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Fundamental Economic Shocks and the Macroeconomy
Charles L. Evans and David A. Marshall
Federal Reserve Bank of Chicago
April 10, 2007

Abstract
This paper asks how macroeconomic and …nancial variables respond to economic impulses. We identify structural economic shocks using a strategy that utilizes measures
of economic shocks explicitly derived from economic models. We use this approach
to identify technology shocks, marginal-rate-of-substitution (labor supply) shocks, and
monetary policy shocks in the context of a Factor Augmented VAR similar to that
developed by Bernanke, Boivin, and Eliasz (2005). We then examine the Bayesian
posterior distribution for the responses of a large number of endogenous macroeconomic and …nancial variables to these three shocks. These shocks account for the
preponderance of output, productivity and price ‡
uctuations. We …nd that technology
shocks have a permanent impact on measures of economic activity, even though this
characteristic of technology shocks is not imposed as an identifying restriction. In contrast, the other shocks have a more transitory impact. Labor inputs have little initial
response to technology shocks; the response builds steadily over the …ve year period.
Consumption has a sluggish response to the technology shock, consistent with a model
of habit formation. Monetary policy has a small response to technology shocks, but
“leans against the wind” in response to the more cyclical labor supply shock. This
shock has the biggest impact on interest rates. Stock prices respond to all three shocks.
A number of other empirical implications of our approach are discussed.
Corresponding Author. Address: Federal Reserve Bank of Chicago, 230 South LaSalle St., Chicago,
IL 60604-1413. Telephone: (312) 322-5102. e-mail: david.marshall@chi.frb.org. We are grateful to Frank
Schorfheide, Mark Watson, and Tao Zha for helpful comments. The opinions in this paper are those of the
authors, and do not re‡ the views of the Federal Reserve Bank of Chicago or the Federal Reserve System.
ect

1. Introduction
This paper investigates how macroeconomic and …nancial variables respond to structural
economic shocks. We use a relatively new and unexplored identi…cation strategy that simultaneously identi…es multiple impulses. Our strategy is linked to economic theory without
being tied rigidly to a particular theoretical model. Furthermore, it minimizes dependence
on arbitrary choices, such as the choice of variables to be included in a vector autoregression
(VAR).
Current methods for identifying and estimating economic shocks have been well-studied
since Sims’ (1980) important contribution. See Stock and Watson (2001) and Christiano,
s
Eichenbaum, and Evans (1999) for recent surveys. A stalwart identi…cation method is to
place zero restrictions on a matrix of contemporaneous impact multipliers in a VAR. Although much has been learned through these methods, such zero restrictions rarely conform
precisely to the equilibrium decision rules of any dynamic stochastic general equilibrium
model (DSGE), a point made by Lucas and Stokey (1987) in response to Litterman and
Weiss (1985). Long-run restrictions are more likely to be compatible with a set of DSGE
models, although subtle changes in model trending details can make these implications fragile, as King and Watson (1997) have discussed relative to Lucas’ theory of the natural rate
s
(1972). Furthermore, economic shocks are often identi…ed one at a time, ignoring potential
correlations across shocks.
We propose an identi…cation strategy that is more closely motivated by the insights
of economic theory without imposing all the restrictions of a particular economic model.
Furthermore, we seek to identify multiple shocks simultaneously, imposing orthogonality
across these shocks.1 Our approach is to use measures of fundamental shocks that are
derived from economic models developed in antecedent literature. We call these“modelbased measures”
.

In particular, we measure technology shocks as Solow residuals and

monetary policy shocks from a Taylor rule speci…cation. In addition, we construct a measure
of shocks to the marginal rate of substitution (MRS) between consumption and leisure using
a procedure similar to Hall (1997). As Hall notes, these shocks can be interpreted as labor
supply shocks.
These measures are potentially noisy. Speci…cally, since they are mutually correlated
it is problematic for our purposes to treat these as clean measures of the true underlying
structural impulses. Instead, we follow the structural VAR (SVAR) literature in assuming
that all structural shocks are mutually orthogonal. We use our model-based shock measures
1
Important recent papers in the literature that identify multiple structural shocks include Gali (1992),
Leeper, Sims, and Zha (1996), and Del Negro, Shorfheide, Smets, and Wouters (2005).

1

to derive the linear combination of VAR innovations that best replicates each structural
impulse. This allows us to compute identi…ed impulse response functions, and relate the
evidence to important macroeconomic questions and alternative models.
In using shock measures derived from economic models, our identi…cation strategy exploits the restrictions implied by economic theory more directly than the typical identifying
strategies used in VAR analysis. However, we do not impose all of the restrictions implied
by these economic models. (For example, we leave the dynamics unrestricted.) In this
sense, our approach is midway between the standard SVAR approach and a fully-articulated
DSGE model. Our approach does require strong assumptions, and we do not assert that it
pointwise dominates other approaches. Nonetheless, it is a plausible approach that di¤ers
from others currently in use, so it could o¤er a di¤erent perspective on economic issues of
interest.2
Evans and Marshall (2003) used a variant of this method to examine a variety of term
structure responses. This paper advances that work along a number of dimensions. First,
we use an alternative, and arguably more robust, set of identifying restrictions. Second,
rather than restricting our information set to a small number of macroeconomic variables, we
incorporate a much larger data set by using the Factor Augmented VAR (FAVAR) approach
of Bernanke, Boivin, and Eliasz (2005). This approach allows us to incorporate enough
information in the VAR residuals to span the true shocks without exhausting our degrees
of freedom. In addition, the approach limits the e¤ect of arbitrary choices regarding which
variables to include in the SVAR. Finally, we move from Evans and Marshall’ (2003) focus
s
on interest rate responses to examine the responses of a wide range of macroeconomic and
…nancial data. This enables us to explore a number of substantive questions that clearly
can bene…t from a multi-shock context.
Speci…c questions we address include the following:
Can a small number of shocks account for most output ‡
uctuation?
How realistic is the traditional focus on technology shocks as drivers of business cycle
variation in output, investment, and labor inputs? (Kydland and Prescott, 1982, and
subsequent RBC literature)
Is it reasonable to associate technology shocks with permanent shocks to output (Blanchard and Quah, 1989; Gali, 1992) or to labor productivity (Gali, 1999; Christiano,
2

In linking identi…cation to the insights of economic theory without tying the identi…cation too tightly to
any single economic model, our approach is related to Del Negro, Shorfheide, Smets, and Wouters (2005).
They use a Bayesian approach to identify a VAR in which the prior distribution is derived from a particular
dynamic general equilibrium model. The strength of the prior determines how tightly the identi…cation is
linked to the underlying model.

2

Eichenbaum, and Vigfuson, 2003), with other shocks (such as “aggregate demand”
shocks) having only transient e¤ects on these variables?
What drives procyclical labor productivity: technology shocks or demand shocks (“labor hoarding”
)?
Are technology shocks contractionary for labor hours and employment (as argued by
Basu, Fernald, and Kimball, 2004, and Gali, 1999), or do these measures of labor
inputs rise contemporaneously with an expansionary technology shock (as argued by
Christiano, Eichenbaum, and Vigfuson, 2003)?
What is the role of monetary policy in aggregate ‡
uctuations?

Is monetary policy

driven largely by responses to economic conditions, or is there an important role for
exogenous monetary policy shocks? Does monetary policy respond di¤erently to technology (“supply” shocks than to labor supply (“demand” shocks? Are monetary
)
)
policy shocks an important source of business cycle variation (as implied by the estimates of Strongin, 1995) or are they rather minor contributors (as discussed by Sims
and Zha, 1998, and Christiano, Eichenbaum, and Evans, 1999)?
What drives ‡
uctuations in the price level and in‡
ation? In particular, what is the
role of real side impulses (such as Phillips curve e¤ects or shocks to marginal costs)?
Are movements in asset prices driven to a signi…cant extent by macroeconomic impulses? Or are asset prices primarily driven by dynamics internal to the …nancial
markets that are largely orthogonal to the macroeconomy? If macro impulses have a
signi…cant role in …nancial markets, which speci…c impulses are most important?
Our results shed light on these questions. We …nd that the three shocks we identify
account for around 72% of the short-run variation in output and over 84% of the variation
in output at longer horizons. In addition, these shocks account for more than 50% of the
long-run variation in in‡
ation, although they account for only about 20% of in‡
ation variation at the 3-month horizon. The MRS shock is an important driver of short-run output
variation, but the e¤ect of the technology shock is much longer-lived. Thus, our evidence
favors the permanent vs. transitory distinction between technology shocks and other shocks,
even though we do not impose this distinction as an identifying restriction. We …nd that
the procyclical response of labor productivity is due almost entirely to procyclical technology shocks. Labor input measures display almost no contemporary response to technology
shocks, but rise gradually in the years following the shock.

3

Similarly, wages have only a

small initial response to technology shocks, even though the technology shocks boost labor’
s
marginal product. Wages then rise monotonically over the next four years.
Monetary policy shocks have a very small impact on real economic activity. While these
shocks do account for a good deal of the short-run variation in the fed funds rate, their impact
is extremely short-lived. Longer-lived policy actions are mostly endogenous responses of the
Fed to other shocks. In particular, the Fed displays a rather small response to technology
shocks, but strongly “leans against the wind” in response to the more cyclical MRS shock.
Finally, while most variation in stock prices is accounted for by sources other than our three
identi…ed shocks, there are a number of intriguing patterns that point to linkages between
…nancial markets and the macroeconomy. In particular: the MRS shock accounts for most
variation in Treasury yields, and all three shocks have signi…cant impacts on stock prices.
The paper is organized as follows. Section 2 describes the basic framework we use.
Section 3 discusses our Bayesian approach to statistical inference. Section 4 describes the
construction of our three model-based shock measures and discusses our FAVAR speci…cation.
Section 5 describes our empirical results, and section 6 concludes.

2. Identifying a Structural VAR using Model-Based Shock Measures
2.1. Basic Framework
We study the responses of macroeconomic and …nancial variables to a set of m fundamental
shocks. Let "t denote the m

1 vector of shocks we wish to identify. It is assumed that "t

is serially uncorrelated, with E"t = 0 and
E"t "0t = I

(2.1)

A key assumption in our approach is that the econometrician observes a m 1 vector t of
model-based measures of these processes. For example, if one element of the "t vector is
an exogenous technology shock, the corresponding observable model-based measure might
be a data series consisting of Solow residuals. Or, if another element of "t were a monetary
policy shock, the corresponding model-based measure might be the residual from an empirical
Taylor rule. These model-based measures may be serially correlated and contaminated with
measurement error. Furthermore, they may not be clean, in the sense that a given element
of

t

may be a function of all of the "t ’ For example, the measured Solow residual series
s.

may be contaminated with monetary policy shocks, as argued by Evans (1992). To capture
these possibilities, we assume that the t vector of model-based shocks is related to the true,
4

unobserved shock vector process "t by
t

= D0 "t + D1 "t

where Dk ; k = 0; :::; K; are m

1

+ ::: + DK "t

K

(2.2)

+ wt

m matrices of parameters and wt is an m

random measurement errors with covariance matrix
E"t wt

j

1 vector of

for which

w

= 0; 8j = 0; 1; 2; :::

(2.3)

We assume that D0 is nonsingular. If D0 is diagonal, then the innovation to a given modelbased shock

i;t

is a function only of its own fundamental shock "i;t (plus the measurement

error wt ). However, if the ith row of D0 is non-diagonal, then the innovation to the shock
i;t

is a function of two or more elements of "t .
In addition to the t vector, the econometrician also observes an n

economic variables, where n

1 vector Yt of

The law of motion for Yt has the following structural

m.

representation:
b
AYt = B(L)Yt

1

"t

+

(2.4)

t

b
where A is an n n nonsingular matrix of parameters, B(L) is an n n matrix of polynomials

in the lag operator, and t is an (n
orthogonal to "t . In particular,
E

1 vector of additional i.i.d. structural shocks

m)

"t

"0t

t

00
t

(2.5)

=I

In the general case, representation (2.4) could be the reduced form of some linearized or loglinearized DSGE model. Alternatively, it could be an atheoretic forecasting model. From
the standpoint of our investigation, t are “nuisance shocks”that we do not seek to identify.
Equation (2.4) can be written as a VAR:
Yt = B(L)Yt
where ut is an n

and

1

(2.6)

+ ut

1 vector of VAR residuals with covariance matrix

u,

b
B (L) = A 1 B(L)
"t

= Aut

t

It is convenient to partition the rows of A as follows:
A"
A

A=
5

(2.7)

where the m

n matrix A" consists of the …rst m rows of A. Notice that
(2.8)

" t = A" u t :

According to equation (2.8), we can recover the structural shocks "t from the VAR residuals
if we can identify the mn elements of the matrix A" . To that end, note that we can combine
equations (2.2) and (2.8) to get
t

where the n

= C0 ut + C1 ut

1

+ ::: + CK ut

K

+ wt

(2.9)

m matrices Ck ; k = 0; :::; K; are de…ned by
Ck

(2.10)

Dk A" ; k = 1; :::; K:

Equation (2.10) with k = 0 means that matrix A" is identi…ed if we can identify the matrices
C0 and D0 . In the next subsection we turn to this task.
2.2. Identi…cation of A"
First, note that equations (2.1) and (2.8) imply that
I = A"

0
u A" :

(2.11)

Equations (2.10) and (2.11) in turn imply
0
D0 D0 = C0

0
u C0

0
u C0 .
0
C0 u C0

which says that D0 is a decomposition of C0

(2.12)
To identify D0 from data, we …rst

impose restrictions su¢ cient to ensure that
can be estimated from the data. We
then impose additional assumptions to ensure that the decomposition in equation (2.12) is
unique.
Let us turn …rst to the estimation of C0

0
u C0 .

Matrix

u

can be estimated in the usual

way from the variance-covariance matrix of the VAR residuals. Estimation of C0 requires an
additional assumption:
E t wt = 0

(2.13)

0
Together, equations (2.3), (2.7), and (2.13) ensure that Eut wt = 0, so we can estimate
Ck ; k = 0; :::; K by regressing t on ut .3
3

OLS estimation of equation (2.9) is consistent, but not e¢ cient. However, using OLS estimation
simpli…es computation of the Bayesian posterior distribution of the model parameters, which we use for
inference. See the appendix for details.

6

While equation (2.13) is a strong restriction, some form of strong exclusion restrictions
must be imposed in virtually any procedure that seeks to identify a small number of shocks
using a large data set. For example, index model approaches, such as Sargent and Sims
(1977) or Stock and Watson (1989), are typically implemented by strongly restricting the
covariances among fundamental shocks and measurement disturbances.
Given the estimates of C0 and u , equation (2.12) represents m(m + 1)=2 restrictions on
the m2 elements of D0 . We can identify D0 if we impose another m(m 1)=2 restrictions on
~
D0 . It is useful to formalize these restrictions by specifying m (m 1) =2 free parameters, d,
n
o
2
~
along with a mapping d : Rm ! Rm(m 1)=2 such that, given d; C0 ; u ; D0 is the solution
to the following system of n2 equations:

~
d (D0 ) = d

(2.14)

0
D0 D0 = C0

0
u C0

For example, one possible set of identifying restrictions could be to require that D0 be lowertriangular.4 These restrictions would be represented in system (2.14) by having the mapping
~
d ( ) pick out the m (m 1) =2 upper triangular elements of D0 , and then setting d equal to
~
a vector of zeros. (In section 4.2, below, we discuss the speci…cation of d ( ) and d that we
actually use in the empirical part of this paper.) Having estimated C0 and identi…ed D0 , we
can then identify A" using equation (2.10), which implies that A" = D0 1 C0 . The structural
shock vector "t can then be identi…ed using equation (2.8).
To compute impulse responses of Yt to "t , rewrite the reduced form (2.6) as
Yt = B(L)Yt

1

+A

1

"t

(2.15)

:

t

Computing impulse responses to "t requires that we know the …rst m columns of A 1 , which
we can denote “[A 1 ]" ” This submatrix can be computed from knowledge of A" using the
.
relation
A

1
"

=

0
u A"

(2.16)

which follows directly from equation (2.11).
Once [A 1 ]" is identi…ed, we can compute the response of any variable zt , even one not
included in the vector Yt . To do so, we augment system (2.6) and (2.7) with another equation
in zt :
Yt
zt
4

=

B(L)
(L)

0
(L)

Yt
zt

1
1

+

A
F

1

0
G

2
4

"t
t
t

3

5:

(2.17)

Evans and Marshall (2003) pursue this strategy after rejecting the testable hypothesis that D is diagonal.

7

In equation (2.17),

(L) and (L) are respectively 1

n and 1

1 vector polynomials in the

lag operator, F and G are 1 n and 1 1 parameter vectors, and t is a serially uncorrelated
disturbance that is also uncorrelated with "t and t . The zero restrictions in equation (2.17)
ensure that, given knowledge of Yt

1

and its lags along with "t and

t,

neither

t,

zt , nor its

lags are needed to determine Yt .
2.3.

Expanding the Information Set

As with any structural VAR, a key requirement of our approach is that the true fundamental
shocks "t are spanned by the VAR residuals ut . To ensure that this is indeed the case, one
would want to incorporate a large number of data series in the VAR. However, to do so
directly would quickly lead to degrees-of-freedom problems. As discussed in Bernanke,
Boivin, and Eliasz (2005), VARs typically used in the literature incorporate no more than 6
to 8 variables.5
To address this problem, we follow Bernanke Boivin, and Eliasz (2005) and implement
equation (2.4) as a Factor Augmented Vector Autoregression (FAVAR). Speci…cally, we use
a set Xt of p observable data series (where p is large), and we assume that Xt is a function
b
of n factors Yt , where n is much smaller than p:
b
Xt = Yt + et :

(2.18)

We assume that et displays weak cross-correlation in the sense of Stock and Watson (1998).
As in Stock and Watson (1998, 2002) and Bernanke Boivin, and Eliasz (2005), we estimate
b
b
Yt as the …rst n principal components of Xt . We then use Yt in equation (2.4) in place of
Yt .

b
Note that this is a two-step procedure: …rst we estimate equation (2.18) to generate Yt ,

and then we estimate equation (2.4) and impose the strategy of section 2.2 to identify the
shocks "t . In using this two-step approach we follow Stock and Watson (1998, 2002). In
principle, one could combine these two steps. However, Bernanke Boivin, and Eliasz (2005)
argue that the gains from doing so appear to be rather small, while the computational burden
increases substantially.6
5

These degrees-of-freedom problems can be mitigated to some extent by imposing a Bayesian prior. For
example, Leeper, Sims and Zha (1996) use this approach to estimate a VAR with 18 variables.
6
b
There is a technical issue in using Yt in place of Yt in equation (2.17): if zt is one of the elements of the
information vector Xt , then it is not clear that the zero restrictions in equation (2.17) will hold. In their
treatment of dynamic factor models, Stock and Watson (2005) test a variety of restrictions of this form.
While they often reject the zero restrictions in a statistical sense, they …nd that the deviations from the
zero restrictions are of no economic signi…cance in virtually all cases. We will continue to impose the zero
restrictions in equation (2.17) as a maintained assumption

8

3. Bayesian Inference
b
Given the Yt series n
estimated in theo
…rst step, the remaining parameters to be determined in
~
the second step are B; u ; C; w ; d , where B contains the coe¢ cients of the lag polynomial
~
B (L) ; C
fCk gK ; and d is the vector of free parameters that identi…es the elements of
k=0

matrix D0 in equation (2.14). A joint prior distribution can be imposed on these parameters,

and the posterior distribution can then be computed. In doing so, we are explicitly treating
b
the generated series Yt as known data. 7
~
Note that the parameter vector d di¤ers from the other parameters. Since m (m 1) =2

restrictions have been imposed on the D0 matrix, the model is exactly identi…ed. Therefore,
the parameters fB; u ; C; w g exhaust the information in the data, so any speci…cation of
~
~
the m (m 1) =2 elements of d is equally likely. Thus the prior on d equals the posterior,
so this prior acts as a way of specifying soft restrictions on the D0 matrix.

The appendix contains a detailed description of how one computes the posterior distribution for fB; u ; C; w g given an uninformative prior on these four parameter elements.
This paper only explores the implications of this uninformative prior. It is straightforward
to amend this procedure for an informative prior.

4. Empirical Implementation
4.1. Model-Based Shock Measures
In our empirical application of the identifying strategy of section 2, we seek to identify three
shocks: a technology shock, a marginal-rate-of-substitution shock that can be interpreted
as a labor supply shock, and a monetary policy shock. To implement the model-based
identi…cation strategy, we need model-based measures of these three shocks. In this section
we describe how we construct these measures.
4.1.1. Technology Shocks
Since Prescott (1986), the driving process for aggregate technology shocks in real business
cycle models has been calibrated to empirical measures of Solow residuals. A large literature,
including Prescott (1986), has noted that a portion of the ‡
uctuations in standard Solow
7

Note, in addition, we are treating the model-based measures t as known, even though, in some cases,
these measures may involve estimated parameters.
An alternative procedure would be to impose a prior on parameter matrices f ; g in equation (2.18),
and then compute the joint posterior over all the parameters. However, these matrices are extremely large.
In our empirical application, is 190 6 and
, the covariance matrix of t , is 190 190. As a result,
this alternative procedure borders on the infeasible.

9

residual measures is endogenous, responding to macro shocks.8 Basu, Fernald, and Shapiro
(2001b) provide a recent estimate of technology innovations that attempts to reduce these in‡
uences. Ignoring industry composition e¤ects, their aggregate analysis speci…es production
as follows:
Yt = zt gt F (vt Kt ; et Nt )
ln zt =

+ ln zt

1

+

(4.1)

T ech;t

where Y , z, v, K; e, and N are the levels of output, technology, capital utilization rate, capital
stock, labor e¤ort, and labor hours.9 The object gt represents costs of adjusting employment
and the capital stock. It is an explicit function of observable data, and is calibrated from
econometric estimates in the literature (see Shapiro (1986) and Basu, Fernald, and Shapiro
(2001a,b)). F is a production function that is homogeneous of degree

1, allowing for the

possibility of increasing returns. Basu, Fernald, and Shapiro (2001a,b)) specify an economic
environment where the unobserved variables v and e can be measured as proportional to
the workweek of labor and capital. Assuming = 1 — constant-returns-to-scale — Basu,
Fernald, and Shapiro (2001b) use time-varying cost shares to compute a quarterly, aggregate
measure of the technology innovation,

T ech;t .

We use Basu, Fernald, and Shapiro’ (2001b) quarterly, aggregate measure of technology
s
for our model-based empirical measure T ech of the aggregate technology shock.10 Although
this quarterly measure includes controls for many latent, endogenous features, data limitations prevent controlling for industry compositional e¤ects. This potentially introduces
measurement error into this series. The data begin in 1965:II and end in 2000:IV.
4.1.2. Marginal-Rate-Of-Substitution Shocks
A shock to the marginal rate of substitution (MRS) between consumption and leisure can
potentially shift aggregate demand for goods and services. Hall (1997), Shapiro and Watson
(1988), and Baxter and King (1990) …nd substantial business cycle e¤ects from empirical
measures of intratemporal marginal rates of substitution between consumption and leisure.
To generate a model-based empirical measure of an MRS shock, we generalize Hall’ (1997)
s
procedure to allow for time-nonseparable preferences.11 Consider a representative consumer
with the following utility speci…cation:
U (Ct ; Nt ) =

Ct
t

bC t
1

8

1
1

Nt1+
1+

For example, see Burnside, Eichenbaum and Rebelo (1993) and Braun and Evans (1998).
Throughout this paper, we omit the time subscript t if no ambiguity is implied.
10
We thank John Fernald for providing us with this time series on technology shocks.
11
Holland and Scott (1998) study a similar MRS shock for the United Kingdom economy.
9

10

ln

t

= (L) ln

t 1

+

(4.2)

M RS;t

where C is the consumption by the representative agent, C represents the per-capita aggregate consumption level, N is labor hours,
M RS

is a serially correlated preference shifter, and

is a serially independent shock. The …rst-order conditions for consumption and labor

hours lead to the following intratemporal Euler equation (or MRS relationship)
Ct

t

bC t

1

=

Nt
where Wt is the real wage and
ln

t

=

t

ln Nt

1
Wt (1

(4.3)

t)

is the labor tax rate. Taking logs, we obtain
lnWt

ln (1

t)

+ ln Ct

bC t

1

:

(4.4)

In equilibrium, the per-capita aggregate consumption equals the consumption levels of the
representative agent, so C = C:
We use equation (4.4) to obtain an empirical measure of ln t . We then compute our
model-based empirical measure M RS;t of the MRS shock as the residual from the OLS
estimate of equation (4:2) : Our data are quarterly and extend from 1964:I to 2000:IV. Consumption is measured by per capita nondurables and services expenditures in chain-weighted
1996 dollars. Labor hours correspond to hours worked in the business sector per capita. The
real wage corresponds to nominal compensation per labor hour worked in the business sector
de‡
ated by the personal consumption expenditure chain price index. The hours and compensation data are reported in the BLS productivity release. Finally, our measure of the
labor tax rate is a quarterly interpolation of the annual labor tax series used in Mulligan
(2002).12 We calibrate the utility function parameters as follows. First, to ensure balanced
growth we set

= 1; corresponding to log utility for consumption services. Second, we use

Hall’ (1997) value for
s

= 1:7, corresponding to a compensated elasticity of labor supply

of 0.6. Finally, we set the habit persistence parameter b = 0:73 as estimated by Boldrin,
Christiano and Fisher (2001).
We measure

M RS

as the residual in equation (4.2). We estimate a sixth-order polynomial

for (L). In addition, the M RS measure

exhibits noticeable low frequency variation, so we

also include a linear time trend in the regression to account for demographic factors that are
beyond the scope of this analysis. If the theoretical variables and data series coincide and
our estimate of (L) is correct, then our measure of

M RS

would equal "M RS : If, however,

our measures of consumption, labor hours, and the spot real wage di¤er from the theory,
then
12

M RS

would represent a noisy measure of "M RS . In order to allow for serially-correlated

We would like to thank Casey Mulligan for providing us with his labor tax rate data.

11

measurement errors in

t,

we use an instrumental variables estimator to estimate (L).13

If our model-based measure M RS were a clean measure of the true structural shock
"M RS , it should be causally prior to any endogenous variables. While we do not use the
model-based measure directly as the structural shock, clearly causal priority is a desirable
characteristic for our

M RS

measure.

Gali, Gertler, and Lopez-Salido (2001) speci…cally

raise this issue with regard to a series similar to our

M RS

measure, questioning whether

it was Granger-causally prior to output, the short-term interest rate, and the term spread.
When we replicate the Gali, Gertler, and Lopez-Salido (2001) causality tests for our M RS
measure, we …nd no evidence that

M RS

is Granger-caused by the variables they consider

(detrended GDP, the federal funds rate, and the term spread). Details of these causality
tests are displayed in Table 1.
Derived this way, our MRS shock has a clear interpretation as a preference shifter. However, macroeconomic researchers have o¤ered several alternative interpretations for the random marginal rate of substitution shifter

t

in equation (4:3).14 First, the home production

literature due to Benhabib, Rogerson, and Wright (1991), Greenwood and Hercowitz (1991),
and Chang and Shorfheide (2003), among others, suggests that t could be a productivity shock to the production of home goods. Second, inertial wage and price contracts will
distort the simple intratemporal Euler equation as it is speci…ed in (4:3) : In particular, in
the Calvo pricing environments considered by Christiano, Eichenbaum, and Evans (2005)
and Galí, Gertler, Lopez-Salido (2001), alternative versions of (4:3) hold. Third, Mulligan
(2002) interprets

t

as re‡
ecting labor market distortions, such as changes in tax rates or

union bargaining power. To the extent that these alternative explanations have di¤erent
theoretical implications for impulse response functions, an empirical analysis of our MRS
shock can help shed light on which explanation seems to be consistent with the aggregate
data.
4.1.3. Monetary Policy Shocks
Unlike the previous two shock measures, there is no well-developed theory that derives
monetary policy shocks from an optimizing framework. However, many theoretical models
assume that the monetary authority sets monetary policy via some variant of a Taylor
(1993) rule. That is, the short-term interest rate is set as an increasing function of both
in‡
ation and the output gap (a measure of the shortfall in economic activity compared to its
13

Our shock identi…cation strategy assumes that the measurement errors in our model-based shocks are
independent of the VAR innovations. Consequently, we use real GDP, the GDP price index, and commodity
prices as instruments.
14
As Hall (1997) pointed out, the greatest amount of evidence against Eichenbaum, Hansen, and Singleton’
s
(1988) preference speci…cations surrounded the intratemporal Euler equation for consumption and leisure.

12

potential). In some speci…cations, lags of the short-term interest rate are included in order
to capture the desire of the monetary authority to smooth changes in the interest rate.15
In these models, the natural speci…cation for monetary policy shocks is the disturbance to
the short-term interest rate that is orthogonal to these systematic components of the Taylor
Rule. We adopt this approach for our model-based measure of the monetary policy shock
MP .

The particular approach we use is to specify a backward-looking Taylor rule, so the
interest rate is a function of current and lagged in‡
ation, as opposed to expected future
in‡
ation. In addition, the output gap is not observed, so some empirical proxy for this gap
variable must be used. In the spirit of taking our model-based measures from approaches
proposed in antecedent literature, we use a gap measure derived from work by Staiger,
Stock, and Watson (1997).

In particular, we measure the gap as the di¤erence between

the current unemployment rate and the Staiger-Stock-Watson measure of the natural rate of
unemployment.16 In addition, we allow the coe¢ cients on in‡
ation and on the gap variable
to be regime dependent. Speci…cally, we allow for three regimes: before 1979:Q4, 1979:Q4
- 1982:Q4, and after 1982:Q4. The speci…c model is as follows:
rf ft =

4
X

j rf ft j

+

j=1

3
X

[

k

(Ik ugapt ) +

k

(Ik t )] +

(4.5)

M P;t

k=1

where rf ft denotes the fed funds rate, ugapt denotes the gap between current unemployment
and the Staiger-Stock-Watson measure of the natural unemployment rate,17

t

denotes the

log change in the GDP de‡
ator, and Ik is an indicator variable for the three regimes. The
data run from 1959:I through 2000:IV.
4.1.4. Correlations among model-based measures
Table 2 displays the correlations among our three model-based measures f

T ech ;

M RS ;

M P g.

As can be seen, the correlations are small but non-zero. As a result, we are reluctant to use
them as clean measures of the true structural shocks "t . Instead, we use them as inputs into
the identi…cation strategy described above in section 2.18 In section 5.8, below, we consider
some interpretive problems that would arise if we were to treat the model-based measures
as error-free measures of the structural shocks.
15

A time-varying in‡
ation target is also sometimes included. See, e.g., Kozicki and Tinsley (2001).
We have experimented with several other speci…cations for the Taylor Rule, including measuring the gap
as detrended output, and using real-time data. The results are very close to those in our baseline speci…cation, except the error bands are somewhat tighter when we use the Staiger-Stock-Watson gap measure.
17
We obtained data on ugapt from Mark Watson’ website.
s
18
Boivin and Giannoni (2006) develop an alternative approach to handling potential mismeasurement of
structural shocks within a fully speci…ed DSGE model.
16

13

4.2. Identifying restrictions
To identify the model, we must impose m (m

1) =2 restrictions on matrix D0 . Since m = 3,

we need 3 restrictions. To motivate the restrictions we impose, note that our procedure is
only likely to be informative if the model-based measures contain a good deal of information
about the shocks they seek to identify. Speci…cally, a shock measure
"i only if most of the variation in

i,

i

is informative about

after controlling for measurement error wt , is accounted

for by "i : Equations (2.2) and (2.1) imply that
vart

1

i;t

wi;t =

m
X

2
D0;ij

(4.6)

j=1

where D0;ij = (i; j)th element of matrix D. We will refer to the left-hand side of equation
(4.6) as the “non-noise variance” of i;t . To ensure that most of this variance is driven by
the own shock "i , we need the fraction of this variance associated with the diagonal element
D0 ;ii to be fairly large. Our restrictions on D0 are motivated by this consideration.

In

particular, we restrict the three diagonal elements such that
D ;2
~
Pm 0 ii 2 = di ; i = 1; 2; 3
D0 ;ij
j=1

(4.7)

~
where di is drawn from a uniform distribution with support [:80; :95]: This ensures that
between 80% and 95% of the non-noise variance of each model-based measure

i

is due to

19

its own shock "i .

4.3. FAVAR Speci…cation
In order to ensure that our information set Xt in equation (2.18) is big enough to span the
space of the shocks "t we seek to identify, we use 190 data series in Xt .

Thirty-six of these

are quarterly data, while 154 are monthly series that have been quarterly averaged. The data
sample is from 1967:Q2 through 2000:Q4. The data series used are listed in Table 1A in the
Data Appendix, along with the transformations used to induce stationarity.20 We set n = 6,
b
and we compute Yt in equation (2.18) as the …rst six principal components of Xt .21 Four
19

Restrictions (2.12) and (4.7) constitute a system of nine equations in the nine unknown elements of D0 .
However, these equations are nonlinear, so there is no guarantee that a solution to this system exists. In
0
practice, for the estimated matrix C0 u C0 (or for the draws of this matrix from its postierior distribution),
~
~
we …nd no di¢ culties solving the system as long as di < 0:95. When di is very near unity for i = 1; 2; 3,
~
however, we …nd that no solution exists. Perhaps this is not surprising, since di = 1, 8i, cannot be a solution
0
to the system if C0 u C0 is non-diagonal.
20
We control for outliers by replacing any data point more than six times the interquartile range (IQR)
above the series median with median + 6 IQR (and analogously for data points more than 6 IQR below
the IQR). All transformed series are then de-meaned and standardized.
21
When we increase the number of principal components to eight, the results are almost identical to those
when six principal components are used. In no case are the substantive implications changed.

14

quarterly lags of each principal component are used in the VAR, equation (2.4). We then use
b
equation (2.17) (substituting Yt for Yt ) to compute the responses to f"T ECH ; "M RS ; "M P g of

a number macroeconomic and …nancial market variables, using the approach of Zha (1999).

The model-based measures only provide useful information for identifying A if they are

correlated with the VAR residuals ut . Table 3 provides evidence on these correlations in the
data we use. It displays the R2 s for the OLS regressions in system (2.9) using our measures
of t . These R2 s show that over 50% of the variation in each model-based measure is
accounted for by the VAR residuals. In addition, the F -statistics testing the hypotheses
that the VAR residuals are uninformative for the

t

measures reject these hypotheses at any

desired signi…cance level. Under our identifying restrictions, these statistics imply that our
measures are potentially informative for the true structural shock vector "t .

5. Empirical Results
The data we use are described in the Data Appendix. Our empirical results are displayed in
Table 4 and Figures 1 - 7. For each endogenous variable listed, Table 4 gives the median
fraction of 3-, 12-, and 60-month ahead forecast variance accounted for by the three identi…ed
shocks, f"M P ; "M RS ; "T ECH g, according to the posterior distribution. The fourth line in each

panel gives the median fraction of each forecast variance accounted for by the three shocks
collectively. The two numbers in parentheses following each median statistic give the 95%
and 5% quantiles of the posterior distribution for each forecast variance fraction.

Figures

1 - 7 display the median impulse responses of selected endogenous variables. The upper and
lower dashed lines give the 95% and 5% quantiles of the response distribution, respectively.
All of these statistics were computed using 500 draws from the posterior distribution of the
model’ parameters.
s
5.1. Long Run Behavior of the Economy
Figure 1 displays the responses of GDP and labor productivity to our three identi…ed shocks
over an 80 quarter horizon. There is clear evidence that technology shocks induce permanent
shifts in the level of GDP and productivity. In contrast, the responses to the MRS shock
and the monetary policy shock appear to display mean reversion, with little evidence of a
permanent level shift for GDP or productivity.
An alternative way of describing the posterior distribution of these long run responses is
in Table 5, which gives the probability that the 80-quarter ahead response exceeds zero. For
the technology shock, we estimate these probabilities at 100% and 99% for GDP and labor
productivity respectively. In contrast, the probability that the 80-quarter ahead responses
15

to "M RS exceeds zero is only 61% for GDP and 19% for productivity; the corresponding
probabilities for "M P are 53% for GDP and 73% for productivity. These results support the
identifying assumption, used by Gali (1992, 1999) and Christiano, Eichenbaum, and Vigfuson
(2003), that only technology shocks induce permanent shifts in output and/or productivity.

5.2. Cyclical Behavior of GDP and its Components
According to Table 4, about 72% of the variance of the 3-month ahead forecast error of GDP
is explained by our three identi…ed shocks. This fraction rises to 84% for the 60-month
ahead forecast error. Recall that there are a total of six VAR innovations, so there are three
remaining sources of variation (the

t

vector) in system (2.4). Thus, our identi…ed shocks do

a reasonable job of accounting for output movements. The technology shock and the MRS
shock are about equally important at the twelve-month horizon. However, at the 5-year
horizon, the technology shock is the predominant driver of output variation. In contrast, the
monetary policy shock accounts for a very small fraction of output variation at all horizons.
This result supports results in Sims and Zha (1998) and Christiano, Eichenbaum, and Evans
(1999) that monetary policy shocks account for, at best, only a small fraction of output
‡
uctuation.
These patterns can also be seen in the GDP responses displayed in Figure 2, which
displays impulse responses over a 20 quarter horizon. Note that the initial responses of GDP
to "T ECH and "M RS are similar in magnitude. However, the response to the technology shock
persists, whereas the response to the MRS shock mean-reverts in 1-1/2 to 2 years. Finally,
a contractionary monetary policy shock dampens GDP, although the posterior distribution
of this response is quite spread out.
Turning to the key components of GDP, Table 4 shows that our three identi…ed shocks
account for over 70% of business …xed investment (equipment and software, investment
structures) variation at the 5-year horizon, and over 60% of the corresponding variation in
total consumption expenditures. Figure 2 shows that the responses of these GDP components
look similar to the GDP responses: permanent response to "T ECH , transient response to
"M RS , negative but relatively small response to contractionary "M P . In contrast, the response
of residential investment to both "T ECH and "M RS mean-revert rather quickly after an initial
positive response. In addition, residential investment displays a more pronounced response
to the contractionary monetary policy shock. These responses re‡ the high interest rate
ect
sensitivity of residential investment. As we shall discuss in section 5.5, below, monetary
policy contracts in response to both an MRS shock and a technology shock, although the

16

second response is with a delay of four to six quarters. These interest rate increases reverse
the initially positive responses of residential investment to "T ECH and "M RS .
One additional noteworthy result from Figure 2 is the gradual, hump-shaped response of
consumption to permanent income drivers. In particular, real compensation has a gradual
but permanent response to the technology shock, implying an substantial increase in permanent income. Thus, it is noteworthy that consumption expenditure has a rather small
response to the technology shock on impact. Thereafter, consumption rises. This sluggish
response of consumption to the technology shock would seem inconsistent with a simple
formulation of the permanent income hypothesis, but would be consistent with the models
of habit formation that are increasingly used in macroeconomic models. (See, for example,
Boldrin, Christiano, and Fisher, 2001; and Fuhrer, 2000.)
5.3. Labor Markets
Figure 3 displays the responses of hours worked, payroll employment, and labor productivity
to our three identi…ed shocks. Note …rst that the MRS shock elicits an immediate rise in both
hours and employment on impact. This e¤ect, however appears to be transient, dissipating
in about two years. In contrast there is virtually no response of hours or employment to
a technology shock on impact.

Thereafter, these measures of labor inputs rise steadily,

reaching a new steady state in about 2 to 2-1/2 years.

On the face of it, the permanent

response of hours to the technology shock contradicts the theoretical premise that hours per
capita should be stationary. This problem is not unique to our identi…cation strategy, but
generally arises in studies that use unadjusted hours data computed by the Bureau of Labor
Statistics. Per-capita hours derived from these data are non-stationary, displaying a trend
of about 0.6% per year.22
The initial response of labor inputs to technology shocks is a matter of some controversy
in the literature. Basu, Fernald, and Kimball (2004) estimate that hours and payrolls fall
with a technology shock on impact. Intuitively, higher productivity enables …rms to meet
demand with less labor. In contrast, Christiano, Eichenbaum and Vigfuson (2003) estimate
a contemporaneous rise in labor inputs in response to a technology shock. Both of these
papers identify the technology shock using long run restrictions, although the way these
restrictions are implemented di¤ers between the two papers. Our identi…cation strategy
does not impose long run restrictions, and our results are intermediate between these two
earlier papers.
22

Ramey and Francis (2006) construct a measure of per capita hours that adjusts for home production
hours, hours spent in school, and other factors. In contrast with the unadjusted BLS data, their measure
appears to be stationary.

17

Another question addressed by Figure 3 is whether the observed procyclicality of labor
productivity is due to “labor hoarding” (a sluggish response of labor demand to cyclical
movements in product demand) or simply due to procyclical technology shocks that directly
drive productivity and output in the same direction. The impulse responses in Figure 3
tend to support the second explanation.

They imply that labor productivity is driven

almost exclusively by technology shocks. In particular, the productivity response to "T ECH
is positive over the …rst year with virtually 100% probability. In contrast, the responses
of productivity to the MRS and monetary policy shocks are small and dissipate quickly.
If labor hoarding were an important factor in explaining procyclical labor productivity, we
would expect to see signi…cant responses of productivity to these non-technology shocks.
Thus, the small responses of productivity to "M RS and "M P provide little support for the
labor hoarding story.
5.4. In‡
ation
According to Table 4, about 60% of the 5-year ahead variation in in‡
ation is explained by our
three identi…ed shocks. The top row of Figure 4, which displays the responses of in‡
ation
to these three shocks, shows that both nominal and real shocks are important for in‡
ation.
In‡
ation rises strongly in response to "M RS . The in‡
ationary response dissipates in two to
three years. As a shock that induces short-term positive responses of both economic activity
and prices, "M RS behaves as what Blanchard (1989) would call an aggregate demand shock.
An expansionary technology shock induces a fall in in‡
ation for about a year and a half.
This would be consistent with a model of monopolistically competitive …rms that set prices
as a markup over marginal cost. After the …rst 6 quarters or so, in‡
ation appears to rise,
and monetary policy responds by contracting.
What appears to be driving this in‡
ation increase is the delayed response of consumption
and business investment demand to the technology shock, discussed above in Section 5.2.
In particular, while the technology shock induces an increase in productive capacity (both
directly and as a result of the investment response), it also induces a rise in demand that
exceeds the rise in capacity over the 5 year horizon displayed in the impulse responses. This
results in an increasing output gap, de…ned as the di¤erence between the actual output and
the long-run sustainable level of output, given current productive capacity. The second row
in Figure 4 displays the response of the output gap (measured as the di¤erence between GDP
and the Congressional Budget O¢ ce’ measure of potential GDP). According to the …gure,
s
the output gap rises steadily for the two years following a technology shock, and remains
elevated for at least another two years. Standard policy analysis would associate this sort
of sustained output gap with in‡
ationary pressures. This sort of association can be justi…ed
18

theoretically in models that generate a New Keynesian Phillips Curve (such as Gali and
Gertler, 1999, and Eichenbaum and Fisher 2004).23
Finally, a notable result in Figure 4 is that a contractionary monetary policy shock is
clearly de‡
ationary, as theory would predict. That is, our identi…cation approach shows no
evidence of Sims’ (1992) “price puzzle” An identi…cation procedure for monetary policy
s
.
shocks is said to display a price puzzle if it implies a pronounced and sustained in‡
ationary
response to a contractionary policy shock. Many procedures used in the literature to identify
monetary policy shocks have this problem. The typical way to avoid a price puzzle is to
include commodity prices, or some other forecaster of in‡
ation, in the VAR. Our procedure
avoids a price puzzle without explicitly including commodity prices. However, the principal
components used in our FAVAR speci…cation may span the information needed to forecast
in‡
ation.
5.5. Monetary Policy
As is common practice, we view the federal funds rate as the indicator of monetary policy.
At short horizons, the most important of our three identi…ed shocks for the federal funds
rate is "M P . Speci…cally, "M P accounts for 34% of the 3-month ahead forecast variance of
the federal funds rate at the median of the posterior distribution. (See Table 4.) By way
of comparison, "T ECH and "M RS account for just 7% and 14% of this variance, respectively.
Figure 5 displays the responses of the funds rate to our three identi…ed shocks. It shows that
the response of the funds rate to the monetary policy shock is extremely short-lived, fully
dissipating in about two quarters. At longer horizons, the MRS shock is by far the most
important determinant of the stance of monetary policy, accounting for 59% of the 5-year
ahead forecast variance of the funds rate (again, at the median of the posterior distribution).
At this 5-year horizon, the corresponding variance percentage attributable to the technology
shock falls to 9%, and the variance percentage of the monetary policy shock declines to 7%.
The response of the funds rate to "M RS follows the qualitative patterns predicted by
a Taylor rule. In particular, the MRS shock induces a rise in both in‡
ation and output
without a concomitant increase in potential output. As a result, a Taylor Rule would predict
monetary tightening. This is precisely what we …nd. In response to an "M RS impulse, the
federal funds rate rises by over 100 basis points over four quarters. This response by the
monetary authority is quite long-lived: the median funds rate remains about 70 basis points
above its starting value even after …ve years. By all appearances, this looks like a classic
23

While Gali and Gertler (1999) and Eichenbaum and Fisher (2004) associate in‡
ationary pressures with
increasing marginal costs, Gali and Gertler (1999) note that there is an approximate log-linear relationship
between marginal costs and the output gap.

19

countercyclical response to a demand shock. What is puzzling about this result is that
the policy response to "M RS is far longer-lived than the corresponding responses of either
in‡
ation or the output gap. This could be interpreted as evidence of policy inertia in the
Fed’ response to in‡
s
ationary pressures.
Finally, Figure 5 shows that monetary policy becomes slightly accommodative on impact
in response to an expansionary technology shock. In particular, the median response of
the federal funds rate to "T ech is a 30 basis point decline. This is not surprising, given the
de‡
ationary impact of "T ech that we saw in Figure 4. Policy does not reliably turn restrictive
until the in‡
ation response turns positive, as described above in section 5.4.
5.6. Treasury Yields
We consider the one-, twelve-, and sixty-month zero-coupon U.S. Treasury yields as computed
in the Fama-Bliss data base from CRSP. According to Table 4, between 66% and 75% of
Treasury yield variation at the …ve-year horizon is explained jointly by our three identi…ed
shocks. The MRS shock is clearly the most important beyond the initial quarters. The last
three rows of Figure 5 give the responses of these yields to the three identi…ed shocks. Notice
that the responses of the intermediate and long rates are similar both in shape and magnitude
to the response of the short rate.

As a result, the MRS shock induces approximately a

parallel shift in the yield curve level. The monetary policy shock is only important at the
very shortest horizon for shortest-term rates (the fed funds rate and the one-month yield)
becoming less important for the longer-term rates. Hence, the monetary policy shock shifts
the yield curve slope.
The yield responses to the technology shock are small and the distribution is spread
around zero. For example, the probability that the one-month yield has a positive average
response over the …rst year is 61%. (The corresponding probability for the 12- and 60month yields are 66% and 53%, respectively.) So it would seem that treasury yields could
easily respond in either direction. Perhaps this is not surprising. As noted by Evans and
Marshall (2003), a technology shock moves real rates and expected in‡
ation in opposite
directions, so the theoretical predictions for nominal yields’ responses are ambiguous. In
Evans and Marshall (2003), the expected in‡
ation e¤ect tended to dominate, so technology
shocks induced a fall in yields. In this study, however, we …nd that these two e¤ects are
of approximately the same magnitude, at least over the …rst year or so.
technology shock has a small e¤ect on nominal yields.

20

As a result, the

5.7. Equity Markets
Our three identi…ed shocks have relatively little explanatory power for stock prices.

As

shown in Table 4, they jointly explain only 26% of stock price variation at the …ve-year
horizon (according to the median of the posterior distribution). They explain even less at
shorter horizons: the corresponding variance fraction explained for the three month forecast
error is only 9%. Thus, most variation in stock prices and returns are driven by factors other
than our three identi…ed impulses.
Having said this, the stock market does display signi…cant responses to all three shocks.
Figure 6 displays the responses of the S&P 500 index, the excess return to the market,
and corporate pro…ts.

The stock market displays a pronounced positive response to an

expansionary technology shock for about a year and a half.

In particular, the median

response of the level of the S&P 500 index over the four quarters averages a bit over one
percentage point, rising to an average of 1.3 percentage points over the …fth through eighth
quarters. The probability that these responses are positive is 96% and 88%, respectively.
This response of the stock price index dissipates in 6 to 8 quarters, perhaps due to the
contractionary response of monetary policy.
The mechanism underlying this stock price response is clear if we regard stock prices
as discounted cash ‡
ows. In response to the technology shock, Figure 6 shows a positive
response of pro…ts (a proxy for cash ‡
ows), while Figure 5 shows a negligible response of
long-term interest rates (a proxy for the discount factor).

It follows that the discounted

present value of the cash ‡ to equity holders must rise.
ow
The response of the stock market to an expansionary MRS shock is rather di¤erent than
the response to a technology shock. There may be a small initial rise in the stock market
upon impact (the error bands are quite wide), but this response is immediately reversed. The
subsequent movement of the stock market is negative, and the market fails to recover its
pre-shock level even after …ve years. This negative outcome for equity markets appears to be
driven by the strong contractionary response of monetary policy along with the concomitant
increase in longer-term interest rates.

In particular, while Figure 6 does show a positive

response of pro…ts to the MRS shock, the response of interest rates is much bigger. The
resulting e¤ect is to decrease the present value of cash ‡
ows to the equity holder. One might
say that while “good news is good news”when the good news is an expansionary technology
shock, “good news is bad news” for the market when the news is an expansionary MRS
shock.24
24

Contrast this result with that in Boyd, Hu, and Jagannathan (2005), where the market responds positively to good economic news in recessions, but tends to respond negatively to good economic news in
expansions.

21

Finally, Figure 6 shows a substantial and fairly long-lived negative response of stock prices
to a contractionary "M P shock. In particular, the median response of the S&P500 index in
the eight quarters following the shock is a decline of over 2 percent. The probability of a
negative response over this period is greater than 98%.

The excess return to the market

portfolio declines by about 70 basis points on impact with negative excess returns persisting
for at least two quarters. These responses are pure discount-rate e¤ects. (The response
of pro…ts to "M P is small and insigni…cant.) All this conforms roughly to the conventional
wisdom that monetary contraction is bad for the stock market.

5.8. Univariate responses to model-based shock measures
A focus of this paper is to use our model-based shock measures

t

to simultaneously identify

all three shocks "t , imposing the restriction that the elements of "t are mutually orthogonal.
An alternative, and simpler, approach would be to compute the responses of macroeconomic
variables directly to the innovation to each element of

t

individually. We call this the

“single- approach” This simpler approach ignores the correlations among the elements
.
of t that are documented in Table 2. It also ignores possible contamination of i;t by
"j;t , j 6= i, and ignores possible measurement error wi;t . In this section, we brie‡ discuss
y
the implications of the single- approach, and contrast its implications with the baseline
approach of Section 2.
To implement the single- approach, we estimate bivariate recursive VARs of the form
i;t

zt
where

i;t

=

i;t 1

(L)

zt

1

+

t;

E

0
t t

(5.1)

=I

is one of our three model-based shock measures, zt is an endogenous variables

whose responses we wish to explore,

t

is a bivariate i.i.d. disturbance, and

triangular matrix. In this structure,

1;t

is interpreted as the shock to

i;t .

is a lower
We use four

quarterly lags in this VAR.
Figure 7 presents selected responses from the single- approach, and contrasts them with
the corresponding responses using the baseline approach described in sections 2 through 4,
above. While most of the responses to the model-based shock measures in framework (5.1)
are qualitatively the same as in our baseline approach, there are several di¤erences worthy
of note. First, and most notably, the in‡
ation response to the shock to M P in framework
(5.1) displays a huge price puzzle. As shown in Figure 7, a contractionary shock to

MP

(“Single-Eta MP shock” induces a signi…cant positive response to both the price level and
)
the in‡
ation rate. In‡
ation remains elevated for at least …ve years after the initial impulse.

22

This contrasts with the negative response to a contractionary "M P in both the price level
and the in‡
ation rate (also displayed in Figure 7).
Second, measures of consumption and investment appear to display permanent responses
to

MP

in framework (5.1), which would seem to violate long run neutrality. Again, these

di¤er from the response patterns to "M P .

(Both are displayed in Figure 7.)

Third, the

federal funds rate displays essentially no response to T ech , the Basu-Fernald-Shapiro technology measure (“Single-Eta Tech shock”in Figure 7). If one believes that an expansionary
technology shock ought to elicit an accommodative policy response, this …nding would be
puzzling.
More generally, if these anomalous responses are interpreted as evidence of misspeci…cation, then one would not want to use the innovations to t as empirical counterparts to the
structural shocks. Our baseline procedure would provide a more satisfactory alternative.

6. Conclusions
In this paper, we have proposed an approach to identifying multiple fundamental macroeconomic shocks. In the introduction, we listed a number of questions that could be fruitfully
addressed by a multiple-shock approach. We …nd that the preponderance of variation in
measures of economic activity can be explained as responses to the three shocks we identify:
technology shocks, shocks to the marginal rate of substitution between consumption and
leisure, and monetary policy shocks. In particular, these three shocks explain over 80% of
the long-run variability in GDP and labor inputs, over 70% of the corresponding variability in the components of business …xed investment, and over 55% of the variability in the
components of consumption and housing.
The traditional emphasis on technology shocks in macroeconomic modelling seems warranted if the focus is on the determinants of long-horizon variability in economic activity.
In the shorter run, a more cyclical driver (here identi…ed as our MRS shock) also needs to
be considered. The association of technology shocks with permanent shocks to output and
productivity is borne out by our analysis.

More transitory responses are associated with

our MRS shock, which is orthogonal to the technology shock.
We …nd no evidence that procyclical labor productivity is driven by “labor hoarding”
.
Such an explanation would imply signi…cant responses of productivity to non-technology
shocks such as our MRS shock. In our results however, the only important driver of productivity is the technology shock. Furthermore, technology shocks are neither expansionary
nor contractionary on impact for labor inputs. Rather, inputs have a negligible contemporaneous response to "T ECH . This result is midway between that found by Basu, Fernald,

23

and Kimball (2004) and that reported by Christiano, Eichenbaum, and Vigfuson (2003).
Monetary policy shocks account for a rather small fraction of output variation. Furthermore, these shocks are important for monetary policy itself only in the short run. Over a
longer horizon, most variation in the federal funds rate is due to the endogenous response of
monetary policy to an MRS shock. The central bank “leans against the wind” in response
to aggregate demand shocks.
About 60% of long-run variation in in‡
ation is explained by our three identi…ed shocks.
Both nominal shocks ("M P ) and real shocks ("T ECH and "M RS ) are important determinants
of price level and in‡
ation. The preponderance of variation in Treasury yields at all maturities is explained by our three shocks, with the MRS shock (which we think of as analogous to
an “aggregate demand”shock) most important. In contrast, most variation in stock prices
and returns is driven by factors other than those identi…ed in this study. Nonetheless, there
is evidence that the stock market displays signi…cant responses to all three shocks. As expected, expansionary technology shocks induce increases in stock prices while contractionary
monetary policy shocks are bad for the market. The market reacts negatively to the “good
news”of an expansionary MRS shock (after 2-3 quarters).
While the results of this paper are intriguing, they raise as many questions as they answer.
Would the results change if more fundamental shocks were added (for example, …scal policy
shocks or investment-speci…c technology shocks)? What is the interpretation of the MRS
shock? We …nd that it behaves rather di¤erently than the technology shock, suggesting that
it probably is not simply a shock to home production technology. But is it best interpreted
as a preference shock (as argued by Hall, 1997), or as a shock to implicit labor taxes or labor
market frictions? Are there other fundamental shocks that can explain the remaining stock
return variation, or does the stock market largely follow its own dynamic, with most of its
volatility orthogonal to the macroeconomy? All of these questions await future work.

24

7. Appendix: Estimation of the Posterior Distribution Assuming
an Uninformative Prior
In this appendix, we construct the posterior distribution for the model parameters f u ; B; w ; Cg ;
b
assuming an uninformative prior. As discussed in Section 3, we treat Yt and t as known

data.

e
It is …rst useful to …x some notation. Let Y ([T + l] n) denote a matrix containing
b
the factor series Yt used in the VAR. (Here, T denotes the number of usable observations, l

denotes the number of lags in the VAR, and n denotes the number of factors in the VAR.) To
write the VAR in regression notation, let q
let the (T

n) matrix of dependent variables in the VAR be denoted Y;

Y

let the (T
2
1
6
6 1
6
6
X 6
6
6
4
1

nl + 1, the number of regressors per equation,

2
6
6
6
6
4

e
Yl+1;1
e
Yl+T;1

3

e
Yl+1;n
e
Yl+T;n

7
7
7
7
5

q) matrix of VAR regressors be denoted X;
e
Yl;1
e
Yl+1;1
e
Yl+T

and let the (T

1;1

e
Yl 1;1
e
Yl;1
e
Yl+T

e
Y1;1
e
Y2;1

e
Yl;2
e
Yl+1;2

e
e
YT;1 Yl+T

2;1

1;2

e
Yl 1;2
e
Yl;2
e
Yl+T

e
Y1;2
e
Y2;2

e
e
YT;2 Yl+T

2;2

m) matrix of model-based shocks be denoted H;
2
3
H

6
6
6
6
4

1;1

1;m

T;1

T;m

w ; B;

u)

= p (Cj

w ; B;

u) p (

25

w jB;

w ; B;

u) ;

u ) p (Bj

All densities in equation (7.1) are conditional on the data fY; X; Hg.
explicitly.

25

1;3

3
e
Y1;n
e 7
Y2;n 7
7
7
7;
7
7
5
e
YT;N

7
7
7:
7
5

Our goal is to compute the joint posterior density p (C;
as follows:25
p (C;

e
Yl;3
e
Yl+1;3

which can be written

u) p (

u)

(7.1)

This dependency is not noted

We assume uninformative priors in the usual way:
prior (

u)

/j

uj

(n+1)=2

(7.2)

prior(B) = constant
prior (

w)

/j

wj

(7.3)

(m+1)=2

(7.4)

prior(C) = constant

(7.5)

The reduced form of the VAR is given by the regression equation
(7.6)

Y = XB + U
where matrix U contains the n

1 i.i.d. error process ut as U = (u1 ; u2 ;

; uT )0 , and it is

assumed that
ut

N (0;

(7.7)

u) :

In equation (7.6), the coe¢ cient matrix B has dimension (q

n). The rows of B correspond
b
to the regressors X; the columns correspond to the n equations. Let B denotes the matrix
of OLS estimates of the VAR slope coe¢ cients
b
B

(X 0 X)

Y

b
XB

1

X 0Y

(7.8)

and let S denotes T times the sample covariance matrix of the VAR disturbances
S

0

Y

b
XB :

b
b
Finally, let Bs and Bs denote the vectors formed by stacking the columns of B and B,

respectively.
Zellner (1971) shows that, given the priors (7.2) and (7.3), the posterior distribution
is inverted Wishart with parameter S. He also shows that, conditional on u , the
b
posterior distribution p (Bs j u ) is multivariate normal with mean Bs and variance-covariance

p(

u)

matrix u (X 0 X) 1 .
We can use Zellner’ (1971) logic to derive the remaining components of the joint posterior
s

distribution (7.1). Equation (2.2) can be written
e
H = U C + W:

(7.9)

e
In equation (7.9), U is a matrix whose columns contain contemporaneous and K lags of U ,
W stacks the m 1 i.i.d. measurement error process wt as W = (w1 ; w2 ; ; wT )0 , and it is
assumed that

W

N (0;
26

w) :

(7.10)

We follow the same steps as we used to derive p (

u)

and p (Bj

u ),

except that we condition

on B. (It turns out that u does not directly a¤ect the conditional distribution of C and
w .) For a given B, let us write
U (B)

and
V (B)

b
C (B)
H

Y

XB

e
e
U (B)0 U (B)

e
b
U (B)C (B)

0

1

H

e
U (B)0 H

e
b
U (B)C (B)

e
(where U (B) contains the contemporaneous and K lags of U (B)). The interpretation of

these objects is as follows: U (B) is the matrix of residuals implied by equation (7.6) given
b
the observed data fY; Xg and a particular choice of B; C (B) is the estimate of C that
one would obtain from U (B) and H if one estimated equation (7.9) via OLS; V (B) is the
moment matrix of n residuals from this OLS estimation of equation (7.9). Conditional
the
o
b
on B, the objects U (B); C (B) ; V (B) are functions of the data, so can be treated as
known quantities.

Therefore, by logic analogous to Zellner (1971), posterior distribution

w jB)

is inverted Wishart with parameter V (B), and posterior distribution p(Cs j w ; B) is
1
b
e
e
multivariate normal with mean C (B) and variance-covariance matrix w U (B)0 U (B)
:
p(

s

One draws from the posterior distribution for fC;

1. Draw

u

w ; B;

ug

as follows:

from the inverted Wishart density with parameter S, which is a function of

data.
2. Given this draw of u ; draw Bs from the multivariate normal distribution with mean
b
Bs and variance-covariance matrix u (X 0 X) 1 .
3. Given this draw of B, draw

w

from the inverted Wishart density with parameter

V (B).
4. Given these draws of B and w , draw Cs from the multivariate normal distribution
1
b
e
e
U (B)0 U (B)
:
with mean C (B)s and variance-covariance matrix w

8. Data Appendix
We use quarterly data from 1967:Q1 through 2000:Q4.26 As described in the text, we use two
(overlapping) data sets. The …rst data set consists of the 190 series used to construct the
26

We start in 1967 because many of the series used to generate the principal components used in the
FAVAR speci…cation are available only from 1967 onward.

27

b
factors in the FAVAR model. Speci…cally, the six factors comprising vector Yt in equation
(2.18) are the …rst six principal components of these 190 data series. 154 of these series
are monthly, and the remaining 36 are quarterly. To facilitate computation of principal

components, each of these data series is rendered stationary. Table 1A lists these data in
detail, along with the stationarity-inducing transformations used.
The second data set is used to construct the series zt (in equation (2.17), whose impulse
responses are to be computed. The data used are as follows:
Data on real GDP and its components (total consumption expenditure, investment in
equipment and software, investment in structures, residential investment) are quarterly
data (seasonally adjusted in chained 2000 dollars) from the Bureau of Economic Analysis (BEA). The output gap is the log of real GDP minus the log of the Congressional
Budget O¢ ce’ measure of potential GDP.
s
Our measure of the price level is the GDP chain-type price index from BEA. The 3
month in‡
ation rate is the log di¤erence of the price level.
Labor productivity is seasonally adjusted business sector output per hour of all persons
(seasonally adjusted) from the Bureau of Labor Statistics (BLS)
Employment is total nonfarm employment, and payroll hours series is the aggregate
total private hours per week index. Both of these are seasonally adjusted data from
the BLS establishment survey.
The real compensation series is business sector real compensation per hour from the
BEA, de‡
ated by the GDP chain-type price index.
The Federal Funds Rate is the e¤ective funds rate from the Federal Reserve Bank of
New York. The 1- 12- and 60-month zero coupon Treasury yields are from the FamaBliss zero coupon bond …les in the CRSP database. The S&P500 Stock Index is from
Standard and Poor’ All of these …nancial data series are converted to quarterly series
s.
by sampling the last business day of each quarter.
Our measure of the excess stock market return is the …rst Fama-French factor from
Kenneth French’ web page
s
http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html

These data are rendered quarterly by sampling the last month of quarter.

28

Pro…ts is the BEA measure of corporate pro…ts (pre-tax) from current production,
seasonally adjusted.
For all series other than the in‡
ation rate, interest rates, and excess stock returns, we
estimate the VAR in log-di¤erences, and then we cumulated the impulse responses to display
the responses of log-levels.

29

References
[1] Basu, S., Fernald, J., and M. Kimball. (2004) Are Technology Improvements Contractionary? Forthcoming in the American Economic Review.
[2] Basu, S., Fernald, J., and Shapiro, M. (2001a) Productivity Growth in the 1990s: Technology, Utilization, or Adjustment? Carnegie-Rochester Conference Series on Public
Policy, December 2001, v. 55, iss. 0, pp. 117-65
[3] Basu, S., Fernald, J. and M. Shapiro. (2001b) Productivity Growth in the 1990s: Updated Estimates. Unpublished memorandum, Federal Reserve Bank of Chicago.
[4] Baxter, M. and King, R. (1990) Productive Externalities and Cyclical Volatility, Working Paper 245, Rochester Center for Economic Research.
[5] Benhabib, J., Rogerson, R., and Wright, R. (1991) Homework in Macroeconomics:
Household Production and Aggregate Fluctuations. Journal of Political Economy, 99,
1166-87.
[6] Bernanke, B.S., Boivin, J., and Eliasz, P. (2005) Measuring the E¤ects of Monetary
Policy: A Factor-Augmented Vector Autoregressive (FAVAR) Approach. Quarterly
Journal of Economics, 120:387-422.
[7] Blanchard, O. J. (1989) A Traditional Interpretation of Macroeconomic Fluctuations
American Economic Review, 79: 1146-1164.
[8] Blanchard, O. J. and D. Quah (1989). The Dynamic E¤ects of Aggregate Demand and
Supply Disturbances. American Economic Review, September 1989, v. 79, iss. 4, pp.
655-73
[9] Boivin, J. and Giannoni, M. (2006) DSGE Models in a Data-Rich Environment.
N.B.E.R. Working Paper No. 02138.
[10] Boldrin, M., Christiano, L., and Fisher, J. (2001) Habit Persistence, Asset Returns, and
the Business Cycle. American Economic Review, 91: 149-166.
[11] Boyd, J., Hu, J., and Jagannathan, R. (2005) The Stock Market’ Reaction to Unems
ployment News: Why Bad News Is Usually Good for Stocks. The Journal of Finance,
v. 60, iss. 2, pp. 649-72.

30

[12] Braun, R.A. and Evans, C.L. (1998) Seasonal Solow Residuals and Christmas: A Case
for Labor Hoarding and Increasing Returns. Journal of Money, Credit, and Banking,
v.30, pp. 306-30.
[13] Burnside, C. Eichenbaum, M., and Rebelo, S (1993) Labor Hoarding and the Business
Cycle, Journal of Political Economy, v. 101, pp. 245-73.
[14] Chang, Y., and Shorfheide, F. (2003) Labor-Supply Shifts and Economic Fluctuations,
Journal of Monetary Economics; v. 50, pp. 1751-68.
[15] Christiano, L., Eichenbaum, M., and Evans, C. (1999) Monetary Policy Shocks: What
Have We Learned and to What End? Handbook of Macroeconomics Vol. 1A, ed. by J.
Taylor and M. Woodford, Amsterdam: Elsevier Science, B.A.
[16] Christiano, L., Eichenbaum, M., and Evans, C. (2005) Nominal Rigidities and the Dynamic E¤ects of a Shock to Monetary Policy, Journal of Political Economy, 113: 1-45
[17] Christiano, L., Eichenbaum, M. and R. Vigfusson (2003). What happens after a technology shock? Unpublished manuscript, Northwestern University.
[18] Del Negro, M., Shorfheide, F., Smets, F., and Wouters, R. (2005). On the Fit and
Forecasting Performance of New Keynesian Models. C.E.P.R Discussion Paper No.
4848.
[19] Eichenbaum, M., and Fisher, J., (2004) Evaluating the Calvo model of sticky prices.
N.B.E.R. Working Paper No. 10617.
[20] Eichenbaum, M. S., Hansen, L. P., and Singleton, K. J. (1988) A Time Series Analysis
of Representative Agent Models of Consumption and Leisure Choice under Uncertainty.
Quarterly Journal of Economics, 103: 51-78.
[21] Evans, C. (1992) Productivity Shocks and Real Business Cycles. Journal of Monetary
Economics 29: 191-209.
[22] Evans, C. and D. Marshall. (2003) Economic Determinants of the Nominal Treasury
Yield Curve. Chicago Fed Working Paper.
[23] Fama, E. and K. French (1993) Common Risk Factors in the Returns on Stock and
Bonds. Journal of Financial Economics, February 1993, v. 33, iss. 1, pp. 3-56
[24] Fuhrer, J.C. (2000), Habit Formation in Consumption and Its Implications for
Monetary-Policy Models. American Economic Review, v. 90, pp. 367-90.
31

[25] Galí, J. (1992) How Well Does the IS-LM Model Fit Post War Data? Quarterly Journal
of Economics, 107: 709 - 738.
[26] Galí, J. (1999) Technology, Employment, and the Business Cycle: Do Technology Shocks
Explain Aggregate Fluctuations? American Economic Review: 249-71.
[27] Galí, J., and Gertler, M., (1999) In‡
ation Dynamics: A Structural Econometric Analysis. Journal of Monetary Economics;v. 44, pp 195-222.
[28] Galí, J., Gertler, M., Lopez-Salido, D. (2001) Markups, Gaps, and the Welfare Costs of
Business Fluctuations NBER Working Paper No. 8850.
[29] Greenwood, J. and Hercowitz, Z. (1991) The Allocation of Capital and Time over the
Business Cycle, Journal of Political Economy, 99: 1188-1214.
[30] Hall, R.E. (1997) Macroeconomic Fluctuations and the Allocation of Time, Journal of
Labor Economics, 15, S223-50.
[31] Holland, A., and Scott, A. (1998) The Determinants of UK Business Cycles, Economic
Journal, 108:1067-92.
[32] King, R. and M. Watson (1997), Testing Long-Run Neutrality. Federal Reserve Bank
of Richmond Economic Quarterly, Summer 1997, v. 83, iss. 3, pp. 69-101
[33] Kozicki, S. and P. Tinsley (2001), Shifting Endpoints in the Term Structure of Interest
Rates. Journal of Monetary Economics, June 2001, v. 47, iss. 3, pp. 613-52
[34] Kydland, F. and E. Prescott (1982) Time-to-build and Aggregate Fluctuations. Econometrica.
[35] Leeper, E., Sims, C., and Zha, T. (1996) What does monetary policy do? Brookings
Papers on Economic Activity, issue 2, pp. 1-63.
[36] Litterman, R. and L. Weiss, (1985), Money, Real Interest Rates, and Output: A Reinterpretation of Postwar U.S. Data. Econometrica, January 1985, v. 53, iss. 1, pp. 129-56
[37] Lucas, R. (1972) Econometric testing of the Natural Rate Hypothesis, in The Econometrics of Price Determination Conference, Otto Eckstein (ed.), Federal Reserve Board
of Governors, Washington, D.C., pp. 50-59.
[38] Lucas, R. and N. Stokey, (1987) Money and Interest in a Cash-in-Advance Economy.
Econometrica, May 1987, v. 55, iss. 3, pp. 491-513
32

[39] Mulligan, C. B. (2002) A Century of Labor-Leisure Distortions. National Bureau of
Economic Research Working Paper: 8774.
[40] Prescott, E. (1986) Theory Ahead of Business Cycle Measurement. Carnegie-Rochester
Conference Series on Public Policy 25: 11-44.
[41] Ramey, V., and N. Francis (2006) A Century of Work and Leisure. NBER W.P. 12264.
[42] Sargent, T.J., and Sims, C.A. (1977) Business cycle modeling without pretending to
have too much a priori economic theory , Federal Reserve Bank of Minneapolis, Working
Paper No. 55.
[43] Shapiro, M.D., (1986) ”
Capital Accumulation and Capital Utilization: Theory and
Evidence,”Journal of Applied Econometrics, v.1, pp. 211-34.
[44] Shapiro, M. and Watson, M. (1988) Sources of Business Cycle Fluctuations. NBER
Macroeconomic Annual, pp. 111-148.
[45] Sims, C. (1980) Macroeconomics and Reality. Econometrica, 48: 1 - 48.
[46] Sims, C. (1992) Interpreting the Macroeconomic Time Series Facts: The e¤ects of monetary policy. European Economic Review, v. 36, pp. 975-1011.
[47] Sims, C. and Zha, T. (1998) Does Monetary Policy Generate Recessions? Federal Reserve Bank of Atlanta Working Paper 98-12.
[48] Staiger, D., Stock, J. H. and Watson, M. W. (1997) The NAIRU, Unemployment and
Monetary Policy; Journal of Economic Perspectives, v. 11, pp. 33-49
[49] Stock, J.H.; Watson, M.W. (1989) New Indexes of Coincident and Leading Economic
Indicators NBER Macroeconomics Annual: pp. 351-94, Cambridge, Mass. and London:
MIT Press
[50] Stock, J.H.; Watson, M.W. (1998) Di¤usion Indexes. NBER Working Paper No.6702.
[51] Stock, J. and M. Watson, (2001), Vector Autoregressions. Journal of Economic Perspectives, Fall 2001, v. 15, iss. 4, pp. 101-15
[52] Stock, J. and M. Watson, (2002), Macroeconomic Forecasting Using Di¤usion Indices,
Journal of Business and Economics Statistics, v. 20, iss. 2, pp. 147-162.

33

[53] Strongin, S. (1995), The Identi…cation of Monetary Policy Disturbances: Explaining
the Liquidity Puzzle. Journal of Monetary Economics, August 1995, v. 35, iss. 3, pp.
463-97
[54] Taylor, J. B. (1993) Discretion Versus Policy Rules in Practice, Carnegie-Rochester
Conference on Public Policy, 39, 195-214.
[55] Zellner (1971), An Introduction to Bayesian Inference in Econometrics, New York:John
Wiley & Sons.
[56] Zha, T. (1999) Block Recursion and Structural Vector Autoregressions, Journal of
Econometrics, 90, 290-316.

34

Table 1: Granger-Causality Tests for MRS Measure
Explanatory # Lags Marginal Signi…cance
Variable
of F-test
Detrended
GDP

4
5
6
4
5
6
4
5
6

Fed Funds
Rate
Term
Spread

Notes:

0.742
0.891
0.715
0.356
0.582
0.510
0.199
0.165
0.202

This table displays the marginal signi…cance of exclusion F-statistics for the

following Granger-Causality regressions

M RS;t

=

N
X

j M RS;t j

+

j Xt j

+ wi;t ;

j=1

where N = 4; 5; or 6; the explanatory variable X is either detrended GDP, the federal funds
rate, or the term spread (de…ned as the di¤erence between the 5-year Treasury Yield and
the federal funds rate); and the F-statistic tests the hypothesis

j

= 0; 8j = 1; :::; N:

Table 2: Correlation Matrix of the Model-Based Shock Measures
M RS

MP
MP
M RS
T ECH

1.0
0.11
1.0
-0.037 0.062

35

T ECH

1.0

Table 3: R2 s For Regression of Model-Based Shock Measures on VAR
Residuals
Shock Measure R2 when regressed on VAR residuals F -test
54.1%
29.7
MP
(0.000)
53.6%
61.2
M RS
(0.000)
52.3%
140.7
T ECH
(0.000)
Notes: The second column displays the R2 s for the regressions
C4 ut

4

+ wt (equation (2.9)), where

t

denotes the 3

t

= C0 ut +C1 ut

1 +:::+

1 vector of model-based measures, ut

denotes the 6 1 vector of VAR residuals, and wt denotes the 3 1 vector of residuals.. The
third column displays the F-statistic testing the hypothesis that the given row of C0 = 0.

36

Table 4
Fraction of Variance of Endogenous Variables Accounted for by the Three
Identified Shocks
Notes: For each of the variables listed, the table gives the median fraction of 3-, 12, and
60-month ahead forecast variance accounted for by the three identified shocks, εMP ,
εMRS , and εTECH, according to the posterior distribution. The fourth line in each panel
gives the median fraction of each forecast variance accounted for by the three shocks
collectively. The two numbers in parentheses following each median statistic give the
95% and 5% quantiles of the posterior distribution for each forecast variance fraction.
These statistics were computed using 500 draws from the posterior distribution of the
model’s parameters.

Real GDP
Steps ahead:

3-month

12-months

60-months

Shock
Shock
Shock
Total

0.049
0.282
0.344
0.721

0.064
0.328
0.422
0.861

0.124
0.107
0.527
0.844

to MP
to MRS
to Tech
of 3 Shocks

(0.233,0.001)
(0.514,0.088)
(0.573,0.151)
(0.779,0.632)

(0.224,0.021)
(0.609,0.087)
(0.702,0.176)
(0.909,0.763)

(0.433,0.014)
(0.411,0.024)
(0.774,0.208)
(0.928,0.648)

Total Consumption Expenditures
Steps ahead:
3-month

12-months

60-months

Shock
Shock
Shock
Total

0.112
0.137
0.372
0.661

0.081
0.060
0.399
0.617

to MP
to MRS
to Tech
of 3 Shocks

0.009
0.305
0.156
0.492

(0.076,0.000)
(0.478,0.121)
(0.332,0.033)
(0.598,0.365)

(0.322,0.014)
(0.369,0.029)
(0.593,0.134)
(0.768,0.497)

(0.330,0.013)
(0.284,0.011)
(0.650,0.162)
(0.791,0.400)

Investment Equip & Software
Steps ahead:
3-month

12-months

60-months

Shock
Shock
Shock
Total

0.027
0.535
0.128
0.721

0.058
0.289
0.303
0.712

to MP
to MRS
to Tech
of 3 Shocks

0.027
0.339
0.015
0.404

(0.116,0.001)
(0.430,0.221)
(0.095,0.000)
(0.488,0.307)

(0.136,0.008)
(0.702,0.307)
(0.357,0.014)
(0.801,0.602)

(0.274,0.011)
(0.576,0.074)
(0.606,0.070)
(0.864,0.490)

Investment Structures
Steps ahead:
3-month

12-months

60-months

Shock
Shock
Shock
Total

0.034
0.346
0.074
0.497

0.030
0.461
0.179
0.735

to MP
to MRS
to Tech
of 3 Shocks

0.031
0.074
0.020
0.138

(0.095,0.001)
(0.137,0.028)
(0.061,0.001)
(0.201,0.089)

(0.186,0.002)
(0.512,0.186)
(0.246,0.005)
(0.626,0.361)

(0.229,0.003)
(0.717,0.185)
(0.488,0.016)
(0.861,0.548)

Residential Investment
Steps ahead:
3-month

12-months

60-months

Shock
Shock
Shock
Total

0.232
0.104
0.225
0.591

0.164
0.240
0.147
0.605

to MP
to MRS
to Tech
of 3 Shocks

0.005
0.245
0.061
0.328

(0.048,0.000)
(0.336,0.133)
(0.179,0.004)
(0.399,0.257)

(0.419,0.086)
(0.233,0.052)
(0.412,0.050)
(0.698,0.459)

(0.340,0.058)
(0.513,0.036)
(0.313,0.039)
(0.808,0.316)

Table 4 (continued)
Labor Productivity
Steps ahead:

3-month

12-months

60-months

Shock
Shock
Shock
Total

0.019
0.019
0.464
0.530

0.041
0.025
0.435
0.536

0.044
0.045
0.337
0.472

to MP
to MRS
to Tech
of 3 Shocks

(0.099,0.000)
(0.118,0.000)
(0.552,0.347)
(0.600,0.446)

(0.190,0.012)
(0.104,0.005)
(0.569,0.289)
(0.652,0.413)

(0.207,0.007)
(0.209,0.008)
(0.537,0.156)
(0.656,0.299)

Payroll Employment
Steps ahead:

3-month

12-months

60-months

Shock
Shock
Shock
Total

0.098
0.522
0.028
0.688

0.031
0.592
0.161
0.821

0.085
0.212
0.440
0.831

to MP
to MRS
to Tech
of 3 Shocks

(0.290,0.007)
(0.655,0.360)
(0.186,0.000)
(0.755,0.601)

(0.139,0.010)
(0.764,0.319)
(0.422,0.029)
(0.882,0.702)

(0.369,0.010)
(0.545,0.050)
(0.741,0.158)
(0.912,0.639)

Payroll Hours
Steps ahead:

3-month

12-months

60-months

Shock
Shock
Shock
Total

0.094
0.537
0.016
0.690

0.040
0.595
0.139
0.816

0.072
0.247
0.405
0.803

to MP
to MRS
to Tech
of 3 Shocks

(0.282,0.007)
(0.673,0.373)
(0.140,0.000)
(0.764,0.583)

(0.147,0.012)
(0.768,0.347)
(0.391,0.026)
(0.884,0.679)

(0.314,0.013)
(0.552,0.068)
(0.715,0.137)
(0.902,0.621)

Real Wage
Steps ahead:

3-month

12-months

60-months

Shock
Shock
Shock
Total

0.046
0.002
0.003
0.055

0.050
0.044
0.013
0.120

0.109
0.167
0.095
0.460

to MP
to MRS
to Tech
of 3 Shocks

(0.094,0.008)
(0.016,0.000)
(0.024,0.000)
(0.106,0.018)

(0.141,0.006)
(0.122,0.009)
(0.042,0.004)
(0.226,0.040)

(0.373,0.006)
(0.443,0.011)
(0.334,0.005)
(0.691,0.198)

Inflation
Steps ahead:

3-month

12-months

60-months

Shock
Shock
Shock
Total

0.045
0.007
0.130
0.199

0.037
0.095
0.194
0.362

0.216
0.164
0.171
0.596

to MP
to MRS
to Tech
of 3 Shocks

(0.162,0.001)
(0.061,0.000)
(0.229,0.035)
(0.307,0.108)

(0.117,0.008)
(0.260,0.022)
(0.356,0.070)
(0.502,0.210)

(0.419,0.067)
(0.370,0.054)
(0.341,0.060)
(0.774,0.390)

Federal Funds Rate
Steps ahead:

3-month

12-months

60-months

Shock
Shock
Shock
Total

0.342
0.141
0.068
0.577

0.147
0.511
0.047
0.726

0.074
0.594
0.090
0.803

to MP
to MRS
to Tech
of 3 Shocks

(0.485,0.186)
(0.329,0.032)
(0.194,0.002)
(0.648,0.498)

(0.302,0.066)
(0.647,0.345)
(0.146,0.010)
(0.795,0.628)

(0.227,0.024)
(0.761,0.302)
(0.351,0.013)
(0.891,0.617)

1-month Treasury Yield
Steps ahead:
3-month

12-months

60-months

Shock
Shock
Shock
Total

0.114
0.378
0.032
0.552

0.071
0.540
0.108
0.751

to MP
to MRS
to Tech
of 3 Shocks

0.164
0.087
0.015
0.281

(0.254,0.084)
(0.189,0.025)
(0.064,0.000)
(0.357,0.211)

(0.248,0.047)
(0.511,0.251)
(0.123,0.009)
(0.641,0.449)

(0.203,0.023)
(0.725,0.262)
(0.376,0.011)
(0.860,0.575)

Table 4 (continued)
12- month Treasury Yield
Steps ahead:
3-month

12-months

60-months

Shock
Shock
Shock
Total

0.150
0.421
0.021
0.624

0.079
0.546
0.077
0.746

to MP
to MRS
to Tech
of 3 Shocks

0.247
0.152
0.008
0.422

(0.373,0.122)
(0.288,0.052)
(0.055,0.000)
(0.504,0.334)

(0.337,0.048)
(0.569,0.251)
(0.128,0.004)
(0.715,0.513)

(0.214,0.026)
(0.741,0.294)
(0.336,0.008)
(0.867,0.570)

60- month Treasury Yield
Steps ahead:
3-month

12-months

60-months

Shock to
Shock to
Shock to

0.121 (0.235,0.084)
0.137 (0.245,0.025)
0.005 (0.047,0.000)

0.133 (0.314,0.026)
0.339 (0.505,0.192)
0.015 (0.088,0.002)

0.076 (0.221,0.023)
0.511 (0.709,0.277)
0.038 (0.210,0.006)

Total of 3 Shocks

0.287 (0.363,0.196)

0.522 (0.628,0.394)

0.662 (0.823,0.467)

S&P500 Stock Index
Steps ahead:

3-month

12-months

60-months

Shock
Shock
Shock
Total

0.040
0.010
0.033
0.094

0.081
0.059
0.049
0.199

0.086
0.092
0.074
0.262

MP
MRS
Tech

to MP
to MRS
to Tech
of 3 Shocks

(0.101,0.008)
(0.046,0.000)
(0.095,0.003)
(0.176,0.047)

(0.172,0.026)
(0.118,0.028)
(0.097,0.019)
(0.334,0.117)

(0.162,0.038)
(0.152,0.040)
(0.138,0.024)
(0.355,0.181)

Excess Stock Market Return
Steps ahead:
3-month

12-months

60-months

Shock
Shock
Shock
Total

0.078
0.043
0.067
0.193

0.081
0.065
0.079
0.233

to MP
to MRS
to Tech
of 3 Shocks

0.066
0.006
0.047
0.132

(0.141,0.017)
(0.044,0.000)
(0.100,0.007)
(0.194,0.076)

(0.143,0.031)
(0.087,0.017)
(0.116,0.025)
(0.266,0.128)

(0.144,0.036)
(0.112,0.033)
(0.134,0.038)
(0.311,0.162)

Table 5: Long-Run Responses to 1 SD Shock
GDP
Productivity
Technology Shock 58 bps (1.00) 31 bps (0.99)
7 bps (0.61) -15 bps (0.19)
MRS Shock
MP Shock
3 bps (0.53) 12 bps (0.73)
Notes: This table gives the median 80-quarter ahead responses of GDP and labor productivity to a one standard deviation impulse to each of the three shocks listed in the
left-most column.

The numbers in parenthesis give the probability that this 80-quarter

ahead response is positive according to the Bayesian posterior distribution.

37

Table 1A: Data Used in Constructing FAVAR Factors

Panel A: Monthly Data Series

Data Description

Transformation

Personal Consumption Expenditures (SAAR, Bil.Chn.2000$)

log 1st diff

Personal Consumption Expenditures: Durable Goods (SAAR, Bil.Chn.2000$)

log 1st diff

Personal Consumption Expenditures: Nondurable Goods (SAAR,Bil.Chn.2000$)

log 1st diff

Personal Consumption Expenditures: Services (SAAR, Bil.Chn.2000$)

log 1st diff

Real Disposable Personal Income (SAAR, Bil.Chn.2000$)

log 1st diff

Value of Public Construction Put in Place (SAAR, Mil.Chn. $)

log 1st diff

Value of Private Construction Put in Place (SAAR, Mil. Chn. $)

log 1st diff

Manufacturers' Shipments of Mobile Homes (SAAR, Thous.Units)

log

Housing Starts (SAAR, Thous.Units)

log

Housing Starts: Midwest (SAAR, Thous.Units)

log

Housing Starts: Northeast (SAAR, Thous.Units)

log

Housing Starts: South (SAAR, Thous.Units)

log

Housing Starts: West (SAAR, Thous.Units)

log

Industrial Production Index (SA, 1997=100)

log 1st diff

Industrial Production: Consumer Goods (SA, 1997=100)

log 1st diff

Industrial Production: Durable Consumer Goods (SA, 1997=100)

log 1st diff

Industrial Production: Nondurable Consumer Goods (SA, 1997=100)

log 1st diff

Industrial Production: Business Equipment (SA, 1997=100)

log 1st diff

Industrial Production: Materials (SA, 1997=100)

log 1st diff

Industrial Production: Durable Goods Materials (SA, 1997=100)

log 1st diff

Industrial Production: Nondurable Goods Materials (SA, 1997=100)

log 1st diff

Industrial Production: Nonindustrial Supplies (SA, 1997=100)

log 1st diff

Industrial Production: Mining (SA, 1997=100)

log 1st diff

Industrial Production: Final Products (SA, 1997=100)

log 1st diff

Industrial Production: Durable Goods [NAICS] (SA, 1997=100)

log 1st diff

Industrial Production: Manufacturing [SIC] (SA, 1997=100)

log 1st diff

Industrial Production: Nondurable Manufacturing (SA, 1997=100)

log 1st diff

Industrial Production: Final Products and Nonindustrial Supplies (SA, 1997=100)

log 1st diff

Industrial Production: Electric and Gas Utilities (SA, 1997=100)

log 1st diff

All Employees: Construction (SA, Thous)

log 1st diff

All Employees: Durable Goods Manufacturing (SA, Thous)

log 1st diff

All Employees: Financial Activities (SA, Thous)

log 1st diff

All Employees: Goods-producing Industries (SA, Thous)

log 1st diff

All Employees: Government (SA, Thous)

log 1st diff

All Employees: Manufacturing (SA, Thous)

log 1st diff

All Employees: Mining (SA, Thous)

log 1st diff

All Employees: Total Nonfarm (SA, Thous)

log 1st diff

All Employees: Nondurable Goods Manufacturing (SA, Thous)

log 1st diff

All Employees: Total Private Industries (SA, Thous)

log 1st diff

All Employees: Retail Trade (SA, Thous)

log 1st diff

All Employees: Service-providing Industries (SA, Thous)

log 1st diff

All Employees: Aggregate of categories

log 1st diff

Civilian Employment: Nonagricultural Industries: 16 yr + (SA, Thous)

log 1st diff

Ratio: Help-Wanted Advertising in Newspapers/Number Unemployed (SA)

log 1st diff

Average Weekly Hours: Overtime: Manufacturing (SA, Hrs)

1st diff

Average Weekly Hours: Manufacturing (SA, Hrs)

1st diff

ISM Mfg: PMI Composite Index (SA, 50+ = Econ Expand)

level

ISM Mfg: Employment Index (SA, 50+ = Econ Expand)

level

ISM Mfg: Inventories Index (SA, 50+ = Econ Expand)

level

ISM Mfg: New Orders Index (SA, 50+ = Econ Expand)

level

ISM Mfg: Production Index (SA, 50+ = Econ Expand)

level

Real Retail Sales: Durable Goods (SA, Mil.Chain.2000$)

log 1st diff

Retail Sales: Retail Trade (SA, Spliced, Mil.Chn 2000$)

log 1st diff

Real Retail Sales: Nondurable Goods (SA, Mil.Chain.2000$)

log 1st diff

Real Inventories: Mfg: Durable Goods Industries (SA, EOP, Spliced, Mil Chn 2000$)

log 1st diff

Real Manufacturing & Trade Inventories: Mfg Industries (SA, EOP, Spliced, Mil.Chn 2000$)

log 1st diff

Real Mfg Inventories: Nondurable Goods Industries (SA, EOP, Spliced, Mil.Chn 2000$)

log 1st diff

Real Inventories: Retail Trade Industries (SA, EOP, Spliced, Mil.Chn 2000$)

log 1st diff

Real Manufacturing & Trade Inventories: Industries (SA, EOP, Spliced, Mil.Chn 2000$)

log 1st diff

Real Inventories: Merchant Wholesale Trade Industries (SA, EOP, Spliced, Mil.Chn 2000$)

log 1st diff

Real Inventories/Sales Ratio: Manufacturing Industries (SA, Spliced, Chained 2000$)

1st diff

Inventories/Sales Ratio: Retail Trade Industries (SA, Spliced, Chained 2000$)

1st diff

Real Manufacturing & Trade: Inventories/Sales Ratio (SA, Spliced, Chained 2000$)

1st diff

Inventories/Sales Ratio: Merchant Wholesale Trade Industries(SA, Chained 2000$)

1st diff

Real Sales: Mfg: Durable Goods Industries(SA, Spliced, Mil.Chn 2000$)

log 1st diff

Real Sales: Manufacturing Industries (SA, Spliced, Mil.Chn 2000$)

log 1st diff

Real Sales: Mfg: Nondurable Goods Industries (SA, Spliced, Mil.Chn 2000$)

log 1st diff

Real Manufacturing & Trade Sales: All Industries (SA, Spliced, Mil.Chn 2000$)

log 1st diff

Real Sales: Merchant Wholesalers: Durable Gds Industrs (SA, Spliced, Mil.Chn 2000$)

log 1st diff

Real Sales: Merchant Wholesale Trade Industries (SA, Spliced, Mil.Chn 2000$)

log 1st diff

Real Sales: Merch Wholesale: Nondurable Goods Industries (SA, Mil.Chn 2000$)

log 1st diff

Real Personal Income Less Transfer Payments (SAAR, Bil.Chn.2000$)

log 1st diff

PCE: Durable Goods: Motor Vehicles and Parts (SAAR, Mil.Chn.2000$)

log 1st diff

Mfrs New Orders: Durable Goods (SA, Mil.Chn.2000.$)

log 1st diff

Manufacturers New Orders: Consumer Goods & Materials (SA, Mil. 1982$)

log 1st diff

Manufacturers New Orders: Nondefense Capital Goods (SA, Mil. 1982$)

log 1st diff

New Pvt Housing Units Authorized by Building Permit (SAAR, Thous.Units)

log

Capacity Utilization: Manufacturing [SIC] (SA, Percent of Capacity)

1st diff

Index of Help-Wanted Advertising in Newspapers (SA,1987=100)

log 1st diff

Civilian Unemployment Rate: 16 yr + (SA, %)

1st diff

University of Michigan: Consumer Expectations (NSA, 66Q1=100)

level

Civilians Unemployed for Less Than 5 Weeks (SA, Thous.)

level

Civilians Unemployed for 15-26 Weeks (SA, Thous.)

level

Civilians Unemployed for 5-14 Weeks (SA, Thous.)

level

Average {Mean} Duration of Unemployment (SA, Weeks)

level

Civilians Unemployed for 15 Weeks and Over (SA, Thous.)

level

Civilians Unemployed for 27 Weeks and Over (SA, Thous.)

level

Adjusted Monetary Base (SA, Mil.$)

log 2nd diff

Adjusted Nonborrowed Reserves of Depository Institutions (SA, Mil.$)

log 2nd diff

Adjusted Nonborrowed Reserves Plus Extended Credit (SA, Mil.$)

log 2nd diff

Adjusted Reserves of Depository Institutions (SA, Mil.$)

log 2nd diff

Adj Monetary Base inc Deposits to Satisfy Clearing Bal Contracts (SA, Bil.$)

log 2nd diff

Money Stock: M1 (SA, Bil.$)

log 2nd diff

Real Money Stock: M2 (SA, Bil.Chn.2000$)

log 1st diff

Money Stock: M3 (SA, Bil.$)

log 2nd diff

Nominal Broad Trade-Weighted Exchange Value of the US$ (JAN 97=100)

log 1st diff

Foreign Exchange Rate: United Kingdom (US$/Pound)

log 1st diff

Moody's Seasoned Aaa Corporate Bond Yield (% p.a.)

1st diff

Moody's Seasoned Baa Corporate Bond Yield (% p.a.)

1st diff

Moody's Seasoned Aaa Corporate Bond Yield - Federal Funds Rate(% p.a.)

level

Moody's Seasoned Baa Corporate Bond Yield - Federal Funds Rate (% p.a.)

level

S&P: Composite 500, Dividend Yield (%)

level

Stock Price Index: Standard & Poor's 500 Composite (1941-43=10)

log 1st diff

S&P: 500 Composite, P/E Ratio, 4-Qtr Trailing Earnings

level

Stock Price Index: NYSE Composite (Avg, Dec. 31, 2002=5000)

log 1st diff

Stock Price Index: Standard & Poor's 400 Industrials (1941-43=10)

log 1st diff

3-Month Treasury Bills, Secondary Market (% p.a.)

1st diff

6-Month Treasury Bills, Secondary Market (% p.a.)

1st diff

3-Month Treasury Bills - Federal Funds Rate, (% p.a.)

level

6-Month Treasury Bills - Federal Funds Rate (% p.a.)

level

1-Year Treasury Bill Yield at Constant Maturity (% p.a.)

1st diff

5-Year Treasury Note Yield at Constant Maturity (% p.a.)

1st diff

1-Year Treasury Bill Yield at Constant Maturity - Federal Funds Rate (% p.a.)

level

5-Year Treasury Note Yield at Constant Maturity - Federal Funds Rate (% p.a.)

level

10-Year Treasury Note Yield at Constant Maturity - Federal Funds Rate (% p.a.)

level

PPI: Crude Materials for Further Processing (SA, 1982=100)

log 2nd diff

PPI: Finished Consumer Goods (SA, 1982=100)

log 2nd diff

CPI-U: Apparel (SA, 1982-84=100)

log 2nd diff

CPI-U: Commodities (SA, 1982-84=100)

log 2nd diff

CPI-U: Durables (SA, 1982-84=100)

log 2nd diff

CPI-U: Services (SA, 1982-84=100)

log 2nd diff

CPI-U: Medical Care (SA, 1982-84=100)

log 2nd diff

CPI-U: All Items Less Food (SA, 1982-84=100)

log 2nd diff

CPI-U: All Items Less Medical Care (SA, 1982-84=100)

log 2nd diff

CPI-U: All Items Less Shelter (SA, 1982-84=100)

log 2nd diff

CPI-U: Transportation (SA, 1982-84=100)

log 2nd diff

PCE: Durable Goods: Chain Price Index (SA, 2000=100)

log 2nd diff

PCE: Personal Consumption Expenditures: Chain Price Index (SA, 2000=100)

log 2nd diff

PCE: Nondurable Goods: Chain Price Index (SA, 2000=100)

log 2nd diff

PCE: Services: Chain Price Index (SA, 2000=100)

log 2nd diff

Avg Hourly Earnings: Construction (SA, $/Hr)

log 2nd diff

Avg Hourly Earnings: Manufacturing (SA, $/Hr)

log 2nd diff

Commercial & Industrial Loans Outstanding (EOP, SA, Mil.Chn.2000 $)

1st diff

Money Stock: M2 (SA, Bil.$)

log 2nd diff

10-Year Treasury Note Yield at Constant Maturity (% p.a.)

1st diff

Federal Funds [effective] Rate (% p.a.)

1st diff

PPI: Intermediate Materials, Supplies and Components (SA, 1982=100)

log 2nd diff

PPI: Finished Goods (SA, 1982=100)

log 2nd diff

ISM: Mfg: Prices Index (NSA, 50+ = Econ Expand)

level

CPI-U: All Items (SA, 1982-84=100)

log 1st diff

Mfrs' New Orders:Durable Goods Industries With Unfilled Orders (SA,Mil$)

log 1st diff

Manufacturers' New Orders (SA, Mil.$)

log 1st diff

Manufacturers' New Orders: Nondurable Goods Industries (SA, Mil.$)

log 1st diff

Mfrs' New Orders:Nondurable Goods Industries W/Unfilled Orders (SA,Mil$)

log 1st diff

Manufacturers' Unfilled Orders: Durable Goods Industries (EOP,SA,Mil.$)

log 1st diff

Manufacturers' Unfilled Orders (EOP, SA, Mil.$)

log 1st diff

Manufacturers' Unfilled Orders:Nondurable Goods Industries (EOP,SA,Mil$)

log 1st diff

Foreign Exchange Rate: Canada (C$/US$)

log 1st diff

Foreign Exchange Rate: Germany (D. Mark/US$)

log 1st diff

Foreign Exchange Rate: Japan (Yen/US$)

log 1st diff

Foreign Exchange Rate: Switzerland (Franc/US$)

log 1st diff

Contracts & Orders: Plant & Equipment (SA, Mil.$)

log 1st diff

Panel B: Quarterly Data
Data Description

Transformation

Business Sector: Compensation per Hour of all Persons (SA,1992=100)

log 1st diff

Business Sector: Real Compensation per Hour of all Persons (SA,1992=100)

log 1st diff

Business Sector: Unit Labor Costs (SA,1992=100)

log 1st diff

Business Sector: Unit Non-Labor Payments (SA,1992=100)

log 1st diff

Non-farm Business Sector: Unit Non-Labor Payments (SA,1992=100)

log 1st diff

Non-financial Corporations: Output per Hour, All employees (SA, 1992=100)

log 1st diff

Non-financial Corporations: Compensation per Hour, All employees (SA, 1992=100)

log 1st diff

Non-financial Corporations: Real Compensation per Hour, All employees (SA, 1992=100)

log 1st diff

Non-financial Corporations: Unit Labor Costs, All employees (SA, 1992=100)

log 1st diff

Non-financial Corporations: Unit Non-Labor Costs, All employees (SA, 1992=100)

log 1st diff

Non-financial Corporations: Total Unit Costs, All employees (SA, 1992=100)

log 1st diff

Business Sector: Real Unit Labor Costs (SA,1992=100)

log 1st diff

Non-financial Corporations: Real Unit Labor Costs, All employees (SA, 1992=100)

log 1st diff

Business Sector: Real Unit Non-Labor Payments (SA,1992=100)

log 1st diff

Non-farm Business Sector: Real Unit Non-Labor Payments (SA,1992=100)

log 1st diff

Non-financial Corporations: Real Unit Non-Labor Costs, All employees (SA, 1992=100)

log 1st diff

Non-financial Corporations: Real Total Unit Costs, All employees (SA, 1992=100)

log 1st diff

Government Total Receipts (SAAR, Bil. $)

log 1st diff

Government Total Expenditures (SAAR, Bil. $)

log 1st diff

Government Net Lending or Net Borrowing (SAAR, Bil. $)

1st diff

GDP Deflator

log 1st diff

Gross Private Domestic Investment: Implicit Price Deflator (SA, 2000=100)

log 1st diff

Private Fixed Investment: Implicit Price Deflator (SA, 2000=100)

log 1st diff

Private Non-residential Fixed Investment: Implicit Price Deflator (SA, 2000=100)

log 1st diff

Private Non-residential Structures: Implicit Price Deflator (SA, 2000=100)

log 1st diff

Private Non-residential Equipment/Software: Implicit Price Deflator (SA, 2000=100)

log 1st diff

Private Residential Investment: Implicit Price Deflator (SA, 2000=100)

log 1st diff

Government Consumption/Gross Investment: Implicit Price Deflator (SA, 2000=100)

log 1st diff

Federal Non-Defense Consumption/Investment: Implicit Price Deflator (SA, 2000=100)

log 1st diff

Imports of Goods & Services: Implicit Price Deflator (SA, 2000=100)

log 1st diff

Exports of Goods & Services: Implicit Price Deflator (SA, 2000=100)

log 1st diff

Non-farm Business Sector: Output per Hour of all Persons (SA,1992=100)

log 1st diff

Non-farm Business Sector: Compensation per Hour of all Persons (SA,1992=100)

log 1st diff

Non-farm Business Sector: Real Compensation per Hour of all Persons (SA,1992=100)

log 1st diff

Non-farm Business Sector: Unit Labor Costs (SA,1992=100)

log 1st diff

Non-farm Business Sector: Real Unit Labor Costs (SA,1992=100)

log 1st diff

Figure 1: Long Horizon Responses
Tech Shock --> GDP

MRS Shock --> GDP

MP Shock --> GDP

1.8

1.8

1.8

1.2

1.2

1.2

0.6

0.6

0.6

0.0

0.0

0.0

-0.6

-0.6

-0.6

-1.2

-1.2

-1.2

3

19

35

51

67

Tech Shock --> Productivity

3

19

35

51

67

MRS Shock --> Productivity

3

19

35

51

67

MP Shock --> Productivity

1.0

1.0

1.0

0.5

0.5

0.5

0.0

0.0

0.0

-0.5

-0.5

-0.5

-1.0

-1.0

-1.0

3

19

35

51

67

3

19

35

51

67

3

19

35

51

67

Figure 2: Cyclical Responses
Tech Shock --> GDP

MRS Shock --> GDP

MP Shock --> GDP

1.8

1.8

1.8

1.2

1.2

1.2

0.6

0.6

0.6

0.0

0.0

0.0

-0.6

-0.6

-0.6

-1.2

1

5

9

13

17

-1.2

Tech Shock --> CONS

1

5

9

13

17

-1.2

MRS Shock --> CONS

1

5

9

13

17

MP Shock --> CONS

1.2

1.2

1.2

0.8

0.8

0.8

0.4

0.4

0.4

0.0

0.0

0.0

-0.4

-0.4

-0.4

-0.8

1

5

9

13

17

-0.8

1

Tech Shock --> BFI

5

9

13

17

-0.8

1

MRS Shock --> BFI

5

9

13

17

MP Shock --> BFI

5.0

5.0

5.0

2.5

2.5

2.5

0.0

0.0

0.0

-2.5

1

5

9

13

17

-2.5

Tech Shock --> RES

1

5

9

13

17

-2.5

1

MRS Shock --> RES

5

9

13

17

MP Shock --> RES

5.0

5.0

5.0

2.5

2.5

2.5

0.0

0.0

0.0

-2.5

-2.5

-2.5

-5.0

-5.0

-5.0

-7.5

1

5

9

13

17

Tech Shock --> Real Compensation

-7.5

1

5

9

13

17

MRS Shock --> Real Compensation

-7.5

1

5

9

13

17

MP Shock --> Real Compensation

1.0

1.0

1.0

0.5

0.5

0.5

0.0

0.0

0.0

-0.5

-0.5

-0.5

-1.0

1

5

9

13

17

-1.0

1

5

9

13

17

-1.0

1

5

9

13

17

Figure 3: Responses of Labor Inputs and Productivity
Tech Shock --> Hours

MRS Shock --> Hours

MP Shock --> Hours

1.5

1.5

1.5

1.0

1.0

1.0

0.5

0.5

0.5

0.0

0.0

0.0

-0.5

-0.5

-0.5

-1.0

-1.0
1

5

9

13

17

Tech Shock --> Employment

-1.0
1

5

9

13

17

MRS Shock --> Employment

1

5

9

13

17

MP Shock --> Employment

1.5

1.5

1.5

1.0

1.0

1.0

0.5

0.5

0.5

0.0

0.0

0.0

-0.5

-0.5

-0.5

-1.0

-1.0
1

5

9

13

17

Tech Shock --> Productivity

-1.0
1

5

9

13

17

MRS Shock --> Productivity

1

5

9

13

17

MP Shock --> Productivity

1.0

1.0

1.0

0.5

0.5

0.5

0.0

0.0

0.0

-0.5

-0.5

-0.5

-1.0

-1.0
1

5

9

13

17

-1.0
1

5

9

13

17

1

5

9

13

17

Figure 4: Responses of Inflation and Output Gap
Tech Shock --> Inflation

MRS Shock --> Inflation

MP Shock --> Inflation

0.50

0.50

0.50

0.25

0.25

0.25

0.00

0.00

0.00

-0.25

-0.25

-0.25

-0.50

-0.50

-0.50

-0.75

-0.75

-0.75

1

6

11

16

1

Tech Shock --> Output Gap

6

11

16

1

MRS Shock --> Output Gap

6

11

16

MP Shock --> Output Gap

1.5

1.5

1.5

1.0

1.0

1.0

0.5

0.5

0.5

0.0

0.0

0.0

-0.5

-0.5

-0.5

-1.0

-1.0

-1.0

1

5

9

13

17

1

5

9

13

17

1

5

9

13

17

Figure 5: Responses of Interest Rates
Tech Shock --> Fed Funds Rate

MRS Shock --> Fed Funds Rate

MP Shock --> Fed Funds Rate

1.5

1.5

1.5

1.0

1.0

1.0

0.5

0.5

0.5

0.0

0.0

0.0

-0.5

-0.5

-0.5

-1.0

-1.0
1

5

9

13

17

-1.0
1

5

9

13

17

1

Tech Shock --> 1 Month Treasury Yield

MRS Shock --> 1 Month Treasury Yield

1.0

1.0

0.5

0.0

-0.5

17

0.0

-0.5

13

0.5

0.0

9

1.0

0.5

5

-0.5

-1.0

-1.0
1

5

9

13

17

Tech Shock --> 12 Month Treasury Yield

MP Shock --> 1 Month Treasury Yield

-1.0
1

5

9

13

17

MRS Shock --> 12 Month Treasury Yield

1

5

9

13

17

MP Shock --> 12 Month Treasury Yield

1.0

1.0

1.0

0.5

0.5

0.5

0.0

0.0

0.0

-0.5

-0.5

-0.5

-1.0

-1.0
1

5

9

13

17

-1.0
1

5

9

13

17

1

Tech Shock --> 5 Year Treasury Yield

MRS Shock --> 5 Year Treasury Yield

0.75

0.75
0.50
0.25
0.00

0.00

-0.25

-0.25

17

0.25

0.00

13

0.50

0.25

9

0.75

0.50

5

-0.25

-0.50

-0.50
1

6

11

16

MP Shock --> 5 Year Treasury Yield

-0.50
1

6

11

16

1

6

11

16

Figure 6: Responses of Equity Markets
Tech Shock --> S&P 500

MRS Shock --> S&P 500

MP Shock --> S&P 500

18

18

18

9

9

9

0

0

0

-9

-9

-9

-18

-18
1

5

9

13

-18

17

Tech Shock --> Excess Stock Return

1

5

9

13

17

1

MRS Shock --> Excess Stock Return

5

9

13

17

MP Shock --> Excess Stock Return

0.90

0.90

0.90

0.45

0.45

0.45

-0.00

-0.00

-0.00

-0.45

-0.45

-0.45

-0.90

-0.90

-0.90

-1.35

-1.35
1

6

11

-1.35

16

1

Tech Shock --> Profits

6

11

16

1

MRS Shock --> Profits

6

11

16

MP Shock --> Profits

5.0

5.0

5.0

2.5

2.5

2.5

0.0

0.0

0.0

-2.5

-2.5

-2.5

-5.0

-5.0
1

5

9

13

17

-5.0
1

5

9

13

17

1

5

9

13

17

Figure 7
Baseline Shocks vs. Single-Eta Shocks
Baseline MP Shock --> Price

Single-Eta MP Shock --> Price

Baseline MP Shock --> Durable Cons.

Single-Eta MP Shock --> Durable Cons.

0.5

0.5

1.8

1.8

0.0

0.0

0.9

0.9

-0.5

-0.5

-0.0

-0.0

-1.0

-1.0

-0.9

-0.9

-1.5

-1.5

-1.8

-1.8

-2.0

-2.0
1

5

9

13

17

Baseline MP Shock --> Inflation

-2.7
1

5

9

13

-2.7

17

Single-Eta MP Shock --> Inflation

1

5

9

13

17

Baseline MP Shock --> Investment E&S

1

5

9

13

17

Single-Eta MP Shock --> Investment E&S

0.4

0.4

2

2

0.2

0.2

1

1

-0.0

-0.0

0

0

-0.2

-0.2

-1

-1

-0.4

-0.4

-2

-2

-0.6

-0.6
1

5

9

13

17

Baseline MP Shock --> Total Cons.

-3
1

5

9

13

17

Single-Eta MP Shock --> Total Cons.

0.4

0.4

-0.0

-3
1

5

9

13

17

1

5

9

13

17

Baseline Tech Shock --> Fed Funds Rate Single-Eta Tech Shock --> Fed Funds Rate

-0.0
0.6

0.0

0.0

-0.4

-0.8

1.2

0.6

-0.4

1.2

-0.8

-1.2

-1.2
1

5

9

13

17

-0.6
1

5

9

13

17

-0.6
1

5

9

13

17

1

5

9

13

17


Federal Reserve Bank of St. Louis, One Federal Reserve Bank Plaza, St. Louis, MO 63102