometrica 53,
129-156.
Long, J. and C. Plosser, 1983, Real business cycles, Journal of Political
Economy 91, 39-69.
Mankiw, N.G., 1989, Real business cycles: a new Keynesian perspective,
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McCallum, B., 1983, A reconsideration of Sims' evidence concerning
monetarism, Economic Letters 13, 167-171.
McCallum, B . , 1989, Real business cycle models, in: R. Barro, editor,
Modern business cycle theory (Harvard University Press), 16-50.
Murphy, K. , A. Shleifer, and R. Vishny, 1989, Building blocks of
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S. Fischer, editors, NBER macroeconomics annual 1989
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Newey, W. and K. West, 1987, A simple, positive definite,
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Prescott, E., 1986, Theory ahead of business cycle measurement,
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25
Footnotes
^The
empirical
approach here
(1990) in three ways:
different;
differs
from Hall
(1988)
and Caballero-Lyons
(1) the instruments and identifying restrictions are
(2) this paper uses quarterly rather than annual data;
Hall-Caballero-Lyons
focus
exclusively
on
contemporaneous
and (3)
correlations,
whereas this paper does not.
2
In a trend-stationary economy,
the
logarithm
(or level)
of z _ is often
^
assumed to be an exogenous, AR(1) process as in Hansen (1985), Hansen-Sargent
(1988), King-Plosser-Rebelo (1988), and McCallum (1989).
3
Referring
e as
to
terminology
productivity
if
the
productivity
e is serially
shock.
I
will
"impulse"
correlated.
refer
is
an
abuse
Nevertheless,
repeatedly
to
e
as
since
the
of
standard
is
the
"impulse,"
irrespective of its serial correlation properties.
4
Specifications of [4] which set jS(L)=0 a priori have also been investigated,
and the conclusions drawn are similar.
^Weaker forms of exogeneity do not seem appropriate here.
Weak exogeneity
and predeterminedness are econometric conditions which determine efficient
estimation techniques (Engle, Hendry, and Richard (1983));
however, admit specifications for e
26
these conditions,
which violate the spirit of RBC models.
Alternative
investigated.
stationary-inducing
In
particular,
transformations
the
basic
of
conclusions
the
of
data
have
been
this
paper
are
unchanged for trend-stationary and Hodrick-Prescott transformations of the
data (including the productivity variable z^).
^All of the test results reported in this paper have been generated using
conditional heteroskedasticity-consistent covariance estimators as suggested
by White (1980) and Hansen (1982).
8
In simple autoregressions with only a univariate x-variable, the exogeneity
hypothesis fails often.
For example, the following variables Granger-cause e
in these autoregressions:
the monetary base (in the 1983:11 period only),
Ml, TBILL, the Federal Funds rate, CPI, GOVT, and OIL.
The Trade deficit did
not Granger-cause e.
9
This evidence in no way rules out the possibility that oil price changes
influence c contemporaneously.
^Confidence
intervals
were
described in Runkle (1987);
computed
by
the
normal
approximation
method
the covariance matrix estimator is conditional
heteroskedasticity-consistent.
^Confidence intervals around the statistic Q * g^(/3) + g2 ( 3 are comPute^
/)
the obvious way,
using the fact that Var(Q)
* Var[g^(/J)]
+ Var[g2 (/?)] +
2Cov[gl09),g2 08)].
12
This conclusion regarding Ml and TBILL continues to hold if the order of
orthogonalization is c, OIL, GOVT, Ml, and TBILL.
27
13
For example, let w ^
and
and
resPect^ve^y•
be the two constructed residuals of [5] using
Then an estimator for the variance of
is the
sample covariance between w ^ and w 2t *
14
As an instrument for the capital stock,
Costello
consumption, but
only
that
data
is
available
(1989) uses electricity
annually.
As
a
quarterly
instrument, I have tried the production of electricity by utility companies.
The correlation between this instrument and the primary capital variable is
.37
(in growth rates).
When this
instrument
is employed,
the exogeneity
hypothesis fails more often than for the case which uses Hours and Output
only.
"^Prescott and Christiano-Eichenbaum assume that only the logarithm of labor
hours is measured with error:
A^(L)=0.
with
their assumptions imply that B^(L)=Bq -Bq L and
Instead, I assume that the growth rate of labor hours is measured
error,
and
allow
serially correlated.
the
measurement
error
process
to
be
arbitrarily
Also, A^(L) ^ 0 is permitted.
^Under the assumption that the technology is accurately specified, issues of
market
power
productivity
play
no
explicit
shocks.
For
role in
the nonexogeneity
example, ina
noncompetitive
of
economy
measured
where
aggregate production takes place according to [1] and [2], if €
is correctly
measured according to
even in the
[3],
it will
survive
exogeneity
tests
presence of market power.
^Twelve measures arise
due to the three
cases:
0 estimated by
0_
^;
(1) 0®.75;
(2)
IV;
labor hours series
(3) time-varying
and (4) variable capacity utilization with 0=.75.
28
and the four
Solow weights
18
This restriction applies regardless of the propagation mechanisms
economy.
and
in the
For example, suppose that the propagation mechanisms lead to m^ ^
^ being correlated with y^+^,
and nt+l’
^
the techn°l°gy
accurately specified and the factors are accurately measured, then A log z _
^ +^
* / + €t+l#
i
^
specification [9],
is uncorrelated with m^ ^ and
19
As in [4], serial correlation in e^ can be accommodated.
Suppose that the
aggregate productivity shock process is given by:
log
=
Z
u
log z
+ u
"it + u2,t-l +
where the {u^}
be
+ n + €
are mean-zero and
p+l,t-p
serially uncorrelated, but the {u.^} may
contemporaneously correlated in the period
(that is, Efu^^u^ t ^]^0, Efu^u^ t 2^^*
in which
etc*)#
they are realized
The ex°geneity tests based
upon [4'] are valid for this more general specification of the omitted real
shock hypothesis.
Also,
setting /3(L)=0 a priori leads to essentially the
same test results as reported in Table 5.
20
Allowing
for
conclusions;
stronger
errors
as
in
Section
detrending
3
for
both
sample
procedures
also
does
results.
in Section
3 does
not
alter
these
in fact, the Granger-causality evidence against exogeneity is
than
alternative
measurement
29
periods.
not
change
Accounting
the
for
qualitative
Since productivity shocks contain predictable components, these results are
consistent with the existence of numerous sources of economic fluctuations.
If nominal variables influence z _ and z _ drives the economy,
^,
^
variables should influence output.
significant
influence
of nominal
Boschen-Mills
variables
on
then nominal
(1988), however,
output.
output effect, however, is a challenge for future research.
find no
Quantifying
this
Presumably, this
will require a structural model which tightly restricts the specifications
and lag lengths assumed here and in Boschen-Mills.
30
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