Investment Shocks and Business Cycles Alejandro Justiniano, Giorgio E. Primiceri, and Andrea ...

53 Pages·2008·0.47 MB·English

by  Alejandro Justiniano

Investment Shocks and Business Cycles
o
g
a
Alejandro Justiniano, Giorgio E. Primiceri,
c
i and Andrea Tambalotti
h
C

f
o

k
n
a
B

e
v

r
e

s
e
R

l
a
r

e
d

e
F WP 2008-12
INVESTMENT SHOCKS AND BUSINESS CYCLES
ALEJANDRO JUSTINIANO, GIORGIO E. PRIMICERI, AND ANDREA TAMBALOTTI
Abstract. Shocks to the marginal e¢ ciency of investment are the most important drivers
of business cycle (cid:135)uctuations in US output and hours. Moreover, these disturbances drive
prices higher in expansions, like a textbook demand shock. We reach these conclusions
by estimating a DSGE model with several shocks and frictions. We also (cid:133)nd that neutral
technologyshocksarenotnegligible,buttheirshareinthevarianceofoutputisonlyaround
25 percent, and even lower for hours. Labor supply shocks explain a large fraction of the
variation ofhoursatvery low frequencies,butnotoverthe businesscycle. Finally,we show
that imperfect competition and, to a lesser extent, technologicalfrictions are the key to the
transmission of investment shocks in the model.
1. Introduction
What is the source of economic (cid:135)uctuations? This is one of the de(cid:133)ning questions of
modern dynamic macroeconomics, at least since Sims (1980) and Kydland and Prescott
(1982). Yet, the literature is far from a consensus on the answer. On the one hand, the
work that approaches this question from the perspective of general equilibrium models tends
to attribute a dominant role in business cycles to neutral technology shocks (see King and
Rebelo (1999) for a comprehensive assessment). On the other hand, the structural VAR
literature usually points to other disturbances as the main sources of business cycles, and
rarely (cid:133)nds that technology shocks explain more than one quarter of output (cid:135)uctuations
(Shapiro and Watson (1988), King, Plosser, Stock, and Watson (1991), Cochrane (1994),
Gali (1999), Christiano, Eichenbaum, and Vigfusson (2004) and Fisher (2006)).
Date: Firstversion: November2007. Thisversion: July 16, 2008. We wish to thank Pedro Amaral, Mark
Gertler, Lee Ohanian, Andrea Ra⁄o, Juan Rubio-Ramirez, Frank Schorfheide, Thijs van Rens, Raf Wouters
and seminar participants at the conference on (cid:147)How Much Structure in Empirical Models?(cid:148)in Barcelona,
Economic Fluctuations & Growth NBER research meeting, Texas Monetary Conference at the Dallas Fed,
Minneapolis Fed, Kansas City Fed, Chicago GSB, Columbia University, Universita(cid:146)Cattolica in Milan and
the IMF for insightful comments. We would also like to thank Frank Smets and Raf Wouters for sharing
their codes and data. The views in this paper are solely the responsibility of the authors and should not be
interpreted as re(cid:135)ecting the views of the Federal Reserve Bank of Chicago, the Federal Reserve Bank of New
York or any other person associated with the Federal Reserve System.
1
INVESTMENT SHOCKS AND BUSINESS CYCLES 2
This paper con(cid:133)rms the SVAR evidence, but it does so from the perspective of a fully
articulated dynamic stochastic general equilibrium (DSGE) model. Our main (cid:133)nding is
that shocks to the marginal e¢ ciency of investment are the key drivers of macroeconomic
(cid:135)uctuations. These shocks a⁄ect the yield of a foregone unit of consumption in terms of
tomorrow(cid:146)scapitalinput. Theliteratureoftenreferstothemasinvestmentspeci(cid:133)ctechnology
shocks,sincetheyareequivalenttoproductivityshocksspeci(cid:133)ctothecapitalgoodsproducing
sector in a simple two-sector economy (Greenwood, Hercowitz, and Krusell (1997)). For
simplicity, we call them investment shocks.
Our(cid:133)ndingsarebasedontheBayesianestimationofaNewNeoclassicalSynthesismodelof
theUSeconomy(GoodfriendandKing(1997)). Themodelincludesarichsetofnominaland
real frictions, along the lines of Christiano, Eichenbaum, and Evans (2005), and is bu⁄eted
by several shocks, as in Smets and Wouters (2007). Among them, a shock to total factor
productivity, or neutral technology shock, as in the RBC literature, an investment shock,
as in Greenwood, Hercowitz, and Hu⁄man (1988) and Greenwood, Hercowitz, and Krusell
(2000), and a shock to labor supply, as in Hall (1997).
According to our estimates, investment shocks account for between 50 and 60 percent of
the variance of output and hours at business cycle frequencies and for more than 80 percent
of that of investment. The contribution of the neutral technology shock is also non-negligible.
It explains about a quarter of the movements in output and consumption, although only
about 10 percent of those in hours. Moreover, this shock generates comovement between
consumption and output, a feature of business cycles that the investment shock has some
trouble replicating.
In this respect, the investment and neutral technology shocks play a complementary role
in our model. The former is mainly responsible for generating the overall volatility and
comovement of output, investment and hours, while the latter contributes a signi(cid:133)cant share
ofthecomovementbetweenoutputandconsumption. Anotheraspectofthiscomplementarity
is that the two disturbances can be characterized as an aggregate demand and aggregate
supplyshockrespectively. Infact,investmentshocksgenerateapositivecomovementbetween
prices and quantities, while technology shocks move the two in opposite directions.
As for the labor supply shock, we show that it is the dominant source of (cid:135)uctuations in
hours at very low frequencies, but not over the business cycle. This is a key contribution
of this paper, especially in light of the emphasis placed by the literature on the role of this
INVESTMENT SHOCKS AND BUSINESS CYCLES 3
shock in business cycles (see, for example, Hall (1997) and Smets and Wouters (2007)). This
role has also been interpreted as a weakness of estimated DSGE models (Chari, Kehoe, and
McGrattan (2008)).
Investment shocks are unlikely candidates to generate business cycles in standard neo-
classical environments. In this framework, a positive shock to the marginal e¢ ciency of
investment increases the rate of return on capital, which induces households to consume less,
but also to work harder. Moreover, with capital (cid:133)xed in the short run, labor productivity
falls and so does the competitive real wage. This is not a recognizable business cycle. In
fact, in neoclassical models, only neutral technology shocks can easily generate the observed
comovement among all these variables. This is because the equality of the marginal rate of
substitution between consumption and leisure and the marginal product of labor imposes
tight restrictions on the relative movements of consumption and hours, as (cid:133)rst pointed out
by Barro and King (1984).
Therefore, to give other shocks a fair chance to be plausible sources of (cid:135)uctuations, our
modeladdstoaneoclassicalcoreanumberofrealandnominalfrictions, suchashabitforma-
tion in consumption, variable capital utilization, investment adjustment costs and imperfect
competition with price stickiness in goods and labor markets. These frictions were originally
proposedintheliteratureasawaytoimprovetheempiricalperformanceofmonetarymodels
(Christiano, Eichenbaum, and Evans (2005)). We show that they also play a crucial role in
turning investment shocks into a viable source of business cycle (cid:135)uctuations.
Among these frictions, we (cid:133)nd that monopolistic competition with sticky prices and wages
isthefundamentalmechanismforthetransmissionofinvestmentshocks. Thisfrictionbreaks
theintratemporale¢ ciencycondition, bydrivinganendogenouswedgebetweenthemarginal
product of labor and the marginal rate of substitution between leisure and consumption. As
a result, the relative movements of consumption and hours are not as tightly linked as in a
perfectly competitive economy. For example, in our estimated model price markups decrease
in response to a positive investment shock, thus increasing labor demand at any given wage.
As a result, consumption, hours, productivity and the competitive real wage can all be
procyclical in response to investment shocks.
INVESTMENT SHOCKS AND BUSINESS CYCLES 4
The prominent role of investment shocks in business cycles implied by our estimates is
consistentwiththeSVARevidenceofFisher(2006)andCanova,Lopez-Salido,andMichelacci
(2006), and broadly in line with the general equilibrium analysis of Greenwood, Hercowitz,
and Krusell (2000). Unlike these authors, however, we do no use direct observations on
the relative price of investment as a measure of investment speci(cid:133)c technological progress.
Instead, we treat the investment shock as an unobservable process, and identify it through
its dynamic e⁄ects on the variables included in the estimation, according to the restrictions
implied by the DSGE model.1 This empirical strategy might be better suited to capture
sources of variation in the marginal e¢ ciency of investment that are not fully re(cid:135)ected in
the variability of the relative price of investment. This would be the case, for example, in
an economy with sticky investment prices, or in which the process of capital accumulation
were subject to more frictions than those we have modeled here, as in Bernanke, Gertler, and
Gilchrist (1999) or Christiano, Motto, and Rostagno (2007).
This paper is also related to a recent literature on the estimation of medium scale DSGE
models (Altig, Christiano, Eichenbaum, and Linde (2005), Del Negro, Schorfheide, Smets,
and Wouters (2007), Gertler, Sala, and Trigari (2007), Justiniano and Primiceri (2007) and
SmetsandWouters(2007)). Wesharewiththisliteraturethebasicstructureofthetheoretical
framework, but we di⁄er from it in three important respects, which summarize our main
contributions. First, we focus the analysis on the origins of business cycle (cid:135)uctuations, which
leads us to emphasize the key role of investment shocks. Second, we investigate how the
departures of our model from the neoclassical benchmark contribute to this result. Finally,
we de-emphasize the contribution of labor supply shocks, by demonstrating that they play a
role only at very low frequencies, but not over the business cycle.
Therestofthepaperisorganizedasfollows. Section2providesthedetailsofthetheoretical
model. Section 3 describes the approach to inference and discusses the (cid:133)t of the estimated
model. Sections 4 and 5 highlight the role of investment shocks in (cid:135)uctuations and the e⁄ect
of frictions on their transmission. Section 6 compares our results to those of Smets and
Wouters (2007). Section 7 compares our estimates of the investment shock to the data on
the relative price of investment. Section 8 conducts a series of robustness checks, including a
detailed comparison with the results of Smets and Wouters (2007). Section 9 concludes.
1 In this respect, our strategy is similar to that followed by Fisher (1997), who infers the properties of
technologicalprogressintheinvestmentsectorthroughaGMMstrategyappliedtomacroeconomicquantities.
INVESTMENT SHOCKS AND BUSINESS CYCLES 5
2. The Model Economy
This section outlines our baseline model of the U.S. business cycle. It is a medium scale
DSGE model with a neoclassical growth core, which we augment with several departures
from the standard assumptions on tastes, technology and market structure(cid:151)(cid:147)frictions(cid:148)for
short(cid:151)now quite common in the literature. This is an ideal framework for the study of
business cycles, for two reasons. First, the model (cid:133)ts the data well, as shown for example by
Del Negro, Schorfheide, Smets, and Wouters (2007) and Smets and Wouters (2007). Second,
it encompasses most of the views on the origins of business cycles proposed in the literature.
The model economy is populated by (cid:133)ve classes of agents. Producers of a (cid:133)nal good,
which (cid:147)assemble(cid:148)a continuum of intermediate goods produced by monopolistic intermediate
goods producers. Households, who consume the (cid:133)nal good, accumulate capital, and supply
di⁄erentiated labor services to competitive (cid:147)employment agencies(cid:148). A Government. We
present their optimization problems in turn.
2.1. Final goods producers. At every point in time t, perfectly competitive (cid:133)rms produce
the (cid:133)nal consumption good Y combining a continuum of intermediate goods Y (i) , i
t f t gi 2
[0;1]; according to the technology
1 1 1+(cid:21)p;t
Yt = Yt(i)1+(cid:21)p;tdi .
(cid:20)Z0 (cid:21)
We assume that (cid:21) follows the exogenous stochastic process
p;t
log(cid:21) = (1 (cid:26) )log(cid:21) +(cid:26) log(cid:21) +" (cid:18) " ,
p;t p p p p;t 1 p;t p p;t 1
(cid:0) (cid:0) (cid:0) (cid:0)
where " is i:i:d:N(0;(cid:27)2). We refer to this as a price markup shock, since (cid:21) is the desired
p;t p p;t
markup of price over marginal cost for intermediate (cid:133)rms. As in Smets and Wouters (2007),
the ARMA(1,1) structure for the desired markup helps capture the moving average, high
frequency component of in(cid:135)ation.
Pro(cid:133)t maximization and the zero pro(cid:133)t condition imply that the price of the (cid:133)nal good,
P , is a CES aggregate of the prices of the intermediate goods, P (i)
t f t gi
1 1 (cid:21)p;t
Pt = Pt(i)(cid:21)p;tdi ,
(cid:20)Z0 (cid:21)
and that the demand function for the intermediate good i is
1+(cid:21)p;t
Pt(i) (cid:0) (cid:21)p;t
(2.1) Y (i) = Y .
t t
P
t
(cid:18) (cid:19)
INVESTMENT SHOCKS AND BUSINESS CYCLES 6
2.2. Intermediate goods producers. A monopolist produces the intermediate good i ac-
cording to the production function
(2.2) Y (i) = max A1 (cid:11)K (i)(cid:11)L (i)1 (cid:11) A F;0 ,
t t(cid:0) t t (cid:0) t
(cid:0)
(cid:8) (cid:9)
whereK (i)andL (i)denotetheamountsofcapitalandlaboremployedby(cid:133)rmi:F isa(cid:133)xed
t t
costofproduction,whichwechoosesothatpro(cid:133)tsarezeroinsteadystate(seeRotembergand
Woodford (1995) and Christiano, Eichenbaum, and Evans (2005)). A represents exogenous
t
labor-augmenting technological progress. Its growth rate (z (cid:1)logA ) follows a stationary
t t
(cid:17)
AR(1) process
z = (1 (cid:26) )(cid:13) +(cid:26) z +" ,
t z z t 1 z;t
(cid:0) (cid:0)
with " i:i:d:N(0;(cid:27)2), which implies that the level of technology is non stationary. This is
z;t z
our neutral technology shock:
AsinCalvo(1983),everyperiodafraction(cid:24) ofintermediate(cid:133)rmscannotoptimallychoose
p
its price, but reset it according to the indexation rule
P (i) = P (i)(cid:25)(cid:19)p (cid:25)1 (cid:19)p,
t t 1 t 1 (cid:0)
(cid:0) (cid:0)
where (cid:25) Pt is gross in(cid:135)ation and (cid:25) is its steady state. The remaining fraction of (cid:133)rms,
t (cid:17) Pt 1
(cid:0)
instead, choosetheirprice, P~(i), bymaximizingthepresentdiscountedvalueoffuturepro(cid:133)ts
t
E 1 (cid:24)s(cid:12)s(cid:21) P~(i) (cid:5)s (cid:25)(cid:19)p (cid:25)1 (cid:19)p Y (i) W L (i)+rkK (i) ,
t p t+s t j=0 t 1+j (cid:0) t+s (cid:0) t t t t
(cid:0)
Xs=0 nh (cid:16) (cid:17)i h io
subject to the demand function 2.1 and the production function 2.2. In this objective, (cid:21)
t+s
is the marginal utility of consumption of the representative households that owns the (cid:133)rm,
while W and rk are the nominal wage and the rental rate of capital.
t t
2.3. Employment agencies. Firms are owned by a continuum of households, indexed by
j [0;1]. Each household is a monopolistic supplier of specialized labor, L (j); as in Erceg,
t
2
Henderson, and Levin (2000). A large number of competitive (cid:147)employment agencies(cid:148)com-
bines this specialized labor into a homogenous labor input sold to intermediate (cid:133)rms, accord-
ing to
1 1 1+(cid:21)w;t
Lt = Lt(j)1+(cid:21)w;tdj .
(cid:20)Z0 (cid:21)
INVESTMENT SHOCKS AND BUSINESS CYCLES 7
Asinthecaseofthe(cid:133)nalgood,thedesiredmarkupofthewageoverthehousehold(cid:146)smarginal
rate of substitution, (cid:21) ; follows the exogenous stochastic process
w;t
log(cid:21) = (1 (cid:26) )log(cid:21) +(cid:26) log(cid:21) +" (cid:18) " ,
w;t w w w w;t 1 w;t w w;t 1
(cid:0) (cid:0) (cid:0) (cid:0)
where " is i:i:d:N(0;(cid:27)2). This is the wage markup shock. We also refer to it as a labor
w;t w
supply shock, since it has the same e⁄ect on the household(cid:146)s (cid:133)rst order condition for the
choice of hours as the preference shock analyzed by Hall (1997).
Pro(cid:133)t maximization by the perfectly competitive employment agencies implies the labor
demand function
1+(cid:21)w;t
Wt(j) (cid:0) (cid:21)w;t
L (j) = L ,
t t
W
t
(cid:18) (cid:19)
where W (j) is the wage received from employment agencies by the supplier of labor of type
t
j, while the wage paid by intermediate (cid:133)rms for their homogenous labor input is
1 1 (cid:21)w;t
Wt = Wt(j)(cid:21)w;tdj :
(cid:20)Z0 (cid:21)
2.4. Households. Each household maximizes the utility function
E 1 (cid:12)sb log(C hC ) ’Lt+s(j)1+(cid:23) ,
t t+s t+s t+s 1
(cid:0) (cid:0) (cid:0) 1+(cid:23)
s=0 (cid:20) (cid:21)
X
where C is consumption, h is the degree of habit formation and b is a shock to the discount
t t
factor, which a⁄ects both the marginal utility of consumption and the marginal disutility of
labor. This intertemporal preference shock follows the stochastic process
logb = (cid:26) logb +" ,
t b t 1 b;t
(cid:0)
with " i:i:d:N(0;(cid:27)2). Since technological progress is non stationary, we work with log
b;t (cid:24) b
utility to ensure the existence of a balanced growth path. Moreover, consumption is not
indexed by j because the existence of state contingent securities ensures that in equilibrium
consumption and asset holdings are the same for all households.
As a result, the household(cid:146)s budget constraint is
P C +P I +T +B R B +Q (j)+(cid:5) +W (j)L (j)+rku K(cid:22) P a(u )K(cid:22) ,
t t t t t t t 1 t 1 t 1 t t t t t t 1 t t t 1
(cid:20) (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) (cid:0)
where I is investment, T are lump-sum taxes, B is holdings of government bonds, R is the
t t t t
gross nominal interest rate, Q (j) is the net cash (cid:135)ow from household(cid:146)s j portfolio of state
t
contingent securities, and (cid:5) is the per-capita pro(cid:133)t accruing to households from ownership
t
of the (cid:133)rms.
INVESTMENT SHOCKS AND BUSINESS CYCLES 8
Households own capital and choose the capital utilization rate, u ; which transforms phys-
t
ical capital into e⁄ective capital according to
K = u K(cid:22) :
t t t 1
(cid:0)
E⁄ective capital is then rented to (cid:133)rms at the rate rk. The cost of capital utilization is a(u )
t t
a (1)
per unit of physical capital. We assume u = 1 in steady state, a(1) = 0 and de(cid:133)ne (cid:31) 00 :
t (cid:17) a0(1)
In our log-linear approximation of the model solution this curvature is the only parameter
that matters for the dynamics.
The physical capital accumulation equation is
I
K(cid:22) = (1 (cid:14))K(cid:22) +(cid:22) 1 S t I ,
t (cid:0) t(cid:0)1 t (cid:0) It 1 t
(cid:18) (cid:18) (cid:0) (cid:19)(cid:19)
where (cid:14) is the depreciation rate. The function S captures the presence of adjustment costs
in investment, as in Christiano, Eichenbaum, and Evans (2005). We assume that, in steady
state, S = S = 0 and S > 0.2
0 00
The investment shock (cid:22) is a source of exogenous variation in the e¢ ciency with which the
t
(cid:133)nal good can be transformed into physical capital, and thus into tomorrow(cid:146)s capital input.
As shown by Greenwood, Hercowitz, and Krusell (1997), (cid:22) is also equivalent to a form of
t
technological progress con(cid:133)ned to the production of investment goods in a simple two-sector
representation of our economy. We assume that it follows the stochastic process
log(cid:22) = (cid:26) log(cid:22) +" ,
t (cid:22) t 1 (cid:22);t
(cid:0)
where " is i:i:d:N(0;(cid:27)2):
(cid:22);t (cid:22)
In terms of wage setting, we follow Erceg, Henderson, and Levin (2000) and assume that
everyperiodafraction(cid:24) ofhouseholdscannotfreelysettheirwage, butsetsthemaccording
w
to the indexation rule
Wt(j) = Wt 1(j)((cid:25)t 1ezt(cid:0)1)(cid:19)w((cid:25)e(cid:13))1(cid:0)(cid:19)w.
(cid:0) (cid:0)
The remaining fraction of households chooses instead an optimal wage by maximizing
E 1 (cid:24)s(cid:12)sb ’Lt+s(j)1+(cid:23) ,
t w t+s (cid:0) 1+(cid:23)
s=0 (cid:26) (cid:27)
X
subject to the labor demand function.
2 Lucca(2005)showsthatthisformulationoftheadjustmentcostfunctionisequivalent(upto(cid:133)rstorder)
to a generalization of the time to build assumption.
INVESTMENT SHOCKS AND BUSINESS CYCLES 9
2.5. Government. A monetary policy authority sets the nominal interest rate following a
Taylor-type rule of the form
1 (cid:26)
R R (cid:26)R (cid:25) (cid:30) Y (cid:30)Y (cid:0) R Y =Y (cid:30)dY
t t 1 t (cid:25) t t t 1
R = R(cid:0) (cid:25) Y Y =Y(cid:0) (cid:17)mp;t,
(cid:18) (cid:19) " (cid:18) t(cid:3)(cid:19) # (cid:20) t(cid:3) t(cid:3)1(cid:21)
(cid:16) (cid:17) (cid:0)
where R is the steady state of the gross nominal interest rate. As in Smets and Wouters
(2007), interest rates responds to deviations of in(cid:135)ation from its steady state, as well as to
the level and the growth rate of the output gap (Y =Y ).3 The monetary policy rule is also
t t(cid:3)
perturbed by a monetary policy shock, (cid:17) , which evolves according to
mp;t
log(cid:17) = (cid:26) log(cid:17) +" ,
mp;t mp mp;t 1 mp;t
(cid:0)
where " is i:i:d:N(0;(cid:27)2 ).
mp;t mp
Fiscal policy is fully Ricardian. The Government (cid:133)nances its budget de(cid:133)cit by issuing
short term bonds. Public spending is determined exogenously as a time-varying fraction of
GDP
1
G = 1 Y ,
t t
(cid:0) g
t
(cid:18) (cid:19)
where the government spending shock g follows the stochastic process
t
logg = (1 (cid:26) )logg+(cid:26) logg +" ,
t g g t 1 g;t
(cid:0) (cid:0)
with " i:i:d:N(0;(cid:27)2).
g;t g
(cid:24)
2.6. Market clearing. The aggregate resource constraint,
C +I +G +a(u )K(cid:22) = Y ,
t t t t t 1 t
(cid:0)
can be derived by combining the Government and the households(cid:146)budget constraints with
the zero pro(cid:133)t condition of the (cid:133)nal goods producers and the employment agencies.
2.7. Model solution. In this model, consumption, investment, capital, real wages and out-
put (cid:135)uctuate around a stochastic balanced growth path, since the level of technology A has
t
a unit root. Therefore, the solution involves the following steps. First, we rewrite the model
in terms of detrended variables. We then compute the non-stochastic steady state of the
transformed model, and log-linearly approximate it around this steady state. Finally, we
solve the resulting linear system of rational expectation equations to obtain its state space
3 The output gap is de(cid:133)ned as the di⁄erence between actual output and the e¢ cient level of output
(Woodford (2003)).