The full text on this page is automatically extracted from the file linked above and may contain errors and inconsistencies.
Federal Reserve Bank of Chicago
Investment Shocks and Business Cycles
Alejandro Justiniano, Giorgio E. Primiceri,
and Andrea Tambalotti
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 ‡
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 …nd that neutral
technology shocks are not negligible, but their share in the variance of output is only around
25 percent, and even lower for hours. Labor supply shocks explain a large fraction of the
variation of hours at very low frequencies, but not over the business cycle. Finally, we show
that imperfect competition and, to a lesser extent, technological frictions are the key to the
transmission of investment shocks in the model.
1. Introduction
What is the source of economic ‡
uctuations? This is one of the de…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 …nds that technology shocks explain more than one quarter of output ‡
uctuations
(Shapiro and Watson (1988), King, Plosser, Stock, and Watson (1991), Cochrane (1994),
Gali (1999), Christiano, Eichenbaum, and Vigfusson (2004) and Fisher (2006)).
Date: First version: November 2007. This version: 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 “How Much Structure in Empirical Models?” 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’ 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‡
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…rms the SVAR evidence, but it does so from the perspective of a fully
articulated dynamic stochastic general equilibrium (DSGE) model. Our main …nding is
that shocks to the marginal e¢ ciency of investment are the key drivers of macroeconomic
‡
uctuations. These shocks a¤ect the yield of a foregone unit of consumption in terms of
tomorrow’ capital input. The literature often refers to them as investment speci…c technology
s
shocks, since they are equivalent to productivity shocks speci…c to the capital goods producing
sector in a simple two-sector economy (Greenwood, Hercowitz, and Krusell (1997)). For
simplicity, we call them investment shocks.
Our …ndings are based on the Bayesian estimation of a New Neoclassical Synthesis model of
the US economy (Goodfriend and King (1997)). The model includes a rich set of nominal and
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…cant share
of the comovement between output and consumption. Another aspect of this complementarity
is that the two disturbances can be characterized as an aggregate demand and aggregate
supply shock respectively. In fact, investment shocks generate a positive comovement between
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 ‡
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 neoclassical 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 …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 …rst pointed out
by Barro and King (1984).
Therefore, to give other shocks a fair chance to be plausible sources of ‡
uctuations, our
model adds to a neoclassical core a number of real and nominal frictions, such as habit formation in consumption, variable capital utilization, investment adjustment costs and imperfect
competition with price stickiness in goods and labor markets. These frictions were originally
proposed in the literature as a way to improve the empirical performance of monetary models
(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 ‡
uctuations.
Among these frictions, we …nd that monopolistic competition with sticky prices and wages
is the fundamental mechanism for the transmission of investment shocks. This friction breaks
the intratemporal e¢ ciency condition, by driving an endogenous wedge between the marginal
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
consistent with the SVAR evidence of Fisher (2006) and Canova, Lopez-Salido, and Michelacci
(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…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‡
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
Smets and Wouters (2007)). We share with this literature the basic structure of the theoretical
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 ‡
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.
The rest of the paper is organized as follows. Section 2 provides the details of the theoretical
model. Section 3 describes the approach to inference and discusses the …t of the estimated
model. Sections 4 and 5 highlight the role of investment shocks in ‡
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
technological progress in the investment sector through a GMM strategy applied to macroeconomic quantities.
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— “frictions” for
short— now quite common in the literature. This is an ideal framework for the study of
business cycles, for two reasons. First, the model …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 …ve classes of agents. Producers of a …nal good,
which “assemble”a continuum of intermediate goods produced by monopolistic intermediate
goods producers. Households, who consume the …nal good, accumulate capital, and supply
di¤erentiated labor services to competitive “employment agencies” A Government. We
.
present their optimization problems in turn.
2.1. Final goods producers. At every point in time t, perfectly competitive …rms produce
the …nal consumption good Yt combining a continuum of intermediate goods fYt (i)gi , i 2
[0; 1]; according to the technology
Yt =
Z
1
1+
1
Yt (i) 1+
p;t
p;t
.
di
0
We assume that
p;t
follows the exogenous stochastic process
log
where "p;t is i:i:d:N (0;
p;t
= (1
2 ).
p
p ) log
p
+
p log
p;t 1
+ "p;t
p "p;t 1 ,
We refer to this as a price markup shock, since
p;t
is the desired
markup of price over marginal cost for intermediate …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‡
ation.
Pro…t maximization and the zero pro…t condition imply that the price of the …nal good,
Pt , is a CES aggregate of the prices of the intermediate goods, fPt (i)gi
Z 1
p;t
1
Pt =
Pt (i) p;t di
,
0
and that the demand function for the intermediate good i is
(2.1)
Yt (i) =
Pt (i)
Pt
1+ p;t
p;t
Yt .
INVESTMENT SHOCKS AND BUSINESS CYCLES
6
2.2. Intermediate goods producers. A monopolist produces the intermediate good i according to the production function
1
Yt (i) = max At
(2.2)
Kt (i) Lt (i)1
At F ; 0 ,
where Kt (i) and Lt (i) denote the amounts of capital and labor employed by …rm i: F is a …xed
cost of production, which we choose so that pro…ts are zero in steady state (see Rotemberg and
Woodford (1995) and Christiano, Eichenbaum, and Evans (2005)). At represents exogenous
labor-augmenting technological progress. Its growth rate (zt
log At ) follows a stationary
AR(1) process
zt = (1
with "z;t i:i:d:N (0;
2 ),
z
z)
+
z zt 1
+ "z;t ,
which implies that the level of technology is non stationary. This is
our neutral technology shock :
As in Calvo (1983), every period a fraction
p
of intermediate …rms cannot optimally choose
its price, but reset it according to the indexation rule
Pt (i) = Pt
where
t
Pt
Pt 1
is gross in‡
ation and
p
1 (i) t 1
1
p
,
is its steady state. The remaining fraction of …rms,
~
instead, choose their price, Pt (i), by maximizing the present discounted value of future pro…ts
Et
1
X
s=0
s s
t+s
p
nh
~
Pt (i)
p
s
1
j=0 t 1+j
p
i
h
Yt+s (i)
io
k
Wt Lt (i) + rt Kt (i) ,
subject to the demand function 2.1 and the production function 2.2. In this objective,
t+s
is the marginal utility of consumption of the representative households that owns the …rm,
k
while Wt and rt are the nominal wage and the rental rate of capital.
2.3. Employment agencies. Firms are owned by a continuum of households, indexed by
j 2 [0; 1]. Each household is a monopolistic supplier of specialized labor, Lt (j); as in Erceg,
Henderson, and Levin (2000). A large number of competitive “employment agencies” combines this specialized labor into a homogenous labor input sold to intermediate …rms, according to
Lt =
Z
0
1
Lt (j) 1+
1
w;t
1+
dj
w;t
.
INVESTMENT SHOCKS AND BUSINESS CYCLES
7
As in the case of the …nal good, the desired markup of the wage over the household’ marginal
s
rate of substitution,
w;t ;
log
w;t
where "w;t is i:i:d:N (0;
follows the exogenous stochastic process
= (1
2 ).
w
w ) log
w
+
w
log
w;t 1
+ "w;t
w "w;t 1 ,
This is the wage markup shock. We also refer to it as a labor
supply shock, since it has the same e¤ect on the household’ …rst order condition for the
s
choice of hours as the preference shock analyzed by Hall (1997).
Pro…t maximization by the perfectly competitive employment agencies implies the labor
demand function
1+ w;t
w;t
Wt (j)
Lt (j) =
Lt ,
Wt
where Wt (j) is the wage received from employment agencies by the supplier of labor of type
j, while the wage paid by intermediate …rms for their homogenous labor input is
Z 1
w;t
1
Wt (j) w;t dj
Wt =
:
0
2.4. Households. Each household maximizes the utility function
Et
1
X
s
bt+s log (Ct+s
hCt+s
1)
'
s=0
Lt+s (j)1+
1+
,
where Ct is consumption, h is the degree of habit formation and bt is a shock to the discount
factor, which a¤ects both the marginal utility of consumption and the marginal disutility of
labor. This intertemporal preference shock follows the stochastic process
log bt =
with "b;t
i:i:d:N (0;
2 ).
b
b log bt 1
+ "b;t ,
Since technological progress is non stationary, we work with log
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’ budget constraint is
s
Pt Ct + Pt It + Tt + Bt
Rt
1 Bt 1
+ Qt
1 (j)
+
t
k
+ Wt (j)Lt (j) + rt ut Kt
1
Pt a(ut )Kt
1,
where It is investment, Tt are lump-sum taxes, Bt is holdings of government bonds, Rt is the
gross nominal interest rate, Qt (j) is the net cash ‡ from household’ j portfolio of state
ow
s
contingent securities, and
of the …rms.
t
is the per-capita pro…t accruing to households from ownership
INVESTMENT SHOCKS AND BUSINESS CYCLES
8
Households own capital and choose the capital utilization rate, ut ; which transforms physical capital into e¤ective capital according to
Kt = u t Kt
1:
k
E¤ective capital is then rented to …rms at the rate rt . The cost of capital utilization is a(ut )
per unit of physical capital. We assume ut = 1 in steady state, a(1) = 0 and de…ne
a00 (1)
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
Kt = (1
where
)Kt
1
+
1
t
S
It
It
It ,
1
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 = 0 and S 00 > 0.2
The investment shock
t
is a source of exogenous variation in the e¢ ciency with which the
…nal good can be transformed into physical capital, and thus into tomorrow’ capital input.
s
As shown by Greenwood, Hercowitz, and Krusell (1997),
t
is also equivalent to a form of
technological progress con…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
where "
;t
is i:i:d:N (0;
t
=
log
t 1
+"
;t ,
2 ):
In terms of wage setting, we follow Erceg, Henderson, and Levin (2000) and assume that
every period a fraction
w
of households cannot freely set their wage, but sets them according
to the indexation rule
Wt (j) = Wt
zt
1 (j) ( t 1 e
1
) w ( e )1
w
.
The remaining fraction of households chooses instead an optimal wage by maximizing
Et
1
X
s s
w bt+s
s=0
'
Lt+s (j)1+
1+
,
subject to the labor demand function.
2 Lucca (2005) shows that this formulation of the adjustment cost function is equivalent (up to …rst order)
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
Rt
=
R
Rt 1
R
R
"
Yt
Yt
t
Y
#1
R
Yt =Yt
Yt =Yt
1
dY
mp;t ,
1
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‡
ation from its steady state, as well as to
the level and the growth rate of the output gap (Yt =Yt ).3 The monetary policy rule is also
perturbed by a monetary policy shock,
log
where "mp;t is i:i:d:N (0;
mp;t
=
mp;t ,
which evolves according to
mp log mp;t 1
+ "mp;t ,
2 ).
mp
Fiscal policy is fully Ricardian. The Government …nances its budget de…cit by issuing
short term bonds. Public spending is determined exogenously as a time-varying fraction of
GDP
1
Yt ,
gt
where the government spending shock gt follows the stochastic process
Gt =
log gt = (1
with "g;t
i:i:d:N (0;
1
g ) log g
+
g
log gt
1
+ "g;t ,
2 ).
g
2.6. Market clearing. The aggregate resource constraint,
Ct + It + Gt + a(ut )Kt
1
= Yt ,
can be derived by combining the Government and the households’ budget constraints with
the zero pro…t condition of the …nal goods producers and the employment agencies.
2.7. Model solution. In this model, consumption, investment, capital, real wages and output ‡
uctuate around a stochastic balanced growth path, since the level of technology At has
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…ned as the di¤erence between actual output and the e¢ cient level of output
(Woodford (2003)).
INVESTMENT SHOCKS AND BUSINESS CYCLES
10
representation. This forms the basis for our estimation procedure, which is discussed in the
next section.
3. Bayesian Inference
3.1. Data and priors. We estimate the model using the following vector of observable
variables
(3.1)
where
[
log Yt ;
log Ct ;
log It ; log Lt ;
log
Wt
;
Pt
t ; Rt ];
denotes the temporal di¤erence operator. The data is quarterly and spans the period
from 1954QIII to 2004QIV. A precise description of the data series used in the estimation
can be found in appendix A.
We use Bayesian methods to characterize the posterior distribution of the structural parameters of the model (see An and Schorfheide (2007) for a survey). The posterior distribution
combines the likelihood function with prior information.4 In the rest of this section we brie‡
y
discuss the speci…cation of the priors.
We …x a small number of parameters to values commonly used in the literature. In particular, we set the quarterly depreciation rate of capital ( ) to 0:025 and the steady state
government spending to GDP ratio (1
1=g) to 0:22, which corresponds to the average value
of Gt =Yt in our sample. Table 1 reports the priors for the remaining parameters of the model.
Although these priors are relatively di¤use and broadly in line with those adopted in previous
studies (Del Negro, Schorfheide, Smets, and Wouters (2007), Levin, Onatski, Williams, and
Williams (2005)), some of them deserve a brief discussion.
For all but two persistence parameters we use a Beta prior, with mean 0:6 and standard
deviation 0:2. One of the two exceptions is neutral technology, which already includes a unit
root. For this reason, the prior for the autocorrelation of its growth rate ( z ) is centered at
0:4 instead. We use 0:4 also to center the prior for the persistence of the monetary policy
shocks, because the policy rule already allows for interest rates inertia.
The intertemporal preference, price and wage markup shocks are normalized to enter with a
unit coe¢ cient in the consumption, price in‡
ation and wage equations respectively (see Smets
and Wouters (2007) and appendix B). The priors on the innovations’ standard deviations
4 In section 8 we show that results are robust to estimating the model by maximum likelihood (i.e. with
‡ priors).
at
INVESTMENT SHOCKS AND BUSINESS CYCLES
11
are quite disperse and chosen in order to generate volatilities for the endogenous variables
broadly in line with the data. The covariance matrix of the innovations is assumed diagonal.
To evaluate jointly the economic content of the priors on the exogenous processes and
the structural parameters, we analyze their implications for the variance decomposition of
the observable variables. This analysis is more useful than a series of comments on the
priors for speci…c coe¢ cients, especially given that the focus of the paper is on the sources
of ‡
uctuations. Turning to table 2; we see that our priors re‡ a view of business cycles in
ect
line with the RBC tradition. The variability of output, consumption, investment and hours
is due for the most part to neutral technology shocks, while the role of investment shocks is
negligible.
3.2. Parameter estimates. In table 1, we report the estimates of the model’ parameters.
s
We present posterior medians, standard deviations and 90 percent probability intervals. In
line with previous studies, we estimate a substantial degree of price and wage stickiness,
habit formation in consumption and adjustment costs in investment (see for example Altig,
Christiano, Eichenbaum, and Linde (2005), Del Negro, Schorfheide, Smets, and Wouters
(2007) and Smets and Wouters (2007)). Capital utilization is not very elastic, as also found
by Del Negro, Schorfheide, Smets, and Wouters (2007). In response to a 1 percent positive
change in the rental rate of capital, utilization increases by slightly less than 0:2 percent.
Our estimates of the income share of capital ( ) and of the Frisch elasticity of labor supply
(1= ) are both lower than the values typically adopted in the RBC literature, but close to
those of Smets and Wouters (2007). In any case, none of our results depend crucially on
these estimates of
and , as we show in section 8.
3.3. Model …t. Given our posterior estimates, how well does the model …t the data? We
address this question by comparing a set of statistics implied by the model to those measured
in the data. In particular, we study the standard deviation and the complete correlation
structure of the observable variables included in the estimation.
Table 3 reports the standard deviation of our seven observable variables, in absolute terms
as well as relative to that of output growth. For the model, we report the median and
the 90 percent probability intervals that account for both parameter uncertainty and small
sample uncertainty. The model overpredicts the volatility of output growth, consumption
and investment, but it matches their relative standard deviations fairly well. The match with
INVESTMENT SHOCKS AND BUSINESS CYCLES
12
hours is close in both cases. There is also a tendency to underpredict the volatility of nominal
interest rates and in‡
ation, which might be due to the fact that the model does not replicate
the very high correlation between these two variables.
With as many shocks as observable variables, why does the model not capture their standard deviation perfectly? The reason is that a likelihood-based estimator tries to match the
entire autocovariance function of the data, and thus must strike a balance between matching
standard deviations and all the other second moments, namely autocorrelations and crosscorrelations. These other moments are displayed in …gure 1, for the data (grey line) and the
model (back line), along with the 90 percent posterior intervals for the model implied by
parameter uncertainty and small sample uncertainty.
Focus …rst on the upper-left 4-by-4 block of graphs, which includes all the quantities in
the model. On the diagonal, we see that the model captures the decaying autocorrelation
structure of these four variables very well. The success is particularly impressive for hours,
for which the model-implied and data autocorrelations lay virtually on top of each other.
In terms of cross-correlations, the model does extremely well for output (the …rst row and
column) and for hours (the fourth row and column), but fails to capture the contemporaneous
correlation between consumption and investment growth. This correlation is slightly positive
in the data, but essentially zero in the model.
In sum, relative to smaller scale RBC models (Cooley and Prescott (1995), King and
Rebelo (1999)), we do slightly worse in matching the properties of consumption, especially
its correlation with investment. However, our model performs considerably better in terms of
hours worked. This is an important result, because one of our main objectives is to investigate
the sources of ‡
uctuations in hours.
With respect to prices, the model is overall quite successful in reproducing the main stylized facts. We emphasize two issues: …rst, the model does not capture the full extent of the
persistence of in‡
ation and the nominal interest rate, even in the presence of in‡
ation indexation and of a fairly high smoothing parameter in the interest rate rule. Second, we match
very closely the correlation between output and in‡
ation, which is highlighted for example
by Smets and Wouters (2007) as an important measure of a model’ empirical success.
s
INVESTMENT SHOCKS AND BUSINESS CYCLES
13
4. Shocks and Business Cycles
In this section, we present the central result of the paper: investment shocks are the most
important source of business cycle ‡
uctuations. First, we document this …nding quantitatively, by looking at the variance decomposition implied by the estimated model. We focus in
particular on output and hours. Second, we provide some intuition for the result by studying
the impulse responses of some key variables to the main shocks in the model. This exercise
also allows us to informally discuss how those shocks are identi…ed by our empirical procedure.
4.1. Variance decomposition. Table 4 reports the contribution of each shock to the unconditional variance of the observable variables included in the estimation. From the …rst
row of the table, we see that investment shocks account for more than 50 percent of the
‡
uctuations in the growth rate of output, by far the largest share. Figure 2 provides a time
series decomposition of this contribution to overall variance by plotting year-to-year GDP
growth in the data (the grey line) and in the model, conditional on the estimated sequence
of the investment shocks alone (the black line). The comovement between the two series is
striking. In particular, investment shocks appear largely responsible for “dragging” GDP
growth down at business cycle troughs. This is especially evident for the last two downturns,
as well as for the recessions of the sixties. The main exceptions are the “twin” recessions
of the early eighties, in which in fact monetary factors are widely believed to have played a
fundamental role.
Looking at the other shocks and variables in table 4, two results stand out. First, the
neutral technology shock remains fairly important in our estimates. It explains around one
quarter of the volatility of output, consumption and real wages. Second, the wage markup
shock, which in this model is indistinguishable from Hall’ (1997) labor supply shock, plays
s
a prominent role in the ‡
uctuations of wages, in‡
ation and especially hours. It accounts for
between one half and two thirds of their volatility.
The variance decomposition of hours in table 4 is puzzling. The investment shock explains
only 20 percent of the volatility of hours, less than half its contribution to output. Yet, the
close comovement of hours and output is perhaps the most notable feature of business cycles.
Table 5 sheds some light on this apparent contradiction, by focusing on ‡
uctuations in the
level of all variables at business cycle frequencies.5
5 We compute the spectral density of the observable variables implied by the DSGE model and transform
it to obtain the spectrum of the level of output, consumption, investment and wages. We de…ne business cycle
INVESTMENT SHOCKS AND BUSINESS CYCLES
14
Over the business cycle, investment shocks explain approximately 60 percent of the ‡
uctuations in hours, as well as 50 percent of those in output and more than 80 percent of those
in investment. We conclude that investment shocks are the leading source of business cycles.
One quali…cation to this result comes from consumption. Investment shocks are responsible
for only a small fraction of its variability, which is instead largely driven by the intertemporal
preference shock. The fact that most movements in consumption come from an otherwise
irrelevant shock is a symptom of the well-known failure of standard consumption Euler equations to capture the empirical relationship between consumption and interest rates, as argued
in Primiceri, Schaumburg, and Tambalotti (2005).
Another interesting result emerging from the comparison of tables 4 and 5 is that the
role of wage markup shocks virtually disappears when we restrict attention to business cycle
frequencies. This is particularly noticeable for hours, with a drop in the share of variance
attributed to wage markup shocks from 65 percent overall to only 6 percent at business cycle
frequencies. Figure 3 clari…es this point by plotting the share of the variance of hours due
to the wage markup shock, as a function of the spectrum frequencies. According to our
de…nition, business cycles correspond to a frequency range between 0:19 and 1:05, which is
highlighted by dotted vertical lines in the picture. The contribution of wage markup shocks
is extremely signi…cant at very low frequencies, but declines steeply as we move towards the
business cycle range, in which it is mostly below 10%.
This result is roughly consistent with Hall’ (1997) …nding of an important role for labor
s
supply shocks in the overall variability of hours, although his cyclical decomposition attributes
a large role to those shocks also at business cycle frequencies, while ours does not. More
recently, Hall (2008) shows that the role of labor supply shocks is signi…cantly diminished in
a model with countercyclical wage markups. As we will see in section 5, the countercyclicality
of markups is also a key ingredient in our results.
4.2. Model dynamics and shock identi…cation. Our results so far suggest that to understand business cycles, we must understand investment shocks, since these shocks are the
largest contributors to ‡
uctuations in several key macroeconomic variables. But what properties of these and the other shocks allow us to separately identify their contributions? This
section provides some intuition for how this identi…cation is achieved, by studying the impulse
‡
uctuations as those corresponding to periodic components with cycles between 6 and 32 quarters, as in Stock
and Watson (1999).
INVESTMENT SHOCKS AND BUSINESS CYCLES
15
responses of several key variables to some of the shocks. In particular, we focus on the three
shocks that are responsible for the bulk of ‡
uctuations according to our estimates. They are
the investment shock, the neutral technology shock and the wage markup (or labor supply)
shock.
Figure 4 reports the impulse responses to the investment shock. Following a positive
impulse, output, hours, investment, real wages and labor productivity all rise persistently
and in a hump-shaped pattern. The reaction in investment is contemporaneous and roughly
proportional to that in output, but larger by a factor of almost …ve. This factor is close to
the ratio of the unconditional volatilities of the two series.
The response of hours is very similar to that of output, in terms of dynamic pro…le and
scale. This accounts for the very similar shares of business cycle ‡
uctuations in output
and hours explained by investment shocks, given that the cyclical components of the two
series have very similar volatilities. The increase in hours is not associated with a drop
in average labor productivity, as would be the case in a standard neoclassical model. The
procyclicality of labor productivity in response to investment shocks is the combined result
of the endogeneity of capital utilization (Greenwood, Hercowitz, and Hu¤man (1988)) and of
the increasing returns implied by the presence of …xed costs in production.
Turning now to consumption, we see an initially ‡ response, followed by a rise after a few
at
quarters. This failure of consumption to comove on impact with the other macroeconomic
variables is the main reason why the investment shock accounts for less then 10 percent of the
movements in consumption, and thus for a smaller share of the variance of output, compared
to investment. Moreover, this lack of comovement, which is especially pronounced for the
consumption-investment pair, given the strong procyclicality of the latter, explains why the
model has some di¢ culty in capturing the correlation between these two variables, as we
pointed out in section 3.3.
Finally, looking at in‡
ation and the nominal interest rate, we see that they both rise
in response to a positive investment shock. In this respect, the investment shock displays
the typical features of a textbook “demand” shock: quantities and prices move in the same
direction, leading to a tightening of monetary policy. In fact, the positive comovement of
prices and quantities is one of the distinguishing characteristics of the investment shock,
when compared to wage markup and neutral technology shocks, whose impulse responses are
depicted in …gures 5 and 6.
INVESTMENT SHOCKS AND BUSINESS CYCLES
16
For example, an increase in the desired wage markup depresses all quantities, but leads
to a fairly persistent increase in real wages and marginal costs. As a consequence, in‡
ation
rises, followed by the nominal interest rate. Moreover, the response in hours, and in all other
quantities, is extremely persistent. This persistence is the source of the large contribution of
the wage markup shock to the low frequency ‡
uctuations in the labor input highlighted in
the previous section.
Similarly, output, consumption and investment all rise in response to a positive neutral
technology shock. Real wages are also procyclical, but their increase lags behind the rise
in the marginal product of labor, so that marginal costs and therefore in‡
ation fall. Most
notably, hours also fall on impact, although they recover after a few periods. The negative
response of hours depends crucially on the presence of imperfect competition, through three
main channels. First, the equilibrium price markup– reciprocal of the real marginal cost–
the
increases, thus counteracting the positive e¤ect of higher productivity on labor demand.
Second, the wage markup (not reported) also increases, thus shifting the labor supply schedule
to the left. Third, the wealth e¤ect on hours is stronger with monopolistic competition, since
positive expected pro…ts increase households’permanent income (Rotemberg and Woodford
(1995)).
The fall in hours in response to a neutral technological improvement is sharply at odds
with the predictions of a standard RBC model, but consistent with a large empirical literature (Gali (1999), Francis and Ramey (2006), Canova, Lopez-Salido, and Michelacci (2006),
Fernald (2007), Basu, Fernald, and Kimball (2007), Gali and Rabanal (2004) and Smets
and Wouters (2007), but see Christiano, Eichenbaum, and Vigfusson (2004), Uhlig (2003)
or Chang and Hong (2006), for the opposite view.). The lack of comovement between output and hours accounts to a large extent for the limited role of neutral technology shocks
as sources of ‡
uctuations in our model. However, these disturbances generate the right comovement between output and consumption. As a result, neutral technology shocks retain a
non-negligible role in the ‡
uctuations of these two variables.
In summary, our analysis proposes a reasonably parsimonious view of the sources of business cycles. Investment shocks impart the main impetus to ‡
uctuations, which spread from
investment to output and hours. Consumption, however, is largely insulated from these
disturbances and its comovement with the rest of the economy is mainly driven by neutral
INVESTMENT SHOCKS AND BUSINESS CYCLES
17
technology shocks. Finally, labor supply shocks account for a large fraction of the movements
in hours, but these are concentrated at very low frequencies.
As for wages and prices, their movement is mainly driven by exogenous variation in desired
markups, as we would expect in an economy in which monetary policy is well calibrated. In
this respect, it is especially remarkable that in‡
ation and wages are almost completely insulated from investment shocks. The fact that these shocks explain close to half of the movements in nominal interest rates suggests that achieving this degree of nominal stabilization
required a fair amount of activism on the part of monetary policy.
5. Inspecting the Mechanism: How Investment Shocks Become Important
In standard neoclassical environments, neutral technology shocks are the most natural
source of business cycles, since they can easily produce comovement of output, consumption,
investment, hours and labor productivity. In fact, Barro and King (1984) show that generating this kind of comovement in response to most other shocks is problematic. In particular,
they explicitly identify investment shocks as unlikely candidates to generate recognizable
business cycles. Their reasoning can be outlined as follows: a positive shock to the marginal
e¢ ciency of investment increases the rate of return on current resources, inducing agents to
postpone consumption. With lower consumption, the marginal utility of income increases,
shifting labor supply to the right– intertemporal substitution e¤ect. Along an unchanged
an
labor demand schedule, this supply shift raises hours and output, but depresses consumption,
wages and labor productivity.6
This is not what happens in our estimated model, though, in which investment shocks
trigger procyclical movements in all the key macroeconomic variables discussed above (see
…gure 4.)7 As a consequence of this signi…cant change in the transmission mechanism with
respect to the neoclassical benchmark, investment shocks emerge from our analysis as the
single most important source of business cycle ‡
uctuations. In this section, we study more
closely how the frictions included in our baseline model contribute to this result. Some of
these frictions, such as endogenous capital utilization and investment adjustment costs, have
been analyzed before in a similar context, most prominently by Greenwood, Hercowitz, and
6 Labor demand is unchanged on impact because the investment shock, unlike a shock to TFP, does not
directly a¤ect the marginal product of labor.
7 Consumption is the only possible exception, since it only increases with a delay of about one year, as we
pointed out in section 4.2.
INVESTMENT SHOCKS AND BUSINESS CYCLES
18
Hu¤man (1988) and Greenwood, Hercowitz, and Krusell (2000). Others, such as monopolistic
competition with sticky prices and wages, have not.8
To organize this discussion, we start from the e¢ ciency equilibrium condition that must
hold in a neoclassical economy:
(5.1)
M RS C ; L
+ +
= MPL L .
With standard preferences and technology, the marginal rate of substitution (M RS) depends
positively on consumption (C) and hours (L), while the marginal product of labor (M P L) is
decreasing in hours. As a result, any shock that boosts hours on impact, without shifting the
marginal product of labor schedule, must also generate a fall in consumption for 5.1 to hold
at the new equilibrium (Barro and King (1984)). This is precisely what happens in response
to investment shocks in a neoclassical model, as we discussed above.
Equation 5.1 also highlights the three margins on which the frictions included in our baseline model must be operating to make the transmission of investment shocks more conformable
with the typical pattern of business cycles. Departures from the standard assumptions on
tastes a¤ect the form of the M RS, technological frictions a¤ect the form of the M P L, while
departures from perfect competition create a wedge between the two.
For instance, with internal habit formation, the M RS also becomes a function of past
and future expected consumption. Intuitively, households become reluctant to sharply adjust
their consumption, which reduces their willingness to substitute over time. As a consequence,
consumption is less likely to fall signi…cantly in response to a positive investment shock.
Endogenous capital utilization, instead, acts as a shifter of the M P L, as …rst highlighted
by Greenwood, Hercowitz, and Hu¤man (1988). An improvement in the e¢ ciency of new
investment increases the utilization of existing capital, due to the drop in its relative value.
Higher capital utilization, in turn, implies an increase in the marginal product of labor,
shifting labor demand to the right. For a given labor supply schedule, this shift implies a
rise in hours and wages, as well as in consumption. Moreover, the increase in the marginal
product of labor with constant returns to scale implies that average productivity also rises.
Finally, monopolistic competition in goods and labor markets drives a wedge between the
M RS and the M P L. Sticky prices and wages make this wedge endogenous, so that equation
8 Rotemberg and Woodford (1995) make the point that endogenous markup variation is an additional
channel through which aggregate shocks might a¤ect ‡
uctuations, especially in employment. However, they
do not consider investment shocks in their analysis.
INVESTMENT SHOCKS AND BUSINESS CYCLES
19
5.1 becomes
(5.2)
! L M RS C ; L
+ +
= MPL L ;
where ! denotes the wedge. In our model, ! is the sum of two equilibrium markups, that of
price over marginal cost and that of real wages over the marginal rate of substitution. If this
markup is countercyclical (i.e. it falls when hours rise, as suggested for example by Rotemberg
and Woodford (1999) and Gali, Gertler, and Lopez-Salido (2007)), consumption and hours
can move together in response to an investment shock, without violating the equilibrium
condition 5.2.
More speci…cally, in our estimated model, a positive investment shock produces a drop in
the price markup, as we can see from the fact that the real marginal cost rises in …gure 4.
This fall in the markup induces a positive shift in labor demand, which ampli…es the shift
associated with changes in utilization. At the same time, the wage markup also falls, shifting
the labor supply schedule to the right. Unlike in the perfectly competitive case, though,
this shift in labor supply is consistent with an increase in hours at an unchanged level of
consumption.
In our economy, the endogeneity of markups is due to price and wage stickiness. However,
equation (5.2) suggests that any other friction resulting in countercyclical markups would
propagate investment shocks in a similar way.
In the rest of this section, we investigate the quantitative role of all these frictions in
turning investment shocks into the dominant source of ‡
uctuations. To this end, we study
the variance decomposition of several restricted versions of the baseline model, in which we
shut down one category of frictions at-a-time. We consider the following groups of frictions.
First, we estimate a model with no habit in consumption, which corresponds to h = 0. Second,
we …x capital utilization and eliminate investment adjustment costs by setting 1= = 0:0001
and S 00 = 0. Third, we consider models with (nearly) competitive labor and goods markets,
by calibrating
w
= 0:01,
w
= 0,
w
= 1:01 and
p
= 0:01,
p
= 0,
p
= 1:01. Finally,
we reduce our model all the way to its standard neoclassical core, by shutting down all the
frictions simultaneously.
The results of this exercise are reported in table 6. The table focuses on the contributions
of investment shocks to the volatility of output and hours at business cycle frequencies, since
INVESTMENT SHOCKS AND BUSINESS CYCLES
20
this is where the importance of these shocks is most evident. First, we observe that removing
any of the frictions reduces the contribution of investment shocks to ‡
uctuations. This is
as expected given our preceding discussion of the e¤ects of the frictions on the transmission
mechanism.
In terms of relative contributions, imperfect competition has the most signi…cant marginal
impact. In the perfectly competitive model, the contribution of investment shocks to ‡
uctuations in output and hours drops to 4 and 8 percent respectively. As apparent from the
case in which we shut down imperfect competition in goods and labor markets separately,
each of these modi…cations produces a roughly equal decline in the importance of investment
shocks. Endogenous utilization and adjustment costs come next. Their exclusion reduces the
contribution of investment shocks to ‡
uctuations in both hours and output by more than
half. The friction that plays the smallest role at the margin is time non-separability.
Finally, the last column in table 6 shows that the contribution of the investment shock
disappears entirely in the frictionless model. This result suggests that our estimation procedure is not unduly a¤ecting our …ndings on the role of this shock in business cycles. When
we restrict ourselves to the standard neoclassical model, we recover what we would expect
in light of the theoretical analysis of Barro and King (1984) and Greenwood, Hercowitz, and
Hu¤man (1988): investment shocks do not play any role in ‡
uctuations.9
Table 6 compares the contribution of investment shocks to business cycles across several
models. In the baseline, investment shocks are paramount, while in some of the restricted
versions they are irrelevant. Therefore, an important question is whether these restricted
models are consistent with the data. The answer is no, as illustrated in table 7, where we
report the log-marginal data density of all the speci…cations described above. The marginal
data density (or marginal likelihood) is the expected value of the likelihood function with
respect to the prior density and is the appropriate way of comparing models from a Bayesian
perspective. According to this comparison, the …t of the baseline model is far superior to
that of any of the alternatives, implying overwhelming posterior odds in its favor.10
9 In the estimated frictionless model, we …nd that the neutral technology and labor supply shocks explain
43 and 47 percent of the variance of output and 4 and 78 percent of that of hours at business cycle frequencies.
10 Del Negro and Schorfheide (2008) discuss reasons why posterior odds should be interpreted with some
care when priors are not adjusted as the model speci…cation is altered.
INVESTMENT SHOCKS AND BUSINESS CYCLES
21
6. A Comparison with Smets and Wouters (2007)
Our results on the role of investment shocks are at odds with those of Smets and Wouters
(2007, SW hereafter). In particular, SW recover a dominant role for the wage markup shock
at medium and long horizons. Moreover, their investment shock accounts for less than 25
percent of ‡
uctuations in GDP at any horizon. In this section, we document the sources of
this discrepancy.
We start by performing our variance decomposition at business cycle frequencies using
SW’ model and the parameter estimates reported in table 1 of their paper. We …nd that
s
the wage markup shock accounts for 11 and 14 percent of the business cycle variance of
output and hours respectively. For output, this share is substantially smaller than that
suggested by the forecast error variance decomposition at medium and long horizons reported
in …gure 1 of SW’ paper. For hours, the discrepancy between spectral and forecast error
s
variance decompositions is even larger.11 Therefore, we conclude that SW’ emphasis on
s
wage markup shocks is mainly due to the di¢ culty in isolating business cycle frequencies
using forecast error variance decompositions. Moreover, when we re-estimate SW’ model,
s
using their observables, but our longer sample from 1954QIII to 2004QIV, the shares of the
wage markup shock in the business cycle variance of output and hours decline to 5 and 7
percent respectively. These numbers are very close to our baseline (table 5).
However, in this case we also …nd a signi…cantly diminished role for the investment shock,
as we show in the …rst column of table 8. The results are almost identical if we use SW’
s
dataset to estimate our model (second column of table 8). This suggests that the minor
di¤erences between the two model speci…cations do not a¤ect the variance decomposition.
Therefore, the remaining discrepancy on the role of investment shocks must be due to the
di¤erences in the de…nitions of the observables.
Compared to us, SW exclude inventories from investment–
although not from output–
and
include purchases of consumer durables in consumption.12 The next two columns of table 8
analyze how the treatment of inventories and durables a¤ects the contribution of investment
shocks to the business cycle volatility of output and hours. In column three, we switch
durables back from consumption into investment, as in our baseline case, but leave inventories
out. In column four we do the opposite and include inventories into investment, but leave
11 Smets and Wouters (2007) do not report the forecast error variance decomposition for hours.
12 SW also use a di¤erent series for hours, but this does not have any material impact on the results.
INVESTMENT SHOCKS AND BUSINESS CYCLES
22
durables in consumption. In the …rst case, the contribution of the investment shock to output
and hours increases to 42 and 47 percent respectively. In the second case, those numbers are
35 and 44 percent. In the last column, we reproduce our baseline variance decomposition,
which attributes 53 and 61 percent of the variance of output and hours to the investment
shock. By comparing these numbers, we conclude that the discrepancy between our results
and SW’ is due almost in equal parts to the di¤erences in the treatment of inventories and
s
durables.
These …ndings suggest that research on the sources of business cycles would bene…t from
more explicit modeling of the behavior of durables and inventories. However, we do not think
they undermine the case for the importance of investment shocks made in this paper, for at
least two reasons. First, our treatment of the data is in line with most of the macroeconomic
literature (see for instance Cooley and Prescott (1995), Christiano, Eichenbaum, and Evans
(2005) or Del Negro, Schorfheide, Smets, and Wouters (2007)). Second, even when considering
SW’ dataset, two key results remain robust. First, the share of variance accounted for by
s
supply shocks–
neutral technology and wage markup shocks–
remains stable around 30 percent
for output and 20 percent for hours. Second, the share of variance accounted for by demand
shocks–
the investment shock and the intertemporal preference shock– also fairly stable
is
around 50 percent for output and 60 percent for hours. The only di¤erence is in the way
in which these shares are apportioned between the investment and intertemporal preference
shock. Not surprisingly, the inclusion of durables and inventories in investment tends to boost
the contribution of the investment shock, at the expense of the preference shock, since these
are two of the most cyclical components of GDP.
7. Investment Shocks and the Relative Price of Investment
In our empirical investigation, we assumed that the marginal e¢ ciency of investment,
t,
follows an exogenous stochastic process. Consequently, we treated the investment shock as
a latent variable in estimation, as in most of the empirical DSGE literature (e.g. Smets and
Wouters (2007) and Del Negro, Schorfheide, Smets, and Wouters (2007)). Another prominent
branch of the literature, however, builds on the observation that this same investment shock
should equal the price of consumption relative to investment in a version of our model with
a competitive investment sector (Greenwood, Hercowitz, and Krusell (1997), Greenwood,
Hercowitz, and Krusell (2000), Fisher (2006)). In this section, we confront this observation
INVESTMENT SHOCKS AND BUSINESS CYCLES
23
by considering a version of the model in which we can explicitly compare the estimated
investment shock and the measured relative price.
This comparison requires a few changes to our baseline framework. First, we must include
a trend in the investment shock process, since the relative price of consumption has been
steadily rising in the postwar period. In this respect, we follow Greenwood, Hercowitz, and
Krusell (2000) and assume that
t
is a trend-stationary process. Moreover, we allow for a
break in the trend in 1982:II, which is consistent with the recent acceleration in the rate
of increase in the relative price noted for example by Fisher (2006). We calibrate the slope
of this broken trend to match the average growth rate of the relative price of consumption
before and after 1982:II.13
In addition, we make a few small modi…cations to the baseline model, along the lines of
Altig, Christiano, Eichenbaum, and Linde (2005). For example, we assume that the cost of
adjusting investment depends on the quantity of investment installed, rather than on its value
in terms of consumption. Therefore, S (It =It
1)
becomes S ( t It ) =
t 1 It 1
, where It is
now the real value of investment in terms of consumption.14 Consistent with this de…nition,
we also de‡ all nominal variables for the estimation by the consumption de‡
ate
ator, on which
we also base our measure of in‡
ation.
The second column of table 8 reports the share of business cycle variance of output and
hours explained by the investment shock in this version of the model. These numbers are
somewhat lower than those in the baseline, but the investment shock remains the single most
important source of ‡
uctuations in both output and investment.15
Next, we compare the smoothed estimate of the investment shock to the relative price of
consumption in the data, both expressed in deviation from the same broken linear trend.
The two series exhibit a similar degree of autocorrelation, but our measure of the investment
shock is considerably more volatile than the relative price, with a standard deviation approximately four times as large. This excess volatility might be due, in part, to the di¢ culty of
measuring the price of investment and of durable consumption goods in a manner consistent
13 We construct this relative price using the chain-weighted de‡
ators for our components of consumption
(non-durables and services) and investment (durables and total private investment).
14 We make three additional small changes to the model, which ensure the existence of a balanced growth
path. We use the deterministic trend in the investment shock process to scale the …xed cost of production
and to index wages, while we scale the cost of capital utilization by the inverse of t itself.
15 We also experimented with a stochastic trend in
t . In that case, the shares of variance of output and
hours explained by the investment shock are even higher (third column of table 8), although the estimated
persistence of the growth rate of the investment shock is also very high.
INVESTMENT SHOCKS AND BUSINESS CYCLES
24
with theory (Gordon (1990), Cummins and Violante (2002)). Another possible interpretation of this …nding is that the smoothed investment shock hides unmodeled frictions in the
capital accumulation process, of the kind considered for example by Christiano, Motto, and
Rostagno (2007).
8. Robustness Analysis
In this section we investigate the robustness of our result to a number of alternative speci…cations of the model. The results of these robustness checks are summarized in table 9, in
which we report the share of the variance of output and hours explained by the investment
shock at business cycle frequencies.
8.1. Standard calibration of capital income share and labor supply elasticity ( =
0:3 and
= 1). Our baseline estimates of the share of capital income ( ) and of the Frisch
elasticity of labor supply (1= ) di¤er from the standard values used in the RBC literature.
To verify that our estimates of
and
do not a¤ect the results too much, we re-estimate
the model calibrating these two parameters at the more typical values of
= 0:3 and
= 1.
The forth column of table 9 shows that the contribution of investment shocks to the business
cycle ‡
uctuations of output and hours is now even larger than in the baseline model.
8.2. No ARMA shocks. Following Smets and Wouters (2007), the baseline model includes
an ARMA(1,1) speci…cation for the wage and price markup shocks. This assumption improves
its …t of the model, but to make sure that it does not drive our results, we also estimate a
version of the model with the more standard assumption that markup shocks are distributed
as an AR(1). As the …fth column in table 9 makes clear, this modi…cation leaves our results
almost unchanged.
8.3. Output growth in the policy rule. We also estimate a model in which the measure
of real activity included in the policy rule is output growth, rather than the output gap, since
both speci…cations are quite common in the literature. Once again, this modi…cation barely
a¤ects the quantitative results (column six in table 9).
8.4. Maximum likelihood. The last robustness check we conduct is with respect to the
priors on the model parameters. In our baseline exercise, we follow the recent literature on
Bayesian estimation of DSGE models and use the prior information reported in table 1. To
verify that the priors are not responsible for our main results, we re-estimate the model by
INVESTMENT SHOCKS AND BUSINESS CYCLES
25
maximum likelihood. Maximizing the likelihood is numerically much more challenging than
maximizing the posterior, since the use of weakly informative priors ameliorates the problems
related to the presence of ‡ areas of the likelihood function and of multiple local modes.
at
These di¢ culties notwithstanding, we were able to compute maximum likelihood estimates
for the model parameters.16 As illustrated in the last column of table 9, these estimates are
entirely consistent with the baseline results. In fact, the investment shock still accounts for
around 60% of the business cycle ‡
uctuations in output and hours.
9. Concluding Remarks
What is the source of business cycle ‡
uctuations? We revisited this fundamental question of
macroeconomics from the perspective of an estimated New Neoclassical Synthesis model. We
found that shocks to the marginal e¢ ciency of investment are the main drivers of movements
in hours, output and investment over the cycle. Imperfect competition with endogenous
markups is crucial for the transmission of these shocks. Neutral technology shocks also
retain a non negligible role in the ‡
uctuations of consumption and output and are mainly
responsible for their comovement. Finally, shocks to labor supply account for a large share of
the variance of hours at very low frequencies, but their contribution over the business cycle
is negligible.
One important quali…cation of these results is that the estimated volatility of the investment shock is much larger than the volatility of the price of investment relative to consumption measured in the data. In a two-sector representation of our model, in which the sector
producing capital goods is perfectly competitive, the two would be the same. There are
several possible reasons for why this is not the case in our set-up. First, measuring the price
of durable goods in a manner consistent with theory is notoriously problematic. Second, a
serious e¤ort at modeling a two-sector economy would probably include sticky prices also in
the capital goods sector. In such a model, we would expect investment prices to be smoother
than marginal costs. Third, the estimated investment shock might hide frictions in the capital accumulation process that we did not consider. Models that explicitly include these type
of frictions, such as that in Christiano, Motto, and Rostagno (2007), therefore represent a
16 More precisely, to maximize the likelihood we need to calibrate {, since the likelihood is not very
informative on this parameter and this creates convergence problems in the maximization routine. Therefore,
we calibrated { = 5, which is our prior mean. This value of { implies a low elasticity of capital utilization,
which makes the propagation of investment shocks if anything more problematic.
INVESTMENT SHOCKS AND BUSINESS CYCLES
26
promising avenue for future research. More generally, our results point to the investment
sector, and to its Euler equation in particular, as the keys to our understanding of business
cycles.
Appendix A. The Data
Our dataset spans a sample from 1954QIII to 2004QIV. All data are extracted from
the Haver Analytics database (series mnemonics in parenthesis).
Following Del Negro,
Schorfheide, Smets, and Wouters (2007), we construct real GDP by diving the nominal series
(GDP) by population (LF and LH) and the GDP De‡
ator (JGDP). Real series for consumption and investment are obtained in the same manner, although consumption corresponds
only to personal consumption expenditures of non-durables (CN) and services (CS), while
investment is the sum of personal consumption expenditures of durables (CD) and gross private domestic investment (I). Real wages correspond to nominal compensation per hour in
the non-farm business sector (LXNFC), divided by the GDP de‡
ator. We measure the labor
input by the log of hours of all persons in the non-farm business sector (HNFBN), divided
by population. The quarterly log di¤erence in the GDP de‡
ator is our measure of in‡
ation,
while for nominal interest rates we use the e¤ective Federal Funds rate. We do not demean
or detrend any series.
Appendix B. Normalization of the Shocks
As in Smets and Wouters (2007), we re-normalize some of the exogenous shocks by dividing
them by a constant term. For instance, one of our log-linearized equilibrium conditions is the
following Phillips curve:
^t =
where
(1
p
(1+
)(1
p
)
p
p
)
1+
Et ^ t+1 +
p
1
1+
^t
1
+ st + ^ p;t ,
^
p
, st is the model-implied real marginal cost and the “hat” denotes
log deviations from the non-stochastic steady state. The normalization consists of de…ning a
new exogenous variable, ^ p;t
^ p;t , and estimating the standard deviation of the innovation
to ^ p;t instead of ^ p;t . We do the same for the wage markup and the intertemporal preference
INVESTMENT SHOCKS AND BUSINESS CYCLES
27
shock, for which we use the following normalizations:
^
w;t
^
bt
0
= @
=
(1
1 + (1 +
(1
w ) (1
1
w)
) (1 + )
w
b ) (e
h b ) (e
e h + e2 + h2
w
1
A ^ w;t
h) ^
bt
These normalizations are chosen in such a way that these shocks enter the wage and consumption equations (respectively) with a unity coe¢ cient. In this way it is easier to choose
a reasonable prior for their standard deviation. Moreover, the normalization is a practical
way to impose correlated priors across coe¢ cients, which is desirable in some cases. For
instance, imposing a prior on the standard deviation of the innovation to ^ p;t corresponds
to imposing prior that allow for correlation between
and the standard deviation of the
innovations to ^ p;t . Often, these normalizations improve the convergence properties of the
MCMC algorithm.
References
Altig, D., L. J. Christiano, M. Eichenbaum, and J. Linde (2005): “Firm-Speci…c Capital, Nominal
Rigidities and the Business Cycle,” NBER Working Paper No. 11034.
An, S., and F. Schorfheide (2007): “Bayesian Analysis of DSGE Models,” Econometric Reviews, 24(2-4),
113–
172, forthcoming.
Barro, R. J., and R. G. King (1984): “Time-Separable Preference and Intertemporal-Substitution Models
of Business Cycles,” Quarterly Journal of Economics, 99(4), 817–
839.
Basu, S., J. Fernald, and M. Kimball (2007): “Are Technology Improvements Contractionary?,” American Economic Review, Forthcoming.
Bernanke, B. S., M. Gertler, and S. Gilchrist (1999): “The Financial Accelerator in a Quantitative
Business Cycle Framework,” in Handbook of Macroeconomics, ed. by J. B. Taylor, and M. Woodford. North
Holland, Amsterdam.
Calvo, G. (1983): “Staggered Prices in a Utility-Maximizing Framework,” Journal of Monetary Economics,
12(3), 383–
98.
Canova, F., D. Lopez-Salido, and C. Michelacci (2006): “On the Robust E¤ects of Technology Shocks
on Hours Worked and Output,” mimeo, Universitat Pompeu Fabra.
Chang, Y., and J. H. Hong (2006): “Do Technological Improvements in the Manufacturing Sector Raise
or Lower Employment?,” American Economic Review, 96(1), 352–
368.
Chari, V., P. J. Kehoe, and E. R. McGrattan (2008): “New Keynesian Models Are Not Yet Useful for
Policy Analysis,” Federal Reserve Bank of Minneapolis Working Paper 664.
INVESTMENT SHOCKS AND BUSINESS CYCLES
28
Christiano, L. J., M. Eichenbaum, and C. L. Evans (2005): “Nominal Rigidities and the Dynamic E¤ect
of a Shock to Monetary Policy,” The Journal of Political Economy, 113(1), 1–
45.
Christiano, L. J., M. Eichenbaum, and R. Vigfusson (2004): “What Happens After a Technology
Shock?,” mimeo, Northwestern University.
Christiano, L. J., R. Motto, and M. Rostagno (2007): “Financial Factors in Business Cycles,” mimeo,
Northwestern University.
Cochrane, J. H. (1994): “Shocks,” Carnegie-Rochester Conference Series on Public Policy, 41, 295–
364.
Cooley, T. F., and E. Prescott (1995): “Economic Growth and Business Cycles,”in Frontiers of Business
Cycle Research, ed. by T. F. Cooley, chap. 1, pp. 1– Princeton University Press, Princeton, NJ.
38.
Cummins, J. G., and G. L. Violante (2002): “Investment-Speci…c Technical Change in the US (1947-2000):
Measurement and Macroeconomic Consequences,” Review of Economic Dynamics, 5(2), 243–
284.
Del Negro, M., and F. Schorfheide (2008): “Forming Priors for DSGE Models (And How It A¤ects the
Assessment of Nominal Rigidities),” mimeo, Federal Reserve Bank of New York.
Del Negro, M., F. Schorfheide, F. Smets, and R. Wouters (2007): “On the Fit and Forecasting Performance of New Keynesian Models,” Journal of Business and Economic Statistics, 25(2), 123–
162, Forthcoming.
Erceg, C. J., D. W. Henderson, and A. T. Levin (2000): “Optimal Monetary Policy with Staggered
Wage and Price Contracts,” Journal of Monetary Economics, 46(2), 281–
313.
Fernald, J. (2007): “Trend Breaks, Long-Run Restrictions, and Contractionary Technology Improvements,”
Federal Reserve bank of San Francisco Working Paper Series, No. 2005-21.
Fisher, J. D. M. (1997): “Relative Prices, Complementarities, and Co-Movement Among Components of
Aggregate Expenditures,” Journal of Monetary Economics, 39(3), 449–
474.
(2006): “The Dynamic E¤ect of Neutral and Investment-Speci…c Technology Shocks,” Journal of
Political Economy, 114(3), 413–
451.
Francis, N. R., and V. A. Ramey (2006): “Measures of Hours Per Capita and their Implications for the
Technology-Hours Debate,” University of California, San Diego, mimeo.
Gali, J. (1999): “Technology, Employment, and the Business Cycle: Do Technology Shocks Explain Aggregate
Fluctuations?,” American Economic Review, 89(1), 249–
271.
Gali, J., M. Gertler, and D. Lopez-Salido (2007): “Markups, Gaps and the Welfare Costs of Business
Fluctuations,” Review of Economics and Statistics, 89(1), 44–
59.
Gali, J., and P. Rabanal (2004): “Technology Shocks and Aggregate Fluctuations: How Well Does the
RBC Model Fit Postwar U.S. Data?,” in NBER Macroeconomics Annual, ed. by M. Gertler, and K. Rogo¤.
Gertler, M., L. Sala, and A. Trigari (2007): “An Estimated Monetary DSGE Model with Unemployment
and Staggered Nominal Wage Bargaining,” mimeo, New York University.
Goodfriend, M., and R. G. King (1997): “The New Neoclassical Synthesis and the Role of Monetary
Policy,” NBER Macroeconomics Annual, 12, 231–
283.
Gordon, R. J. (1990): The Measurement of Durable Goods Prices. University of Chicago Press, Chicago, IL.
INVESTMENT SHOCKS AND BUSINESS CYCLES
29
Greenwood, J., Z. Hercowitz, and G. W. Huffman (1988): “Investment, Capacity Utilization, and the
Real Business Cycle,” American Economic Review, 78(3), 402–
417.
Greenwood, J., Z. Hercowitz, and P. Krusell (1997): “Long Run Implications of Investment-Speci…c
Technological Change,” American Economic Review, 87(3), 342–
362.
(2000): “The role of investment-speci…c technological change in the business cycle,” European Economic Review, 44(1), 91–
115.
Hall, R. E. (1997): “Macroeconomic Fluctuations and the Allocation of Time,”Journal of Labor Economics,
15(2), 223–
250.
(2008): “Sources and Mechanisms of Cyclical Fluctuations in the Labor Market,” mimeo, Stanford
University.
Justiniano, A., and G. E. Primiceri (2007): “The Time Varying Volatility of Macroeconomic Fluctuations,” American Economic Review, Forthcoming.
King, R. G., C. I. Plosser, J. H. Stock, and M. W. Watson (1991): “Stochastic Trends and Economic
Fluctuations,” American Economic Review, 81(4), 819–
840.
King, R. G., and S. T. Rebelo (1999): “Resuscitating Real Business Cycles,” in Handbook of Macroeconomics, ed. by J. B. Taylor, and M. Woodford, Amsterdam. North-Holland.
Kydland, F. E., and E. C. Prescott (1982): “Time to Build and Aggregate Fluctuations,”Econometrica,
50(6), 1345–
70.
Levin, A. T., A. Onatski, J. C. Williams, and N. Williams (2005): “Monetary Policy Under Uncertainty
in Micro-Founded Macroeconometric Models,” in NBER Macroeconomics Annual.
Lucca, D. O. (2005): “Resuscitating Time to Build,” mimeo, Board of Governors of the Federal Reserve
System.
Primiceri, G. E., E. Schaumburg, and A. Tambalotti (2005): “Intertemporal Disturbances,” mimeo,
Northwestern University.
Rotemberg, J. J., and M. Woodford (1995): “Dynamic General Equilibrium Models with Imperfectly
Competitive Product Markets,” in Frontiers of Business Cycle Research, ed. by T. F. Cooley, chap. 9, pp.
243–
293. Princeton University Press, Princeton, NJ.
(1999): “The Cyclical Behavior of Prices and Costs,” in Handbook of Macroeconomics, ed. by J. B.
Taylor, and M. Woodford, chap. 16, pp. 1051–
1135. Elsevier.
Shapiro, M. D., and M. Watson (1988): “Sources of Business Cycle Fluctuations,” in NBER Macroeconomics Annual, pp. 111–
148. MIT Press, Cambridge, Massachusetts.
Sims, C. A. (1980): “Macroeconomics and Reality,” Econometrica, 48(1), 1–
48.
Smets, F., and R. Wouters (2007): “Shocks and Frictions in US Business Cycles: A Bayesian Approach,”
American Economic Review, 97(3), 586–
606, forthcoming.
Stock, J. H., and M. W. Watson (1999): Business Cycle Fluctuations in US Macroeconomic Time Serieschap. 1, pp. 3– Elsevier.
64.
Uhlig, H. (2003): “Do Technology Shocks Lead to a Fall in Total Hours Worked?,” mimeo, University of
Chicago.
INVESTMENT SHOCKS AND BUSINESS CYCLES
30
Woodford, M. (2003): Interest and Prices: Foundations of a Theory of Monetary Policy. Princeton University Press, Princeton, NJ.
Federal Reserve Bank of Chicago
E-mail address: ajustiniano@frbchi.org
Northwestern University, NBER and CEPR
E-mail address: g-primiceri@northwestern.edu
Federal Reserve Bank of New York
E-mail address: andrea.tambalotti@ny.frb.org
Table 1: Prior densities and posterior estimates for baseline model with all frictions
Posterior
Prior
2
Prior
Density 1
Mean
Std
Median
Capital Share
N
0.30
0.05
0.17
0.006 [ 0.16
ιp
Price indexation
B
0.50
0.15
0.24
0.073 [ 0.14 , 0.39 ]
ιw
Wage indexation
B
0.50
0.15
0.11
0.029 [ 0.06 , 0.16 ]
γ
SS technology growth rate
N
0.50
0.03
0.48
0.023 [ 0.44 , 0.52 ]
h
Consumption habit
B
0.50
0.10
0.79
0.023 [ 0.76 , 0.83 ]
λp
SS mark-up goods prices
N
0.15
0.05
0.25
0.032 [ 0.19 , 0.30 ]
λw
SS mark-up wages
N
0.15
0.05
0.15
0.033 [ 0.07 , 0.19 ]
logL ss
SS leisure
N
396.83
0.50
397.16
0.480 [ 396.4 , 398.0 ]
100(π-1)
SS quarterly inflation
N
0.50
0.10
0.71
0.078 [ 0.56 , 0.82 ]
100( β-1- 1) Discount factor
G
0.25
0.10
0.14
0.045 [ 0.07
ν
Inverse Frisch elasticity
G
2.00
0.75
3.59
0.674 [ 2.63 , 4.84 ]
ξp
Calvo prices
B
0.66
0.10
0.84
0.016 [ 0.82 , 0.87 ]
ξw
Calvo wages
B
0.66
0.10
0.71
0.019 [ 0.68 , 0.74 ]
χ
Elasticity capital
utilization costs
G
5.00
1.00
5.80
1.001 [ 4.38 , 7.58 ]
S''
Investment adjustment
costs
G
4.00
1.00
2.95
0.301 [ 2.43 , 3.39 ]
Φp
Taylor rule inflation
N
1.70
0.30
1.97
0.144 [ 1.71 , 2.20 ]
Φy
Taylor rule output
N
0.13
0.05
0.05
0.012 [ 0.03 , 0.07 ]
Φ dy
Taylor rule output growth
N
0.13
0.05
0.23
0.016 [ 0.21
0.26 ]
ρR
Taylor rule smoothing
B
0.60
0.20
0.81
0.016 [ 0.79
0.84 ]
Coefficient
Description
α
( Continued on the next page )
Std
[
5
,
95
]
0.18 ]
0.22 ]
Table 1: Prior densities and posterior estimates for baseline model with all frictions
Posterior
Prior
2
Prior
Density 1
Mean
Std
Median
Monetary Policy
B
0.40
0.20
0.16
0.048 [ 0.07
0.22 ]
ρz
Neutral Technology
growth
B
0.40
0.20
0.23
0.043 [ 0.15
0.30 ]
ρg
Government spending
B
0.60
0.20
0.99
0.001 [ 0.99
0.99 ]
ρμ
Investment
B
0.60
0.20
0.73
0.031 [ 0.68
0.78 ]
ρp
Price mark-up
B
0.60
0.20
0.94
0.017 [ 0.91
0.96 ]
ρw
Wage mark-up
B
0.60
0.20
0.98
0.003 [ 0.98
0.99 ]
ρb
Intertemporal preference
B
0.60
0.20
0.65
0.027 [ 0.60
0.68 ]
θp
Price mark-up MA
B
0.50
0.20
0.78
0.010 [ 0.76
0.79 ]
θw
Wage mark-up MA
B
0.50
0.20
0.95
0.002 [ 0.94
0.95 ]
σ mp
Monetary policy
I
0.10
1.00
0.22
0.012 [ 0.21
0.25 ]
σz
Neutral Technology
growth
I
0.50
1.00
0.89
0.049 [ 0.81
0.98 ]
σg
Government spending
I
0.50
1.00
0.35
0.017 [ 0.32
0.38 ]
σμ
Investment
I
0.50
1.00
6.01
0.505 [ 5.02
6.79 ]
σp
Price mark-up
I
0.10
1.00
0.14
0.002 [ 0.14
0.15 ]
σw
Wage mark-up
I
0.10
1.00
0.24
0.003 [ 0.23
0.24 ]
σb
Intertemporal preference
I
0.10
1.00
0.04
0.001 [ 0.04
0.04 ]
Coefficient
Description
ρ mp
(log) Likelihood at median
Std
[
5
95
,
-1094.7
Calibrated coefficients: depreciation rate (δ) is 0.025, g implies a SS government share of 0.22
Relative to the text, the standard deviations of the innovations are scaled by 100 for the estimation, which is reflected in the prior and
posterior estimates.
1
2
N stands for Normal, B Beta, G Gamma and I Inverted-Gamma1 distribution
Median and posterior percentiles from 2 chains of 120,000 draws generated using a Random walk Metropolis algorithm, where we
discard the initial 20,000 and retain one in every 20 subsequent draws. Additional longer chains produced almost identical posterior
moments.
]
Table 2: Prior variance decomposition for observable variables in the baseline model
Medians and [5,95] prior percentiles
Series \ Shock
Policy
Neutral
Government
Investment
Output growth
0.01
0.26
0.23
0.00
0.00
0.01
0.08
[0.00,0.33]
[0.02,0.88]
[0.02,0.85]
[0.00,0.04]
[0.00,0.14]
[0.00,0.39]
[0.00,0.74]
0.01
0.31
0.00
0.00
0.00
0.00
0.42
[0.00,0.34]
[0.01,0.93]
[0.00,0.11]
[0.00,0.03]
[0.00,0.09]
[0.00,0.27]
[0.02,0.98]
0.01
0.38
0.00
0.03
0.00
0.01
0.04
[0.00,0.45]
[0.01,0.95]
[0.00,0.13]
[0.00,0.43]
[0.00,0.25]
[0.00,0.69]
[0.00,0.93]
0.02
0.17
0.07
0.01
0.00
0.04
0.05
[0.00,0.54]
[0.00,0.90]
[0.00,0.68]
[0.00,0.13]
[0.00,0.29]
[0.00,0.92]
[0.00,0.81]
0.00
0.73
0.00
0.00
0.04
0.09
0.00
[0.00,0.03]
[0.10,0.99]
[0.00,0.03]
[0.00,0.01]
[0.00,0.50]
[0.01,0.71]
[0.00,0.17]
0.01
0.11
0.01
0.00
0.08
0.08
0.03
[0.00,0.66]
[0.00,0.86]
[0.00,0.19]
[0.00,0.08]
[0.00,0.79]
[0.00,0.95]
[0.00,0.81]
0.02
0.15
0.02
0.00
0.02
0.03
0.11
[0.00,0.43]
[0.00,0.92]
[0.00,0.34]
[0.00,0.14]
[0.00,0.50]
[0.00,0.88]
[0.00,0.94]
Consumption growth
Investment growth
Hours
Wage growth
Inflation
Interest Rates
Price mark-up Wage mark-up
Preference
Notice that median shares need not add up to one. This is particularty true with the a-priori (as opposed to posterior) variance decompositions, due to the skeweness
induced by the dispersed prior distribution for the standard deviation of the shocks. Mean shares add up to one, and for the case of the investment shocks do not exceed
3 percent for output and hours.
Table 3: Standard deviations and relative standard deviations in
the data and in the baseline model with all frictions
1
Relative standard deviation 2
Standard deviation
Baseline Model
Series
Data
Median
Output growth
0.94
Consumption growth
[
Baseline Model
]
Data
Median
1.14
[ 1.00 , 1.31 ]
1.00
1.00
0.51
0.72
[ 0.62 , 0.82 ]
0.54
0.63
[ 0.53 , 0.74 ]
Investment growth
3.59
4.59
[ 3.95 , 5.36 ]
3.83
4.03
[ 3.61 , 4.50 ]
Hours
4.11
4.47
[ 3.09 , 6.75 ]
4.39
3.91
[ 2.79 , 5.81 ]
Wage growth
0.55
0.66
[ 0.59 , 0.75 ]
0.59
0.58
[ 0.50 , 0.67 ]
Inflation
0.60
0.49
[ 0.39 , 0.63 ]
0.64
0.43
[ 0.34 , 0.56 ]
Interest Rates
0.84
0.66
[ 0.52 , 0.83 ]
0.90
0.58
[ 0.45 , 0.74 ]
5
,
95
1
[
5
, 95 ]
For each parameter draw, we generate 1000 samples of the observable series implied by the model with same length as our
dataset (202 observations) after discarding 50 initial observations. For the relative standard deviations, for each replication and
parameter draw we take the ratio of the standard deviation of each series to that of output. Table reports median and 5th and 95th
percentile together with the corresponding moments in the data.
2
Standard deviation relative to the standard deviation of output growth
Table 4: Posterior variance decomposition for observable variables in the baseline model
Medians and [5,95] posterior percentiles
Series \ Shock
Policy
Neutral
Government
Investment
Output growth
0.04
0.20
0.07
0.51
0.04
0.05
0.09
[ 0.03, 0.06]
[ 0.15, 0.25]
[ 0.06, 0.08]
[ 0.45, 0.57]
[ 0.03, 0.05]
[ 0.03, 0.07]
[ 0.07, 0.11]
0.02
0.26
0.02
0.07
0.01
0.09
0.53
[ 0.01, 0.03]
[ 0.21, 0.32]
[ 0.02, 0.03]
[ 0.04, 0.11]
[ 0.00, 0.01]
[ 0.06, 0.13]
[ 0.46, 0.60]
0.03
0.05
0.00
0.87
0.03
0.01
0.01
[ 0.02, 0.04]
[ 0.04, 0.07]
[ 0.00, 0.00]
[ 0.84, 0.89]
[ 0.02, 0.04]
[ 0.01, 0.01]
[ 0.01, 0.02]
0.02
0.03
0.02
0.20
0.05
0.65
0.02
[ 0.02, 0.04]
[ 0.02, 0.04]
[ 0.01, 0.03]
[ 0.12, 0.30]
[ 0.03, 0.07]
[ 0.52, 0.77]
[ 0.01, 0.03]
0.00
0.29
0.00
0.03
0.22
0.46
0.00
[ 0.00, 0.00]
[ 0.23, 0.34]
[ 0.00, 0.00]
[ 0.02, 0.04]
[ 0.18, 0.27]
[ 0.42, 0.50]
[ 0.00, 0.00]
0.03
0.07
0.00
0.06
0.24
0.56
0.02
[ 0.02, 0.06]
[ 0.05, 0.11]
[ 0.00, 0.00]
[ 0.03, 0.11]
[ 0.17, 0.32]
[ 0.44, 0.68]
[ 0.01, 0.03]
0.10
0.05
0.01
0.45
0.02
0.24
0.11
[ 0.08, 0.14]
[ 0.04, 0.08]
[ 0.01, 0.01]
[ 0.34, 0.57]
[ 0.02, 0.04]
[ 0.13, 0.37]
[ 0.08, 0.15]
Consumption growth
Investment growth
Hours
Wage growth
Inflation
Interest Rates
Notice that median shares need not add up to one, although mean shares do.
Price mark-up Wage mark-up
Preference
Table 5: Variance decomposition at business cycle frequencies1 in the baseline
model with all frictions
Medians and [5,95] posterior percentiles
Output
Policy
Neutral
Government
Investment
0.05
0.24
0.02
0.53
0.05
0.04
0.07
[ 0.04, 0.07]
Series \ Shock
Price mark-up Wage mark-up
Preference
[ 0.18, 0.30]
[ 0.01, 0.02]
[ 0.45, 0.61]
[ 0.03, 0.07]
[ 0.03, 0.06]
[ 0.05, 0.09]
0.27
0.02
0.08
0.01
0.08
0.51
[ 0.21, 0.33]
[ 0.02, 0.03]
[ 0.05, 0.14]
[ 0.00, 0.01]
[ 0.05, 0.12]
[ 0.42, 0.59]
0.03
0.06
0.00
0.85
0.04
0.01
0.01
[ 0.02, 0.04]
Investment
0.02
[ 0.01, 0.03]
Consumption
[ 0.04, 0.09]
[ 0.00, 0.00]
[ 0.81, 0.89]
[ 0.02, 0.05]
[ 0.01, 0.01]
[ 0.01, 0.02]
0.61
0.06
0.06
0.08
[ 0.54, 0.67]
[ 0.04, 0.08]
[ 0.03, 0.08]
[ 0.06, 0.11]
0.00
0.39
0.00
0.04
0.31
0.25
0.00
[ 0.30, 0.47]
[ 0.00, 0.00]
[ 0.02, 0.07]
[ 0.24, 0.38]
[ 0.21, 0.31]
[ 0.00, 0.01]
0.03
0.14
0.00
0.07
0.40
0.31
0.02
[ 0.10, 0.19]
[ 0.00, 0.00]
[ 0.04, 0.13]
[ 0.32, 0.49]
[ 0.25, 0.38]
[ 0.01, 0.03]
0.18
0.09
0.01
0.48
0.04
0.04
0.15
[ 0.14, 0.23]
Interest Rates
0.02
[ 0.02, 0.03]
[ 0.02, 0.05]
Inflation
0.10
[ 0.08, 0.13]
[ 0.00, 0.01]
Wages
0.06
[ 0.05, 0.09]
Hours
[ 0.07, 0.12]
[ 0.00, 0.01]
[ 0.41, 0.56]
[ 0.03, 0.06]
[ 0.03, 0.06]
[ 0.11, 0.19]
Since reporting median shares, these need not add up to one, although mean shares do.
1
Decomposition of the variance corresponding to periodic components with cycles of between 6 and 32 quarters, obtained using the spectrum of the
DSGE model and an inverse first difference filter for output, consumption, investment and wages to obtain the levels. The spectral density is computed
from the state space representation of the model and 500 bins for frequencies covering that range of periodicities. Results are identical to those that
would result from repeatedly simulating the observables, obtaining the levels and then applying a Band-Pass filter. Variance shares for periods of 2 to 32
quarters obtained with the spectrum implied by the DSGE, or by HP filtering the model observables (transformed to levels where appropriate) deliver a
very similar decomposition.
Table 6: Variance share for output and hours at business cycle frequencies1 explained by investment shocks for
alternative specifications without some frictions
Baseline
No habits 2
No investment
costs and
variable capital
utilization 3
Perfectly
competitive
goods and labor
markets 4
Perfectly
competitive
goods markets5
Perfectly
competitive
labor market 6
Frictionless
model 7
Output
0.53
0.38
0.23
0.04
0.30
0.31
0.02
Hours
0.61
0.50
0.30
0.08
0.50
0.41
0.03
Series
1
Share of the variance of output (level) and hours, corresponding to periodic components of cycles between 6 and 32 quarters explained by investment shocks alone.
Obtained using the spectrum from the state-space representation of the DSGE. Variance decompositions are performed at the mode of each specification.
2
h calibrated at 0.01
3
S'' calibrated at 0.01, 1/χ calibrated at 0.001
4
λ w, ξ w, ι w, λ p , ξ p and ι p calibrated at 0.01
5
λ w, ξ w and ι w calibrated at 0.01
6
λ p, ξ p and ι p calibrated at 0.01
7
combines the calibration for all specifications above, except baseline
Table 7: Log-Marginal Data Densities for baseline and
alternative specifications without some frictions
Specification
Log Marginal 1
Baseline
-1215.10
No habits
-1316.75
No investment costs and variable capital
utilization
-1298.04
Perfectly competitive goods and labor
markets
-1466.52
Perfectly competitive goods markets
-1433.42
Perfectly competitive labor market
-1283.19
Frictionless model
1521 88
-1521.88
1
Except for the baseline, the log marginal data density is computed using
the Metropolis-Laplace approximation at the posterior mode. The
specification favored by the data attains the highest marginal density.
ifi ti f
d b th d t tt i th hi h t
i l d it
Full set of parameter estimates is available from the authors upon request
Table 8: Variance share of output and hours at business cycle frequencies1 explained
by investment shocks using alternative models and datasets
Model
Smets and
Wouters
Ours
Investment
includes
inventories but
not consumer
durables
Baseline:
investment
includes
inventories and
consumer
durables
Smets and
Wouters
Smets and
Wouters
Investment
includes
consumer
durables but not
inventories
Output
0.23
0.18
0.42
0.35
0.53
Hours
0.26
0.21
0.47
0.44
0.61
Dataset
Series
1
Share of the variance of output (level) and hours, corresponding to periodic components of cycles between 6 and 32 quarters
explained by investment shocks alone. Obtained using the spectrum from the state-space representation of the DSGE. Variance
decompositions are performed at the mode of each specification.
Table 9: Robustness check for the variance share of output and hours at business cycle
1
frequencies explained by investment shocks
Baseline
Trend
stationary
investment
shock 2
Stochastic trend
investment
shock 3
v = 1 and
α = 0.3
Output
0.53
0.40
0.56
Hours
0.61
0.45
0.70
No MA
components 4
Taylor rule
with output
growth 5
MLE 6
0.66
0.52
0.49
0.60
0.77
0.56
0.54
0.64
Series
1
Share of the variance of output (level) and hours, corresponding to periodic components of cycles between 6 and 32 quarters explained by
investment shocks alone. Obtained using the spectrum from the state-space representation of the DSGE. Variance decompositions are
performed at the mode of each specification.
2
Model with broken linear trend in investment shocks (break occurs in 1982q2)
3
Model with stochastic trend in investment shocks
4
Moving average component for price and wage mark-up shocks calibrated to zero.
5
Taylor rule responds to observable output growth instead of the output gap.
6
Baseline specification estimated by maximum likelihood.
Fig 1: Autocorrelation for baseline specification, dsge median (dark), dsge 5-95 (dotted) & data (grey)
dYt,dYt-k
dYt,dCt-k
dYt,dIt-k
1
0.2
0.8
0.4
0.5
0.6
0.2
0
0
0
2
4
dCt,dYt-k
2
4
0
dCt,dCt-k
0.5
0
2
-0.2
4
0
dIt,dYt-k
2
4
0
dIt,dCt-k
2
4
0
-0.2
0
2
4
0
Ht,dYt-k
2
4
0
Ht,dCt-k
2
0.4
0.2
0
0
2
4
0
dWt,dYt-k
2
4
4
2
4
0
dPt,dCt-k
4
0
nomRt,dYt-k
2
4
nomRt,dCt-k
2
-0.2
2
4
0
-0.2
0
2
4
2
2
4
0
2
0
4
2
4
4
4
0
2
4
0
dPt,dWt-k
2
4
4
0.6
0.4
0.2
0
0
2
4
0
nomRt,dWt-k
2
4
0
nomRt,dPt-k
2
4
nomRt,nomRt-k
1
0.6
0.4
-0.2
4
2
dPt,nomRt-k
0.5
0
2
0
dPt,dPt-k
0.2
0
4
1
-0.2
-0.4
4
2
0.1
0
-0.1
-0.2
-0.3
0
2
4
dWt,nomRt-k
-0.4
4
0.2
0
0
dWt,dPt-k
-0.2
2
2
Ht,nomRt-k
0
0
0
0.6
0.4
0.2
0
-0.2
-0.4
dWt,dWt-k
0
2
4
-0.4
2
Ht,dPt-k
4
2
0
0
0.5
0
0
dIt,nomRt-k
0.2
0
-0.2
-0.4
-0.6
nomRt,Ht-k
0
4
-0.2
Ht,dWt-k
0.6
0.4
0.2
0
-0.2
0.2
0
0
4
1
nomRt,dIt-k
0.2
-0.2
0
4
0.4
0.2
0
2
0.2
0
-0.2
-0.4
0
2
0
-0.1
-0.2
-0.3
dPt,Ht-k
-0.2
0
dIt,dPt-k
0.2
4
0
-0.4
2
4
0.4
dPt,dIt-k
-0.2
0
2
0.2
0
2
dIt,dWt-k
0.3
0.2
0.1
0
-0.1
0
0
dPt,dYt-k
0.1
0
-0.1
-0.2
-0.3
0
dWt,Ht-k
0.2
0
2
4
0
dWt,dIt-k
0.2
0
4
0.4
0.4
0.2
2
dCt,nomRt-k
0
0.2
0
4
-0.2
0
dWt,dCt-k
0.4
2
2
0.2
-0.4
0.8
0
0
dCt,dPt-k
0
Ht,Ht-k
0.3
0.2
0.1
0
4
-0.2
1
0.2
2
0.4
Ht,dIt-k
0.4
-0.4
0
0
0
4
4
0.2
0.1
0
-0.1
-0.2
-0.3
0.5
0
2
dCt,dWt-k
dIt,Ht-k
0.2
-0.2
-0.4
0
0.4
dIt,dIt-k
1
0.8
0.6
0.4
0.2
0
4
dCt,Ht-k
0
0
0
2
0.3
0.2
0.1
0
-0.1
0.2
0.4
0
-0.3
0
4
-0.2
0
dCt,dIt-k
1
0.2
2
dYt,nomRt-k
-0.1
0.2
-0.2
0
0
dYt,dPt-k
0.4
0
0.4
0.2
dYt,dWt-k
dYt,Ht-k
0.5
0.2
0
2
4
0
2
4
0
2
4
legend: dY=output growth, dC=consumption growth, dI=investment growth, H=hours, dW=wages growth, dP=inflation, nomR=nominal interest rate
Figure 2: Year−to−year output growth, actual data and
counterfactual explained by investment shocks
8
6
4
2
0
−2
−4
Only investment shocks
Data
−6
1955
1960
1965
1970
1975
1980
1985
1990
1995
2000
2005
Figure 3: Variance share of Hours explained by
wage mark-up shocks at all frequencies
0.9
0.8
0.7
variance share
0.6
0.5
0.4
0.3
0.2
0.1
0.5
1
1.5
frequency 2
2.5
3
Computed at the median of the paremeter estimates.
Vertical dashed lines mark the frequency band associated with business cycles of 6 to 32 quarters.
Figure 4: Impulse responses to an investment shock
output
consumption
1.4
1.2
0.4
1
0.2
0.8
0.6
0
0.4
0
5
10
15
0
5
investment
10
15
10
15
hours
1
6
4
0.5
2
0
0
0
5
10
15
0
5
wages
inflation
0.3
0.06
0.2
0.04
0.02
0.1
0
0
5
10
15
0
interest rate
5
10
15
marginal cost
0.2
0.2
0.15
0.15
0.1
0.1
0.05
0.05
0
0
5
10
15
0
5
10
15
labor productivity
0.4
0.3
Median (solid) and 5-95 posterior bands (dashed)
0.2
0.1
0
5
10
15
Figure 5: Impulse responses to a wage mark-up shock
output
consumption
-0.2
-0.2
-0.4
-0.4
-0.6
-0.6
-0.8
-0.8
-1
0
5
10
15
0
5
investment
10
15
10
15
hours
0
-0.2
-0.5
-0.4
-1
-0.6
-1.5
-0.8
0
5
10
15
0
5
wages
inflation
0.15
0.4
0.3
0.1
0.2
0.05
0.1
0
5
10
15
0
interest rate
5
10
15
marginal cost
0.08
0.4
0.3
0.06
0.2
0.04
0.1
0
5
10
15
0
5
10
15
labor productivity
0
Median (solid) and 5-95 posterior bands (dashed)
-0.05
-0.1
0
5
10
15
Figure 6: Impulse responses to a neutral technology shock
output
consumption
1.4
1.2
1
1
0.8
0.8
0.6
0.6
0.4
0.4
0
5
10
15
0.2
0
5
investment
10
15
10
15
hours
2.5
0.2
2
0
1.5
−0.2
1
−0.4
0
5
10
15
0
5
wages
inflation
1.2
0
1
−0.02
0.8
−0.04
0.6
−0.06
0.4
−0.08
0.2
0
5
10
15
0
interest rate
5
10
15
marginal cost
0.02
0
0
−0.2
−0.02
−0.04
−0.4
−0.06
−0.6
−0.08
0
5
10
15
0
5
10
15
labor productivity
1.2
1
Median (solid) and 5−95 posterior bands (dashed)
0.8
0
5
10
15
Working Paper Series
A series of research studies on regional economic issues relating to the Seventh Federal
Reserve District, and on financial and economic topics.
Firm-Specific Capital, Nominal Rigidities and the Business Cycle
David Altig, Lawrence J. Christiano, Martin Eichenbaum and Jesper Linde
WP-05-01
Do Returns to Schooling Differ by Race and Ethnicity?
Lisa Barrow and Cecilia Elena Rouse
WP-05-02
Derivatives and Systemic Risk: Netting, Collateral, and Closeout
Robert R. Bliss and George G. Kaufman
WP-05-03
Risk Overhang and Loan Portfolio Decisions
Robert DeYoung, Anne Gron and Andrew Winton
WP-05-04
Characterizations in a random record model with a non-identically distributed initial record
Gadi Barlevy and H. N. Nagaraja
WP-05-05
Price discovery in a market under stress: the U.S. Treasury market in fall 1998
Craig H. Furfine and Eli M. Remolona
WP-05-06
Politics and Efficiency of Separating Capital and Ordinary Government Budgets
Marco Bassetto with Thomas J. Sargent
WP-05-07
Rigid Prices: Evidence from U.S. Scanner Data
Jeffrey R. Campbell and Benjamin Eden
WP-05-08
Entrepreneurship, Frictions, and Wealth
Marco Cagetti and Mariacristina De Nardi
WP-05-09
Wealth inequality: data and models
Marco Cagetti and Mariacristina De Nardi
WP-05-10
What Determines Bilateral Trade Flows?
Marianne Baxter and Michael A. Kouparitsas
WP-05-11
Intergenerational Economic Mobility in the U.S., 1940 to 2000
Daniel Aaronson and Bhashkar Mazumder
WP-05-12
Differential Mortality, Uncertain Medical Expenses, and the Saving of Elderly Singles
Mariacristina De Nardi, Eric French, and John Bailey Jones
WP-05-13
Fixed Term Employment Contracts in an Equilibrium Search Model
Fernando Alvarez and Marcelo Veracierto
WP-05-14
1
Working Paper Series (continued)
Causality, Causality, Causality: The View of Education Inputs and Outputs from Economics
Lisa Barrow and Cecilia Elena Rouse
WP-05-15
Competition in Large Markets
Jeffrey R. Campbell
WP-05-16
Why Do Firms Go Public? Evidence from the Banking Industry
Richard J. Rosen, Scott B. Smart and Chad J. Zutter
WP-05-17
Clustering of Auto Supplier Plants in the U.S.: GMM Spatial Logit for Large Samples
Thomas Klier and Daniel P. McMillen
WP-05-18
Why are Immigrants’ Incarceration Rates So Low?
Evidence on Selective Immigration, Deterrence, and Deportation
Kristin F. Butcher and Anne Morrison Piehl
WP-05-19
Constructing the Chicago Fed Income Based Economic Index – Consumer Price Index:
Inflation Experiences by Demographic Group: 1983-2005
Leslie McGranahan and Anna Paulson
WP-05-20
Universal Access, Cost Recovery, and Payment Services
Sujit Chakravorti, Jeffery W. Gunther, and Robert R. Moore
WP-05-21
Supplier Switching and Outsourcing
Yukako Ono and Victor Stango
WP-05-22
Do Enclaves Matter in Immigrants’ Self-Employment Decision?
Maude Toussaint-Comeau
WP-05-23
The Changing Pattern of Wage Growth for Low Skilled Workers
Eric French, Bhashkar Mazumder and Christopher Taber
WP-05-24
U.S. Corporate and Bank Insolvency Regimes: An Economic Comparison and Evaluation
Robert R. Bliss and George G. Kaufman
WP-06-01
Redistribution, Taxes, and the Median Voter
Marco Bassetto and Jess Benhabib
WP-06-02
Identification of Search Models with Initial Condition Problems
Gadi Barlevy and H. N. Nagaraja
WP-06-03
Tax Riots
Marco Bassetto and Christopher Phelan
WP-06-04
The Tradeoff between Mortgage Prepayments and Tax-Deferred Retirement Savings
Gene Amromin, Jennifer Huang,and Clemens Sialm
WP-06-05
2
Working Paper Series (continued)
Why are safeguards needed in a trade agreement?
Meredith A. Crowley
WP-06-06
Taxation, Entrepreneurship, and Wealth
Marco Cagetti and Mariacristina De Nardi
WP-06-07
A New Social Compact: How University Engagement Can Fuel Innovation
Laura Melle, Larry Isaak, and Richard Mattoon
WP-06-08
Mergers and Risk
Craig H. Furfine and Richard J. Rosen
WP-06-09
Two Flaws in Business Cycle Accounting
Lawrence J. Christiano and Joshua M. Davis
WP-06-10
Do Consumers Choose the Right Credit Contracts?
Sumit Agarwal, Souphala Chomsisengphet, Chunlin Liu, and Nicholas S. Souleles
WP-06-11
Chronicles of a Deflation Unforetold
François R. Velde
WP-06-12
Female Offenders Use of Social Welfare Programs Before and After Jail and Prison:
Does Prison Cause Welfare Dependency?
Kristin F. Butcher and Robert J. LaLonde
Eat or Be Eaten: A Theory of Mergers and Firm Size
Gary Gorton, Matthias Kahl, and Richard Rosen
Do Bonds Span Volatility Risk in the U.S. Treasury Market?
A Specification Test for Affine Term Structure Models
Torben G. Andersen and Luca Benzoni
WP-06-13
WP-06-14
WP-06-15
Transforming Payment Choices by Doubling Fees on the Illinois Tollway
Gene Amromin, Carrie Jankowski, and Richard D. Porter
WP-06-16
How Did the 2003 Dividend Tax Cut Affect Stock Prices?
Gene Amromin, Paul Harrison, and Steven Sharpe
WP-06-17
Will Writing and Bequest Motives: Early 20th Century Irish Evidence
Leslie McGranahan
WP-06-18
How Professional Forecasters View Shocks to GDP
Spencer D. Krane
WP-06-19
Evolving Agglomeration in the U.S. auto supplier industry
Thomas Klier and Daniel P. McMillen
WP-06-20
3
Working Paper Series (continued)
Mortality, Mass-Layoffs, and Career Outcomes: An Analysis using Administrative Data
Daniel Sullivan and Till von Wachter
The Agreement on Subsidies and Countervailing Measures:
Tying One’s Hand through the WTO.
Meredith A. Crowley
WP-06-21
WP-06-22
How Did Schooling Laws Improve Long-Term Health and Lower Mortality?
Bhashkar Mazumder
WP-06-23
Manufacturing Plants’ Use of Temporary Workers: An Analysis Using Census Micro Data
Yukako Ono and Daniel Sullivan
WP-06-24
What Can We Learn about Financial Access from U.S. Immigrants?
Una Okonkwo Osili and Anna Paulson
WP-06-25
Bank Imputed Interest Rates: Unbiased Estimates of Offered Rates?
Evren Ors and Tara Rice
WP-06-26
Welfare Implications of the Transition to High Household Debt
Jeffrey R. Campbell and Zvi Hercowitz
WP-06-27
Last-In First-Out Oligopoly Dynamics
Jaap H. Abbring and Jeffrey R. Campbell
WP-06-28
Oligopoly Dynamics with Barriers to Entry
Jaap H. Abbring and Jeffrey R. Campbell
WP-06-29
Risk Taking and the Quality of Informal Insurance: Gambling and Remittances in Thailand
Douglas L. Miller and Anna L. Paulson
WP-07-01
Fast Micro and Slow Macro: Can Aggregation Explain the Persistence of Inflation?
Filippo Altissimo, Benoît Mojon, and Paolo Zaffaroni
WP-07-02
Assessing a Decade of Interstate Bank Branching
Christian Johnson and Tara Rice
WP-07-03
Debit Card and Cash Usage: A Cross-Country Analysis
Gene Amromin and Sujit Chakravorti
WP-07-04
The Age of Reason: Financial Decisions Over the Lifecycle
Sumit Agarwal, John C. Driscoll, Xavier Gabaix, and David Laibson
WP-07-05
Information Acquisition in Financial Markets: a Correction
Gadi Barlevy and Pietro Veronesi
WP-07-06
Monetary Policy, Output Composition and the Great Moderation
Benoît Mojon
WP-07-07
4
Working Paper Series (continued)
Estate Taxation, Entrepreneurship, and Wealth
Marco Cagetti and Mariacristina De Nardi
WP-07-08
Conflict of Interest and Certification in the U.S. IPO Market
Luca Benzoni and Carola Schenone
WP-07-09
The Reaction of Consumer Spending and Debt to Tax Rebates –
Evidence from Consumer Credit Data
Sumit Agarwal, Chunlin Liu, and Nicholas S. Souleles
WP-07-10
Portfolio Choice over the Life-Cycle when the Stock and Labor Markets are Cointegrated
Luca Benzoni, Pierre Collin-Dufresne, and Robert S. Goldstein
WP-07-11
Nonparametric Analysis of Intergenerational Income Mobility
with Application to the United States
Debopam Bhattacharya and Bhashkar Mazumder
WP-07-12
How the Credit Channel Works: Differentiating the Bank Lending Channel
and the Balance Sheet Channel
Lamont K. Black and Richard J. Rosen
WP-07-13
Labor Market Transitions and Self-Employment
Ellen R. Rissman
WP-07-14
First-Time Home Buyers and Residential Investment Volatility
Jonas D.M. Fisher and Martin Gervais
WP-07-15
Establishments Dynamics and Matching Frictions in Classical Competitive Equilibrium
Marcelo Veracierto
WP-07-16
Technology’s Edge: The Educational Benefits of Computer-Aided Instruction
Lisa Barrow, Lisa Markman, and Cecilia Elena Rouse
WP-07-17
The Widow’s Offering: Inheritance, Family Structure, and the Charitable Gifts of Women
Leslie McGranahan
WP-07-18
Demand Volatility and the Lag between the Growth of Temporary
and Permanent Employment
Sainan Jin, Yukako Ono, and Qinghua Zhang
WP-07-19
A Conversation with 590 Nascent Entrepreneurs
Jeffrey R. Campbell and Mariacristina De Nardi
WP-07-20
Cyclical Dumping and US Antidumping Protection: 1980-2001
Meredith A. Crowley
WP-07-21
The Effects of Maternal Fasting During Ramadan on Birth and Adult Outcomes
Douglas Almond and Bhashkar Mazumder
WP-07-22
5
Working Paper Series (continued)
The Consumption Response to Minimum Wage Increases
Daniel Aaronson, Sumit Agarwal, and Eric French
WP-07-23
The Impact of Mexican Immigrants on U.S. Wage Structure
Maude Toussaint-Comeau
WP-07-24
A Leverage-based Model of Speculative Bubbles
Gadi Barlevy
WP-08-01
Displacement, Asymmetric Information and Heterogeneous Human Capital
Luojia Hu and Christopher Taber
WP-08-02
BankCaR (Bank Capital-at-Risk): A credit risk model for US commercial bank charge-offs
Jon Frye and Eduard Pelz
WP-08-03
Bank Lending, Financing Constraints and SME Investment
Santiago Carbó-Valverde, Francisco Rodríguez-Fernández, and Gregory F. Udell
WP-08-04
Global Inflation
Matteo Ciccarelli and Benoît Mojon
WP-08-05
Scale and the Origins of Structural Change
Francisco J. Buera and Joseph P. Kaboski
WP-08-06
Inventories, Lumpy Trade, and Large Devaluations
George Alessandria, Joseph P. Kaboski, and Virgiliu Midrigan
WP-08-07
School Vouchers and Student Achievement: Recent Evidence, Remaining Questions
Cecilia Elena Rouse and Lisa Barrow
WP-08-08
Does It Pay to Read Your Junk Mail? Evidence of the Effect of Advertising on
Home Equity Credit Choices
Sumit Agarwal and Brent W. Ambrose
WP-08-09
The Choice between Arm’s-Length and Relationship Debt: Evidence from eLoans
Sumit Agarwal and Robert Hauswald
WP-08-10
Consumer Choice and Merchant Acceptance of Payment Media
Wilko Bolt and Sujit Chakravorti
WP-08-11
Investment Shocks and Business Cycles
Alejandro Justiniano, Giorgio E. Primiceri, and Andrea Tambalotti
WP-08-12
6
@FedFRASER