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S tic k y P r ic e a n d L im ite d P a r t ic ip a t io n
M o d e ls o f M o n e y : A C o m p a r i s o n
Lawrence J. Christiano, Martin Eichenbaum
and Charles L. Evans
sank of chi'
Working Papers Series
Macroeconomic Issues
Research Department
Federal Reserve Bank of Chicago
Decem ber 1996 (W P -96-28)
. HU |
FEDERAL RESERVE BANK
OF CHICAGO
S tic k y P r ic e a n d L im ite d P a r tic ip a tio n M o d e ls o f
M oney:
Law rence J. C hristiano*
A
C o m p a ris o n *
M artin Eichenbaum *
C harles L. Evans§
D ecem ber 1996
A bstract
We provide new evidence that models of the monetary transmission mechanism
should be consistent with at least the following facts. After a contractionary monetary
policy shock, the aggregate price level responds very little, aggregate output falls,
interest rates initially rise, real wages decline by a modest amount, and profits fall. We
compare the ability of sticky price and limited participation models with frictionless
labor markets to account for these facts. The key failing of the sticky price model lies in
its counterfactual implications for profits. The limited participation model can account
for all the above facts, but only if one is willing to assume a high labor supply elasticity
(2 percent) and a high markup (40 percent). The shortcomings of both models reflect
the absence of labor market frictions, such as wage contracts or factor hoarding, which
dampen movements in the marginal cost of production after a monetary policy shock.
*We are grateful for helpful discussions with y.V. Chari, Francesco Giavazzi, Christopher Sims, Tao Zha,
and an anonymous referee. W e thank Wendy Edelberg for superb research assistance and Sarah IVeier for
editorial advice. Christiano and Eichenbaum thank the National Science Foundation for financial support.
The views expressed herein are those of the authors and not necessarily those of the Federal Reserve Banks
of Chicago and Minneapolis or the Federal Reserve System.
^Northwestern University, Federal Reserve Banks of Chicago and Minneapolis, and NBER.
^Northwestern University, Federal Reserve Bank of Chicago, and NBER.
^Federal Reserve Bank of Chicago.
1. I n t r o d u c t i o n
Plausible models of the monetary transmission mechanism should be consistent with at least
the following facts about the effects of a contractionary monetary policy shock:
• Aggregate price level initially responds very little.
• Aggregate output falls.
• Interest rates initially rise.
• Real wages decline by a modest amount.
• Profits fall.
In this paper, we provide new evidence to document these facts and we assess the ability
of sticky price and limited participation models to account for them. A generic failing of the
sticky price model is its implication that profits rise after a contractionary monetary policy
shock. In contrast, the limited participation model is capable of accounting for all of the
above facts, but only if one is willing to assume an implausibly high labor supply elasticity
(e.g., 2 percent) and a high average markup (e.g., 40 percent). In our view, it is unlikely
that any model which allows for only one type of friction will be able to account for all of
the facts in a plausible way. But our results suggest that limited participation models may
be a more useful starting point than sticky price models.
To assess the effects of an exogenous shock to monetary policy, we use close variants
of the policy shock measures developed in Christiano, Eichenbaum, and Evans (1996) and
Sims and Zha (1995). Since the first three facts listed above are extensively documented in
the literature, we focus the bulk of our empirical analysis on real wages and profits. Using
both aggregate and sectoral data, we show that a contractionary monetary policy shock is
associated with a small decline in real wages and a sharp, persistent drop in profits.
2
Based on our empirical analysis, we take as given the five facts listed above. We then turn
to the question: W hat type of frictions are likely to be helpful in accounting for these facts?
The first fact leads us to dismiss the Lucas (1972) model of money from consideration. This
is because the engine driving the signaling problem at the core of that model is an immediate
movement in the price level after a monetary policy shock. Such price movements are not
observed in the postwar U.S. data. The fourth fact leads us to dismiss simple sticky wage
models from consideration. Those types of models imply that real wages rise, not fall, after
a contractionary monetary policy shock.1
In light of these considerations, we concentrate on two frictions that have received sub
stantial attention in the recent literature. The first friction is that some firms do not imme
diately adjust prices in response to monetary policy shocks while ex post, output is demand
determined. The effect of this friction is that aggregate output falls in response to a mon
etary contraction. The second friction is that households do not immediately adjust their
nominal saving in response to monetary policy shocks. The effect of this friction is that
monetary contractions disproportionately affect the reserves of banks and, hence, the supply
of loanable funds. The result is a rise in interest rates which induces firms who need working
capital to cut back on their scale of operations, and aggregate output declines.
While these two frictions are by no means mutually exclusive, we find it useful to initially
analyze them in isolation. We do this by considering separately, the consequences of intro
ducing each of them into a single, benchmark model.2 The model economy is populated by
xBy simple sticky wage models we have in mind models which do not allow significant countercyclical
markups. See Romer (1996, chap. 5.4) for further discussion.
2Our benchmark model economy is closely related to the one considered by Blanchard and Kiyotaki
(1987); Chari, Christiano, and Eichenbaum (1995); Chari, Kehoe, and McGrattan (1996); Cho and Cooley
(1995); Ireland (1995); King and Watson (1996); Ohanian, Stockman, and Kilian (1995); and Woodford
3
an infinitely lived representative agent, a monetary authority, a competitive producer of final
goods, and a continuum of intermediate good producers, each of whom are monopolists. In
addition, there is a financial intermediary, which intermediates cash loans from households
to intermediate good firms. The household purchases the final consumption good, supplies
labor to intermediate good firms, and lends funds to the financial intermediary. The financial
intermediary combines funds received from households with lump-sum injections of money
from the government and makes loans to intermediate good firms. These firms need loans
because they must pay labor costs before they sell their output. The size of the money
transfers from the monetary authority to the financial intermediary is the only source of
uncertainty in the model economy.
In the
s tic k y p r ic e
version of the model, the sequence of events within a period is as
follows. First, intermediate good producers set their prices. Then the current-period money
growth rate is realized. Finally, all other model variables are realized, with the output of
the intermediate good producers being demand determined.
In the
lim ite d p a r tic ip a tio n
version of the model, goods prices are flexible, but we incor
porate the second type of monetary friction discussed above. As in Lucas (1990), Christiano
(1991), Fuerst (1992), and Christiano and Eichenbaum (1992, 1994, 1995), we do this by
assuming that, in any given period, households must determine how much money to deposit
with financial intermediaries prior to the realization of the money shock.
We analyze how the model economies respond to an exogenous shock in the growth rate
of money. Our findings can be summarized as follows. The key failing of the sticky price
model is its implication that profits rise after a monetary contraction. This is true across
(1996).
4
a broad set of parameter values and perturbations of the model. The intuition is quite
simple. Since output is demand determined, a monetary contraction leads to a substantial
decline in the resources used by intermediate good producers. This, in the absence of labor
market frictions or an extremely high elasticity of labor supply, leads to a substantial fall in
wages and marginal costs, along with a sharp rise in the markup. Although revenues fall,
cost considerations dominate and profits rise. We conclude that sticky prices alone are not
sufficient to account for the key facts. Like Romer (1996, chap. 6.12), we suspect that labor
market frictions, which have the effect of inhibiting cyclical movements in marginal costs by
mimicking very high labor supply elasticities, need to be embedded in the current generation
of general equilibrium sticky price models.3
We reach the same conclusion with the limited participation model, but the path by
which we reach it is different. The limited participation model does at least as well, if
not better, than the sticky price model. For this model, we find that if one is willing
to assume a high labor supply elasticity (e.g., 2 percent) and a reasonably high markup
(e.g., 40 percent), then the limited participation model can account for all of the stylized
facts we stress above. Specifically, a contractionary shock to the growth rate of money has
essentially no contemporaneous impact on the price level and drives wages, profits, output,
and employment down, while driving the rate of interest up. But if one is not willing to
accept high markups and labor supply elasticities, then the model has difficulty in generating
a large output effect and a small price effect from a monetary policy shock. As with the
3Romer (1996) argues his case in a different, but related way. He shows in a particular class of model
economies that absent labor market frictions, what he views as implausibly large menu costs, are required
to rationalize the sticky price assumption. The logic of his argument, like ours, focuses on the response of
firms’marginal costs to monetary shocks.
5
sticky price models, it seems important to embed labor market frictions, which have the
effect of mimicking a high elasticity of labor supply into the current generation of limited
participation models. We conclude that general equilibrium models which allow for only one
type of friction cannot convincingly account for the salient facts about how the economy
responds to an unanticipated monetary policy shock.
The previous remarks may seem to suggest that we could remedy the shortcomings of
the limited participation model by requiring a subset of the intermediate good firms to set
their price in advance. However, we find that this change has only a relatively small impact
on the equilibrium price and output response to a monetary policy shock. This is true even
when as many as 80 percent of the intermediate good firms set their price in advance. The
basic reason is as follows. For the subset of the firms who set prices in advance, the output
effect of a contractionary policy shock is greater than in the equilibrium when all firms set
prices flexibly. But the large drop in employment of labor and capital by fixed price firms
leads to a large drop in the marginal cost of production. This in turn leads flexible price
firms to drop their prices by a large amount and to actually increase output. This effect
accounts for the small impact on aggregate price and output dynamics of the introduction
of price setters and operates through the general equilibrium impact of a monetary shock on
marginal costs. This basic result holds, even if there is limited mobility of capital and labor
between the fixed and sticky price sectors of the economy. We conclude that embedding
labor market frictions in the limited participation model is likely to prove a more fruitful
way of remedying its shortcomings than allowing for sticky prices.
The finding that flexible price setters adjust their prices by more, the larger is the fraction
of firms which fix prices in advance, also holds in a version of the sticky price model in which
6
only a fraction of the firms set prices in advance. In our view, this finding calls into question
the basic appeal of the sticky price model. Presumably, the appeal of th at model rests on
the notion th at flexible price firms act more like fixed price firms the larger is the fraction
of the firms in the economy who set their price in advance. The opposite is true for the
environments that we consider.4
The remainder of this paper is organized as follows. In Section 2, we discuss the monetary
policy shocks used in our empirical analysis and present our empirical results. In Section 3, we
present the theoretical models. In Sections 4 and 5, we discuss qualitative and quantitative
properties of the models, respectively. Our concluding remarks appear in Section 6.
2. T h e E m p i r i c a l Effects o f M o n e t a r y P o l i c y S h o c k s
2.1. P olicy Shock M easures
In our empirical analysis, we use two measures of shocks to monetary policy. These are close
variants of measures developed in Christiano, Eichenbaum, and Evans (1996) (CEE) and
Sims and Zha (1995) (SZ). Both procedures posit that the Federal Reserve System follows
an interest rate targeting rule and that the monetary policy shock is a disturbance to that
rule. They differ on the assumptions made to identify that shock.
C h r is t ia n o , E ic h e n b a u m , a n d E v a n s P o lic y S h o c k s
4These considerations suggest changing our environment to allow for factors which increase complementar
ity among price setters. This could, for example, be achieved by assuming that intermediate good producers
use the output of other intermediary good producers as inputs to production. (See Basu (1995).) It would be
of interest to explore the implications of this model modification in our environment. However, experiments
reported in Chari, Kehoe, and McGrattan (1996) suggest that the gains from this modification may not be
large.
7
CEE identify a monetary policy shock with the disturbance term in the following interest
rate targeting rule:
Rt
where
Rt
is the federal funds rate,
=
ip is a
available to the monetary authority when
that is orthogonal to the elements of
Rt
Clt .
+
(2.1)
£st
linear function, Ot summarizes the information
Rt
is set, and
e 3t
is a serially uncorrelated shock
(CEE also work with a version of (2.1), where
is replaced by a measure of the nonborrowed reserves of banks.) The orthogonality
restriction on
variable,
R t,
e 3t
corresponds to a particular recursiveness assumption: the monetary policy
is contemporaneously affected by the date
t
variables in
Clt ,
but those variables
are not contemporaneously affected by the monetary policy shock. The advantage of this
recursiveness assumption is that it justifies estimating
squares regression of
Rt
e 3t
as the residual in an ordinary least
on fi£. The impulse response of a variable to a policy shock can be
measured by the coefficients in the regression of the variable on current and lagged values of
the fitted residuals in (2.1).
In practice, we estimate the impulse response functions by an asymptotically equivalent
procedure based on a Vector Autoregressive Representation (VAR) for a vector of variables,
Zt.
(For the details of this procedure, see CEE.) In our benchmark VAR,
Zt
includes the log
of real GDP, the log of the GDP deflator, an index of the change in sensitive commodity
prices, the federal funds rate, the log of nonborrowed reserves, the log of total reserves, and
the first difference of the log of M2. We structure the VAR so that it captures the CEE
recursiveness assumption, and specifies that the contemporaneous variables in fi£ are the
first three variables in
Z t.
The rationale for this specification is discussed in CEE. To assess
8
the effect of a monetary policy shock on real wages, we add the log of real wages to
Zt.
To
assess the effect of a policy shock on the share of profits in output, we add the ratio of profits
to nominal GNP to
nominal GNP from
Z tQ.
We exclude contemporaneous real wages and the ratio of profits to
The estimation period is from 1965Q3 to 1995Q2, and the VARs have
a lag length of four. (See Appendix A for a detailed description of the data.)
S im s -Z h a P o lic y S h o ck s
Although the recursiveness assumption implicit in the CEE procedure buys considerable
simplicity, it may come at the cost of specification error. For this reason, we also consider SZ
policy shocks, which do not make the recursiveness assumption. The cost, however, is that
SZ must identify a broader set of economic relationships than do CEE and these additional
identifying assumptions could also entail specification error. For example, SZ assume that
contemporaneous output does not enter the monetary policy rule, but it does enter the
money demand equation. (See Appendix B for further details.)
SZ assume a monetary policy rule of the form
Rt —
Here,
g
<?(©t) +
(2-2)
£st-
is a linear function, and ©t summarizes the variables that the policymakers look at
when setting the target interest rate,
R t.
SZ identify
Rt
with the three-month rate of return
on Treasury bills. The information set, ©t, is composed of time
t
values of crude materials
prices and M2, and lagged values of the Treasury bill rate, intermediate materials prices,
the aggregate price level, real wages, aggregate output, crude materials prices, M2, and a
measure of personal bankruptcies.
9
Under SZ’s assumptions, all of the variables in
Zt
can respond contemporaneously to a
monetary policy shock. Because the monetary policy shock is not orthogonal to the elements
of ©t, it cannot be identified with the residuals in a least squares regression of
Rt
on the
elements of ©t. The exact SZ procedure for identifying the policy shock is summarized in
Appendix B. The associated impulse response functions are estimated using standard VAR
methods. As in SZ, our VAR has four lags, and the estimation period is the same as for the
CEE system.
Our version of SZ does not include their measure of personal bankruptcies, since we did
not have access to this data. In addition, we work with the first difference of the log of M2.
We do this to facilitate comparisons with the CEE results. In addition, we do not impose the
overidentifying restrictions used by SZ that the demand for real balances has a coefficient of
one on contemporaneous real income.5 To assess the effect of a monetary policy shock on
the ratio of profits to nominal GNP, we amend the SZ system in a way that is summarized
in Appendix B.
2.2. The Effects of M onetary Policy Shocks on Wages and Profits
In this section, we report the effects of a contractionary monetary policy shock on real wages
and corporate profits. To help assess the properties of our benchmark policy shock measures,
Figure 1 displays the effects of contractionary benchmark CEE and SZ policy shocks on var
ious economic aggregates. Solid lines report point estimates of dynamic response functions.
Dashed lines denote a 95 percent confidence interval for the dynamic response functions.6
5Comparing the estimated dynamic response functions to a monetary shock in our benchmark system
with those in SZ, it can be verified that these three perturbations make very little difference to the results.
6The 95 percent confidence intervals for the CEE impulse response functions in Figures 1-8 are computed
using the following bootstrap Monte Carlo procedure. We first construct 1000 time series on the vector
10
Since close variants of these response functions are discussed in CEE and SZ, we comment
on them only briefly here.
The main consequences of a contractionary benchmark CEE policy shock can be summa
rized as follows. First, there is a persistent rise in the federal funds rate and a persistent drop
in nonborrowed reserves and the growth rate of M2. After a one-quarter delay, the shock also
leads to a persistent decline in total reserves. Second, after a delay of two quarters, there is
a sustained decline in real GDP.7 Third, after an initial delay, the policy shock generates a
persistent decline in the index of commodity prices. The GDP deflator is flat for roughly a
year and a half before it declines. Fourth, we cannot reject the hypothesis that a monetary
policy shock has no effect on real balances in the long run.
The main consequences of a contractionary benchmark SZ policy shock can be summa
rized as follows. First, there is a persistent decline in the growth rate of M2 and a rise in
the interest rate. Second, there is a persistent decline in the GDP deflator and the prices of
Zt,each of length T, where T denotes the number of observations in our data sample. Let {ut}T=i denote
the vector of residuals from the estimated VAR. We construct 1000 sets of new time series of residuals,
{ u t ( j ) } J L . i , j = 1,. . . , 1000. The t th element of { u t ( j ) } J = x isselected by drawing randomly, with replacement,
from the set of fitted residual vectors, { ut}J-i. For each {^(i)}^!, we construct a synthetic time series
of Z t ,denoted
using the estimated V A R and the historical initial conditions on Z t .Second, we
reestimate our V A R using { Z t { j ) } J Li and the historical initial conditions and calculate the implied impulse
response functions for j = 1,..., 1000. For each fixed lag, we calculated the 2bth lowest and 975t/l highest
value of the corresponding impulse response coefficient across all 1000 synthetic impulse response functions.
The boundaries of the confidence intervals in the figures correspond to a graph ofthese coefficients. The solid
line reports our point estimate of the impulse response function. For the most part, these point estimates
are quite similar to the mean value of the simulated impulse response functions. There is some evidence of
bias, especially in Figure 7, which displays the results for our aggregate measures of profits. Interestingly,
the evidence of bias suggests that our point estimates understate the magnitude of the drop in profits after
a monetary contraction.
The bands for the SZ impulse response functions are computed using the procedure described in Sims and
Zha (1995a). The reported bands are two standard deviations about the mean of the impulses. As in the
case of CEE, the solid line reports our point estimate of the impulse response function.
7The asymmetry in the confidence bands suggests that our estimate ofthe response of G D P to a monetary
policy shock is biased toward zero. Thus, a bias-adjusted estimator would indicate a stronger negative
response of G D P to a contractionary monetary policy shock. The same istrue for the response of aggregate
profits to a monetary policy shock. (See Figure 7.)
11
intermediate goods and crude materials. Third, after a delay, the shock generates a persis
tent decline in real GDP. Finally, note that the benchmark measure of real wages (average
hourly earnings of private nonagricultural production workers divided by the GDP deflator)
is basically unaffected by the SZ policy shock. Overall, the qualitative response of the system
to a policy shock is quite similar for the CEE and SZ policy shock measures. However, the
estimated SZ policy shocks are somewhat smaller than the estimated CEE policy shocks.
For example, the impact effect of a CEE policy shock on the federal funds rate is about 70
basis points, while the impact of a SZ policy shock on the three-month Treasury bill rate is
about 40 basis points. In addition, the impulse response functions associated with the SZ
policy shocks are estimated somewhat less precisely than the ones associated with the CEE
policy shocks.
Figure 2 reports the response of different measures of real wages to contractionary CEE
and SZ policy shocks. Rows 1-6 report the response of five measures of aggregate real wages:
(1) the benchmark measure we discuss above, (2) average hourly earnings of production
workers in the private nonagricultural sector deflated by the Bureau of Labor Statistics
using an index derived from the Consumer Price Index for Urban Wage Earners and Clerical
Workers, (3) average hourly earnings of production workers in the manufacturing sector
divided by the GDP deflator, (4) average hourly earnings of production workers in the
manufacturing durable goods sector divided by the GDP deflator, and (5) average hourly
earnings of production workers in the manufacturing nondurable goods sector divided by the
GDP deflator.
The key results can be summarized as follows. First, with two exceptions, regardless
of which policy shock or which measure of real wages we work with, according to the point
12
estimates, a contractionary monetary policy shock leads to a persistent decline in real wages.
The exceptions are that measures (1) and (5) of real wages appear roughly unaffected by
a SZ policy shock. Second, for both policy shock measures, manufacturing real wages fall
more sharply than economywide wage measures. Finally, within manufacturing, real wages
fall more sharply in the durable good industries than in the nondurable good industries.
Generally speaking, the decline in real wages following a SZ policy shock is smaller and less
precisely estimated than the decline following a CEE policy shock.
Next, we consider the response of real wages at the two-digit SIC industry level to a
contractionary policy shock, where real wages are measured as gross average hourly earnings
of production and nonsupervisory workers, deflated by the GDP deflator. Figure 3 reports
the response of real wages to a contractionary CEE policy shock for 10 two-digit SIC code
nondurable good industries.8 Figure 4 reports the analog results for a contractionary SZ
policy shock. Figure 5 reports the response of real wages to a contractionary CEE policy
shock for 10 two-digit SIC code durable good industries.9 Figure 6 reports the analog results
for a SZ policy shock.
The key results can be summarized as follows. First, real wages in all but one of each of
the nondurable and durable good industries (leather and leather products, and instruments
and related products, respectively) fall after a contractionary CEE policy shock. Second, the
declines are greater in the durable good industries than in the nondurable good industries.
8Food and Kindred Products, SIC 20; Tobacco, SIC 21; Textile Mill Products, SIC 22; Apparel and Other
Textiles, SIC 23; Paper and Allied Products, SIC 26; Printing and Publishing, SIC 27; Chemicals and Allied
Products, SIC 28; Petroleum and Coal, SIC 29; Rubber and Miscellaneous Plastic Products, SIC 30; and
Leather and Leather Products, SIC 31.
9Lumber and Wood Products, SIC 24; Furniture and Fixtures, SIC 25; Stone, Clay, and Glass, SIC 32;
Primary Metal Industries, SIC 33; Fabricated Metal Industries, SIC 34; Machinery-Except Electrical, SIC
35; Electric and Electronic Equipment, SIC 36; Transportation Equipment, SIC 37; Instruments and Related
Products, SIC 38; and Miscellaneous Manufacturing, SIC 39.
13
T h ir d , fo r b o th in d u s tr ie s , th e r e s u lts a re m o re m ix e d fo r th e S Z p o lic y s h o c k m e a su re .
Integrating across all of our results, we conclude there is substantial evidence in support
of the view that real wages fall in response to a contractionary monetary policy shock. There
is no evidence to support the view that real wages rise in response to such a shock.
We now discuss the response of profits to a monetary policy shock. Figure 7 reports the
response of seven different measures of profits to contractionary CEE and SZ policy shocks:
(1) total before-tax profits, (2) total after-tax profits, (3) net domestic profits after taxes, (4)
nonfinancial net domestic after-tax profits, (5) total after-tax profits net of interest costs, (6)
net after-tax domestic profits net of interest costs, and (7) nonfinancial after-tax domestic
profits net of interest costs. The last three measures of profits are of some interest because
they allow us to isolate the role that interest rate costs play in the response of profits to a
contractionary policy shock. Notice that regardless of which measure we work with, both
CEE and SZ contractionary monetary policy shocks lead to a persistent decline in profits.
This is true even when we construct profits in a way that does not take into account interest
costs. The dynamic impulse response functions of SZ are estimated less precisely than in
the case of CEE.
Next, we consider the response of profits at the sectoral level to contractionary CEE and
SZ policy shocks. Figure 8 reports the response of before-tax profits in five sectors of the
economy: manufacturing, nondurables, durables, retail, and transportation and utilities. As
above, profits are calculated as a fraction of nominal GDP. Notice that for the CEE policy
shock measures, profits in manufacturing, durable goods, and the retail sector experience
persistent drops after a contractionary policy shock. This is not true for nondurable goods
and transportation and utilities. While profits appear to rise in these industries, one cannot
14
reject the hypothesis that profits are unaffected by the policy shock. The results with the SZ
policy shock measures are consistent with those of the CEE policy shock measures, although
again the dynamic response functions are estimated less precisely. Figures 7 and 8 provide
strong evidence th at profits fall after a contractionary policy shock.
Based on the evidence reported in this section, we conclude that business cycle models
ought to have the implication th at output, real wages, and profits fall in response to a
contractionary policy shock. For a substantial period of time, the aggregate price level
should not respond. While there is uncertainty about the response of real wages, plausible
theories will not have the implication th at real wages rise after a contractionary policy shock.
3. O u r S t i c k y P r i c e a n d L i m i t e d P a r t i c i p a t i o n M o d e l s
In this section, we describe our fixed price and limited participation models, which correspond
to two specifications of the sequence of events in a basic, benchmark model. We first present
the problems faced by the agents in our model, and we then discuss our equilibrium concept.
3.1. Final G ood Firm s
At time
t,
a final consumption good,
Yt ,
is produced by a perfectly competitive firm. The
firm does so by combining a continuum of intermediate goods, indexed by
i
6 (0,1), using
the technology
where 1 < // < oo, and
P it
denote the time
t
Yu
denotes the time
t
input of intermediate good
price of the consumption good and intermediate good
15
i.
i,
Let
Pt
and
respectively.
P r o fit m a x im iz a tio n im p lie s th e E u le r e q u a tio n
(3.2)
\ p j
Yt
According to (3.2), the demand for intermediate good i is a decreasing function of the relative
price of that good and an increasing function of aggregate output,
Yt.
Integrating (3.2) and
imposing (3.1), we obtain the following relationship between the price of the final good and
the price of the intermediate good:
-i(i-p)
h
i
:
(3.3)
p ^ rd i
3.2. Interm ediate G ood Firms
Intermediate good
i
is produced by a monopolist who uses the following technology:
K ? ,N
}r -
*
if
> 4
Y it= {
0,
where 0 <
a
< 1. Here,
Na
and
Ku
(3.4)
otherwise
denote time
t
labor and capital used to produce the
i th
intermediate good. The parameter </>denotes a fixed cost of production. We rule out entry
and exit into the production of intermediate good
i.
Intermediate firms rent capital and labor in perfectly competitive factor markets. Eco
nomic profits are distributed to the firms’ owner, the representative household, at the be
ginning of time period
by
rt
and
W t,
t +
1. We denote the time
t
rental rate on capital and the wage rate
respectively. Workers must be paid in advance of production. As a result,
16
firms need to borrow their wage bill,
W tN n ,
from the financial intermediary at the beginning
of the period. Repayment occurs at the end of time period
Consequently, the firm’s total time
t
costs are given by
t
at the gross interest rate,
R t W t N it
+
r t K it .
R t.
Their cost function
is given by
C (r„
where
A
=
put, given
^ ( q) >so that the time
Y it
> 0, is
(3.5)
R ,W „ Y „ ) = A ( r t ) a (W t R t ) 1- a (Yu + 4 )
M C ( r t ) R tW t )
=
t
marginal cost of producing additional out
A r f ^ W tR t) 1 - 0 -
A convenient representation of this
expression, which holds in equilibrium, is given by
M C ( r t , R tW t)
where
Nt
=
j^ N tW
tR t
(3.6)
denotes aggregate employment, and we take into account our assumption that the
aggregate stock of capital is a constant, unity.10
In the version of the model where prices are set flexibly, profit maximization leads the
intermediate good firm to set its price equal to a constant markup over marginal cost:
P it = f iM C t.
(3.7)
In the version of the model where the firm sets its price prior to the realization of the
10To obtain this expression, we note that an efficiency condition of firm t € (0,1) is r t / ( W t Rt) =
[a/(l — a)] N u / K u . The implied equality of firm labor-to-capital ratios implies that this expression holds
for the aggregate ratio of labor to capital; N t/ K t . To obtain (3.6), we substitute this expression with the
aggregate variables into A r f ( W t R t ) l ~a and take into account the equilibrium condition, K t = 1.
17
m o n e y s h o c k , it d o e s so to o p tim iz e th e a p p ro p ria te ly w e ig h te d e x p e c ta tio n o f p ro fits:
•nt+i
[PayB -
subject to the demand equation, (3.2). Here,
of the representative household. The
other than
Pu
and
Yu
i th
(3.8)
C(rt>B,W „«,)]
UCtt+i
denotes the time t + 1 marginal utility
intermediate good firm takes prices and quantities
as given and beyond its control. The weights on profits in (3.8) cor
respond to the marginal utility of a dollar to the firm’s owner, the representative household,
and the dating reflects our assumption (displayed below) that the household cannot spend
its date
t
profits until date
t
+ 1. Under these circumstances, the firm is led to set its price
equal to a constant markup over a weighted expectation of marginal cost:
P it
(3.9)
—fJ.Et-iu>t M C t
where
ut
E t-1
(3.10)
DP-1 \X
P .+ l
Yt
As (3.10) makes clear, in setting its price, the firm places a great deal of weight on
states of the world where aggregate demand,
Yt ,
and
P it
=
Pt,
for
i
in
is large.
Expressions (3.2), (3.7), and (3.9) indicate that in equilibrium,
Yu = Yt ,
M Ct
N it = N t , K&
=
K t,
€ (0,1). Note that although final goods are priced flexibly,
in equilibrium they inherit whatever inflexibility there is in intermediate good prices. (See
(3.3).)
18
3.3. F in a n c ia l In te rm e d ia ry
At time
a perfectly competitive financial intermediary receives deposits,
t,
household and lump-sum cash injections,
X t,
I t,
from the
from the monetary authority. These funds
are supplied to the loan market at the gross interest rate,
R t.
Demand in the loan market
comes from the intermediary good producers who seek to finance their wage bill,
W tN t .
Loan
market clearing requires
(3.11)
W t N t = It + X t .
At the end of the period, the intermediary pays
and distributes
R tX t
R tIt
to households in return for their deposits
to households in the form of profits.
3.4. H ouseholds
At time
t,
the representative household ranks alternative streams of consumption and hours
worked according to the criterion function:
OO
(3.12)
E t Y . e ‘U ( C „ t ,N „ , ) .
j-o
Here, 0 <
(3 <
1, C* denotes time
t
units of consumption,
Nt
denotes time
t
hours of work,
and
U (C , N )
= log
C - ^ N '+ *
1
19
(3.13)
In (3.13), V'o > 0, and
ip >
0. Specification (3.13) has the convenient feature that the house
hold has a well-defined static labor supply function, whose elasticity,
l/ip ,
is a constant.11
In our quantitative analysis, we also consider an alternative specification of utility.
The household is endowed with
Kt
units of capital, which it supplies inelastically to a
competitive rental market in which the rental rate is denoted by r t . To simplify the analysis,
we assume there exists no technology for increasing the aggregate stock of capital and that
the rate of depreciation is zero. As a result, the per capita stock of capital is a constant,
and we specify this to be unity. We assume there is no market in which agents can trade
ownership claims on capital. This is without loss of generality, since we assume all agents
are identical.
The household supplies
Nt
units of labor at the nominal wage rate,
W t,
and faces the
following cash constraint on its consumption purchases:
(3.14)
P t C t < W t N t + M t - It-
Here,
Mt
denotes the household’s beginning-of-period t holdings of cash, and
It
denotes time
11We can reconcile our model with balanced growth as follows. First, we think of (3.13) as the indirect
utility function for a household whose actual utility function is
log (C
+ C n) -
7 log
/ N 1+^
\
+ NnJ
where N n and C n denote nonmarket hours worked and consumption, respectively. Second, suppose the
home production function is C n = ipoNn. Proceeding as in Benhabib, Rogerson, and Wright (1991), it is
straightforward to show that the indirect utility function in C and N is
108 ( r h ) - T"*
) + ( 1 - 7) l o i ( c - * . £ 9 ? ) .
We get a balanced growth path in which labor does not grow, and all other quantities grow at a positive
rate by assuming that intermediate good firm technologies and the home production function shift up at the
same, constant rate.
20
t
dollars sent to the financial intermediary. Constraint (3.14) implies that time period
t
wage earnings are payable to the household in time to satisfy its time t cash constraint. The
household’s money holdings evolve according to
M t+1 = [WtNt + M t
—
It
— P tC t]
+
r tK t
+ Rt [It +
X t]
+ Dt
(3.15)
where D t and R tX t denote time t profits received from intermediate good producers and
financial intermediaries, respectively.
The household maximizes (3 .12), subject to (3.13)-(3.15). In both versions of the model,
C t,N t , and M t+ 1 are chosen after the realization of the time t monetary shock. This is also
true for
It
in the fixed price model. In the limited participation version of the model,
is set before the realization of the period
t
It
monetary shock. For convenience, the timing
assumptions in the two models are summarized in Figure 9.
The first-order-necessary condition associated with the household’s choice of N t is given
by
Wt
tp o N f.
(3.16)
Pt
In the sticky price version of the model, the Euler equation for It is given by
U ct
—R t E t
Pt
fiU c,t+l
P t +1
(3.17)
According to (3.17), the household equates the marginal utility of a dollar deposited with
the financial intermediary at time t to the time t + 1 expected marginal utility of the returns
21
from that deposit. In the limited participation version of the model, the Euler equation for
It
is given by
P
U a
_p
D PU c,t+ 1
(3.18)
t+l
3.5. M onetary A uthority
W e assume that the growth rate of money,
xt
=
X t/ M t
= (M
t+ i
—
is the realization
of an exogenous, three-state Markov chain with an unconditional mean growth rate of fxx .
W e discuss the details of this process in the next subsection. There, we also discuss the
relationship between the representation of monetary policy used in the model and the interest
rate targeting representation we adopt in our empirical analysis.
3.6. Equilibrium and Com putation
Let
Z t
denote the vector of nominal variables (excluding
period stock of money. Let
Zt
=
Q t
R t)
scaled by the beginning-of-
denote the other variables. Thus,
[Pu, P t , W t , r t , I t , X t \ /M t , Q t
—[-Rt>Ct, Yt, Yu, K ^ ,
K t, Nt, Ait,], where
i
€ (0,1).
To define equilibrium, we find it convenient to adopt a notation that allows us to be more
precise about the price and commodity space. Let s£denote the history of exogenous shocks
up to time
Z ( s t)
and
A
sequence-of-markets equilibrium is a set of history-contingent sequences,
Q ( s l ),
with the properties: (i) given the prices, the quantities solve the household
t.
and final good firm problems for each possible s t ; (ii) given the final good and factor prices,
the
i th
intermediary good price, output, and inputs solve the intermediary firm’s problem
22
for each
i
6 (0 ,1) for each possible s*; and (iii) the loan market-clearing condition, (3.11),
and the resource constraints are satisfied,
Jo N ^ s ^ d i
=
C ( s *)
= y(sf) and JjJK i ( s f ) d i
K ( s t) = 1,
=
N ( s t) , for all s l , and all t. Part (iii) of our definition of equilibrium incorporates
our assumption that the per capita stock of capital is unity at each date. W e confine
ourselves to symmetric equilibria, in which P i ( s *) = P(s4), Y ( s l)
N i ( a *) =
=
Y^s*), K ^ s * )
1,and
N ( s *), for all i .
To describe how we compute equilibrium, we define the state variables,
Under our assumptions on the money growth process,
Any set of nine
Qa
=
Z3
and
Q 3s
induces sequences,
{ Z ( s t),
s
s
= (x_i, re).
can take on nine possible values.
Q(s‘); all s*}.12 W e compute
Za
and
s such that the implied price and quantity sequences are a competitive equilibrium. In the
sticky price model,
P /M
(the second element in Z s) is restricted to vary with x_j only. In
the limited participation model,
Q a ’s
I/M
is restricted to be a function of x_i only. The
Zs
and
are computed as the solution to a particular set of nonlinear equations: the first-order
conditions and resource constraints for each possible s.
4. Q u a l i t a t i v e P r o p e r t i e s o f t h e S t i c k y P r i c e
a n d L i m i t e d Participation M o d e l s
In this section, we discuss the qualitative properties of our models. W e begin by comparing
the nature of the output response to a money shock in the two models. W e then discuss the
interest rate and profit response to a monetary shock in the limited participation model. In
analyzing this response, we pay particular attention to the role played by the magnitude of2
1
12Here, s‘= (so,«i,. ••,««). s t
=
(x t- i , x t).
23
the labor supply elasticity and the markup.
4.1. The O utput Effects o f a M oney Shock in the Two M odels
W e combine (3.11) (evaluated at equality) and (3.14) to obtain
P tC t = M t + X t .
(4.1)
This equation must hold for interior equilibria of both versions of the model. Relation (4.1)
defines a parabola in a graph with P t on the vertical axis and C t (or, output, Yt , since the two
are the same in our model) on the horizontal axis. This curve is depicted by the downwardsloped line labeled D D in Graph 1. The curve D D shifts to the right for higher values of X t ,
just as the aggregate demand equation in an intermediate macroeconomics textbook does.
In the sticky price model, equilibrium output, Y , can be thought of as the intersection of the
curve D D and another curve, which is horizontal at the predetermined price level. In Graph
1,this horizontal curve is labeled S S . As in the standard intermediate textbook treatment,
the sticky price model depicts the economy’s response to a money injection as a move along
a fixed and horizontal short-run aggregate supply curve.13 So, for a money injection given
by X
t,
for X ' t
equilibrium output is given by Y . The curve D 'D ' graphs the relationship P t =
> X t.
The equilibrium level of output that obtains for this larger money injection,
Y ' , is given by the intersection of D ' D 1 with S S .
The limited participation model takes a very different position on the short-run supply
13Below, we also consider a version of the sticky price model in which not all firms set prices in advance.
In this version of the model, the short-run aggregate supply curve is, in effect, positively sloped. This change
does not affect the comments we make here.
24
curve. One way to think of this model is that its short-run supply curve, labeled
S S
in
Graph 2 ,is vertical and shifts right with a money injection. A monetary injection operates
in part like a technology shock: it reduces production costs by driving down the equilibrium
rate of interest. The vertical curve S ' S ' corresponds to the vertical supply curve that obtains
for X [
> X t.
If the supply-side effect associated with the monetary shock is sufficiently large,
then the equilibrium contemporaneous price response to the money injection could be zero
or even negative.
To understand the supply-side effect of a monetary policy shock in the limited partici
pation model, it is useful to understand its impact on the labor market. Relations (3.6) and
(3.7) imply that in equilibrium, labor demand is given by
W t
Pt
(1 -
g ) N t~a
pR t
Relation (4.2) can be expressed as a labor demand schedule in real wage-employment space.
This schedule is depicted by the downward-sloped line in Graph 3 labeled D
Other things
D .
equal, a decrease in the interest rate shifts the labor demand curve to the right. These effects
occur because the firm equates the value of labor’s marginal product to a markup over the
cost of hiring labor, inclusive of financing costs.
Relation (3.16), the household Euler equation for N
t,
defines a static upward-sloped labor
supply schedule. This schedule is depicted by the upward-sloped solid line in Graph 3 labeled
SS. For a given level of R
t,
equilibrium employment is given by the intersection of the static
labor demand and supply schedules. A lower value of the interest rate, R !
< R,
with a rightward shift in the labor demand schedule (to the curve labeled
25
is associated
D 1D ' )
and an
increase in the real wage and employment. This induces a rightward shift in the aggregate
supply curve in the price level/output plane.
4.2. T he O utput, Interest R ate, and Profit Effects o f a
M onetary P olicy Shock in th e Limited Participation M odel
An important shortcoming of the previous intuition about the limited participation model
is that it is based on an exogenous shift in the interest rate. In fact, the rate of interest
is jointly determined with employment and output. To obtain intuition about the general
equilibrium effects of a monetary shock, it is useful to consider a simplified version of the
model in which 0 = 0.
Taking the ratio of the labor market-clearing condition, (3.11), to the cash equation, (4.1)
we obtain
W tN t _
r
r
*’ ‘
Pt C t
It + X t
Mt + X t'
The variable, rt,denotes the ratio of funds passing through the loan market to funds passing
through the goods market. Since I t
< M t,
and these two variables are predetermined relative
to X(, a contractionary policy shock causes Tt to fall. That is, a monetary contraction creates
a relative shortage of liquidity in financial markets. This leads to a reduction in employment
and output, as is explained in Christiano (1991), Christiano and Eichenbaum (1992, 1995),
and Fuerst (1992). To see this, we substitute out for the real wage using the labor supply
equation, (3.16), make use of N t ~ a =
C t, K t
= 1,and rearrange, to obtain:
(4.4)
N t =
26
Note that the size of the decrease in employment associated with a given reduction in X
t
monotonically increases in the labor supply elasticity, 1 / ip . With the labor supply elasticity
large enough, and
a
small enough, the equilibrium response of employment to a money
shock can be made arbitrarily large for given Tt. Since P t = (M
t + X t)/ N } ~ Q,
this suggests
there exists a value of ip for which the equilibrium price level does not respond to X
t.
This
reasoning abstracts from general equilibrium effects of ip on the level of Tt. But we assume
these are negligible, since the nonstochastic steady-state level of rt, T, and the value of
d T t/ d x t ,
evaluated in steady state, is invariant to ip.
To determine the effect of a contractionary monetary policy shock on the rate of interest,
note that
N fa
=
C t/ N t,
when
K t
= 1 and
<p =
W tN t
0 ,so that
_ 1-
P tC t
a
(J-Rt
rearranging this equation, we obtain
1 —a
/*Tt
Rt =
Since d T t / d x t
>
0 for I t
< M t,
(4.6)
(4.6) establishes that in this version of the model, a monetary
contraction must drive the equilibrium rate of interest up.
Next, we consider the impact of a monetary shock on profits. The time t economic profit
of intermediate good producers equals their total revenues minus total costs:
P tY t -
R tW tN t -
r tK t
=
27
P tY t -
M C t {Yt + 4>).
Recall from Section 2 th at the measure of profits we use in our empirical analysis corresponds
to accounting profits. While our empirical measure of profits nets out depreciation costs, a
large portion of the return to capital (e.g., dividends) is not treated as a cost. To adjust our
model-based measure of economic profits to bring it closer in line with the empirical measure
of profits, we add
r tK t
to economic profits. This actually overadjusts our measure of profits,
because some components of rent to capital are treated as costs in our empirical measure of
profits. However, one of our key conclusions is that the sticky price model counterfactually
implies that profits rise after a monetary contraction. If anything, our treatment of the return
to capital in profits biases our results in favor of the sticky price model. To summarize, the
empirical measure of profits that we adopt is
7rt =
where the equilibrium condition,
K t
P t Yt - M C t (Y t + 4>) + r t
(4.7)
= 1, is imposed.
To determine the impact of a monetary shock on 7Tt, we note that (4.7) for the limited
participation model reduces to
7h
= (M t + X t)
1
1.
+
ccN }~ Q
(4.8)
where the first term uses (4.1) and (3.7), and the last term corresponds to the equilibrium
rent on capital. Equations (4.4) and (4.8) indicate that profits necessarily fall in response to
a fall in
X t.
Note that when
after a decline in
rt
is added to economic profits, it exacerbates the decline in 7rt,
x t.
28
It is of interest to understand the influence of the markup on the equilibrium effects of a
monetary policy shock. Prom (4.4), it is clear that the effect on output of a monetary policy
shock,
d Y t/ d x t ,
can be decomposed into two components: (i) the effect of x t on
the effect of Tt on
N t.
Changes in
fi
affect
dY t/d x t
and (ii)
exclusively via the first channel. Prom
(4.3), we see th at in our model, Tt corresponds to the share of labor in gross output. Not
surprisingly, the larger is
fxXt
fi,
the smaller is the steady-state value of I\ (See (??).) Given
a smaller value of T corresponds to a smaller value of J/M , the fraction of households’
beginning-of-period stock of money sent to the financial sector. The smaller is
I /M
, the
larger is the impact of a given monetary injection on the pool of funds passing through the
financial intermediary that are lent to firms. This implies that
turn leads to a rise in
d N t/ d x t
and
d Y t/ d x t
d r t/ d x t
is larger, which in
(at least when evaluated in steady state). In
this way, an increase in the markup raises the employment and output effects of a monetary
policy shock. Note that the effect of an increase in /z on
the effect of an increase in
l/ip .
d N t/ d x t
and
d Y t/ d x
is similar to
However, the mechanisms by which these effects occur are
different. As we note above, changes in the labor supply elasticity have a negligible impact
on the magnitude of d T t / d x t and a relatively large impact on
d N t/d x t.
We conclude this section by noting that equation (4.8) implies that the increase in d N t / d x t
associated with a larger value of /z also implies that a given monetary shock has a larger
impact on profits. In addition, it is easy to verify that
d R t/d x t
is increasing (in absolute
value) in /z, at least when evaluated in nonstochastic steady state. As is the case regarding
dY t/d x t
and
d N t/d x t,
the effects of an increase in /z are similar to those of an increase in
1/i p , but the mechanisms by which these effects occur are different.
29
5. Q u a n t i t a t i v e P r o p e r t i e s o f t h e S t i c k y P r i c e
a n d L i m i t e d Participation M o d e l s
Before presenting the quantitative properties of the model, we discuss how values are assigned
to the parameters.
5.1. Param eter Values
To compute the response of the system to monetary shocks, we require values for the models’
parameters. In this section, we describe the benchmark values we use in our experiments.
The models’ structural parameters consist of /3 , a , ip, (jl, <j>, ip0 , and the parameters governing
the evolution of
x t.
We set the discount parameter /3 to (1.03)~‘25. The parameter V'o is
chosen so that, conditional on the assigned values for the other parameters, employment in
nonstochastic steady state is unity.
The elasticity of labor supply with respect to the real wage rate is equal to
l/ip .
The
value of this elasticity is controversial. Most microeconomic studies estimate it to be quite
small. Typically, estimated labor supply elasticities for males are near 0. (See Card (1991),
Killingsworth (1983), and Pencavel (1986).) Estimates of labor supply elasticities for females
typically fall in the range 0.5-1.5. (See, for example, Killinsgworth and Heckman (1986).)
At the macroeconomic level, authors in the real business cycle literature typically work
with labor supply elasticities that are much higher than those emerging from the labor liter
ature. For example, the parameter estimates in Christiano and Eichenbaum (1992a) imply
a Frisch labor supply elasticity in excess of 5.0. Authors such as Hansen (1985) assume indi
visibilities in labor supply and a market structure that breaks the connection between indi
30
vidual and aggregate labor supply elasticities. Given Hansen’s functional-form assumptions,
the Frisch labor supply elasticity of the fictitious representative consumer whose preferences
are used to compute the aggregate equilibrium is infinite. So, the range of elasticities that
are used in the literature is enormous. We use a benchmark value for
ip
equal to 1.0, which
corresponds to a labor supply elasticity of 1.0. We demonstrate th at the models’ empirical
performance depends sensitively on this parameter by displaying results for a range of values
for
ip.
Next, we consider the parameters
fj,
and
<p.
For intermediate good firms which set their
price flexibly, /x corresponds to the markup in each period. For firms which set their price
prior to the realization of a money shock, /x corresponds roughly to their average markup.14
To discuss the relevant empirical range of values for /x and
production function of a typical intermediate good firm as
= K a N 1~a .
<p,
it is useful to represent the
Y — F (K , N )
—<p, where
F (K , N )
Profit maximization implies
Fk
r
= /x - and
RW
Fn =
(5.1)
when firms set prices flexibly. This relation only holds approximately otherwise, though for
the purposes of the following discussion, we assume the relation is exact. Let
derivative of
F
with respect to
J
Fj
denote the
€ (K , N ) . By our linear homogeneity assumption for
Fk K
+
Fn N
Y
F
~ Y ‘
F
:
(5.2)
14The correspondence is only approximate, since from (3.9), E P u = y.Eu)t M C t = f i C o v ( u ti M C t ) + l i E M C t
unless C ov(u jtl M C t ) = 0.
7^ f i E M C t ,
31
After (5.1) is substituted into the left side of (5.2), it implies that
Ml
where
s„
is the share of economic profits,
(5-3)
~ s *) = y
P Y — r K —R W N ,
in total nominal output. Basu
and Fernald (1994), Hall (1988), and Rotemberg and Woodford (1995), among others, argue
that sw is close to zero. Setting
sn
= 0, we obtain
, ,
**
since
Y
1
+ Y
(5.4)
l-4 >
= 1 — (f>, given our procedure for choosing
ipQ.
Our reading of the literature is that
there is very little independent evidence on fi and ^ . 15 For our benchmark parameterization,
we follow Hornstein (1993) in adopting the value,
fi
= 1.20. Given our diffuse priors on the
size of •£, we also consider a range of other values of fi. We do this both with and without
imposing (5.4).
We now consider the parameterization of the finite-state Markov chain for x t . We suppose
xt
e {Hx - <t, fix, fix
i , j = 1,2,3,
and
+ a },
x (j)
and let
nx
= {7r? }, where 7r? = prob{xt+i =
x (j)\x t
corresponds to fix — a, fix,and fix + a, respectively, for
In our benchmark specification we set
fix =
0.02 and
a
= ®(0)> f°r
j = 1,2,3.
= 0.017. Also, we specify that
xt
is iid by setting each entry in 7T1 to 1/3. We also consider an alternative parameterization
in which money growth is positively autocorrelated. For this, we assume the elements of
7T1 are symmetric, so that there are five free parameters in the stochastic process for {x£}:
three in 7T1 and the two in
x (j),
for j
=
1,2,3. We determine these by requiring that (1) the
15See Rotemberg and Woodford (1995) for a brief review of the literature.
32
autocorrelation of
xt
be 0.5, (2) the standard deviation of the error in regressing
xt
on one
lag of itself be 0.01, (3) {xt} have the kurtosis of a normal distribution, namely, 3.0, and (4)
the mean growth rate of x t is 0.02. Finally, we arbitrarily set the 1, 2 elements of ir to 1/3.16
Our specification of the Markov chain for
xt
implies that the growth rate of money has a
first-order autoregressive representation (AR(1)), with an AR coefficient equal to either 0.0 or
0.5. At first glance, this parameterization might appear to be inconsistent with the empirical
analysis of Section 2, where we consider monetary policy rules that are highly reactive to
the state of the economy. Indeed, the view taken in both CEE and SZ is that the aim
of monetary policy is to bring about a particular relationship between various endogenous
variables. These relationships are given by (2.1) and (2.2), respectively. However, for either
of these relationships to hold in equilibrium, the growth rate of money must respond to
current and past exogenous shocks (e.g., innovations in preferences, technology, sunspots,
monetary policy shocks) in an appropriate way. Under the identifying assumptions of CEE
and SZ, an estimate of the way
xt
responds to current and past monetary policy shocks
is given by the estimated dynamic response function of
xt
to a policy shock. Christiano,
Eichenbaum and Evans (1996a) argue that when money is measured by M2, a reasonable
time series representation for the response of x t to a policy shock is an (AR(1)) with an AR
coefficient equal to 0.5. (For details, see Christiano, Eichenbaum, and Evans (1996a).)17
16For further details about the procedure for parameterizing a three-state Markov chain, see Christiano
/ 0.58 0.33 0.08 \
(1990). We use ttx =
0.08 0.83 0.08 j , and x t G {0.0,0.02,0.04}.
\ 0.08 0.33 0.58 /
17The argument in Christiano, Eichenbaum and Evans (1996a) can be summarized very simply, with the
aid of a money demand equation in a diagram with the nominal interest rate on the vertical axis and the
money stock on the horizontal axis. Suppose, in the spirit of Section 2, th at policy is represented as an interest
rate target, with ip = 0 in (2.1) and two possible values for e4 :
Then policy can be represented by
two horizontal lines, with intercepts R h = e j and R l = ela . Denote the equilibrium money stocks associated
with these two interest rates by M h and M l . Then we have two equivalent ways to represent policy. One is
33
We emphasize two points about our parameterization of monetary policy. First, we do
not adopt the AR(1) specification based on an appeal to the univariate properties of the raw
M2 growth data. Such a procedure would be hard to square with our empirical analysis,
according to which monetary policy is reactive to the state of the economy. Second, there is
an important caveat to our analysis: when M2 in the CEE or SZ analysis is replaced by Ml
or the monetary base, then the AR(1) representation we use to model the response of money
growth to policy shocks is rejected by the data. In this case, a better approximation is a
short-moving average representation in which the response of x t to a policy shock is initially
small and then becomes larger. An important topic for further research is the extent to
which the results we discuss below are robust to alternative specifications for the growth
rate of money.
Finally, we turn to the parameter,
a.
Estimates in Christiano (1988, footnote 3), based
on the National Income and Product Accounts, suggest that the share of income going to
labor,
W t N t / ( P t Yt ),
averages roughly 0.64. In the version of our model with
<f>
0, (4.5)
becomes
r
i-«
'
( iR t
n
\~ °
already cited, namely two horizontal lines with intercepts,
The other represents monetary policy
by a money supply rule with vertical lines at M h and M l . Corresponding to these two equivalent ways of
representing policy, there are two methodologies for testing the model. (Here ‘model’ refers to the downwardsloped money demand schedule.) One way is to specify policy as {F P ^ R 1} and verify th at the
predicted by the theoretical money demand curve holds in the data. This is equivalent to incorporating the
interest rate rule into the model and verifying th at the impulse response from monetary policy shocks to
money in the model matches the one estimated from the data. Alternatively, one could specify policy as
{ M h1M 1} and verify th at
holds in the data. The methodology we adopt in this paper is in the
spirit of the latter.
34
o r,
a fte r
u s in g
(5 .4 )
a n d
im p o s in g
th a t
in
s te a d y
a
= 1 —K T .
Given the parameter values already specified,
r = 0.64, (5.5) implies
a =
s ta te ,
R
N t=
1 , w e
o b ta in
(5.5)
= (1 +
fix ) / P —
0.34. In our calculations, we use
a
1.0276. Given this and
= 0.36.
5.2. R esults
Our results are reported in Tables 1 and 2, which display the contemporaneous equilibrium
response of the system to an unanticipated fall in the growth rate of the money stock from
fix
to
In those tables,
fix — a .
dp
denotes the percentage change in the price level associated
with a 1 percent unanticipated change in the end-of-period stock of money. Specifically,
dp =
where
s
=
p
log(p'/p)/log((l +
denotes the price level in state
(fix , f i x — cr).
The variables
fix ) / { l + fix - a ) )
s = (fix ,f ix ),
dc, d n , d w , d n ,
and
and
pi
dM C
denotes the price level in state
refer to the analogous responses
of consumption, employment, the real wage, profits, and marginal cost, respectively. The
variable
dR
represents the simple change in the nominal rate of interest, scaled by log((l +
M i)/(l +
—cr)). The variable
x
in Table 1 denotes the level of the markup when money
growth is fix — a in the current period and when growth is
fix
in the previous period. Tables
1 and 2 report results for the sticky price and limited participation versions of our model,
respectively.
3 5
5.2.1. T he Sticky P rice M odel
The two most salient failings of the benchmark sticky price model are its counterfactual
implications that profits
r is e
and the interest rate f a ils in response to a monetary contraction.
For example, Panel A of Table 1 indicates that for the benchmark parameter values, an
unanticipated 1 percent contraction in the money stock generates a 2.95 percent rise in
economic profits and a 79-basis-point fall in the interest rate. We consider each of these
failings in turn and show th at the model’s counterfactual implication for the interest rate
can be overturned, but its counterfactual implication for profits is more fundamental.
To understand the benchmark sticky price model’s implications for the response of profits
to a contractionary monetary policy shock, we recall that in equilibrium, time
t
profits can
be written as
ivt = ( M t + X t )
Pt ~ M C A
M C t <j) +
r t.
(5.6)
Pt
Here, we make use of the fact that
(3.6),
M Ct
=
P tC t
=
Mt
+
X t.
In what follows it is useful to recall
j^ N fW tR t.
As we noted, the price of the final good inherits the inflexibility of intermediate good
prices, so that
dp
= 0. Consequently, consumption and output fall by the same percentage
as the money stock. Since output in the intermediate good industry is lower, aggregate
employment is also lower. In the sticky price model, this corresponds to a movement along
the aggregate supply curve of labor. Given our assumed labor supply elasticity, this generates
a large fall in the real wage equal in magnitude to the percentage decline in employment (1.30
percent). W ith the interest rate, the real wage rate, and employment falling, marginal costs
decline, and the markup rises by six percentage points, from 1.20 to 1.26. In equilibrium, the
36
rental rate, r t , is given by r t =
the fall in
rt
so it too falls. The rise in the markup overwhelms
and output. The result is that profits rise after a monetary contraction.
The previous discussion suggests a variety of perturbations to assess the robustness of this
result. The perturbations which we consider are motivated by a desire to identify versions of
the model in which marginal costs fall by less after a monetary contraction. The first set of
changes we consider are variations in the elasticity of labor supply. Panel B of Table 1 reveals
that increasing the elasticity of labor supply does reduce the fall in wages and mitigates the
rise in profits. However, even if we increase the elasticity to the incredible value of 10.0, we
still do not overturn the basic result that profits rise after a contractionary monetary shock.
In Table 1, Panels C and D and row 2 of Panel E document that the profit result is robust
to variations in
fj,
and 0. Panel C varies
fj.
while changing 0 according to (5.4) and holding
all other parameter values at their benchmark values. Panel D varies /z, holding all other
parameters (including 0) fixed at their benchmark values. Row 2 of Panel E sets 0 = 0,
holding all other parameter values to their benchmark values.
The next perturbation we consider is an increase in the power on labor in the production
function. With a reduction in curvature on labor in the production function, a 1 percent fall
in consumption requires a smaller decline in
N t.
For a given elasticity of labor supply, this
means that the real wage falls less in response to the contractionary money shock. Other
things the same, this reduces the downward pressure on the markup and marginal costs and
the upward pressure on profits. There is, however, a key countervailing force. As
a
goes to
zero, the capital costs drop from profits. The first row of Panel E of Table 1 reveals that
the latter effect dominates by a large margin. Now, with
contractionary monetary policy shock.
37
a =
0, profits almost triple after a
Next, we consider the effect of reducing the percentage of firms that set prices in advance.
First, we consider the case in which 80 percent of the firms set prices according to (3.9), and
20 percent set prices flexibly, according to (3.7). When a subset of firms set prices flexibly,
output and employment ought to fall by less in response to an unanticipated monetary
contraction. This should reduce the downward pressure on marginal costs and thereby lessen
the upward pressure on profits. The first row of Panel F reports results for this case and
verifies the previous conjectures: the rise in profits is now less than the rise for the benchmark
model. However, the impact on the magnitude of the rise in profits is small. Further
reductions in the number of price setters are likely to produce additional improvements in
the model’s predictions for the response of profits. However, these improvements come at a
severe cost: a given reduction in the fraction of price setters produces a disproportionately
large fall in the price level and a disproportionate dampening in the response of output to a
contractionary monetary policy shock. This reflects the absence of strategic complementarity
in price setting in our model. With a 1 percent money contraction, a given flexible price setter
drops its price by more, the larger is the fraction of firms fixing prices. This happens because
the larger is the fraction of firms fixing prices, the greater is their reduction in output with
a given money contraction and, therefore, the greater is the general equilibrium reduction in
marginal costs when they employ fewer factors of production. This accounts for the greater
reduction in price by the flexible price firms, who simply set price as a given markup over
marginal costs. A further discussion of what happens in our model economy when there is a
mixture of flexible and fixed price firms appears below. The second row of Panel F reports
results for the case in which 20 percent of the firms set price in advance. Consistent with the
discussion above, this economy looks very much like a standard cash-in-advance economy.
38
Profits do fall after a contraction, but now
= —0.91 and
dp
dc —
—0.09.
All versions of the sticky price model that we have considered so far imply that the interest
rate falls with a monetary contraction. There are two reasons to consider perturbations of
the model in which the interest rate rises after a monetary contraction. First, this finding
is consistent with the data. Second, the interest rate decline is partially responsible for the
fall in marginal costs and the rise in profits that occur in the benchmark model after a
contractionary monetary policy shock.
We can reverse the implications of the benchmark model for the interest rate with the
following utility function:
C 1-7
U { C ,N )
1— 7
1+
(5.7)
ip
To see this, we note th at the household’s Euler equation, (3.17), and PtCt =
C t U c,t = (3 R tA ,
The fact that
A
where
A
=
M t+2/ M t+1
Mt+ Xt
.
imply
(5.8)
is constant reflects the benchmark model’s iid assumption on the growth
rate of money. Relations (5.7) and (5.8) imply
C l^
‘
Since
Pt
and
Mt
[M t + X t I1'7
PA
0 A P ? -'’
are predetermined relative to
down for 7 > 1 and has no impact on
Rt
X t,
'
it follows that an increase in
Xt
drives
Rt
for 7 = 1 .
Rows 3-5 of Panel E of Table 1 report the results we obtain when adopting specification
(5.7) of the utility function for the basic sticky price model. Row 3 reports results for the
39
case 7 =
if;
= 1 . As expected, the interest rate is unaffected by a contractionary monetary
policy shock. The basic result that profits rise after a monetary contraction is unaffected.
Indeed, the rise in profits is even larger than in the benchmark model.
The basic intuition for this result is as follows. With the new utility function, the house
hold’s Euler equation for labor is given by
7T =
This resembles the labor supply equation in the benchmark model, (3.16), with one impor
tant difference: a decrease in consumption shifts the labor supply curve to the right. It is
still the case that a 1 percent decrease in the money supply produces a 1 percent drop in
consumption. Since the production technologies in the two specifications are identical, the
drop in employment must be the same. But with the new labor supply curve, the drop in
consumption leads to a larger fall in the real wage rate and marginal cost. This explains why
the markup and profits rise by even more than in the benchmark specification. (See row 1
of Panel A of Table 1 .)
Row 4 of Panel E presents results for the same specification as row 3, except that 7 = 2.
Now the interest rate actually rises in response to the monetary contraction. However, this
effect is offset by a greater fall in the wage rate. The consequence is that profits continue to
rise. Row 5 allows for a money growth rate process where the Wold representation is a firstorder autoregression with a lag coefficient equal to 0.5 and an innovation standard deviation
of 0.01. Despite the anticipated inflation effects that now come into play, the interest rate
continues to rise. The counterfactual implications for profits are not affected.
40
To summarize our results, we find that the sticky price model fails on two key dimensions
of the data. First, it implies that profits rise after an unanticipated monetary contraction.
Second, and closely related, for plausible labor supply elasticities, it implies large declines
in the wage rate following a contractionary monetary policy shock. An additional source
of concern about the sticky price model is that the benchmark version implies th at interest
rates fall after a contractionary monetary policy shock. We did identify a perturbation to
the model that remedies this shortcoming. However, it exacerbates the other two empirical
shortcomings of the model.
5.2.2. T he Lim ited Participation M odel
In this section, we consider the ability of the limited participation version of the model to
account, at least in a stylized way, for the empirical regularities we document above. We
show that this version of the model does at least as well, if not better than the sticky price
model. Specifically, it has no difficulty generating a rise in the interest rate and a fall in
profits after a contractionary monetary policy shock. Moreover, it is capable of producing
small price and large output responses, but its ability to do so depends on the assumed labor
supply elasticities and markups.
Our quantitative results for the benchmark specification are reported in the first row of
Panel A of Table 2. The key features are as follows. In contrast to the benchmark sticky
price model, the interest rate rises, and profits fall, in response to a 1 percent permanent
reduction in the money stock. The key failing of the benchmark model is that the primary
impact of the policy shock is on prices and not on output. Specifically, prices fall by 0.62
percent, and output falls by 0.38 percent.
41
We now consider a series of perturbations motivated by the desire to increase the output
response and decrease the price response of the system to a monetary policy shock. Panel
B of Table 2 reports the results of varying the elasticity of labor supply. As expected,
based on the reasoning that leads to equation (4.4), perturbations which increase the value
of
l/ip
work in the right direction. Indeed, at a labor supply elasticity of 5.0, the output
response is so large (—1.1 percent) that prices actually rise in response to an unanticipated
contractionary monetary policy shock. For all labor supply elasticities reported, the interest
rate rises and profits fall in response to the shock.
Panel C of Table 2 reports the results of varying the markup. As in Panel C of Table
1, we simultaneously change
4> so
that there are no economic profits in steady state. Two
key features of the results are worth noting. First, increases in the markup move the model
in the desired direction. Specifically, the sensitivity of the price level to the policy shock
declines, while the sensitivity of output rises. Second, if we set the markup to 1.4, the value
Rotemberg and Woodford (1995) assume, we can lower the labor supply elasticity to 2.0
and obtain the result that the price level moves very little in response to a contractionary
monetary policy shock
(d p =
—0.08 percent, and
dc
= —0.92 percent). While this labor
supply elasticity is high relative to some micro-based estimates, it is small relative to the
range considered in the real business cycle literature.
Panel D reports the results of varying the markup, holding
<f> constant
value. Consistent with the discussion in Section 4.B, an increase in
p
at its benchmark
(i) increases the extent
of the fall in employment, consumption and the real wage, (ii) increases the rise in the
interest rate, and (iii) mutes the fall in the price level. Comparing Panels C and D, we see
that decreases in
<f>,
per se, have the same qualitative effect on the response of the system to
42
a contractionary policy shock as an increase in
fi.
A different way to see this is to compare
the results for the benchmark parameter values of row 1 of Panel A with the results in row
2 of Panel E, which are obtained with the benchmark parameter values except that
<j> is
set
to zero.
For completeness, Panel E of Table 2 reports the results of the experiments analogous
to those analyzed in Panel E of Table 1. The two main findings are as follows. First,
when we increase the share of labor, this leads to a deterioration of the benchmark model’s
performance. Specifically, prices respond by more to a contractionary monetary policy shock.
Moreover, profits actually rise. Second, the effect of moving to the alternative functional
form for utility has relatively little impact on the model’s performance. Relative to the
benchmark model, the output effect is somewhat weaker, and the price effect is somewhat
stronger. This is consistent with the intuition we offer above, according to which the change
in functional form has effects similar to a reduction in the labor supply elasticity.
One obvious perturbation of the limited participation model is to assume that a subset of
the intermediate good firms set their price in advance of the realization of x t , thus magnifying
the effect of a policy shock on aggregate output. Panel F considers the consequences when
we assume that 80 percent of the intermediate good firms set prices in advance. The first row
reports the impact of the change on our benchmark specification. Interestingly, the impact is
quite small. With the change, the price and output responses are —0.48 and —0.52 percent,
respectively. These are to be compared with the —0.62 and —0.38 figures from Panel A. The
reason that adding price setters does little to reduce the price effect of a money shock is very
similar to the reasoning we use to explain the consequences of reducing the percentage of
price setters in the sticky price model from 100 percent to 80 percent. (See Panel F of Table
43
1.) For the 80 percent of firms who set prices in advance in the limited participation model,
the output effect of a money contraction is greater than in the equilibrium when each firm
sets prices flexibly. In particular, their output falls by 3.4 percent and their employment falls
by 3.0 percent. The key to understanding the relatively small effect of a money contraction
on aggregate output and the relatively large effect on the price level is to consider the price
and output response of the other 20 percent of intermediate good producers who set prices
flexibly. The large drop in employment by the fixed price firms leads to a large drop in
the marginal cost of production. According to Panel A, the marginal cost of production
falls by 0.62 percent when all prices are set flexibly. In contrast, marginal costs fall by 2.06
percent when 80 percent of firms fix prices in advance. This drop in marginal costs leads
the flexible price firms to drop their prices by 2.06 percent and to actually increase output
and employment by 8.96 percent and 7.46 percent, respectively. In effect, it is the complete
absence of strategic complementarity in price setting that accounts for the small impact of
price setting in the model: flexible price setters are encouraged to reduce prices by more, the
larger is the fraction of firms which fix prices in advance. For completeness, row 2 of Panel F
reports results for the case in which 20 percent of the firms set price in advance. Consistent
with the discussion above, the results are extremely similar to those which we obtain when
none of the firms set price in advance. (See row 1 of Panel A of Table 2.)
The previous reasoning suggests that introducing sticky price firms into the limited par
ticipation model would have a greater impact on reducing the price effect of a money shock,
if we incorporate limitations on the intersectoral mobility of factors of production. To in
vestigate this possibility we study a version of the limited participation model in which the
allocation of labor and capital to fixed and flexible price firms is predetermined relative
44
to the realization of the monetary policy shock. See Appendix
for details. Panel
C
G
of
Table 2 reports the response of the previous model economy to a monetary policy shock
that assumes our benchmark parameter values and th at 20 percent of the firms set prices in
advance. Comparing these results to row 2 of Panel F of Table 2, we see th a t introducing
limited intersectoral mobility does reduce the magnitude of
nitude of d c and
dn.
dp
and does increase the mag
However, these effects are small and come at a large cost: the interest
rate falls, and profits rise after a contractionary shock.
The introduction of limitations on intersectoral mobility of production factors evidently
helps very little. To gain intuition into this result, we recall that fixed price firms substan
tially reduce their use of productive resources when there is a monetary contraction. Absent
limitations on intersectoral mobility, this results in a large flow of resources from the fixed
price sector to the flexible price sector. The resulting downward pressure on factor costs
encourages flexible price firms to cut prices and expand output. Limitations on the inter
sectoral mobility of factors moderate this phenomenon: labor and capital released from the
fixed price sector cannot find their way to the flexible price sector in the period of a monetary
shock. As a result, the contraction of the fixed price sector does not release capital and labor
for use in the flexible price sector. However, the limited intersectoral mobility assumption
does not. restrict the intersectoral flow of cash. The contraction of the fixed price sector
results in a drop in the demand for money by firms in that sector. This demand by firms
appears to reduce the equilibrium interest rate, which drives down marginal costs of flexible
price firms and encourages them to cut prices and increase output.18
We now summarize our results for the limited participation model. Our major finding
18The percentage change in the marginal costs of the two sectors are d M C u
4 5
=
—5.73 and d M C it = —7.56.
is as follows. If one is willing to assume a high labor supply elasticity (e.g., 2 percent)
and a reasonably high markup (e.g., 40 percent), then the limited participation model can
account in a stylized way for the facts we stress in this section. Specifically, an iid shock to
the growth rate of money has essentially no contemporaneous impact on the price level and
drives wages, profits, output, and employment down, while driving the rate of interest up. If
one is not willing to accept high markups and labor supply elasticities, then the model has
difficulty generating a large output effect and a small price effect from a monetary policy
shock.
6. C o n c l u s i o n
In this paper, we assessed the ability of two classes of models to account for the salient facts
about how the economy responds to an unanticipated monetary policy shock. Each class
of models stresses a particular type of friction that generates monetary nonneutrality. The
first friction is sticky good prices. The second is a friction in financial markets. Both models
suffer from related shortcomings. In our view, a model that convincingly accounts for the
key effects of a monetary policy shock will have to allow for labor market frictions which
increase the effective elasticity of labor supply, in addition to one of the two frictions we
consider in this paper.
The key problem with the sticky price model is that it cannot account for the fact that
profits fall after a contractionary monetary policy shock. Indeed, the model has the per
verse implication that profits actually rise after such a shock. This happens because, absent
labor market frictions or an implausibly high labor supply elasticity, marginal costs fall
46
and markups rise sharply after a contractionary monetary policy shock. The presence of
wage contracts is one obvious friction which would help overturn the model’s counterfactual
implications. If these wage contracts had the property that employment falls after a con
tractionary policy shock but the wage does not, then marginal costs would not drop by as
much after a contractionary monetary policy shock, and profits might not rise. Allowing for
endogenous capacity utilization might also render the sticky price model consistent with the
key facts. As Burnside and Eichenbaum (1996) stress, with endogenous capacity utilization,
the supply of capital services to the economy is no longer predetermined in any given pe
riod. Consequently, employment and marginal costs would not fall so much in response to
a contractionary policy shock. This could overturn the sticky price model’s counterfactual
implications for profits.
The key problem with the limited participation model is that it cannot account for the
fact that prices do not immediately respond to a monetary shock, at least not with a plausible
labor supply elasticity. Allowing for wage contracts which effectively increased the response
of employment to monetary shocks, would clearly improve the model’s performance. So too
would endogenous capacity utilization that magnifies the response of output to shocks. An
important additional advantage of allowing for endogenous capacity utilization is that it
could render both the sticky price and limited participation models consistent with the fact
that labor productivity is procyclical.
4 7
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J o u rn a l o f E c o n o m ic T h e o ry
50 (2): 237-
Ohanian, L.H.; Stockman, A.; and Kilian, L. 1995. The effects of real and monetary shocks
in a business cycle model with some sticky prices. J o u rn a l o f M o n e y , C red it, a n d
B a n k in g 27 (4) (November, Part 2), 1209-34.
P e n c a v e l,
0 .
J .
1 9 8 6 .
A s h e n fe lte r
3 -1 0 2 .
L a b o r
a n d
s u p p ly
o f m e n :
A
su rv e y .
R .
L a y a rd ,
H a n d b o o k s
N o rth -H o lla n d :
E ls e v ie r
S c ie n c e .
4 9
in
In
Handbook of Labor Economics,
E c o n o m ic s
S e rie s ,
n o .
5 ,
V o l.
1,
e d .
p p .
Romer, D. 1996.
A d v a n c e d M a c ro e c o n o m ic s.
New York: McGraw Hill.
Rotemberg, J., and Woodford, M. 1995. Dynamic general equilibrium models with im
perfectly competitive product markets. In F ro n tie rs o f B u s in e s s C y c le R esea rch , ed.
Thomas F. Cooley, pp. xvi and 419. Princeton: Princeton University Press.
Sims, C., and Zha, T. 1995. Does monetary policy generate recessions? Manuscript. Yale
University.
_________ . 1995a. Error bands for impulse responses. Working Paper 95-6. Federal
Reserve Bank of Atlanta.
U.S. Department of Commerce. Bureau of Economic Analysis. 1985. Corporate profits:
Profits before tax, profits tax liability, and dividends. Methodology Paper Series MP-2.
Washington, D.C.: GPO.
Woodford, M. 1996. Control of the public debt: A requirement for price stability. Manu
script. Princeton University.
50
A p p e n d ix A : D a t a S o u rc e s
We use the following time series to estimate the CEE policy shock measures.
Logged GDP in fixed-weight 1987 dollars, seasonally adjusted (SA); logged GDP deflator
derived from nominal GDP and GDP in fixed-weight 1987 dollars, SA; change in index of
sensitive materials prices, including commodity prices, smoothed; federal funds rate; logged
nonborrowed reserves, SA; logged total reserves, SA; and the change in the log of M2, SA.
These data series are taken from the Federal Reserve Board’s macroeconomic database.
The following time series are used to estimate the SZ policy shock measures.
Logged producer price index crude materials, SA; logged producer price index intermedi
ate materials, SA; logged GDP in fixed-weight 1987 dollars, SA; logged GDP deflator derived
from nominal GDP and GDP in fixed-weight 1987 dollars, SA; three-month Treasury bill
rate; and change in the log of M2, SA. These data series are taken from the Federal Reserve
Board’s macroeconomic database. Logged average hourly earnings of private nonagricultural
production workers are divided by the GDP deflator, SA, and are derived from the Citibase
data set.
The following measures of real wages are used in our estimation exercises.
Average hourly earnings (AHE) of private nonagricultural production workers (from
1964:Q1 to 1995:2); AHE of private nonagricultural production workers, are deflated by
the Bureau of Labor Statistics using a derivation of the Consumer Price Index for Urban
Wage Earners and Clerical Workers (from 1964:Q1 to 1992:3); AHE of manufacturing sector;
AHE of manufacturing durable goods sector; AHE of manufacturing nondurable goods sec
tor; AHE of food and kindred product sector; AHE of tobacco manufacturing sector; AHE
of textile mill products sector; AHE of apparel and other textile products sector; AHE of
paper and allied products sector; AHE of printing and publishing sector; AHE of chemicals
and allied products sector; AHE of petroleum and coal products sector; AHE of rubber and
miscellaneous plastics products sector; AHE of leather and leather products sector; AHE of
lumber and wood products sector; AHE of furniture and fixtures sector; AHE of stone, clay,
and glass products sector; AHE of primary metal industries sector; AHE of fabricated metal
products sector; AHE of machinery sector-except electrical; AHE of electric and electronic
equipment sector; AHE of transportation equipment sector; AHE of instruments and related
products sector; and AHE of miscellaneous of durable manufacturing goods sector. All wages
are taken from the Citibase data set and are seasonally adjusted. All wage data are divided
by the GDP deflator and are logged, except where noted.
The profit data we use in our analysis are accounting profits, namely income earned in
current production. (See U.S. Department of Commerce (1985).) The following measures of
corporate profits are used in our empirical exercises.
Profits before tax with inventory valuation and capital consumption adjustment, SA;
Profits after tax with inventory valuation and capital consumption adjustment, SA; Net
domestic profits after tax with inventory valuation and capital consumption adjustment, SA;
Nonfinancial net domestic profits after tax with inventory valuation and capital consumption
adjustment, SA; Profits after tax excluding net interest costs, SA; Net domestic profits after
tax excluding net interest costs, SA; Nonfinancial net domestic profits after tax excluding
net interest costs, SA; Domestic manufacturing profits before tax with inventory valuation
adjustment, SA; Domestic durable goods manufacturing profits before tax with inventory
51
valuation adjustment, SA; Domestic nondurable goods manufacturing profits before tax with
inventory valuation adjustment, SA; Domestic transportation and public utilities profits
before tax with inventory valuation adjustment, SA; Domestic retail trade profits before
tax with inventory valuation adjustment, SA. All profit series data taken from the Federal
Reserve Board’s macroeconomic database.
As explained in U.S. Department of Commerce (1985) for corporate profits with inventory
valuation adjustment and capital consumption adjustment, profits are measured as receipts
less expenses as defined in federal tax law. However, receipts exclude capital gains and
dividends received, expenses exclude depletion and capital losses, inventory withdrawals are
valued at current replacement cost, and depreciation is on a consistent accounting basis and
valued at current replacement cost.
5 2
A p p e n d ix B : S im s -Z h a I d e n tif ic a t io n S c h e m e
In this appendix, we describe the identification scheme underlying our version of the SZ
policy shock measure. Suppose that the economy is described by a structural model of the
form
B q Zt = B \ Z t — \ + ....+ B q Z t — q + £ f
(6*1)
Here, Z t denotes an l dimensional vector of observable variables, B { is an l by l dimensional
matrix, i € [1, ...,g], the diagonal elements of B are unity, B o is assumed to be invertible,
and e t is an l dimensional vector of structural disturbances to the economy. The vector e t is
assumed to be uncorrelated with Z t ~ j , for all j > 0, and the covariance matrix of et ,
q
E £ t£'t =
A
(6.2)
is diagonal. The diagonal elements of A are the variances of the structural shocks to the
economy. Relation (6.1) implies the following reduced-form VAR for Z t :
Zt
— A \ Z t - l + ... +
A qZ t-q
+
Uf.
(6.3)
The covariance matrix, E, of u t is
(6.4)
The
Ai
s are given by
(6.6)
A =
The disturbance term
ut
is related to et via the relationship
ti, =
B 0 'e ,.
(6.6)
The vector Z t includes the log of crude materials prices (Pcm), the first difference of the
log of M2 (M2), the three-month Treasury bill rate ( T b i l l ) , the log of intermediate materials
prices ( P i m ) , the log of the implicit GDP deflator (P), the log of real wages ( W / P ) , and the
log of real GDP (Y ). Sims and Zha (1995) achieve identification by the following specification
53
of the
Bq
matrix:
-
r
£Pcm
Bn
£ 12
£ 13
£ 14
£ 15
£ ie
Bn
Upon
£m d
0
£22
£23
0
£2 5
0
£27
UM2
£m p
B 31
B 32
£33
0
0
0
0
UTbill
B 41
0
0
£44
£45
£46
Bn
Upim
Bn
0
0
0
£55
£56
Bn
Up
Bei
0
0
0
0
Bee
Bn
Uw/p
Bn
0
0
0
0
0
Bn
Uy
=
£pim
£p
u/p
Sy
(6.7)
along with the overidentifying restriction that £25 = £27 = —£ 22- We refer the reader to
Sims and Zha (1995) for a discussion of this identification scheme. In our version of SZ, we
do not impose restrictions on £25 and £ 27.
For our analysis of profits, we augment the vector Z t to include the ratio of profits to
GDP ( P r o f ) . Identification in the 8-variable system is achieved by adding an eighth row
and column to £0 in (6.7) for £ p rof and U p roj. The additional nonzero elements in Bo are
£ 18,£ 48,£ 58,£68, £ 78,£ 81, and £««.
A p p e n d ix C : T h e L im ite d I n te r s e c to r a l M o b ility M o d e l
We describe the version of the model in which the intersectoral allocation of productive
resources is predetermined relative to the realization of a monetary shock. We denote the
sector of the economy in which intermediate good firms set prices flexibly and the sector in
which they set prices in advance as sector 1 and 2, respectively. We assume that fraction v
and (1 —v ) of the population work in sectors 1 and 2, respectively. The assumption that v
is not a state-dependent choice of the household captures limited intersectoral immobility of
labor. We modify the preferences of the representative household as follows:
U (C ,N
u
N 2) =
log j c - u
l + rf>
N l +*
- (1 “
v)
^0 tvrl+lfr
1 + Tp * }
(6.8)
where N i denotes hours of work in sectors i = 1,2, respectively. The time t wage rate in
sector i is given by W a , where 7 = 1,2. The cash constraint on the household’s consumption
purchases, (3.14), is replaced by the constraint
P tC t
5!
v W itN n
+ (1 —v ) W
2 tN 2 t
4-
M t — I t•
(6.9)
The household is endowed with one unit of capital, which it allocates to capital markets in
the two sectors of the economy subject to the constraint
v K \t
+ (1 —v ) K 2 t
—
1.
(6.10)
Here, K u denotes the amount of capital supplied to sector i = 1,2. The time t rental rate
on capital in sector i is given by r u , where i = 1,2. The household chooses K u before the
time t realization of X t - This assumption captures limited intersectoral mobility of capital.
W e replace (3.15), which governs the evolution of the household’s money holdings, with
M t+1 =
[ v W l t N u + ( l - v ) W 2tN 2t + M t - I t - P tC t]
(6.11)
-\- T \ tv K \ t + (1 —v ) r 2tK 2t 4- R t [ I t + Xt] + D u + D 2t.
Here, D u and D 2t denote time t profits from intermediate good producers in the two sectors.
The household maximizes (6.8), subject to (6.9) - (6.11). It chooses C t , N u , N 2t, and
M t+i after the realization of X t . It chooses I t , K u , and K 2t before the realization of X t .
The first-order necessary conditions associated with the household’s choice of N u are
given by
= iM tf
(6.12)
where i — 1,2. The Euler equation for I t is still given by (3.18). The household’s Euler
equations for K u and K 2t imply that
E<-1% ^ , , - r«) = 0.
•ft+l
(6.13)
The problem of the final good firm is unaffected, so that the demand equation for inter
mediate good i is still given by (3.2). The problems of the intermediate good firms in the
two sectors are the same as we describe in Section 3 of the paper. As before, we confine
ourselves to symmetric equilibria. Let K u and N u denote the amount of capital and labor
hired by the typical firm in sector i — 1,2. Firms’Euler equations for K u and N u imply
Tu
W itR t
a
_
1
N it
- a K it
where i = 1,2. The typical firm in the flexible price sector continues to set its price as a
constant markup over marginal cost, according to (3.7). The typical firm in the inflexible
price sector continues to set its price as a constant markup over a weighted expectation of
marginal cost, according to (3.9) and (3.10). Marginal cost for the two types of firms is given
55
by
M C “ A ( w itR t) W , , R ‘
where i = 1,2, and where
by
A
(6.15)
is defined immediately after (3.5). Economywide output is given
(6.16)
Yt =
and the economywide price level is given by
l-n
Pt-
v p j r + ( i - v )P i
(6.17)
The loan market-clearing condition (3.11) is replaced by
v W ltN lt + (1 - v ) W 2tN 2t = I t + X t .
(6.18)
Finally, the definition of an equilibrium is the same as that given in Section 3, except that
W t and r t are replaced by (Wit, W2f) and (rlt,r 2t), respectively. Aggregate employment
is given by N t = v N u + (1 — v ) N 2t, while we define the aggregate wage rate by W t =
( v W i t N u + (1 —v ) W 2tN 2t) / N t . We compute an equilibrium by solving a suitably modified
version of the nonlinear equations discussed in Section 3.
56
Tablel
Responses to a Monetary Contraction-Fixed Price Model
dp
dc
dn
dw
dM C
dR
Panel A: Benchmark Parameter Values
0.00 -1.00 -1.30
-1.30
-2.54 --0.79
Panel B: Different Labor Supply Elasticities
0.00 •-1.00 -1.30 -12.99 -14.20 -0.75
1/ip = 0.1
0.00 -1.00 -1.30
-2.60
-3.85 -.080
l / i p = 0.5
0.00 -1.00 -1.30
-0.26
-1.44 -0.73
1/^ = 5
0.00 -1.00 -1.30
-0.13
-1.29 -0.71
l/v> = 10
Panel C: Different Markup Values
0.00 -1.00 -1.55
-1.55
-3.02 -0.93
p = 1.01
0.00 -1.00 -1.30
-1.30
-2.54 -0.79
p = 1.20
0.00 -1.00 -1.11
-2.23 -0.73
-1.11
p = 1.40
0.00 -1.00 -0.78
-0.78
-1.75 -0.71
p = 2.00
Panel D: Different Markup Values, Benchmark <p
0.00 -1.00 -1.30
-2.70 -0.95
-1.30
p = 1.01
0.00 -1.00 -1.30
-1.30
-2.43 -0.68
p = 1.40
0.00
-1.00
-1.30
-1.30
-2.25
-0.50
p = 2.00
Panel E: Miscellaneous
0.00 -1.00 -0.83
-0.83
-1.56 -0.74
Q= 0
0.00 -1.00 -1.56
-1.56
-2.85 -0.74
</>= 0
0.00
0.00 -1.00 -1.30
-2.30
-2.77
Modified Preferences, 7 = 1
0.00 -1.00 -1.30
-3.30
-2.77
1.04
Modified Preferences, 7 = 2
1.04
0.00 -1.00 -1.30
-3.30
-2.77
Modified Preferences, 7 = 2
X
dn
1.26
2.95
1.64
1.30
1.24
1.23
15.94
4.91
1.19
0.94
1.07
1.26
1.46
2.07
3.92
2.95
2.26
1.15
1.07
1.47
2.09
6.25
1.61
0.26
1.24 198.61
1.27
2.06
1.27
3.30
3.30
1.27
1.27
3.30
(Persistent Shocks)
80% Price Setters
20% Price Setters
Panel F: Partial Price Setting
-0.40 -0.60 -0.72
-0.72
-0.10
-0.91 -0.09 -0.10
-1.86 -0.48
—1.12 -0.08
1.24
1.21
1.25
-0.67
Table 2
Responses to a Monetary Contraction - Limited Participation Model
dp ,
dc
dn
dw
dM C
dR
Panel A: Benchmark Parameter Values
-0.62 -0.38 -0.50 -0.50 -0.62
0.70
Panel B: Different Labor Supply Elasticities
-0.95 -0.05 -0.06 -0.60 -0.95
0.64
i fi> = o.i
-0.79 -0.21 -0.28 -0.55 -0.79
0.67
1/0 = 0.5
0.10 -1.10 -1.43 -0.29
0.10
0.83
1/0 = 5
0.43 -1.43 -1.86 -0.19
0.43
0.89
1/0 = 10
Panel C: Different Markup Values
0.64
-0.71 -0.29 -0.45 -0.45 -0.71
p = 1.01
-0.62 -0.38 -0.50 -0.50 -0.62
0.70
p = 1.20
-0.50
-0.50
-0.56
-0.56
-0.50
0.78
p = 1.40
-0.08 -0.92 -1.02 -0.51 -0.08
0.91
p = 1.40,1/0 = 2
0.11 -1.11 -0.86 -0.86
0.11
1.22
p = 2.00
-0.54 -0.46 -0.36 -0.72 -0.54
0.87
p = 2.00,1/0 = .5
Panel D: Different Markup Values, Benchmark 0
-0.78 -0.22 -0.29 -0.28 -0.78
0.40
p = 1.01
-0.45 -0.55 -0.72 -0.72 -0.45
1.02
p = 1.40
0.07 -1.07 -1.40 -1.40
0.07
1.98
p = 2.00
Panel E: Miscellaneous
-0.96 -0.04 -0.03 -0.03 -0.96
0.04
a = 0
-0.56 -0.44 -0.69 -0.69 -0.56
0=0
0.98
Modified Preferences, 7 = 1 -0.76 -0.24 -0.31 -0.54 -0.76
0.68
Modified Preferences, 7 = 2 -0.83 -0.17 -0.22 -0.56 -0.83
0.66
Modified Preferences, 7 = 2 -0.83 -0.17 -0.22 -0.56 -0.83
0.66
dn
- l.n
-1.01
-1.06
-1.33
-1.43
-1.01
-1.11
-1.26
-1.47
-2.00
-1.41
-1.12
-1.11
-1.00
24.44
-1.00
-1.07
-1.05
-1.05
(P e r sis te n t S h o c k s)
80% Price Setters
20% Price Setters
20% Price Setters
Panel F: Partial Price Setting
-0.48 -0.52 -0.57 -0.57 -2.06 -0.81
-0.61 -0.39 -0.50 -0.50 -0.75
0.56
Panel G: Limited Intersectoral Mobility
* -0.64
-0.53 -0.47 -0.59 -0.50
1.35
-0.87
0.14
*Marginal cost responses are not reported because they differ across the fixed and flexible price firms.
Graph 1
Equilibrium Price and Output In the Sticky Price Model
Graph 2
Equilibrium Price and Output inthe Limited Participation Model
Graph 3
Equilibrium Real Wage and Employment Inthe
Limited Participation Model
F ig u re 1
C E E an d SIM S-ZH A S y ste m s R e sp o n s e s to P o licy S h o c k s
i
I
CEE Policy Shock *«> change in M2
Fig u re 2
A g g reg ate R eal W age R e sp o n se s to P o licy S h o c k s
CEE
Privatenonagrlcuttural sector wagedeflatedbyGDP
SIM S-2H A
Privatenonagricuttural sector wagedeflatedbyGDP
0.36 ------------- =
---------- -
■ojx J
1
— ......................... .
6
.—
11
. - - r v c
16
rr.
21
Averagehourlyearnings deflatedbyCPIU-wageearners
ManufacturingwagedeflatedbyGDP
ManufacturingwagedeflatedbyGDP
Durablegoods wagedeflatedbyGDP
Durablegoods wagedeflatedbyGDP
Nondurablegoods wagedeflatedbyGDP
Nondurablegoods wagedeflatedbyGDP
percent
percent
AveragehourlyearningsdeflatedbyCPIU-wageearners
Fig u re 3
Tw o-Digit N ondurable G o o d S IC R eal W age R e sp o n s e s to C E E P o licy S h o c k s
PrintingandPublishing
Tobacco
ChemicalsandAlliedProducts
TextileMill Products
PetroleumandCoal
Apparel andother Textiles
Rubber andMiscellaneous Plastic Products
Paper andAlliedProducts
Leather andLeather Products
p e rce n t
p ercen t
p e rce n t
p ercen t
FoodandKindredProducts
s
i
Figure 4
Two-Digit Nondurable Good SIC Real Wage Responses to SZ Policy Shocks
Foodand KindredProducts
PrintingandPublishing
0 .9 0
0 .4 S
0.00
-0 .4 5
•0 .9 0
Tobacco
ChemicalsandAlliedProducts
Apparel andother Textiles
Rubber andMiscellaneous Plastic Products
Paper andAlliedProducts
Leather andLeather Products
OSO
02S
0.00
■0.25
•0 .5 0
0 .3 2
0 .1 6
0.00
•0 .1 6
•0 3 2
0 .4
0.2
0.0
•02
•0.4
0 .4 0
0.00
•0 .4 0
-0 .6 0
Fig u re 5
Tw o-D igit D u rab le G o o d S IC R eal W age R e sp o n s e s to C E E P o licy S h o c k s
Machinery- except electrical
Lumber andWoodProducts
006 -
v
\
____ ____
0 .0 0 *
V
\
-0 .0 8 -
___ _______ _
\
|
5.
^
-0 .1 6 \ \
-0 0 4 -
------ --------
v\
-
^ ___
—
-
—
- 0 .3 2 -
ElectricandElectronicEquipment
FurnitureandFixtures
i
£
Stone, Clay, andGlass
TransportationEquipment
I
&
PrimaryMetal Industries
Instruments andRelatedProducts
FabricatedMetal Industries
Miscellaneous Manufacturing
%
H
&
!
i
F ig u re 6
Tw o-D igit D u rab le G ood S IC R e al W age R e sp o n s e s to S Z P o licy S h o c k s
LumberandWoodProducts
Machinery- except electrical
FurnitureandFixtures
ElectricandElectronicEquipment
Stone, Clay, andGlass
TransportationEquipment
PrimaryMetal Industries
InstrumentsandRelatedProducts
FabricatedMetal Industries
Miscellaneous Manufacturing
§
i
percentageofOOP
percentageofOOP
percentageofOOP
F ig u re 7
A g g reg ate Profit R e sp o n s e s to P o licy S h o c k s
CEE
SIM S-ZH A
*
i
percentageofGDP
Nonfinancial net domestic profits after taxes
0
percentageofODP
1
percentageofOOP
's
*
Nonfinancial net domestic profits excluding net Interest co sts
Nonfinancial net dom estic profits excluding net interest c o sts
percentageofOOP
0.60
§
■8
■
1
0.60-i
o.x -
’°3°
■0.60quarter
F ig u re 8
S e cto ra l P ro fit R e sp o n s e s to P o licy S h o c k s
CEE
SIM S-ZH A
Manufacturing
Durables
Durables
Retail
Retail
Transportation&Utilities
Transportation&Utilities
percentage of GOP
percentage of GOP
percentage of GOP
percentage of GOP
percentage of GDP
Manufacturing
Figure 9
Sequence of Events in Period t in the TVvo Models
Sticky Price Model
Intermediate goods
prices, Plt, set
Money growth rate,
x t, realized
I------------ 1-------------------------------------1-----------
All other date t
variables determined
--------------1------------ 1
t+1
t
Limited Participation Model
Household deposit
with financial
intermediary, lt, set
Money growth rate,
x (, realized
All other date t
variables determined
I------------ 1------------
---------- 1-----------
-------------->------------ 1
t+ 1
t
@FedFRASER