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Federal Reserve Bank of Chicago

Two Flaws in Business Cycle
Accounting
Lawrence J. Christiano and Joshua M. Davis

WP 2006-10

Two Flaws In Business Cycle Accounting∗
Lawrence J. Christiano†

Joshua M. Davis‡

October 18, 2006

Abstract
Using ‘business cycle accounting’ (BCA), Chari, Kehoe and McGrattan (2006)
(CKM) conclude that models of financial frictions which create a wedge in the intertemporal Euler equation are not promising avenues for modeling business cycle dynamics.
There are two reasons that this conclusion is not warranted. First, small changes in the
implementation of BCA overturn CKM’s conclusions. Second, one way that shocks to
the intertemporal wedge impact on the economy is by their spillover effects onto other
wedges. This potentially important mechanism for the transmission of intertemporal
wedge shocks is not identified under BCA. CKM potentially understate the importance
of these shocks by adopting the extreme position that spillover effects are zero.

∗

The first author is grateful for the financial support of a National Science Foundation grant. We are
grateful for several key discussions with Mark Gertler, as well as for discussions with Martin Eichenbaum.
†
Northwestern University, National Bureau of Economic Research.
‡
Northwestern University.

1. Introduction
Chari, Kehoe and McGrattan (2005) (CKM) argue that a procedure they call Business Cycle
Accounting (BCA) is useful for identifying promising directions for model development.1 The
key substantive finding of CKM is that financial frictions like those analyzed by Carlstrom
and Fuerst (1997) (CF) and Bernanke, Gertler and Gilchrist (1999) (BGG) are not promising
avenues for studying business cycles. Based on our analysis of business cycle data for the
US in the 1930s and for the US and 14 other OECD countries in the postwar period, we find
that the CKM conclusion is not warranted.
The BCA strategy begins with the standard real business cycle (RBC) model, augmented
by introducing four shocks, or ‘wedges’. A vector autoregressive representation (VAR) for
the wedges is estimated using macroeconomic data on output, consumption, investment
and government consumption.2 The macroeconomic data are assumed to be observed with a
small measurement error whose variance is fixed a priori. The fitted wedges have the property
that when they are fed simultaneously to the augmented RBC model, the model reproduces
the four macroeconomic data series up to the small measurement error. The importance of
a particular wedge is determined by feeding it to the model, holding all the other wedges
constant, and comparing the resulting model predictions with the data. One of the wedges,
the intertemporal wedge, is the shock that enters between the intertemporal marginal rate of
substitution in consumption and the rate of return on capital. CKM argue that this wedge
contributes very little to business cycle fluctuations, for the following two reasons: (i) the
wedge accounts for only a small part of the movement in macroeconomic variables during
recessions and (ii) the wedge drives consumption and investment in opposite directions,
while these two variables display substantial positive comovement over the business cycle.
CKM assert that their conclusions are robust to various model perturbations, including the
introduction of adjustment costs in investment.
There are two reasons that BCA does not warrant being pessimistic about the usefulness of models of financial frictions such as those proposed in CF or BGG. First, CKM’s
conclusions are not robust to small changes in the way they implement BCA. For example,
when we redo CKM’s calculations for the 1982 recession, we reproduce their finding that the
intertemporal wedge accounts for essentially no part of the decline in output below trend
at the trough of the recession. When we introduce a modest amount of investment adjustment costs, the intertemporal wedge accounts for a substantial 34 percent of the drop in
output at the trough of the recession.3 We then consider an alternative specification of the
intertemporal wedge which is at least as plausible as the one CKM work with. CKM define
the intertemporal wedge as an ad valorem tax on the price of investment goods. We argue
that the CF and BGG models motivate considering an alternative formulation in which the
1
This strategy is closely related to that advocated in Parkin (1988), Ingram, Kocherlakota and Savin
(1994), Hall (1997), and Mulligan (2002).
2
The last variable includes government consumption and net exports.
3
Our adjustment costs are ‘modest’ in two senses. First, they imply a steady state elasticity of the
investment-capital ratio to the price of capital equal to unity. This lies in the middle of the range of
empirical estimates reported in the literature. Second, the adjustment cost function has the property that
the quantity of resources lost due to investment adjustment costs is small, even in the wake of the enormous
decline in investment in the early 1930s (see section 4 below for a detailed discussion).

2

wedge is modeled as a tax on the gross rate of return on capital. When we work with this alternative formulation, the intertemporal wedge accounts for 26 percent of the drop in output
at the trough of the 1982 recession. But, when we also drop CKM’s model of measurement
error, that quantity jumps to 52 percent. Notably, the CKM model of measurement error is
overwhelmingly rejected in the post war US data. So, BCA actually places a range of 0 to
52 percent on the fraction of the drop in output accounted for by the intertemporal wedge in
the 1982 recession. This range is sufficiently wide to comfortably include most views about
the importance of the intertemporal wedge.
We show that, at a qualitative level, economic theory predicts the lack of robustness in
BCA that we find. The intertemporal wedge associated with different perturbations of the
RBC model represent different ways of bundling the fundamental economic shocks to the
economy. As a result, the BCA experiment of feeding measured wedges to an RBC model
represents fundamentally different economic experiments under alternative specifications of
the RBC model. Since the experiments are different, the outcomes are expected to be
different too. Our results show that these expected differences are quantitatively large enough
to overturn CKM’s conclusions.
Second, CKM’s analysis ignores that the financial shocks which drive the intertemporal
wedge may have spillover effects onto other wedges.4 It is not possible to determine the
magnitude of these effects with BCA, because BCA leaves the fundamental shocks to the
economy unidentified. In fact, the VAR for the wedges estimated under BCA is consistent
with a wide range of possible spillover patterns. In terms of CKM’s conclusion (i) above,
we show that the financial shocks which drive the intertemporal wedge could account for
as much as 70-100 percent of reductions in output in US recessions, including the Great
Depression. We obtain the same finding for several other countries in the OECD. Regarding
CKM’s conclusion (ii), we show that once spillover effects are taken into account, financial
shocks which drive the intertemporal wedge can drive consumption and investment in the
same direction.
CKM understand that the fundamental economic shocks are not identified under BCA.
However, the implications they draw from this observation are very different from the ones
we draw. They say, ‘Our method is not intended to identify the primitive sources of shocks.
Rather, it is intended to help understand the mechanisms through which such shocks lead to
economic fluctuations.’5 We find that, without the ability to identify the economic shocks,
a potentially important part of the mechanism by which these shocks affect the economy the spillover effects - is also not identified. In effect, BCA offers a menu of observationally
equivalent assessments about the importance of shocks to the intertemporal wedge. By
focusing exclusively on the extreme case of zero spillovers, CKM select the element in the
menu which minimizes the role of intertemporal shocks. We show that there are other
elements in that menu which assign a very large role to intertemporal shocks.
4

Recent developments in economic modeling suggest a variety of mechanisms by which these spillover
effects can occur. For example, it is known that in models with Calvo-style wage-setting frictions (see,
e.g., Erceg, Henderson and Levin (2000)), a shock outside the labor market can trigger what looks like a
preference shock for labor, or a ‘labor wedge’. Similarly, variable capital utilization can have the effect that
a non-technology shock triggers a move in measured TFP, or the ‘efficiency wedge’.
5
The quote is taken from the CKM introduction. It summarizes CKM’s comments in section 3 of their
paper.

3

Following is an outline of the paper. In the following section, we describe the model used
in the analysis. In section 3, we elaborate on the observational equivalence results discussed
above. In section 4, we discuss our model solution and estimation strategy. In section 5 we
discuss the lack of identification of spillover effects in BCA. In section 6 we discuss the wedge
decomposition under BCA and our modification to take into account spillovers. Section 7
displays the results of implementing BCA on various data sets. Concluding remarks appear
in section 8. Additional technical details appear in three Appendices.

2. The Model and the Wedges
This section describes the model used in the analysis. In addition, we discuss the wedges
and, in particular, our two specifications of the intertemporal wedge.
According CKM’s version of the RBC model, households maximize:
E

∞
X
t=0

(β (1 + gn ))t [log ct + ψ log (1 − lt )] , 0 < β < 1,

where ct and lt denote per capita consumption and employment, respectively. Also, gn is the
population growth rate and ψ > 0 is a parameter. The household budget constraint is
ct + (1 + τ x,t ) xt ≤ rt kt + (1 − τ l,t ) wt lt + Tt ,
where Tt denotes lump sum taxes, xt denotes investment and τ l,t denotes the labor wedge.
Here, kt denotes the beginning-of-period t stock of capital divided by the period t population.
The variable, τ x,t , is CKM’s specification of the intertemporal wedge. The technology for
capital accumulation is given by:
µ ¶
xt
kt ,
(2.1)
(1 + gn ) kt+1 = (1 − δ) kt + xt − Φ
kt
where Φ (ζ) is symmetric about ζ = b, where b is the steady state investment-capital ratio. In
addition, to ensure that Φ has no impact on steady state, we suppose that Φ (b) = Φ0 (b) = 0.
The household maximizes utility by choice of {ct , kt+1 , lt , xt } , subject to its budget constraint, the capital evolution equation, the laws of motion of the wedges and the usual
inequality constraints and no-Ponzi scheme condition.
The resource constraint is:
ct + gt + xt = y (kt , lt , Zt ) = ktα (Zt lt )1−α ,

(2.2)

where
Zt = Z̃t (1 + gz )t ,
and Z̃t , the ‘efficiency’ wedge, is an exogenous stationary stochastic process. In the resource
constraint, gt denotes government purchases of goods and services plus net exports, which
is assumed to have the following trend property:
gt = g̃t (1 + gz )t ,
4

where g̃t is a stationary, exogenous stochastic process and gz ≥ 0.
Combining firm and household first order necessary conditions for optimization in the
case Φ = 0,
−ul,t
= (1 − τ l,t ) yl,t
uc,t
uc,t = βEt uc,t+1

(2.3)

h
³
´
³
´
i
xt+1
t+1
t+1
+ Φ0 xkt+1
yk,t+1 + (1 + τ x,t+1 ) Pk0 ,t+1 1 − δ − Φ xkt+1
kt+1
(1 + τ x,t ) Pk0 ,t

(2.4)

where uc,t and −ul,t are the derivatives of period utility with respect to consumption
and leisure, respectively. In addition, yl,t and yk,t are the marginal products of labor and
capital, respectively. Also, the price of capital, Pk0 ,t , is
Pk0 ,t =

1
³

1 − Φ0

xt+1
kt+1

´.

(2.5)

The equilibrium values of {ct , kt+1 , lt , xt } are computed by solving (2.1), (2.2), (2.3), (2.4),
subject to the transversality condition and the following law of motion for the exogenous
shocks:
⎛
⎞
log Z̃t
⎜ τ l,t ⎟
0
0
⎟
st = [I − P ] P0 + P st−1 + ut , st = ⎜
(2.6)
⎝ τ x,t ⎠ , Eut ut = QQ = V,
log g̃t
where P0 is the 4 × 1 vector of unconditional means for st and
¸
∙
¸
∙
Q̄ 0
P̄ 0
, Q=
.
P =
0 q44
0 p44

(2.7)

Here, P is stationary and P̄ is not otherwise restricted. The symmetric matrix, V, in (2.6)
must satisfy the zero restrictions implicit in QQ0 = V, and the zeros in the lower diagonal
part of Q in (2.7). We follow CKM in implementing the zero restrictions in our analysis
of the US Great Depression. We do this in our analysis of OECD countries as well. In
our analysis of postwar US data, we allow all elements of P and all elements in the lower
triangular part of Q to be non-zero. The parameters of (2.6) are P0 , P, and V, possibly with
the indicated zero restrictions on V and the zero and stationarity restrictions on P.
We consider an alternative specification of the intertemporal wedge. Our specification is
motivated by our analysis of the version of the CF model with adjustment costs and by our
analysis of BGG. In Appendix A, we derive equilibrium conditions for a version of the CF
model with Φ 6= 0. We establish a proposition displaying a set of wedges which, if added
to the RBC economy, ensure that the equilibrium allocations of the RBC economy coincide
with those of our version of the CF economy with investment adjustment costs. We show
that the intertemporal wedge has the following form:
¡
¢ k
uc,t = βEt uc,t+1 1 − τ kt+1 Rt+1
,
(2.8)
5

where,
Rtk =

h
³ ´
³ ´ i
yk,t + Pk0 ,t 1 − δ − Φ xktt + Φ0 xktt xktt
Pk0 ,t−1

(2.9)

Note that in the alternative formulation, the wedge is a tax on the gross return to capital, in
contrast to CKM’s value-added tax on investment purchases, τ x,t . In Appendix A we show
that the CF model with adjustment costs implies τ kt+1 is a function of uncertainty realized
at date t, but not at date t + 1.6 We follow CKM in presuming that all wedges implied by
the CF financial frictions apart from the intertemporal wedge, 1 − τ kt+1 , are quantitatively
small and can be ignored.
In Appendix B we derive the intertemporal wedge associated with the BGG model. That
model also implies that the intertemporal wedge enters as 1−τ kt+1 in (2.8). The only difference
is that under BGG, τ kt+1 is a function of the period t + 1 realization of uncertainty.7
In our alternative specification of the intertemporal wedge, we allow τ kt to respond to
current and past information. This assumption encompasses both the CF and BGG financial
friction models, since the econometric estimation is free to produce a τ kt whose response to
current information is very small.

3. General Observations on the Robustness of BCA to Modeling
Details
In later sections, we show that the conclusions of BCA for the importance of the intertemporal wedge are not robust to alternative specifications of the intertemporal wedge, and to
alternative specifications of investment adjustment costs. This finding may at first seem puzzling in light of a type of observational equivalence result emphasized in CKM. An example
of this type of result which occurs when BCA is done with a linearly approximated RBC
model is the following. Consider an RBC economy with, say, no investment adjustment costs
(i.e., Φ = 0) and a particular time series representation for the wedges. After introducing
adjustment costs (i.e., Φ 6= 0), one can find a new representation of the intertemporal wedge
which ensures that the equilibria of the economies with and without adjustment costs coincide.8 This is an observational equivalence result because it implies that the likelihood of a
6

That appendix provides a careful derivation of our result, because our finding for the way the intertemporal wedge enters (2.8) differs from CKM’s finding. CKM consider the case, Φ = 0, in deriving the wedge
representation of the CF model. The results for the Φ = 0 and Φ 6= 0 cases are qualitatively different.
When Φ = 0 capital producers simply produce increments to the capital stock, which capital owners add
to the existing undepreciated capital by themselves. When Φ 6= 0, old capital is a fundamental input in
the production of new capital. In this case, we assume that the capital producers must purchase the economy’s entire stock of capital in order to produce new capital, so that their financing requirements and the
associated frictions are different. There are perhaps other ways of arranging the production of new installed
capital when Φ 6= 0. We find our way convenient because it results in an intertemporal wedge that virtually
coincides with the one we derive for BGG
7
CKM derive the intertemporal wedge for a version of the BGG model in which banks have access to
complete state-contingent markets. Our wedge formula applies to the model analyzed in BGG, which does
not permit complete markets.
8
Here, we make use of our asumption that analysis is done using log-linear approximation. In this case,
the only effect of the change in Φ is to change the rate of return on capital. For example, in the linear

6

set of allocations is invariant to the presence of adjustment costs. This case of adjustment
costs is just example of the type of observational equivalence result we have in mind. For
example, consider an RBC economy in which the intertemporal wedge is of the τ x,t type
emphasized by CKM. Given a specification of the joint time series representation of τ x,t and
the other wedges, the τ x,t RBC model implies a set of equilibrium allocations. Now consider
an alternative RBC economy in which the intertemporal wedge is of the τ kt type. There
exists a specification of the joint stochastic process for τ kt and the other wedges having the
property that the equilibrium allocations in the τ kt RBC model coincide with those in the τ x,t
RBC model. Again, this stochastic process is identified from the requirement that the after
tax rates of return in the two economies coincide. In both of the above examples, it is clear
that the observational equivalence result depends on the assumption that the time series
representations used for the shocks are sufficiently flexible to accommodate any specification
for the stochastic process of the wedges.9
We wish to stress here that the equilibrium observational equivalence result does not
imply a ‘BCA robustness result’. In particular, the outcome of BCA (i.e., the outcome of
feeding fitted wedges, one at a time, to a model) is not expected to be robust to the specification of investment adjustment costs, or to whether the intertemporal wedge is modeled as
τ x,t or τ kt . There are two reasons for this lack of robustness. One is practical and reflects that
the analyst must confine him/herself to a specific parametric time series representation of
the wedges, thus potentially ruling out one of the conditions of the observational equivalence
result. The other, deeper, reason is the one mentioned in the introduction. Even if the
analyst uses a completely flexible time series representation of the wedges, the intertemporal
wedge represents a different bundle of fundamental shocks under alternative perturbations
of the model. Feeding the measured intertemporal wedge to an RBC model under alternative model perturbations represents a different experiment and so is expected to produce a
different outcome.
To illustrate these observations, suppose the data are generated by an RBC model in
which intertemporal wedge is the τ kt type, with a certain specification of the adjustment cost
function, Φ. The joint time series representation of the wedges is given by (2.6), in which P
and Q are diagonal. Thus, each wedge is uncorrelated with all other wedges, at all leads and
lags. In this case, BCA has a clear interpretation: when the estimated intertemporal wedge
is fed to the baseline RBC model, the simulations display the model’s response to a particular
history of past innovations to that wedge alone. Suppose the econometrician is provided with
an infinite amount of data, but misspecifies the adjustment cost function, Φ. As in BCA,
the econometrician only estimates the joint time series representation of the wedges, and
holds the misspecified Φ and other nonstochastic parts of the economy fixed. We assume
that the econometrician’s time series representation for the wedges is sufficiently flexible
to encompass the quasi-true time series of the wedges that is implied by the observational
equivalence result. We obtain insight into BCA by deriving that time series representation.
The requirement that the after tax rates of return in the econometrician’s model coincide
approximation the law of motion for the capital stock, (2.1), is always linear and invariant to a.
9
This is a special case of a well-known result that econometric identification often hinges on having
sufficient restrictions on the unobserved shocks.

7

with the true after tax rate of return implies, using (2.9):
h
³ ´
³ ´ i
xt
0 xt xt
0 ,t 1 − δ − Φ̄
y
+
P̄
+
Φ̄
k,t
k
¡
¢
kt
kt
kt
h
³ ´
³ ´ i.
1 − τ kt+1 = 1 − τ̄ kt+1
yk,t + Pk0 ,t 1 − δ − Φ xktt + Φ0 xktt xktt

(3.1)

Here, a − over a variable indicates the value of the variable in the true model and absence of
a − indicates the value estimated by the econometrician who misspecifies Φ. The endogenous
variables on the right side of the equality in (3.1) are specific functions of the history of the
innovations driving the wedges in the actual economy. Then, according to (3.1), the adjusted
time series representation of τ kt is the convolution of these functions with the function on
the right of the equality in (3.1). We derive this map from the fundamental innovations in
the economy to τ kt using linearization.
Consider the true specification of Φ and the true joint time series representation of the
wedges, st , given in (2.6). Let zt denote the list of endogenous variables in the model, i.e.,
zt = (ct , xt , kt+1 , lt , τ kt ), where the quantity variables are measured in log deviations from
steady state and τ kt is in deviation from steady state. The equilibrium conditions of zt may
be written in the form:
Et [α0 zt+1 + α1 zt + α2 zt−1 + β 0 st+1 + β 1 st ] = 0, with st = P st−1 + Qεt .
´0
³
Here, st = log Z̃t , τ l,t , τ̄ kt , log g̃t . The expectational difference equation is composed of
the intertemporal first order condition (2.8), the intratemporal first order condition (2.3),
the law of motion for capital (2.1), the resource constraint, (2.2), and the mapping from
τ̄ kt to τ kt , (3.1), all after suitable log-linearization. The solution to this system is written
zt = Azt−1 + Bst , or, when expressed in moving average form10 :
zt = [I − AL]−1 B [I − P L]−1 Qεt .
Let τ denote the 5-dimensional column vector with all zeros, except a 1 in the 5th location.
Then, the time series representation for τ kt is
τ kt = τ [I − AL]−1 B [I − P L]−1 Qεt .
This is the convolution of (3.1) with the time series representation of the (linearized) variables in (3.1). Let ν denote the 3 by 4 matrix constructed by deleting the third row of
the 4-dimensional identity matrix and let St denote the 3 dimensional vector obtained by
deleting τ̄ kt from st . We conclude that the econometrician who misspecifies Φ will estimate
the following joint time series representation for the wedges in his misspecified model:
µ k ¶ ∙
¸
τt
τ [I − AL]−1 B
[I − P L]−1 Qεt .
=
St
ν
¢
¡
By inspection, it is clear that in general, the new joint series representation of τ kt , St has
a moving average component. To see this, it is useful to examine the iid case, P = 0 and
10

For further discussion, see Christiano (2002).

8

Q = I. Note first that τ [I − A]−1 B has the following form:
⎡
⎤−1
⎡
1 0 −L Laa3313−1 0 0
1 0 −a13 L 0 0 0
⎢ 0 1 −L a23
⎢ 0 1 −a23 L 0 0 0 ⎥
0 0
⎢
⎥
⎢
⎢ 0 0 − La133 −1 0 0
⎥
⎢
0 0 1 − a33 L 0 0 0 ⎥
⎢
La33 −1
τ [I − A]−1 B = τ ⎢
a43
⎢ 0 0 −a43 L 1 0 0 ⎥ B = τ ⎢
1 0
0
0
−L
⎢
La33 −1
⎥
⎢
⎢
a53
⎣ 0 0 −a53 L 0 1 0 ⎦
⎣ 0 0 −L La33 −1 0 1
0 0 −a63 L 0 0 1
0 0 −L Laa3363−1 0 0
£
¤
0 0 −a63 L 0 0 1 B
=
£
B51 − a63 B31 L B52 − a63 B32 L B53 − a63 B33 L B54 − a63 B34 L
=

⎤

0
0
0
0
0
1
¤

⎥
⎥
⎥
⎥
⎥B
⎥
⎥
⎦
,

where Bij denotes the ij th element of B. We conclude that the new joint representation of
the wedges is:
¢ ¸
µ k ¶ ∙ ¡
τt
B51 − a63 B31 L B52 − a63 B32 L B53 − a63 B33 L B54 − a63 B34 L
εt .
=
St
ν
Note that the intertemporal wedge has a pure, first order moving average representation,
even though τ kt in the correctly specified economy is iid and a function only of the third
element of εt . Evidently, the wedges in the misspecified economy do not obey the same first
order VAR(1) representation that st does. Thus, the analyst who is restricted VAR(1) (or,
VAR(q), q < ∞) representations for the wedges misrepresents the reduced form of the data.
Under these circumstances, it is not surprising that the conclusions of BCA will be different,
across different specifications of Φ.
Now, suppose that the analyst adopts a sufficiently flexible time series representation
of the wedges, so that the specification error described in the previous paragraph does not
occur. The intertemporal wedge, τ̄ kt , computed by the econometrician working with the
correct specification of Φ is a function of just the current realization of the third element of
εt . In the alternative specification, τ kt is a function of the entire history of all elements of εt .
Clearly, feeding the estimated intertemporal wedge to the model is a different experiment
across the two different specifications of Φ. This is why we do not expect the results of BCA
to be robust to perturbations in the RBC model.

4. Model Solution and Estimation
Here, we describe how we assigned values to the model parameters. A subset of the parameters were not estimated. These were set as in CKM:
β = 1/1.03, α = 0.35, δ = 0.0464, ψ = 2.24,
gn = 0.015, gz = 0.016.

(4.1)

Here, β, δ, gn , and gz are expressed at annual rates. These are suitably adjusted when we
analyze quarterly data. The first subsection below discusses the estimation of the parameters
of the exogenous shocks, P0 , P, and V, using data on output, consumption, investment and
9

government consumption plus net exports. Estimation is carried out conditional on a parameterization of the adjustment cost function. The parameterization of the adjustment cost
function is discussed in the second subsection. The third subsection rebuts some criticisms
of the investment adjustment cost function expressed in CKM. Their criticisms suggest that
investment adjustment costs are, in effect, a ‘nonstarter’. Since they are not empirically interesting, they therefore do not constitute a compelling basis for criticizing BCA. We explain
why we disagree with this assessment.
4.1. Estimating the Parameters of the Time Series Representation of the Wedges
For the US Great Depression, we used annual data covering the period, 1901-1940.11 Quarterly data covering the period 1959Q1-2004Q3 were used for the US and quarterly data over
various periods were used on 14 other OECD countries.12 Following CKM, the elements of
the matrices, P and V are estimated subject to the zero restrictions described in section 2,
and to the restriction that the maximal eigenvalue of P not exceed 0.995.
The first step of estimation is to set up the model’s solution in state space - observer
form:
Yt = H (ξ t ; γ) + υ t
¡
¢
ξ t = F ξ t−1 ; γ + ηut
µ ¶
0̃
, Eυ t υ 0t = R, Eut u0t = V,
γ = (P, P0 , V ) , η =
I
where 0̃ is a 1 × 4 vector of zeros and ξ t is the state of the system:
¶
µ
log k̃t
,
ξt =
st
where k̃t = kt / (1 + gz )t . Also, Yt is the observation vector:
⎛
⎞
log ỹt
⎜ log x̃t ⎟
⎟
Yt = ⎜
⎝ log lt ⎠ ,
log g̃t

(4.2)
(4.3)

(4.4)

(4.5)

where x̃t = xt / (1 + gz )t . Finally, υ t is a 4 × 1 vector of measurement errors, with
R = 0.0001 × I4 ,

(4.6)

where I4 is the four-dimensional identity matrix and CKM set the scale factor exogenously
(see CKM (technical appendix, page 16)). We refer to this specification of R as the ‘CKM
11

These data were taken from CKM, as supplied on Ellen McGrattan’s web site.
US data are the data associated with the CKM project, and were taken from Ellen McGrattan’s web
page. With two exceptions, data for other OECD countries were taken from Chari, Kehoe and McGrattan
(2002), also on Ellen McGrattan’s web site. Data on hours worked were taken from the OECD productivity
database. These data are annual and were converted to quarterly by log-linear interpolation. Population
data were taken from the OECD national databases and log-linearly intertpolated to quarterly.
12

10

measurement error assumption’. We repeat the analysis under CKM measurement error, as
well as with R = 0.
As noted in the introduction, the CKM specification of measurement error has an impact
on the analysis. CKM do not explain why they include measurement error, nor do they
discuss the a priori evidence which leads them to the specific values they choose for the
measurement error variance.13 We do have reason to believe the data are measured with
error. However, we know of no reason to take seriously the notion that CKM’s specification
even approximately captures actual data measurement error.14
We implement BCA using first and second-order approximations to the model’s equilibrium conditions. Consider the first order approximation. In this case, the representation of
the policy rule is:
log k̃t+1 = (1 − λ) λ0 + λ log k̃t + ψst ,
(4.7)
where λ0 and λ are scalars and ψ is a 1 × 4 row vector. Then, (4.2)-(4.3) can be written:
ξ t = F0 + F1 ξ t−1 + ηεt ,
¸
¸
∙
∙
(1 − λ) λ0
λ ψ
,
, F1 =
F0 =
0 P
(I − P ) P0
where F0 is a 5 × 1 column vector, and F1 is a 5 × 5 matrix. Also,
Yt = H0 + H1 ξ t + υ t ,

(4.8)

where H0 is a 4 × 1 column vector and H1 is a 4 × 4 matrix. The Gaussian likelihood is
constructed using F0 , F1 , H0 , H1 , V, R, and Y = (Y1 , ..., YT ) (see Hamilton (1994)). These
in turn can be constructed using γ, R. Thus, the likelihood can be expressed as L (Y |γ; R) .
For the nonlinear case, we use the algorithm in Schmitt-Grohe and Uribe (2004) to obtain
second order approximations to the functions, F and H in (4.2) and (4.3). It is easy to see
that even if ut is Normally distributed, Yt will not be Normal in this nonlinear system.
We nevertheless proceed to form the Gaussian density function using the unscented filter
described in Wan and van der Merwe (2001). It is known that under certain conditions,
Gaussian maximum likelihood estimation has the usual desirable properties, even when the
data are not Gaussian.
4.2. Investment Adjustment Costs
To analyze the version of the model with adjustment costs, we must parameterize the investment adjustment cost function, Φ. Our calibration is based on our interpretation of the
variable, Pk0 ,t . On this dimension, the CF and BGG models differ slightly (for details, see
Appendices A and B). Both agree that Pk0 ,t is the marginal cost, in units of consumption
13

As already noted, other parameter values are also fixed in the analysis, such as production function
parameters. Dogmatic priors like this can perhaps be justified by appealing to analyses based on other data,
such as observations on income shares. We are not aware of any such argument, however, that can be used
as a basis for adopting the dogmatic priors in (4.6).
14
Based on what we know about the way data are collected, there is strong a priori reason to question the
CKM model of measurement error. For a careful discussion, see Sargent (1989).

11

goods, of producing new capital when only (2.1) is considered.15 However, in the CF model,
financial frictions introduce a wedge between the market price of capital and Pk0 ,t . Still, in
practice the discrepancy between Pk0 ,t and the market price of new capital in the CF model
with adjustment costs may be quantitatively small. To see this, it is instructive to consider
the response of the variables in the CF model (where Pk0 ,t = 1 always) to a technology shock.
According to CF (see Figure 2 in CF), the contemporaneous response of the market price
of capital is only one-tenth the contemporaneous response of investment. That simulation
suggests that the distinction between Pk0 ,t and the market price of capital may not be large
in the CF model.
In the BGG model, financial frictions arise inside the relationship between the managers
of capital and banks, and so the frictions do not open wedge between the marginal cost of
capital and Pk0 ,t . As a consequence, Pk0 ,t corresponds to the market price of capital in the
BGG model.
Under the interpretation of Pk0 ,t as the market price of capital, we can calibrate Φ based
on empirical estimates of the elasticity of investment with respect to the price of capital (i.e.,
Tobin’s q). From (2.5), this is
d log (xt /kt )
1
.
= 00
d log Pk0 ,t
Φ (b) b

(4.9)

According to estimates reported in Abel (1980) and Eberly (1997), Tobin’s q lies in a range
of 0.6 to 1.4. Interestingly, if we just consider the period of largest fall in the Dow Jones
Industrial average during the Great Depression, 1929Q4 to 1932Q4, the ratio of the percent
change in investment to the percent change in the Dow is 0.68.16 This is an estimate of
Tobin’s q under the assumption that the movement in the Dow reflects primarily the price
of capital, and not its quantity.17 This estimate lies in the middle of the Abel-Eberly range
of estimates. A unit Tobin’s q elasticity implies Φ00 (b) = 1/b.
Another factor impacting on our choice of Φ00 (b) is the model’s implication for the rate
of return on capital, Rk . Figure 1A shows the results corresponding to Tobin’s q elasticities
1/2, 1, 3 and ∞ (the latter corresponds to Φ00 (b) = 0). For each elasticity, the model
was estimated using the linearization strategy and using quarterly US data covering the
period 1959QIV-2003QI. For these calculations, the only feature of Φ that is required is the
value of Φ00 (b) . The model-based estimate of Rtk , (2.9), was computed using the two-sided
Kalman smoother.18 The US data on Rtk were constructed using Robert Shiller’s data on
real dividends and real stock prices for the S&P composite index. In the case of both modelbased and actual Rtk , we report centered, equally weighted, 5 quarter moving averages. Note
that without adjustment costs, the model drastically understates the volatility in Rtk . With
15

It is easy to verify that Pk0 ,t in (2.1) corresponds to the price of investment goods (i.e., unity) divided
by the marginal product of investment goods in producing end of period capital.
16
This is the ratio of the log difference in investment to the log difference in the Dow, over the period
indicated. Both variables were in nominal terms.
17
By associating the model’s capital stock with what is priced in the Dow, we are implicitly taking the
position that capital in the model corresponds to both tangible and intangible capital.
18
See Hamilton (1994) for a discussion. The two-sided smoother is required because we do not use empirical
data on the capital stock, which is an input in (2.9). Presumably, the smoother estimates the capital stock
by combining the investment data with the capital accumulation equation.

12

a Tobin’s q elasticity of 3 (i.e., Φ00 (b) = 1/(3b)) the model still substantially understates
that volatility. With an elasticity around unity, the model begins to reproduce the volatility
of Rk , though it is still somewhat low. Only with an elasticity around 1/2 does the model
nearly replicate the volatility of Rk . These results reinforce our impression that the data
suggest a Tobin’s q elasticity of unity or less. To be conservative, we work with an elasticity
of unity.
4.3. Responding to CKM’s Criticisms About Adjustment Costs
CKM criticize the use of adjustment costs with a unit Tobin’s q elasticity for two reasons.
According to their first critique, adjustment costs with a unit Tobin’s q elasticity imply
that an unreasonably large amount of resources are absorbed by adjustment costs during
collapse of investment in the Great Depression. This conclusion is based on the arbitrary
assumption that the adjustment cost function, Φ, is globally quadratic. But, we show that
other functional forms for Φ can be found with the property, Φ00 (b) = 1/b, whose global
properties do not imply that an inordinate amount of resources were used up in investment
adjustment costs in the Great Depression. Second, CKM assert that an adjustment cost
formulation which implies a static relationship between the investment-capital ratio and
Tobin’s q is empirically implausible. But, we show that BCA lacks robustness even with
the specification of adjustment costs proposed in Christiano, Eichenbaum and Evans (2004),
which does not imply a static relationship the investment-capital ratio and Tobin’s q. This
adjustment cost function, in which adjustment costs are a function of the change in the flow
of investment, also does not imply that an inordinate amount of resources were used up in
adjustment costs during the collapse of investment in the 1930s.19
The globally quadratic adjustment cost formulation adopted by CKM is:
µ
¶2
µ ¶
a xt
xt
=
−b ,
Φ
kt
2 kt
so that Φ00 (b) = a. Imposing that Tobin’s q elasticity is unity, the resources lost to adjustment
costs, as a fraction of output, is given by:
µ ¶
x
1
xt
= (λt − 1)2
,
(4.10)
Φ
kt
2
yµt
according to (2.1). Here, x/y is the steady state investment to output ratio. In (4.10),
we have used x = bk in the steady state. Here, λt is the time t investment-capital ratio,
expressed as a ratio to its steady state value, b. Also, µt is the output-capital ratio, expressed
as a ratio to its steady state value, y/k. Figure 6 indicates that output was 10 percent below
trend in 1930, and then fell another 10 percent in each of 1931 and 1932. In 1933, the trough
of the Depression, it fell yet another 5 percent, so that by 1933 output was a full 35 percent
19

This adjustment cost function has the additional advantage that it receives empirical support from the
analysis of housing investment (see Rosen and Topel (1988)) and aggregate Tobin’s q data (see Matsuyama
(1984)), in addition to the empirical evidence in Christiano, Eichenbaum and Evans (2006). Also, this
adjustment cost formulation has economically interesting microfoundations, as shown in Lucca (2006) and
Matsuyama (1984).

13

below trend. The drop in investment was even more dramatic. In 1930, 1931, 1932 and
1933 it was about 30, 50, 70 and 70 percent below trend, respectively. Using our capital
accumulation equation, we infer that the stock of capital was 10 percent below trend in 1933.
Since investment was 70 percent below its trend in 1933 and the capital stock was 10
percent its trend then, we infer that the investment to capital ratio is 60 percent below steady
state, i.e., λ1933 = 0.40. Output was 35 percent below steady state in 1933, and we infer that
the output-capital ratio was 25 percent below trend, so that µ1933 = 0.75. Substituting these
into (4.10),
µ ¶
1
xt
= (0.40 − 1)2 (0.23) /0.75 = 0.055,
Φ
kt
2
or 5.5 percent. Given that output was 35 percent below trend in 1933, the implication is that
16 percent of the drop in output reflected resources lost to adjustment costs associated with
the low level of investment. To see how sensitive this conclusion is to the choice of functional
form for Φ, consider Figure 1B, which graphs (4.10) for 100λt ranging from 40 percent to
160 percent, holding x/ (yµt ) fixed at 0.31. Note how the quadratic curve hits the vertical
axis at 5.5 percent. The other curve in Figure 1B coincides with the quadratic function
for λt roughly in its range for postwar business cycles. Outside this range, the alternative
function is flatter than the quadratic, and it hits the vertical axis at 2.5 percent. The
alternative adjustment cost function has a much more modest implication for the amount
of resources lost to adjustment costs as investment collapsed in the Great Depression. Yet,
the implications of the model with the alternative adjustment cost function for postwar
business cycles coincides with the implications of the model with the quadratic adjustment
cost function.20
To address CKM’s second concern about adjustment costs, we also considered the following formulation:
"
µ
¶2 #
xt
a
xt .
−1
(1 + gn ) kt+1 = (1 − δ) kt + 1 −
2 xt−1
With this formulation of adjustment costs, investment responds differently to permanent
and temporary changes in the price of capital. This addresses one of CKM’s concerns about
investment adjustment costs. To address the other concern, we needed to assign a value to
a. For this, we estimated the parameters of the joint time series representation of the wedges
for various values of a, using postwar US data. We found that with a = 3.75 the model’s
implications for the volatility of the rate of return on capital virtually coincides with the
implications of our baseline model with a unit Tobin’s q elasticity. We then used the Balke
and Gordon quarterly data on investment and output in the 1930s to compute the fraction
of output lost due to adjustment as investment plunged at the start of the Great Depression.
We found that the largest fraction of output lost due to adjustment costs in the period
1929Q1-1933Q1 was 1.46 percent. According to the Balke and Gordon data, investment
20

The alternative adjustment cost function is a 10th degree polynomial, and so it has a continuous derivative
of every order. It was constructed as follows. We constructed a ‘target’ function by splicing the quadratic
function in the range, λ ∈ (0.85, 1.15) , with straight lines on either end. The straight lines have slope equal
to that of the quadratic function at the point where they meet. The 10th degree polynomial was fit by
standard Chebyshev interpolation.

14

rose sharply starting in 1933Q2. Adjustment costs were larger then, but adjustment costs in
expansions are less of a concern to CKM.21 We conclude that with the alternative adjustment
costs, neither of CKM’s two objections apply.
Significantly, our finding that BCA is sensitive to the presence of adjustment costs is
also true when the adjustment costs are in terms of the change in investment. Ignoring the
spillover effects between wedges, as CKM do, we calculated the percent of the fall in output
due to the intertemporal wedge at the trough of five postwar US recessions. For the 1970,
1974, 1980, 1990 and 2000 recessions, the percentages are 17, 30, 14, 26, and 43, respectively.
All these are substantial amounts and certainly do not warrant the CKM conclusion that
financial frictions which manifest themselves primarily in the intertemporal wedge are not
worth pursuing.

5. Identification, the Importance of Financial Frictions and BCA
In the introduction we discussed the sense in which the importance of financial frictions is
not identified under BCA. We explain this here. We describe a statistic which we use to
characterize the importance of financial frictions. We show that a range of values for this
statistic is consistent with the same value of the likelihood function.
Until now, the basic shocks driving the system have been ut in (2.6). The interactions
among these shocks are left almost completely unrestricted under BCA. In part, this is
because the ut ’s are found to be highly correlated in practice. This correlation is assumed to
reflect that the elements of ut are overlapping combinations of different fundamental economic
shocks. Because fundamental economic shocks are assumed to be primitive and to have
separate origins, they are often assumed to be uncorrelated. We make this uncorrelatedness
assumption here. Denote the 5×1 vector of fundamental economic shocks by et . We normalize
their variances to unity, so that Eet e0t = I. We assume that the fundamental shocks are
related to the ut ’s by the following invertible relationship:
ut = Cet , Eet e0t = I, CC 0 = V,

(5.1)

where C has the structure of Q in (2.7).22 It is well known that even with a particular
estimate of V in hand, there are many C’s that satisfy CC 0 = V . Alternative specifications
of C that preserve the property, CC 0 = V, are observationally equivalent with respect to a
set of observations, Y = (Y1 , ..., YT ). Because this property plays a key role in our analysis,
it is useful to state it as a proposition:
21

According to Balke and Gordon’s data, per capita real investment, including durable goods, (1929
dollars), was 44, 65, 119, and 83 in the first to fourth quarters of 1933. Our estimate of the percent of
aggregate output lost to adjustment costs is 0.77, 3.09, 17.04, and 1.69 for each of the four quarters in 1933.
The number for 1933Q3 is very large. However, we note that it is generated by a rise in investment, not a
fall. In addition, we are suspicious that investment rose 83 percent in 1933Q3 and then fell about 30 percent
in 1933Q4. This sharp volatility is consistent with the possibility that measurement error overstated the
level of invesment in 1933Q3.
22
We are assuming that the fundamental economic shocks can be recovered from the space of current and
past shocks. Lippi and Reichlin (1993) challenge this assumption and discuss some of the implications of its
failure. See also Sims and Zha (1996) and Fernandez-Villaverde, Rubio-Ramirez and Sargent (2006).

15

Proposition 1. Consider a set of model parameter values, γ = (P, P0 , V ), with likelihood
value, L (Y |γ; R) . Perturbations of C such that CC 0 = V have no impact on the likelihood,
L.
Obviously, Proposition 1 applies for both the linear and the nonlinear strategies we use to
approximate the likelihood. Although BCA makes many detailed economic assumptions
(e.g., details about utility and technology), it does not make the assumptions needed to
identify the fundamental economic disturbances, et , to the economy.
We suppose, for the purpose of our discussion, that the third element in et corresponds
to the financial frictions shock which originates in the intertemporal wedge, which is the
third element of st .23 To discuss the difficulty of pinning down the importance of financial
frictions, it is useful to develop a constructive characterization of the family of C’s that
satisfy (5.1).24 Write
C = C̄W,
(5.2)
where W is any orthonormal matrix and C̄ is the unique lower diagonal matrix with nonnegative diagonal elements having the property that C̄ C̄ 0 = V . Although each C in (5.2) is
observationally equivalent by Proposition 1, each C implies a different et . To see this, note
that for any sequence of fitted disturbances, ut , one can recover a time series of et using
et = C −1 ut = W 0 C̄ −1 ut .

(5.3)

To see how many et ’s there are, for given V and sequence ut , let
⎡
⎤
a
b
c d
1 ⎢
e f ⎥
⎢ −b a
⎥,
W =
2a ⎣ −c −e a g ⎦
−d −f −g a

where g = (cf −de)/b. It is easy to verify that W is orthonormal for each θ = (a, b, c, d, e, f ) .
For a fixed set of observed ut , t = 1, ..., T, there is a different sequence, et , t = 1, ..., T,
associated with almost all θ ∈ R6 . According to Proposition 1, the likelihood of the data
based on the linear approximation is constant with respect to variations in θ.
We are now in a position to describe our measure of the importance of financial frictions.
This measure combines the two mechanisms by which financial frictions can matter. The first
is that financial frictions represent a source of shocks (see Figure 2). For us, the stand-in for
these shocks is e3t . These operate on the economy by driving the intertemporal wedge, s3t , (see
(i) in Figure 2) and through spillover effects onto other wedges ((iii) in Figure 2). The second
mechanism reflects that financial frictions modify the way non-financial friction shocks, e1t ,
e2t , e4t , affect the economy. They do so by inducing movements in the intertemporal wedge
(see (ii) in Figure 2). Our measure of the importance of financial frictions is the ratio of what
the variance of HP-filtered output would be if only the financial frictions were operative, to
23

In an agency cost model, these shocks could be perturbations to the variance of idiosyncratic disturbances
affecting entrepreneurs, or to the survival rate of entrepreneurs. See Christiano, Motto and Rostagno (2004,
2006) for examples.
24
Here, we follow the strategy pursued in Uhlig (2002).

16

the total variance of HP-filtered output. We construct this formally as follows. The wedges,
st , have the following moving average representation (here, we ignore constant terms):
st = [I − P L]−1 Qεt = F (L)εt ,
say. Define
s̃t = F̃ (L) εt .
Here, F̃ (L) denotes the version of F (L) in which all elements have been set to zero, except
those in the third column and the third row (i.e., F̃ (L) is F (L) with the (i, j) elements
set to zero, for i, j = 1, 2, 4.) The dynamics of s̃t reflect the mechanisms by which the
financial frictions affect the wedges. The fact that the 3, 3 element of F (L) is kept in F̃ (L)
means that the financial friction shock is permitted to exert its effect on the intertemporal
wedge, s3t . The fact that we keep the other elements of the third column of F (L) means
that we include in F̃ (L) the spillover effects from the financial friction shock to the other
wedges. Regarding the other elements of εt , F̃ (L) only includes their spillover effects onto
the intertemporal wedge. This is our way of capturing the notion that financial frictions
modify the transmission of non-financial shocks. Although s̃t represents the component of
st corresponding to financial frictions, it is important to bear in mind that it is not an
orthogonal decomposition of st .25 For example, it is possible for the variance of s̃t to exceed
that of st .
Write (4.7) in lag operator form:
log k̃t =

γL
st ,
1 − λL

and express the linearized observer equation, (4.8), as follows:
Yt = h0 st + h1 log k̃t + υ t
where h0 is a 4 × 4 matrix and h1 is a 4 × 1 column vector. Then,
Yt = H(L)F (L) εt + υ t ,
where
H(L) = h0 + h1

γL
.
1 − λL

The representation of Yt that reflects only the financial frictions is denoted Ỹt , and is as
follows:
Ỹt = H(L)F̃ (L) εt + υ t .
(5.4)
The spectral densities of Ỹt and Yt are, respectively,
¡
¢ ¡ ¢0 ¡ ¢0
SỸ (ω) = H(e−iω )F̃ e−iω F̃ eiω H eiω + R
25

¡
¢ ¡ ¢0 ¡ ¢0
SY (ω) = H(e−iω )F e−iω F eiω H eiω + R.

That is, s̃t and st − s̃t are correlated. Since var (st ) = var (s̃t ) + var (st − s̃t ) + 2cov (s̃, st − s̃t ) , it is
possible for var (s̃t ) > var (st ) if the covariance term is sufficiently negative.

17

The variance of Yt , denoted C0 , can be computed by solving the following expression for
large N :
N

−1
2
1
2 X
1
2πj
C0 = SY (ω 0 ) +
re (SY (ωk )) + SY (ωN/2 ), ωj =
.
N
N k=1
N
N

The variance of Ỹt , C̃0 , can be computed in an analogous way.
Our measure of the importance of financial frictions, f, is the 1,1 element of C̃0 , which
we denote C̃011 . Our measure of financial frictions scales this by the 1,1 element of C0 :
f=

C̃011
.
C011

(5.5)

Since it is a ratio of variances, f must be positive. However, because (5.5) is not based on an
orthogonal decomposition, f may be larger than unity. The importance of financial frictions
is not identified, because almost all perturbations in θ imply different values of f, but the
same value of the likelihood, by Proposition 1.

6. Wedge Decompositions
We describe decompositions of the data during a recession which begins in period t = t1
and ends in period t = t2 . CKM’s strategy, which we call the ‘baseline decomposition’, is as
follows. CKM ask how the recession would have unfolded if only the wedge, s3t , evolved as
it did and the other wedges remained constant at their values at the start of the recession.
We find the sequence, εt , t = t1 , ..., t2 which has the property that when this is input into
(2.6), the third element of the simulated st , t = t1 , ..., t2 , coincides with its estimated values
and the other elements of st are fixed at their value at t = t1 .
We investigate an alternative strategy for assessing the role of financial frictions, which
recognizes the roles played by these frictions discussed in the introduction and in section
5. Such a strategy would choose a value for the rotation parameter, θ and use the implied
sequence of et ’s to simulate (5.4). However, because F̃ is an infinite-ordered moving average
representation, we decided this strategy is impractical and we devised a closely related one
instead. The strategy we implemented (‘rotation decomposition’) recognizes that financial
shocks drive both the intertemporal wedge and have spillover effects on other wedges. But,
it does not capture the spillover effects from other shocks onto the intertemporal wedge. In
this sense our rotation decomposition understates the role of financial frictions. However,
we mitigate the latter effect by working with the rotation, θ, which maximizes the role of
financial frictions, f.
The rotation decomposition is constructed as follows. We compute ut , t = t1 , ..., t2 , and
the value, θ∗ , of θ ∈ R6 which maximizes f in (5.5). Then, we fix W and compute the
implied sequence, et , for t = t1 , ..., t2 using (5.3) and the value of C implied by (5.2). Next,
set to zero all but the third element in et . After that, we compute the implied sequence of
∗
disturbances, uθt , t = t1 , ..., t2 using (5.1). Here, the superscript θ∗ highlights the dependence
on the rotation parameter, θ∗ . For input into our state space - observer system, (4.3)-(4.2),
∗
∗
∗
we require εt . We compute a sequence, εθt , t = t1 , ..., t2 using εθt = C −1 uθt .
18

7. Empirical Results
This section documents two problems with BCA: conclusions are sensitive to modeling details
and to the position one takes on spillover effects. In the first subsection we discuss the results
for US postwar recessions. We then consider postwar recessions in the remaining OECD
countries. Finally, we consider the US in the Great Depression.
7.1. US Postwar Recessions
7.1.1. Sensitivity of Baseline Decomposition to Modeling Details
In our analysis of the post-war US data, we examine five recessions. The 1982 recession,
which is emphasized in CKM, is highlighted in the text. Details about the other post war US
recessions are provided in Appendix C. Consider Table 1, which presents summary results for
the 1982 US recession. The statistic reported in Table 1 is the fraction of the decline in output
at the recession trough which is accounted for by the intertemporal wedge. The trough of the
recession is defined as the quarter when detrended output achieves its minimum value. Panel
1a displays results based on the CKM specification of the intertemporal wedge (i.e., τ xt ) and
Panel 1b displays results for the alternative specification (τ kt ). In addition, results based on
the baseline and rotation decompositions and with and without investment adjustment costs
are reported. Finally, the table shows the impact of including CKM measurement error at
the estimation stage of computing the wedges.
Turning to the CKM version of the wedge in Panel 1a we see that, regardless of whether
measurement error is included in the analysis, adjustment costs make a substantial difference. Without investment adjustment costs, the intertemporal wedge contributes essentially
nothing to the decline in output (or investment) in the 1982 recession. With adjustment
costs, the intertemporal wedge accounts for roughly 30 percent of the decline in output at
the trough of that recession. Evidently, adjustment costs have a very large impact on inference. At the same time, the impact of measurement error is nil, when we work with the
CKM version of the intertemporal wedge.
Turning to the alternative specification of the intertemporal wedge, in Panel 1b we see
that measurement error now matters a great deal. For example, with no measurement error
and with adjustment costs, the intertemporal wedge accounts for over half the decline in
output at the trough of the 1982 recession. With measurement error, that number falls to
a much smaller (though still substantial!) 22 percent. The first column in the table shows
that the CKM measurement error specification is strongly rejected by a likelihood ratio test
whether or not adjustment costs are included in the analysis. So, the likelihood directs us
to pay attention to the results without measurement error.
The results in Panel 1b show how much the specification of the intertemporal wedge
matters. When CKM measurement error is used and there are no adjustment costs, the
alternative formulation of the intertemporal wedge accounts for a substantial 24 percent of
the drop in output at the trough of the 1982 recession. This stands in sharp contrast with
the nearly zero percent drop implied by the CKM measure of that wedge. Interestingly,
with the alternative measure of the wedge and with CKM measurement error, adjustment
costs matter very little. When we set measurement error to zero (inducing a very large jump

19

in the likelihood!) then adjustment costs matter a great deal, even with the alternative
specification of the intertemporal wedge.
A more complete representation of our findings is reported in Figure 3, which displays
results for the baseline decomposition of US data in the 1982 recession. To save space,
Figure 3 reports results only for the alternative specification of the intertemporal wedge.
The alternative version of the wedge is of special interest because of its conformity with the
model in BBG.
In Figure 3, the circles indicate the zero line. The line with diamonds indicates the
evolution of the data in response to all the wedges. By construction, the line with diamonds
corresponds to the actual (detrended) data. The line marked with stars indicates the baseline
decomposition when we estimated the model with the CKM specification of measurement
error. The left column of graphs indicates results based on setting adjustment costs in
investment to zero (i.e., Φ = 0). The right column of graphs indicates results based on setting
adjustment costs in investment to a level which implies a Tobin’s q elasticity of unity. Note
that for results based on estimation using the CKM measurement error specification, the
intertemporal wedge accounts for relatively little of the movement in output, investment,
hours worked and consumption. This conclusion is not sensitive to the introduction of
adjustment costs in investment.
The line in Figure 3 indicated by pluses displays results based on estimation with measurement error set to zero. In the left column, we see that if the only wedge that had been
active in the 1982 recession had been the intertemporal wedge, the US economy would have
experienced a substantial boom (this can also be seen in Table 1). Investment would have
been massively above trend, and consumption would have been massively below trend. These
results show how sensitive BCA can be to seemingly minor details. Measurement error is
very small under the CKM measurement error specification, yet it has a large impact on the
outcome of BCA.
Measurement error also has a big impact on the assessment of the importance of adjustment costs. Comparing results in the left and right columns of Figure 3, we see that when
measurement error is set to zero in estimation, then adjustment costs make a big difference to
the assessment of the importance of the intertemporal wedge. The boom in output produced
by the intertemporal wedge in the absence of adjustment costs becomes a recession when
adjustment costs are turned on. As noted above, with adjustment costs the intertemporal
wedge accounts for a very substantial 52 percent of the drop in output at the trough of the
1982 recession.
Results for four other US postwar recessions are presented in the appendix, and they
generally support our findings for the 1982 recession: BCA results sensitive to the position
taken on measurement error, the specification of the intertemporal wedge and on adjustment
costs in investment.
7.1.2. The Potential Importance of Spillovers
The evidence for the 1982 recession in Figure 3 and for the other recession episodes is that
the intertemporal wedge, when it has any impact at all, drives consumption and investment
in opposite directions. At first, this may seem damaging to the proposition that shocks
which drive the intertemporal wedge are important in business cycles, because consumption
20

and investment are both procyclical in the data. This section shows that the oppositesigned response of consumption and investment is simply an artifact of ignoring spillover
effects. Once spillover effects are taken into account, the evidence from BCA is consistent
with consumption and investment responding with the same sign to an intertemporal wedge
shock.
We quantify the potential importance of spillover effects by considering our rotation decomposition, discussed in section 6. Table 1 indicates that the intertemporal wedge accounts
for almost the whole of the 1982 recession under the rotation decomposition, under almost
all model perturbations. The one exception occurs in the case of no measurement error, no
adjustment costs and τ kt intertemporal wedge.
We can see the results more completely for the alternative representation of the wedge,
in Figure 4 (from here on, only results for the alternative representation of the wedge are
presented). The left column of that figure reproduces the results of CKM’s baseline decomposition from Figure 3. The right column displays the results based on the rotation
decomposition. All results in Figure 4 are based on setting measurement error to zero.
This is consistent with our remarks above, according to which CKM’s measurement error
specification has no a priori appeal, and it is overwhelmingly rejected in the post war data.
What we see in the right column of Figure 4 is that the estimated financial shock accounts
for nearly the whole of the 1982 recession. Also, the financial shock drives consumption and
investment in the same directions. This reflects the operation of spillover effects. We stress
that the likelihood of the model on which the results in the left and right columns are based
is the same. BCA provides no way to select between the two.
7.2. OECD Postwar Recessions
The results for postwar recessions in OECD countries for which we have data are summarized
in Table 2, panel A (no adjustment costs) and Table 2, panel B (adjustment costs). For each
country the entry represents the average of a statistic over all the recessions for which we
have data. The statistic is the fraction of the decline in output in the trough of a recession,
due to the intertemporal wedge. This is measured, as indicated in the table, according to the
baseline or rotation decomposition.26 In each panel, the bottom row is the weighted mean
of the corresponding column entries. The weight for a given country is proportional to the
number of recessions in that country’s data.27
Consider first the case where the BCA methodology is closest to CKM, i.e., the case with
measurement error, no investment adjustment costs and the baseline wedge decomposition.28
26

The numbers for the United States are different from what is reported in Table 1, because all results
in Table 2 are based on P and Q matrices with the zero restrictions indicated in (2.7). In addition, the
numbers in Table 2 reflect an average over all recessions in the sample for each country, while Table 1 only
pertains to the 1982 recession.
27
For Belgium, we only have data for the 1990 recession; for Canada, the 1980 and 1990 recessions; for
Denmark, the 1990 recession; for Finland, the 1974 and 1990 recessions; for France, the 1980 and 1990
recessions; for Germany, the 1990 recession; for Italy, the 1980 and 1990 recessions; for Japan, the 1990
recession; for Mexico, the 1990 recession; for Holland, the 1980 and 1990 recessions; for Norway, the 1990
recession; for Spain, the 1974 and 1990 recessions; for Switzerland, the 1990 recession; for the UK, the 1974,
1980, and 1990 recessions.
28
However, recall that we now consider the alternative type of wedge, the τ kt wedge motivated by the CF

21

Note that there are numerous countries with fractions that are well above zero. Some are
even above unity, which means that when the intertemporal wedge is fed to the RBC model,
the model on average predicts bigger recessions than actually occurred. Overall, the average
contribution of the intertemporal wedge to the fall in output in a trough is a substantial 22
percent.
As we found for the United States in the 1982 recession, when we then drop measurement
error we find that the intertemporal wedge on average predicts an output boom in the OECD
recessions for which we have data (Panel A, right portion). Although the measurement error
used in the analysis is quite small, the outcome of BCA is evidently very sensitive to it.
Now consider what happens when we introduce adjustment costs, in Panel B. When we
include measurement error in the analysis, there are several countries in which the intertemporal wedge plays a substantial role in recessions. However, there are several where the
intertemporal wedge actually predicts a significant boom. As a result, the average contribution of the intertemporal wedge to business cycles across all countries is now about zero.
When we now drop measurement error, the importance of the wedge jumps substantially for
several countries. For example, it jumps from 15 percent to 46 percent in the United States
and 33 percent to 75 percent in Canada. Some, however, such as Switzerland, go from 31
percent to -14 percent when measurement error is dropped. As a result, the overall average
is a more modest jump of 16 percent.
Turning to the rotation wedge, we see that under that decomposition, the intertemporal
wedge assumes a very large role in most countries. It is logically possible that the entire
effect of this substantial importance assigned to financial shocks is due to spillover effects.
In this case, one might be tempted to conclude that these are not actually shocks to the intertemporal wedge itself, and are better thought of as shocks to other wedges. To investigate
this, we computed the ratio of the variance in HP filtered output due only to the spillover
effects of financial shocks, to the total variance in HP filtered output due to financial frictions. This ratio is reported in the column, ‘ratio’, in Table 2. Note that in the case of no
measurement error and investment adjustment costs, the ratio is only 30 percent for the US.
Evidently, in US business cycles, the great importance assigned to financial shocks is not
coming primarily from spillover effects. In other countries, the ratio is greater than unity,
suggesting that spillovers are substantial (see Belgium, Germany and the UK). However,
on average the ratio is only 60 percent, suggesting that the financial shocks identified in
our rotation decomposition operate on the economy primarily by their direct impact on the
intertemporal wedge.
We conclude that our findings for the postwar US also hold up on average across the
other countries in the OECD.
7.3. US Great Depression
We now consider results for the US Great Depression. In this episode, the data exhibit substantial fluctuations and so it is perhaps not surprising that there is evidence of inaccuracy in
the linear approximation of our model’s solution. To quantify the degree approximation error
we first estimate the capital stock for each date in the sample, by a two-sided Kalman proand BGG models.

22

jection using the state-space representation of our model.29 This, together with the realized
wedges for each date, provided us with an estimate of the model’s state for each date in the
sample. Then, for each t we used the approximate policy rule to compute (ct , kt+1 , lt , xt , yt )
as a function of the date t state. We then computed the percent change in each of these
5 variables required for the four equilibrium conditions, (2.1), (2.2), (2.3), (2.8), plus the
production function to be satisfied as a strict equality at t. For each t these calculations
were done under the assumption that the period t + 1 decisions are made using the approximate solution. Figure 5 shows that outside the 1930s, the approximation error associated
with the linearized policy rule is for the most part fairly small. In the period of the 1930s,
however, the approximation error becomes large, briefly reaching 65 percent for investment.
We report the same measure of approximation error for the second order approximation to
the model solution. In this case, the approximation errors are considerably smaller. Because
of this evidence that the first order approximation has substantial approximation error, and
because the second order approximation appears to be noticeably more accurate, we only
display results for the Great Depression based on the second order approximation.
Consider the results in Figure 6. The left column displays the baseline decomposition
and shows that the intertemporal wedge accounts for a substantial 21 percent of the fall in
output in the Great Depression. In addition, that wedge drives consumption and investment
in opposite directions. When we allow for spillovers using the rotation decomposition, we
find that financial shocks may account for as much as 92 percent of the fall in output at
the trough of the Great Depression.30 Moreover, shocks to the intertemporal wedge drive
consumption and investment in the same direction. We also did the calculations using the
CKM measurement error and the results appear in Figure A9 in Appendix C. The results
reported there are qualitatively similar to what emerges from Figure 6.
We conclude that results for the Great Depression are consistent with the findings for the
postwar period. Taken as a whole, the evidence from BCA is consistent with the proposition
that shocks to the intertemporal wedge play a significant role in business fluctuations.

8. Conclusion
Chari, Kehoe and McGrattan (2006) advocate the use of business cycle accounting to identify
directions for improvement in equilibrium models. As a demonstration of the power of the
approach, they argue that BCA can be used to rule out a prominent class of financial friction
models. In particular, they conclude that models of financial frictions which create wedges
in the intertemporal Euler equation are not promising avenues for understanding business
cycle dynamics.
We have described two flaws in BCA which undermine its usefulness. First, consistent
with economic theory, the results of BCA are not robust to small changes in the modeling
environment. Second, BCA necessarily misses key mechanisms by which financial shocks
which drive the intertemporal wedge affect the economy. The empirical correlations among
29

Essentially, this involves using measured investment to compute the capital stock using the capital
accumulation equation.
30
Given the nonlinearity of the model, we could not compute the rotation decomposition as we did for
postwar data. Instead, we computed the rotation that minimized the sum of squared deviations between the
actual data and the predicted data using the estimated wedges.

23

wedges are consistent with the possibility that the financial shocks which drive the intertemporal wedge have important spillover effects on other wedges. These spillover effects are
not identified under BCA. However, spillover effects are potentially so important that the
evidence is consistent with the proposition that financial shocks are the major driving force
in postwar recessions in the US and many OECD countries, as well as in the US Great
Depression.
Fortunately, there are alternative ways to investigate whether given model features are
useful in business cycle analysis. An approach which does not involve so many of the detailed
model assumptions used by BCA, but which does incorporate the sort of assumptions needed
to identify spillover effects, uses vector autoregressions.31 An alternative approach works with
fully specified, structural models. With the recent advances in computational technology
and in economic theory, exploration of alternative models is relatively costless. A full set of
references to the literature that explores the sort of financial frictions which are the object
of interest in CKM would be too lengthy to include here. See Carlstrom and Fuerst (1997),
Bernanke, Gertler and Gilchrist (1999), Christiano, Motto and Rostagno (2004, 2006) and
Queijo (2005), and the references they cite.
Another approach uses a natural way to confront one of the identification problems with
BCA. Absent direct observations, it is difficult to identify the intertemporal wedge and the
rate of return of capital separately. However, as stressed in Cochrane and Hansen (1992),
rates of return are the one type of economic variable on which we have excellent observations.
For example, rates of return do not have the problems of interpretation associated with
wages and they do not have the measurement error problems associated with observations
on quantities like consumption and investment. The recent work of Primiceri, Schaumburg
and Tambalotti (2005) carries out an analysis that is similar to business cycle accounting,
except that they make use of direct measures of rates of return. They find that the estimates
of τ kt (which they call ‘preference shocks’) assign that variable an important role in business
cycle fluctuations.32 A related approach is taken recently in Christiano, Motto and Rostagno
(2006), who also include rates of return in the analysis. In addition, they integrate an explicit
model of financial frictions and so are able to relate τ kt directly to primitive, uncorrelated
financial shocks. When they feed the individual shocks to the model, holding other shocks
fixed, they find that the financial shocks are an important driving force in business cycles.
31
32

For a recent review, see Christiano, Eichenbaum and Vigfusson (2006).
This approach is related to that of Hansen and Singleton (1982, 1983).

24

A. Appendix A: The Carlstrom-Fuerst Financial Friction Wedge
This section considers a version of the CF model, modified to include the adjustment costs
in capital studied in CKM. We identify the version of the RBC model with wedges whose
equilibrium coincides with that of the CF model with adjustment costs. We state the result
as proposition A.3. For the RBC wedge economy to have the same equilibrium as the
CF economy with adjustment costs requires several wedges and other adjustments. We
then describe the parameter settings required in the original CF model to ensure that the
adjustments primarily take the form of a wedge in the intertemporal Euler equation, and
nowhere else. In this respect we follow the approach taken in CKM. To simplify the notation,
we set the population growth rate to zero throughout the discussion in the appendix.
A.1. RBC Model With Adjustment Costs
To establish a baseline, we describe the version of the RBC model with adjustment costs.
Preferences are:
∞
X
E0
β t u (ct , lt ) .
t=0

The resource constraint and the capital accumulation technology are, respectively,
ct + xt ≤ ktα (Zt lt )1−α

and

¶
xt
kt+1 = (1 − δ) kt + xt − Φ
kt .
kt
The first order necessary conditions for optimization are:
µ ¶α
−ul,t
kt
= (1 − α)
Zt1−α
uc,t
lt
¢
uc,t+1 ¡
k
1 + Rt+1
,
1 = βEt
uc,t
µ

(A.1)
(A.2)

(A.3)
(A.4)

where the gross rate of return on capital is:
³
´α−1
kt+1
α Zt+1
+ Pk,t+1
lt+1
k
=
.
1 + Rt+1
Pk0 t
where Pk0 ,t is defined in (2.5) and
∙
µ
¶
µ
¶
¸
xt+1
xt+1 xt+1
0
Pk,t+1 = Pk0 ,t+1 1 − δ − Φ
+Φ
.
kt+1
kt+1 kt+1

(A.5)

In the following two subsections, we argue that the CF financial frictions act like a tax
k
k
, in (A.4). In particular, 1 + Rt+1
is replaced by
on the gross return on capital, 1 + Rt+1
¡
¢
¡
¢
k
1 + Rt+1
1 − τ kt .

This statement is actually only true as an approximation. Below we state, as a proposition,
what the exact RBC model with wedges is, which corresponds to the CF model. We then
explain the sense in which the wedge equilibrium just described is an approximation.
25

A.2. The CF Model With Adjustment Costs
Here, we develop the version of the CF model in which there are adjustment costs in the
production of new capital. The economy is composed of firms, an η mass of entrepreneurs and
a mass, 1 − η, of households. The sequence of events through the period proceeds as follows.
First, the period t shocks are observed. Then, households and entrepreneurs supply labor and
capital to competitive factor markets. Because firm production functions are homogeneous,
all output is distributed in the form of factor income. Households and entrepreneurs then sell
their used capital on a capital market. The total net worth of households and entrepreneurs at
this point consists of their earnings of factor incomes, plus the proceeds of the sale of capital.
Households divide this net worth into a part allocated to current consumption, and a part
that is deposited in the bank. Entrepreneurs apply their entire net worth to a technology
for producing new capital. They produce an amount of capital that requires more resources
than they can afford with only their own net worth. They borrow the rest from banks.
At this point the entrepreneur experiences an idiosyncratic shock which is observed to him,
while the bank can only see it by paying a monitoring cost. This creates a conflict between
the entrepreneur and the bank which is mitigated by the bank extending the entrepreneur a
standard debt contract. After capital production occurs, entrepreneurs sell the new capital,
and pay off their bank loan. Households receive a return on their deposits at the bank, and
use the proceeds to purchase new capital. Entrepreneurs use their income after paying off
the banks to buy consumption goods and new capital. All the newly produced capital is
purchased by households and entrepreneurs, and all the economy’s consumption goods are
consumed. The next period, everything starts all over.
We now provide a formal description of the economy. The household problem is
max

{cc,t ,kct+1 }∞
t=0

∞
X

β t u (ct , lt ) ,

t=0

subject to:
ct + qt kc,t+1 ≤ wtc lt + [rt + Pk,t ] kc,t

(A.6)

where ct and kc,t denote household consumption and the household stock of capital, respectively. In addition, and lt denotes household employment, wtc denotes the household’s
competitive wage rate, Pk,t denotes the price of used capital and qt denotes the price of capital available for production in the next period (the reason for not denoting this price by Pk0 ,t
will be clear momentarily). After receiving their period t income, households allocate their
net worth (the right side of (A.6)) to ct and the rest, wtc lt + [rt + Pk,t ] kc,t − ct , is deposited in
a bank. These deposits earn a rate of return of zero. This is because markets are competitive
and the opportunity cost to the household of the output they lend to the bank is zero. Later
in the period, when the deposit matures, the households use the principal to purchase kc,t+1
units of capital. The first order conditions of the household are (A.6) with the equality strict
and:
∙
¸
uc,t+1 rt+1 + Pk,t+1
(A.7)
1 = Et β
uc,t
qt
−ul,t
= wte ,
(A.8)
uc,t
26

where uc,t and −ul,t denote the time t marginal utilities of consumption and leisure, respectively.
The η entrepreneurs’ present discounted value of utility is:
E0

∞
X

(βγ)t cet .

t=0

After the period t shocks are realized, the net worth of entrepreneurs, at , is:
at = wte + [rt + Pk,t ] ket ,
where wte is the wage rate earned by the entrepreneur, who inelastically supplies his one
unit of labor. The entrepreneur uses the at consumption goods, together with a loan from
the bank to purchase the inputs into the production of capital goods. Entrepreneurs have
access to the technology for producing capital, (2.1). The technology proceeds in two stages.
In the first stage, the entrepreneur produces an intermediate input, it . In the second stage,
that input results in ωit units of capital, which has a price, in consumption goods, qt . The
random variable, ω, is independently distributed across entrepreneurs, has mean unity, and
cumulative density function,
Ψ (z) ≡ prob [ω ≤ z] .
The entrepreneur who wishes to produce it units of the capital input faces the following
cost function:
∙
¶
¸
µ
ϕx,t
ϕk,t ,
C (it ; Pk,t ) = min Pk,t ϕk,t + ϕx,t + λt it − (1 − δ) ϕk,t − ϕx,t + Φ
ϕk,t ,ϕx,t
ϕk,t
where the constraint is that the object in square brackets is no less than zero. In addition,
ϕk,t and ϕx,t denote the quantity of old capital and investment goods, respectively, purchased
by the entrepreneur. The first order conditions for ϕk,t and ϕx,t are:
∙
µ
¶
µ
¶
¸
ϕx,t
ϕx,t ϕx,t
0
+Φ
(A.9)
Pk,t = λt 1 − δ − Φ
ϕk,t
ϕk,t ϕk,t
∙
µ
¶¸
ϕx,t
0
,
(A.10)
1 = λt 1 − Φ
ϕk,t
respectively. The reason for denoting the time t price of old capital by Pk,t is now apparent.
Substituting out for λ in (A.9) from (A.10), we see that the formula for Pk,t here coincides
with with the one implied by (A.5). The reason for not denoting the price of new capital by
Pk0 ,t is also apparent. Comparing (A.10) with (2.5) we see that the formula for λt coincides
with the formula for Pk0 ,t in the standard RBC model with adjustment costs. However, the
equilibrium value of qt will not coincide with λt here. This is because λt does not capture all
the costs of producing new capital. It measures the marginal costs implied by the production
technology. However, as discussed in detail in CF, it is missing the marginal cost that arises
from the conflict between entrepreneurs and banks. This has the consequence that the
production of capital necessarily involves some monitoring, and therefore also involves some
destruction of capital.
27

Solving (A.10) for xt /kt in terms of λt , and using the result to substitute out for ϕx,t /ϕk,t
in (A.9):
⎡
Ã1
!2
!Ã 1
!⎤
Ã1
−1
−1
a λt − 1
λt
+b ⎦
+ a λt
Pk,t = λt ⎣(1 − δ) −
2
a
a
a

Solving this for λt , provides the marginal cost function for producing it :

(A.11)

λt = λ (Pk,t ) .

Because all entrepreneurs face the same Pk,t , they will all choose the same ratio, ϕx,t /ϕk,t ,
regardless of the scale of production, it . Moreover, that ratio must be equal to the ratio of
aggregate investment to the aggregate stock of capital.
The constant returns to scale feature of the production function implies that the total
cost of producing it is:
½
λ (Pk,t ) it a > 0
C (it ; Pk,t ) =
it
a=0

Consider an entrepreneur who has at units of goods and wishes to produce it ≥ at , so that the
entrepreneur must borrow λ (Pk,t ) it − at from the bank. Following CF, we suppose that the
entrepreneur receives a standard debt contract. This specifies a loan amount and an interest
rate, Rta , in consumption units. If the revenues of the entrepreneur turn out to be too low for
him to repay the loan, then the entrepreneur is ‘bankrupt’ and he simply provides everything
he has to the bank. In this case, the bank pays a monitoring cost which is proportional to
the scale of the entprepeneur’s project, µiat . We now work out the equilibrium value of the
parameters of the standard debt contract.
The value of ω such that entrepreneurs with smaller values of ω are bankrupt, is ω̄ at ,
where
[λ (Pk,t ) it − at ] Rta = ω̄ at it qt .
Using this we find that the average, across all entrepreneurs with asset level at , of revenues
is:
Z ∞
Z ∞
Z ω̄at
a
a
ωdF (ω) −
Rt (λ (Pk,t ) it − at ) dF (ω) − it qt
ωdF (ω)
it qt
ω̄ a
t

0

= it qt f

0

(ω̄at ) ,

where
f

(ω̄at )

=

Z

∞

ω̄a
t

ωdΦ (ω) − ω̄at (1 − Φ (ω̄at )) .

The average receipts to banks, net of monitoring costs, across loans to all entprepreneurs
with assets at is:
∙Z ω̄at
¸
a
a
qt it
ωdΦ (ω) − µΦ (ω̄ t ) + [λ (Pk,t ) it − at ] Rta [1 − Φ (ω̄ at )]
0

= qt iat g (ω̄ at ) ,

28

where
g (ω̄at )

=

Z

ω̄ a
t

0

ωdΦ (ω) − µΦ (ω̄ at ) + ω̄ at [1 − Φ (ω̄at )] .

The contract with entrepreneurs with asset levels, at , that is assumed to occur in equilibrium is the one that maximizes the expected state of the entrepreneur at the end of the
contract, subject to the requirement that the bank be able to pay the household a gross
rate of interest of unity. The interval during which the entrepreneur produces capital is one
in which there is no alternative use for the output good. So, the condition that must be
satisfied for the bank to participate in the loan contract is:
qt it g (ω̄at ) ≥ λ (Pk,t ) it − at .
The contract solves the following Lagrangian problem:
it qt f (ω̄ at ) + µ [qt it g (ω̄ at ) − λ (Pk,t ) it + at ] .
max
a
ω̄t ,it

The first order conditions for ω̄ at and it are, after solving out for µ and rearranging:
f 0 (ω̄at )
[qt g (ω̄ at ) − λ (Pk,t )]
a
0
g (ω̄ t )
at
=
λ (Pk,t ) − qt g (ω̄at )

qt f (ω̄ at ) =
it

(A.12)
(A.13)

From (A.12), we see that ω̄ at = ω̄ t for all at , so that Rta = Rt for all at . It then follows from
(A.13) that the loan amount is proportional to at . As in the no adjustment cost case in CF,
these two properties imply that in studying aggregates, we can ignore the distribution of
assets across entrepreneurs.
The expected net revenues of the entrepreneurs, expressed in terms of at , are, after making
use of (A.13):
qt f (ω̄ t )
at .
(A.14)
it qt f (ω̄t ) =
λ (Pk,t ) − qt g (ω̄t )
At the end of the period, after the debt contract with the bank is paid off, the entrepreneurs
who do not go bankrupt in the process of producing capital have income that can be used
to buy consumption goods and new capital goods:
½
it qt ω − Rt (λ (Pk,t ) it − at ) ω ≥ ω̄ t
cet + qt ket+1 ≤
.
(A.15)
0
ω < ω̄t

An entrepreneur who is bankrupted in period t must set cet = 0 and ket+1 = 0. In period
e
t + 1, these entrepreneurs start with net worth at+1 = wt+1
. Entrepreneurs who are not
bankrupted in period t can purchase positive amounts of cet and ke,t+1 (except in the nongeneric case, ω = ω̄ t ). For these entrepreneurs, the marginal cost of purchasing ke,t+1 is qt
units of consumption. The time t expected marginal payoff from ke,t+1 at the beginning of
period t + 1 is Et [rt+1 + Pk,t+1 ] . In each aggregate state in period t + 1, the entrepreneur
expands his net worth by the value of [rt+1 + Pk,t+1 ] in that state. This extra net worth
can be leveraged into additional bank loans, which in turn permit an expansion in the
29

entrepreneur’s payoff by investing in the capital production technology. The expected value
of this additional payoff (relative to date t + 1 idiosyncratic uncertainty) corresponds to the
coefficient on at in (A.14). So, the expected rate of return available to entrepreneurs who
are not bankrupt in period t is:
∙
¸
rt+1 + Pk,t+1
Et
(A.16)
× ζ t+1 ,
qt
which they equate to 1/(βγ). Here,
ζ t+1

∙

¸
qt+1 f (ω̄ t+1 )
= max
,1 .
λ (Pk,t+1 ) − qt+1 g (ω̄ t+1 )

The expression to the left of ‘×’ in (A.16) is the rate of return enjoyed by ordinary households.
The reason that ζ t+1 cannot be less than unity is that and entprepeneur can always obtain
unity, simply by consuming his net worth in the following period and not producing any
capital. Averaging over all budget constraints in (A.15):
cet + qt ket+1 =

qt f (ω̄ t )
at .
λ (Pk,t ) − qt g (ω̄t )

Here, cet and ke,t+1 refer to averages across all entrepreneurs.
Output is produced by goods-producers using a linear homogeneous technology,
y (kt , lt , η, Zt ) = ktα ((1 − η) Zt lt )1−α−ζ η ζ ,

(A.17)

where kt is the sum of the capital owned by households and the average capital held by
entrepreneurs:
kt = (1 − η) kct + ηke,t .

The argument, η, in y is understood to apply to the second occurrence of η. The arguments
in the production function reflect our assumption that the entrepreneur supplies one unit of
labor, and households supply lt units of labor. Profit maximization implies:
yk,t = rt , yl,t = wtc , y3,t = wte .

(A.18)

We now collect the equilibrium conditions for the economy. The production of new capital
goods by the average entrepreneur is:
Z ∞
Z ω̄t
ωdF (ω) − µit
dF (ω)
it
0

0

= it [1 − µF (ω̄t )] .

Since there are η entprepreneurs, the total new capital produced is kt+1 = ηit [1 − µF (ω̄t )] ,
so that
∙
µ ¶ ¸
xt
kt [1 − µF (ω̄ t )] .
(A.19)
kt+1 = (1 − δ) kt + xt − Φ
kt
The resource constraint is:
(1 − η) ct + ηcet + xt = ktα ((1 − η) Zt lt )1−α−ζ η ζ .
30

(A.20)

Substituting (A.18) into (A.7) and (A.8):
1 = βEt

uc,t+1 yk,t+1 + Pk,t+1
uc,t
qt

−ul,t
= yl,t .
uc,t

(A.21)
(A.22)

The budget constraint of the entrepreneur is:
cet + qt ket+1 = λ (Pk,t )

kt+1
qt f (ω̄t )
η [1 − µF (ω̄ t )]

(A.23)

The efficiency conditions associated with the contract are:
f 0 (ω̄t )
[qt g (ω̄ t ) − λ (Pk,t )]
g0 (ω̄ t )
kt+1
at
=
η [1 − µF (ω̄t )]
λ (Pk,t ) − qt g (ω̄ t )
at = y3,t + yk,t ket + Pk,t ket
qt f (ω̄ t ) =

(A.24)
(A.25)
(A.26)

The intertemporal efficiency condition for the entrepreneur is (assuming the condition, ζ t+1 ≥
1, is not binding):
∙
¸
Fk,t+1 + Pk,t+1
1
qt+1 f (ω̄t+1 )
Et
=
(A.27)
×
qt
λ (Pk,t+1 ) − qt+1 g (ω̄ t+1 )
γβ
Taking the ratio of (A.9) to (A.10), we obtain:
³ ´
³ ´
1 − δ − Φ xktt + Φ0 xktt xktt
³ ´
Pk,t =
1 − Φ0 xktt

(A.28)

The 10 variables to be determined with the 10 equations, (A.19)-(A.28) are: ct , ce,t , xt , kt ,
ke,t , lt , Pk,t , qt , ω̄t , at .
It is convenient to define a sequence of markets equilibrium formally. Let st denote a
history of realizations of shocks. Then,

Definition A.1. An equilibrium of the CF economy with adjustment costs is a sequence of
prices, {Pk (st ) , q (st ) , we (st ) , wc (st ) , r (st )} , quantities, {c (st ) , ce (st ) , x (st ) , k (st ) , ke (st ) , l (st ) , a (st )} ,
and {ω̄ (st )} such that:
(i) Households optimize (see (A.21), (A.22))
(ii) Entrepreneurs optimize (see (A.23), (A.26), (A.27), (A.28))
(iii) Firms optimize (see (A.18))
(iv) Conditions related to the standard debt contract are satisfied (see (A.24), (A.25))
(v) The resource constraint and capital accumulations equations are satisfied (see (A.19),
(A.20))
31

A.3. The CF Model as an RBC Model with Wedges
We now construct a set of wedges for the RBC economy in section A.1, such that the
equilibrium for the distorted version of that economy coincides with the equilibrium for the
CF economy. We begin by constructing the following state-contingent sequences:
¡ ¢
¡ ¡ t ¢¢
ē s ,
ψ st = 1 − µF ω
(A.29)
t
t
¡ ¢
ψ (s ) q̃ (s )
³
´ − 1,
τ x st =
t
λ P̃k,t (s )
¡ ¢
θ st
¡ ¢
G st
¡ ¢
T st
¡ ¢
D st

P̃k (st ) τ x (st )
,
r̃ (st )
¡ ¡ ¢
¡ ¢¢
= η c̃e st − c̃ st ,
¡ ¢
¡ ¢ ¡ ¢
¡ ¢ ¡ ¢ ¡
¢
= G st − τ x st x̃ st − θ st r̃ st k̃ st−1 ,
¡ ¢
= w̃e st η,
=

ē and P̃k correspond to the objects without ‘ ˜· ’ in a CF equilibrium.
where q̃, c̃e , c̃, w̃e , r̃, k̃, x̃, ω
Also, λ is the function defined in (A.11). In this subsection, we treat D, ψ, θ, τ x , G and T
as given exogenous stochastic processes, outside the control of agents. Here, D, G, and T
represent exogenous sequences of profits, government spending and lump sum taxes. Also,
θ and τ x are tax rates on capital rental income and investment good purchases. Finally, ψ
is a technology shock in the production of physical capital.
Consider the following budget constraint for the household:
¡ ¢¢ ¡ ¢
¡ ¢ ¡
(A.30)
c st + 1 + τ x st x st
¡ t¢ ¡ t¢
¡ t¢
¡ t¢
¡
¡ t ¢¢ ¡ t ¢ ¡ t−1 ¢
+w s l s −T s +D s .
≤ 1−θ s r s k s

Here, r is the rental rate on capital, w is the wage rate, and l measures the work effort of the
household. Each of these variables is a function of st and is determined in an RBC wedge
economy. At time 0 the household takes prices, taxes and k (s−1 ) as given and chooses c, k
and l to maximize utility:
∞ X
X
t=0

st

¡ ¢ ¡ ¡ ¢ ¡ ¢¢
β t π st u c st , l st

subject to the budget constraint, no-Ponzi game and non-negativity constraints. Here, π (st )
is the probability of history, st .
Households operate the following backyard technology to produce new capital:
¶
∙
µ
¸
¡ t−1 ¢
¡ t¢
¡ t¢
¡ t¢
¡ t¢
x (st )
k
s
k s = (1 − δ) k s + x s − Φ
ψ
s .
(A.31)
k (st−1 )

32

The first order necessary conditions for household optimization are:
¡ ¢
¡ ¢ ¡ ¢
(A.32)
ul st + uc st w st = 0,
¡ t¢
1 + τ x (st )
0 s
P
(A.33)
k
ψ (st )
X
¡
¢ uc (st+1 ) £ ¡ t+1 ¢ ¡
¡ t+1 ¢¢ ¡
¡ t+1 ¢¢ ¡ t+1 ¢¤
=
βπ st+1 |st
r
s
1
−
θ
s
+
1
+
τ
s
Pk s
,
x
uc (st )
t+1 t
s

|s

where
¡ ¢
Pk st ≡

1−δ−Φ

µ

x(st )
k(st )

¶

1 − Φ0

0

µ

x(st )
k(st )

+Φ
³ t ´
x(s )
k(st−1 )

¶

x(st )
k(st )

.

(A.34)

Equation (A.32) is the first order condition associated with the optimal choice of l (st ) .
Equation (A.33) combines the first order order conditions associated with the optimal choice
of x (st ) and k (st ) . Also,
¡ ¢
1
³ t ´,
Pk0 st ≡
(A.35)
x(s )
1 − Φ0 k(s
t−1 )

is the pre-tax marginal cost of producing new capital, in units of the consumption good. In
addition, π (st+1 |st ) ≡ π (st+1 ) /π (st ) is the conditional probability of history st+1 given st .
The technology for firms is taken from (A.17):
y (k, l, η, Z) = kα ((1 − η) Zl)1−α−ζ η ζ ,
where, as before, the third argument in y refers only to the second occurrence of η. There are
three inputs: physical capital, household labor and another factor whose aggregate supply
is fixed at η. Profit maximization leads to:
¡ ¢
¡ ¢
¡ ¢
¡ ¢
¡ ¢
¡ ¢
(A.36)
r st = yk st , w st = yl st , we st = yη st .

The household is assumed to own the representative firm, and it receives the earnings of
η in the form of lump-sum profits, D (st ) . We do allow allow trade in claims on firms, a
restriction that is non-binding on allocations because the households are identical.
We now state the equilibrium for the RBC wedge economy:

Definition A.2. An RBC wedge equilibrium is a set of quantities, {c (st ) , l (st ) , k (st ) , x (st )} ,
and prices {Pk (st ) , Pk0 (st ) , r (st ) , w (st )} , and a set of taxes, profits and government spending, {G (st ) , τ x (st ) , θ (st ) , T (st )} , technology shocks, {Z (st ) , ψ (st )} , such that
(i) The quantities solve the household problem given the prices, taxes, profits, government
spending and the shock to the backyard investment technology
(ii) Firm optimization is satisfied
(iii) Relations (A.29) is satisfied, for given state-contingent sequences, q̃, c̃e , c̃, w̃e , r̃, k̃,
ē and P̃k .
x̃, ω
33

The variables to be determined in an RBC wedge equilibrium are c, l, k, x, Pk , Pk0 , r and
w. The 8 equations that can be used to determine these are (A.30)-(A.36). It is easily verified
that c, l, k, x, Pk , r and w coincide with the corresponding objects in a CF equilibrium. In
addition, Pk0 coincides with λ (Pk ) in a CF equilibrium. To see this, one verifies that the
equilibrium conditions in the RBC wedge economy coincide with the equilibrium conditions
in the CF economy. First, (A.31) coincides with (A.19). After using (A.36), we see that
(A.32) coincides with (A.22). Consider the household budget equation evaluated at equality.
Substituting out for lump sum transfers:
¡ ¢ ¡
¡ ¢¢ ¡ ¢
c st + 1 + τ x st x st
¢
¡ ¢ ¡ ¢
¡
¡ ¢¢ ¡ ¢ ¡
= 1 − θ st r st k st−1 + w st l st
¡ ¢ ¡ ¢
¡ ¢ ¡ ¢ ¡
¢
¡ ¢
¡ ¢
τ x st x st + θ st r st k st−1 + we st η + G st ,
or,

¡ ¢
¡ ¢
¡ ¢
(1 − η) c st + x st + ηce st
¢
¡ ¢ ¡ ¢
¡ ¢
¡ ¢ ¡
= r st k st−1 + w st l st + we st η
¢ ¡ ¢
¡ ¢¢
¡ ¡
= y k st−1 , l st , η, Z st ,

(A.37)

by linear homogeneity. Here, Z (st ) = Z (st ) , where st is the realization of period t uncertainty.
Equation (A.37) coincides with (A.20). Substitute out for θ and τ x from (A.29) into (A.33),
and rearranging, we obtain:
"
#
uc (st+1 ) r (st+1 ) + Pk (st+1 )
1 = Et
.
1+τ x (st )
uc (st )
Pk0 (st )
t
ψ(s )

Note that by definition of 1 + τ x (st ) in (A.29),
¡ t ¢ Pk0 (st ) q (st )
1 + τ x (st )
0
P
.
=
k s
ψ (st )
λ (Pk,t (st ))

Combining (A.11) and (A.10), we find that λ (Pk,t (st )) = Pk0 (st ) , so that the household’s
intertemporal Euler equation reduces to (A.21), or (after making use of (A.36)):
∙
¸
¡ t ¢¢
uc (st+1 ) yk (st+1 ) + Pk (st+1 ) ¡
k
1−τ s
Et
= 1,
(A.38)
uc (st )
Pk0 (st )

where

¡ ¢
1 − τ st =

ψ (st )
.
1 + τ x (st )
We conclude that conditions (A.19)-(A.22) in the CF economy are satisfied. The remaining
equilibrium conditions are satisfied, given (A.29). We state this result as a proposition:
k

Proposition A.3. Consider a CF equilibrium, and a set of taxes, technology shocks and
transfers computed in (A.29). The objects, {c (st ) , l (st ) , k (st ) , x (st )} , {Pk (st ) , r (st ) , w (st )}
and Pk0 (st ) = λ (Pk (st )) in the CF equilibrium correspond to an RBC wedge equilibrium.
For η and ζ close to zero and ψ close to unity, the RBC wedge equilibrium converges to
the equilibrium conditions of the RBC model with adjustment costs in section A.1 with a
wedge, 1 − τ k , in the intertemporal Euler equation, (A.4).
34

B. Appendix B: The Bernanke-Gertler-Gilchrist Financial Friction
Wedge
In this section we briefly review the BGG model and derive the RBC wedge model to which
it corresponds. In the model there are households, capital producers, entrepreneurs and
banks. At the beginning of the period, households supply labor to factor markets, and
entrepreneurs supply capital. Output is then produced and an equal amount of income
is distributed among households and entrepreneurs. Households then make a deposit with
banks, who lend the funds on to entrepreneurs. Entrepreneurs have a special expertise in
the ownership and management of capital. They have their own net worth with which to
acquire capital. However, it is profitable for them to leverage this net worth into loans from
banks, and acquire more capital than they can afford with their own resources. The source of
friction is a particular conflict between the entrepreneur and the bank. In the management
of capital, idiosyncratic things happen, which either make the management process more
profitable than expected, or less so. The problem is that the things that happen in this
process are observed only by the entrepreneur. The bank can observe what happens inside
the management of capital, but only at a cost. As a result, the entrepreneur has an incentive
to underreport the results to the bank, and thereby attempt to keep a greater share of the
proceeds for himself. To mitigate this conflict, it is assumed that entrepreneurs receive a
standard debt contract from the bank.
The capital that entrepreneurs purchase at the end of the period is sold to them by
capital producers. The latter use the old capital used within the period, as well as investment
goods, to produce the new capital that is sold to the entrepreneurs. Capital producers have
no external financing need. They finance the purchase of used capital and investment goods
using the revenues earned from the sale of new capital.
The budget constraint of households is:
ct + Bt+1 ≤ (1 + Rt ) Bt + wt lt + Tt ,
where Rt denotes the interest earned on deposits with the bank, bt denotes the beginningof-period t stock of those deposits, wt denotes the wage rate, lt denotes employment and Tt
denotes lump sum transfers. Subject to this budget constraint and a no-Ponzi condition,
households seek to maximize utility:
E0

∞
X

β t u (ct , lt ) .

t=0

Households’ first order conditions, in addition to the transversality condition, are:
uc,t = βEt uc,t (1 + Rt+1 )
−ul,t
= wt .
uc,t
Firms have the following production function:
yt = ktα (Zt lt )1−α = y (kt , lt , Zt ) .
35

They rent capital and hire labor in perfectly competitive markets at rental rate, rt , and wage
rate, wt , respectively. Optimization implies:
yk,t = rt , yl,t = wt .
Capital producers purchase investment goods, xt , and old capital, kt , to produce new
capital, kt+1 , using the following linear homogeneous technology:
µ ¶
xt
kt+1 = (1 − δ) kt + xt − Φ
kt .
kt
The competitive market prices of kt and kt+1 are Pk,t and Pk0 ,t , respectively. Capital producer
optimization leads to the following conditions:
∙
µ ¶
µ ¶ ¸
xt
xt xt
1
0
³ ´ 1−δ−Φ
Pk,t =
+Φ
kt
kt kt
1 − Φ0 xktt
Pk0 ,t =

1 + gn
³ ´.
1 − Φ0 xktt

At the end of period t, entrepreneurs have net worth, Nt+1 , and it is assumed that
Nt+1 < Pk0 ,t kt+1 . As a result, in an equilibrium in which the entire stock of capital is to be
owned and operated, entprepreneurs must borrow:
bt+1 = Pk0 ,t kt+1 − Nt+1 .

(B.1)

As soon as an individual entrepreneur purchases kt+1 , he experiences a shock, and kt+1
becomes kt+1 ω. Here, ω is a random variable that is iid across entrepreneurs and has mean
unity. The realization of ω is unknown before the loan is made and it is known only to the
entrepreneur after it is realized. The bank which extends the loan to the entrepreneur must
pay a monitoring cost in order to observe the realization of ω. The cumulative distribution
function of ω is F, where
Pr ob [ω < x] = F (x) .
Entrepreneurs receive a standard debt contract from their bank, which specifies a loan
amount, bt+1 , and a gross rate of return, Zt+1 , in the event that it is feasible for the entrepreneur to repay. The lowest realization of ω for which it is feasible to repay is ω̄t+1 ,
where
¡
¢
k
ω̄t+1 1 + Rt+1
(B.2)
Pk0 ,t kt+1 = Zt+1 bt+1 .

For ω < ω̄t+1 the entrepreneur simply pays all its revenues to the bank:
¡
¢
k
1 + Rt+1
ωPk0 ,t kt+1 .

In this case, the bank monitors the entrepreneur. Following BGG, we assume that monitoring
costs are a fraction, µ, of the total earnings of the entrepreneur:
¡
¢
k
µ 1 + Rt+1
ωPk0 ,t kt+1 .
36

At time t the bank borrows bt+1 from households. In each state of t + 1 the bank pays
households
(1 + Rt+1 ) bt+1
(B.3)
units of currency. The bank’s source of funds in each state of period t+1 is the earnings from
non-bankrupt entrepreneurs plus the earnings of bankrupt entrepreneurs, net of monitoring
costs:
Z ω̄t+1
¡
¢
k
[1 − F (ω̄ t+1 )] Zt+1 bt+1 + (1 − µ)
ωdF (ω) 1 + Rt+1
(B.4)
Pk0 ,t kt+1 .
0

We follow BGG, who implicitly suppose that at date t there are no state-contingent markets
for currency in date t + 1. As a consequence, (B.3) must not exceed (B.4) in any date t + 1
state. This condition, together with competition among banks, leads to:
Z ω̄t+1
¢
¡
k
[1 − F (ω̄ t+1 )] Zt+1 bt+1 + (1 − µ)
Pk0 ,t kt+1 = (1 + Rt+1 ) bt+1 .
ωdF (ω) 1 + Rt+1
0

¡
¢
k
Substituting from (B.2) for Zt+1 bt+1 and dividing by 1 + Rt+1
Pk0 ,t kt+1 :
¶
µ
Z ω̄t+1
bt+1
1 + Rt+1
[1 − F (ω̄ t+1 )] ω̄t+1 + (1 − µ)
ωdF (ω) =
.
k
1 + Rt+1 Pk0 ,t kt+1
0

We conclude that the gross return on capital can be expressed:
¡
¢¡
¢
k
,
1 + Rt+1 = 1 − τ kt+1 1 + Rt+1

where the ‘wedge’, 1 − τ kt+1 , satisfies:
µ
¶
Z ω̄t+1
Pk0 ,t kt+1
k
1 − τ t+1 =
[1 − F (ω̄ t+1 )] ω̄t+1 + (1 − µ)
ωdF (ω) .
Pk0 ,t kt+1 − Nt+1
0

The wedge, τ kt , contains two additional endogenous variables, Nt+1 and ω̄ t+1 . These are
determined in general equilibrium by the introduction of two additional equations: the condition associated with the fact that the standard debt contract maximizes the utility of the
entrepreneur, as well as the law of motion for entrepreneurial net worth.
The resource constraint for this economy is:
ct + Gt + xt = ktα (Zt lt )1−α ,
where Gt includes any consumption of entrepreneurs, as well as monitoring costs incurred
by banks. As long as these latter can be ignored, then the BGG financial friction is to, in
k
effect, introduce a tax on the rate of return on capital in, 1 + Rt+1
, in (A.4). In particular,
k
1 + Rt+1 is replaced by
¡
¢¡
¢
k
1 + Rt+1
1 − τ kt+1 .
Note there is a slight difference with CF financial frictions in that the latter imply the tax
rate is not a function of period t + 1 uncertainty, while the BGG frictions imply that in
general it is a function of this uncertainty.
37

C. Appendix C: Other Empirical Results
Figures A1 - A9 display additional results for US recessions. Figures A1-A8 pertain to four
postwar US recessions. Figures A1 - A4 are the analog of Figure 3 for the 1982 recession.
Figures A5 - A8 are the analog of Figure 4. Figure A9 is the analog of Figure 6 for the US
Great Depression, except that it is based on BCA, when measurement error is set to zero in
estimation.

38

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41

Table 1: Summary of Results for the 1982 US Recession
Panel 1a: CKM Version of Intertemporal Wedge (τ x,t )
CKM measurement error No measurement error
baseline rotation
baseline rotation
Tobin’s q elasticity = ∞
-0.03

0.92

0.047

0.96

Tobin’s q elasticity = 1
0.31

1.02

0.28

1.05

Panel 1b: Alternative Version of the Wedge (BGG, τ kt )
Likelihood ratio test of
CKM measurement error No measurement error
CKM measurement error baseline rotation
baseline rotation
Tobin’s q elasticity = ∞
481

0.24

1.32

-1.31

-0.01

Tobin’s q elasticity = 1
541

0.22

1.05

0.53

0.93

Notes: (1) Likelihood ratio statistic - twice difference between the log likelihood
under estimation with CKM measurement error specification, and under estimation
with measurement error set to zero; (2) CKM measurement error: results based
on estimation with CKM specification of R in (3.6),
(3) No measurement error: based on estimation subject to R = 0, (4) baseline
decomposition - see text, (5) rotation - rotation of shocks which maximizes
importance of financial frictions, as defined in text.

1

Table 2: Alternative Version of the Wedge (BGG, τ kt )
Panel A: Tobin’s q Elasticity = ∞
CKM Measurement Error
No Measurement Error

Country
United States
Belgium
Canada
Denmark
Finland
France
Germany
Italy
Japan
Mexico
Netherlands
Norway
Spain
Switzerland
England
Weighted Mean

Baseline

Rotation

Ratio

Baseline

Rotation

Ratio

0.24
0.61
0.20
0.39
1.18
0.13
0.44
-4.83
-0.00
0.00
2.50
1.27
1.49
-0.14
0.25
0.22

0.90
0.83
1.11
1.15
1.58
1.63
1.10
1.85
1.02
1.06
3.02
-0.23
1.51
0.95
1.10
1.30

0.49
0.28
0.69
0.00
0.13
0.96
0.77
0.00
1.01
1.00
0.04
0.00
0.00
1.03
0.60
0.44

-1.11
-1.12
-0.51
0.18
0.24
-3.10
-1.87
-0.19
0.27
-0.07
-0.01
-0.56
-0.00
-0.24
0.04
-0.59

-0.15
0.24
0.95
1.11
1.31
1.59
-3.29
1.38
1.67
1.05
1.25
0.79
1.66
0.89
1.19
0.80

1.29
0.31
1.25
0.92
0.44
0.41
0.00
0.45
1.41
1.00
0.68
0.90
0.97
1.01
0.89
0.85

Panel B: Tobin’s q Elasticity = 1
CKM Measurement Error
No Measurement Error

Country
United States
Belgium
Canada
Denmark
Finland
France
Germany
Italy
Japan
Mexico
Netherlands
Norway
Spain
Switzerland
England
Weighted Mean

Baseline

Rotation

Ratio

Baseline

Rotation

Ratio

0.15
-0.09
0.33
0.14
-6.25
1.45
0.33
0.66
0.71
-0.04
0.76
-0.06
1.93
0.31
-0.01
-0.01

0.89
0.85
1.26
1.05
-5.72
1.43
1.08
1.29
1.05
0.92
1.25
1.10
1.28
1.11
1.07
0.61

0.73
1.01
0.55
0.99
0.02
0.02
1.32
0.41
1.12
1.06
0.43
0.91
0.03
0.67
0.91
0.61

0.46
-0.69
0.75
-0.17
-0.60
1.13
-0.08
-0.51
0.23
0.40
0.04
-0.29
0.67
-0.14
-0.08
0.16

0.85
1.25
1.86
0.95
0.49
0.99
0.90
3.72
2.06
1.04
1.51
1.53
1.29
1.38
1.26
1.37

0.30
1.39
0.39
1.12
0.33
0.02
1.22
0.11
1.01
0.41
0.65
0.78
0.96
0.24
1.24
0.60

1

-6
1960

1990

2000

-2

-2

1980

0

0

1970

2

2

-6
1960

-4

4

4

-4

6

6

Tobin's q elasticity = 3
data

8

8

2000

10

1990

10

1980

-6
1960

-4

12

1970

Tobin's q elasticity = 1/2
data

-2

0

2

4

6

8

10

12

1960

-5

0

5

10

12

1970

1970

1990

2000

1980

1990

2000

Tobin's q elasticity = infinity
data

1980

Tobin's q elasticity = 1
data

Figure 1A: Actual and Model Rates of Return, Different Tobin's q Elasticities

Adjustment costs, as percent of aggregate output

0
40

1

2

3

4

5

60

80
100
120
Investment-capital ratio, as a percent of steady state, 100 O t

Quadratic Adjustment Costs
Alternative Adjustment Costs

140

Figure 1B: Implications of Quadratic and Alternative Adjustment Cost Functions, Each Having Unit Tobin's q Elasticity

160

(iii)

(ii)

(*)

(i)

Propagation

Intertemporal wedge:
shock that enters
intertemporal Euler
equation

Other wedges: shock in
intratemporal Euler
equation, shock in
resource constraint

Wedges,
or Shocks

(*) movements in other wedges due to other disturbances
(i) movements in the intertemporal wedge due to financial disturbances
(ii) movements in the intertemporal wedge due to spillover effects from standard
disturbances
(iii) movements in other wedges due to spillovers from financial disturbances

Financial friction
disturbances
(monitoring costs,
entrepreneurial risk,
etc.)

Other disturbances
(tastes, government
spending, technology,
etc.)

Fundamental
Economic
Disturbances

Figure 2: The propagation of economic disturbances through wedges

Output

1.1

1983

1983

1984

1984

1985

1985

1

0.8

0.9

1

1980

1981

1982

1983

1984

1985

1985

0.94

0.96

0.98

1

1.02

0.94
1984

0.95
1983

0.96

1
1982

0.98

1.05

1981

1

1.1

1980

1.02

1.15

0.8
1982

1982

1

1981

1981

0.92

0.94

0.96

0.98

1

0.9

1980

1980

Tobin's Q Elasticity = f

1980

1980

1980

1980

Figure 3: Raw Data ('All Wedges') and Various Counterfactual Simulations

1.5

2

0.95

1

1.05

Investment

Hours

Consumption

1981

1981

1981

1981

1982

1982

1982

1982

1983

1983

1983

1983

1984

1984

1984

1984

Tobin's Q Elasticity = 1

1985

1985

1985

1985

Intertemporal Wedge, ME = 0
Intertemporal Wedge, ME = CKM
All Wedges
Baseline

1980

1981 1982 1983 1984
BASELINE DECOMPOSITION

1985

1980 1981 1982 1983 1984 1985
Wedge=-0.32052 R2=0.44068 E=-1.0051

1980 1981 1982 1983 1984 1985
Wedge=0.91634 R2=0.85922 E=1.2317

1980 1981 1982 1983 1984 1985
Wedge=1.1727 R2=0.93033 E=1.1072

0.94

0.96

0.98

1

0.95

1

1.05

0.8

0.9

1

1.02
1
0.98
0.96
0.94
0.92

1980

1981 1982 1983 1984
ROTATION DECOMPOSITION

1985

1980 1981 1982 1983 1984 1985
Wedge=1.0783 R2=0.96272 E=0.83927

1980 1981 1982 1983 1984 1985
Wedge=0.54225 R2=0.75622 E=0.83027

1980 1981 1982 1983 1984 1985
Wedge=0.87435 R2=0.98008 E=1.1342

Wedge=0.92998 R2=0.87408 E=0.80766

All Wedges
Intertemporal Wedge
Baseline

Note (1) wedge - fraction of fall in raw data at the trough for output accounted for by the intertemporal wedge; (2) R2 - R-square in regression of raw data on
wedge component throughout recession episode; (3) E - slope coefficient in preceding regression

0.94

0.96

0.98

1

1.02

0.94

0.96

0.98

1

1.02

0.8

0.9

1

0.92

0.94

0.96

0.98

1

Wedge=0.52742 R2=0.86969 E=2.0858

Figure 4: Raw Data ('all wedges') and Two Counterfactual Wedges, Tobin's q = 1, No Measurement Error

GDP

INVESTMENT

HOURS

CONSUMPTION

1920
year

1930

1930

1940

-70
1900

1920
year

-12
1900

-40

-30

-20

-10

0

10

20

-6
1900

-60

1910

1940

-4

-2

0

2

4

-10

nonlinear
linear

Figure 5C: Percent Euler Errors, Hours

1910

nonlinear
linear

Figure 5A: Percent Euler Errors, Output

-50

-6

-4

-2

0

2

4

6

-8
1900

-6

-4

-2

0

2

4

-8

percent

percent

percent
percent

1920
year

1930

1910

nonlinear
linear

1920
year

1930

Figure 5D: Percent Euler Errors, Investment

1910

nonlinear
linear

Figure 5B: Percent Euler Errors, Consumption

1940

1940

1930
1932
1934
1936
1938
BASELINE NONLINEAR DECOMPOSITION

1940

0.8

0.9

1930

1930

1930

1930

2

1932
1934
1936
1938
ROTATION DECOMPOSITION

1932
1934
1936
1938
Wedge=0.88939 R2=0.95465 E=0.9339

1932
1934
1936
1938
Wedge=1.0148 R2=0.90315 E=0.88801

1932
1934
1936
1938
Wedge=0.95715 R2=0.946 E=0.91713

Wedge=0.92051 R2=0.94612 E=0.99907

1940

1940

1940

1940

Note: (1) wedge - fraction of fall in raw data at the maximum for output accounted for by the intertemporal wedge; (2) R - R-square in regression of raw
data on wedge component throughout recession episode; (3) E - slope coefficient in preceding regression.

0.8

0.9

1

1

0.8

0.8
1940

0.9

0.9

1930
1932
1934
1936
1938
Wedge=-0.20084 R2=0.18331 E=0.95868

1

1

0.4

0.4
1940

0.6

0.6

1932
1934
1936
1938
Wedge=0.30211 R2=0.3634 E=1.2732

0.8

0.8

1930

1

1

0.7

0.7
1940

0.8

0.8

1932
1934
1936
1938
Wedge=0.62184 R2=0.96296 E=1.3631

0.9

0.9

1930

1

1

Wedge=0.21241 R2=0.9 E=4.1234

All Wedges
Intertemporal Wedge
Baseline

Figure 6: Wedges, US Great Depression Based on Second Order Approximation to Model, CKM Measurement Error, Tobin's q Elastic ity = 1

GDP

INVESTMENT

HOURS

CONSUMPTION

Output

1970 1970.5 1971 1971.5 1972 1972.5 1973 1973.5

1970 1970.5 1971 1971.5 1972 1972.5 1973 1973.5

1970 1970.5 1971 1971.5 1972 1972.5 1973 1973.5

Tobin's Q Elasticity = f

1

1.02

1.04

0.96

0.98

1

0.85

0.9

0.95

1

1.05

0.96

0.97

0.98

0.99

1

Tobin's Q Elasticity = 1

Intertemporal Wedge, ME = 0
Intertemporal Wedge, ME = CKM
All Wedges
Baseline

1970 1970.5 1971 1971.5 1972 1972.5 1973 1973.5

1970 1970.5 1971 1971.5 1972 1972.5 1973 1973.5

1970 1970.5 1971 1971.5 1972 1972.5 1973 1973.5

Figure A1: Raw Data ('all wedges') and Various Counterfactual Simulations

0.96

0.98
1970 1970.5 1971 1971.5 1972 1972.5 1973 1973.5
1970 1970.5 1971 1971.5 1972 1972.5 1973 1973.5
Notes: (1) ME = CKM - model estimation using CKM measurement error assumption, (2) ME = 0 - model estimation using no measurement error;
(3) Tobin's Q elasticity = f - investment adjustment costs set to zero, =1 means investment adjustment costs implies a unit Tobin's Q elasticity

0.98

1

1.02

1.04

1.04
1.02
1
0.98
0.96
0.94

0.8

0.9

1

1.1

1.2

0.96

0.98

1

1.02

Investment

Hours

Consumption

Output

1975

1975

1975

1976

1976

1976

1976

1977

1977

1977

1977

1978

1978

1978

1978

1979

1979

1979

1979

1974

0.96

0.98

1

1.02

0.94
1974

0.96

0.98

1

1974

0.8

0.9

1

1974

0.94

0.96

0.98

1

1975

1975

1975

1975

1976

1976

1976

1976

1977

1977

1977

1977

Tobin's Q Elasticity = 1

1978

1978

1978

1978

1979

1979

1979

1979

Intertemporal Wedge, ME = 0
Intertemporal Wedge, ME = CKM
All Wedges
Baseline

Notes: (1) ME = CKM - model estimation using CKM measurement error assumption, (2) ME = 0 - model estimation using no measurement error;
(3) Tobin's Q elasticity = f - investment adjustment costs set to zero, =1 means investment adjustment costs implies a unit Tobin's Q elasticity

1974

0.9

0.95

1

0.95
1974

1

1.05

1.1

0.8
1974

1

1.2

1.4

1.6

1975

Tobin's Q Elasticity = f

Figure A2: Raw Data ('all wedges') and Various Counterfactual Simulations

1974

0.95

1

1.05

Investment

Hours

Consumption

1993

1994

1995

1996

1990

1990

1990

1991

1991

1991

1992

1992

1992

1993

1993

1993

1994

1994

1994

1995

1995

1995

1996

1996

1996

0.98

1

1.02

0.98

1

1.02

0.9

0.95

1

1.05

1.1

1990

1990

1990

1990

1991

1991

1991

1991

1992

1992

1992

1992

1993

1993

1993

1993

1994

1994

1994

1994

1995

1995

1995

1995

Tobin's Q Elasticity = 1

1996

1996

1996

1996

Intertemporal Wedge, ME = 0
Intertemporal Wedge, ME = CKM
All Wedges
Baseline

Notes: (1) ME = CKM - model estimation using CKM measurement error assumption, (2) ME = 0 - model estimation using no measurement error;
(3) Tobin's Q elasticity = f - investment adjustment costs set to zero, =1 means investment adjustment costs implies a unit Tobin's Q elasticity

0.92

0.94

0.96

0.98

1

1.02

1.06
1.04
1.02
1
0.98

1

1.2

1.4

0.96
1992

0.96

1991

0.97

0.98

0.99

1

0.98

1990

Tobin's Q Elasticity = f

1

1.02

1.04

1.06

Figure A3: Raw Data ('all wedges') and Various Counterfactual Simulations

Output

Investment

Hours

Consumption

2001

2001

2001

2002

2002

2002

2003

2003

2003

2004

2004

2004

1

1.01

1.02

0.94
2000

0.96

0.98

1

2000

0.9

0.95

1

2000

0.96

0.98

1

2001

2001

2001

2002

2002

2002

2003

2003

2003

Tobin's Q Elasticity = 1

2004

2004

2004

Intertemporal Wedge, ME = 0
Intertemporal Wedge, ME = CKM
All Wedges
Baseline

0.99
2000
2001
2002
2003
2004
2000
2001
2002
2003
2004
Notes: (1) ME = CKM - model estimation using CKM measurement error assumption, (2) ME = 0 - model estimation using no measurement error;
(3) Tobin's Q elasticity = f - investment adjustment costs set to zero, =1 means investment adjustment costs implies a unit Tobin's Q elasticity

0.9

0.95

1

2000

0.95

1

1.05

2000

1

1.2

1.4

0.95
2000

1

1.05

Tobin's Q Elasticity = f

Figure A4: Raw Data ('all wedges') and Various Counterfactual Simulations

Output

Investment

Hours

Consumption

1970 1970.5 1971 1971.5 1972 1972.5 1973 1973.5
Wedge=-1.3684 R2=0.8418 E=-1.7295

1970 1970.5 1971 1971.5 1972 1972.5 1973 1973.5
Wedge=0.86917 R2=0.047532 E=-0.22102

0.98

1

1.02

1.04

0.95

1

1.05

1.1
1.05
1
0.95
0.9

0.96

1970 1970.5 1971 1971.5 1972 1972.5 1973 1973.5
Wedge=1.8908 R2=0.8928 E=0.94042

1970 1970.5 1971 1971.5 1972 1972.5 1973 1973.5
Wedge=0.33269 R2=0.096766 E=-0.17023

1970 1970.5 1971 1971.5 1972 1972.5 1973 1973.5
Wedge=0.85782 R2=0.89838 E=0.63298

Wedge=0.84853 R2=0.68226 E=0.48347

All Wedges
Intertemporal Wedge
Baseline

1970 1970.5 1971 1971.5 1972 1972.5 1973 1973.5
1970 1970.5 1971 1971.5 1972 1972.5 1973 1973.5
ROTATION DECOMPOSITION
BASELINE DECOMPOSITION
Note: (1) wedge - fraction of fall in raw data at the minimum for output accounted for by the intertemporal wedge; (2) R2 - R-square in regression of raw
data on wedge component throughout recession episode; (3) E - slope coefficient in preceding regression

1

1.02

1.04

0.96

0.98

1

0.85

0.9

0.95

1

1.05

0.96

1970 1970.5 1971 1971.5 1972 1972.5 1973 1973.5
Wedge=1.1739 R2=0.9543 E=0.83222

1

0.98
0.98

1.02

0.99

0.97

1.04

1

Wedge=0.51776 R2=0.81035 E=1.755

Figure A5: Raw Data ('all wedges') and Three Counterfactual Simulations, Tobin's q = 1, Measurement Error = 0

GDP

INVESTMENT

HOURS

CONSUMPTION

1975
1976
1977
1978
BASELINE DECOMPOSITION

1975
1976
1977
1978
Wedge=-0.64169 R2=0.9046 E=-1.4053

1975
1976
1977
1978
Wedge=1.0115 R2=0.71279 E=1.2569

1975
1976
1977
1978
Wedge=1.0623 R2=0.94465 E=1.1827

1979

1979

1979

1979

1974

0.96

0.98

1

1.02

1974

0.95

1

1.05

1974

0.8

0.9

1

1974

0.94

0.96

0.98

1

1.02

1975
1976
1977
1978
ROTATION DECOMPOSITION

1975
1976
1977
1978
Wedge=1.2428 R2=0.97723 E=0.7265

1975
1976
1977
1978
Wedge=0.62893 R2=0.66166 E=0.62529

1975
1976
1977
1978
Wedge=0.84323 R2=0.96326 E=1.0121

Wedge=1.1106 R2=0.87098 E=0.65491

1979

1979

1979

1979

All Wedges
Intertemporal Wedge
Baseline

2
Note: (1) wedge - fraction of fall in raw data at the minimum for output accounted for by the intertemporal wedge; (2) R - R-square in regression of raw
data on wedge component throughout recession episode; (3) E - slope coefficient in preceding regression

1974

0.96

0.98

1

1.02

0.94
1974

0.96

0.98

1

1974

0.8

0.9

1

1974

0.94

0.96

0.98

1

Wedge=0.59855 R2=0.79206 E=2.1862

Figure A6: Raw Data ('all wedges') and Three Counterfactual Simulations, Tobin's q = 1, Measurement Error = 0

GDP

INVESTMENT

HOURS

CONSUMPTION

1
0.98
0.96

0.98

0.97

0.96

1990

1990

1991 1992 1993 1994 1995 1996
Wedge=-0.5154 R2=0.59606 E=-0.72926

1991 1992 1993 1994 1995 1996
Wedge=0.81405 R2=0.62805 E=1.5112

0.98

1

1.02

0.98

1

1.02

1.04

1.06

0.9

1990

1990

1990

1991 1992 1993 1994 1995 1996
Wedge=0.97365 R2=0.60399 E=0.34821

1991 1992 1993 1994 1995 1996
Wedge=0.72304 R2=0.81966 E=0.62709

1991 1992 1993 1994 1995 1996
Wedge=0.87084 R2=0.96598 E=1.1944

Wedge=0.97262 R2=0.64538 E=0.41595

All Wedges
Intertemporal Wedge
Baseline

1991 1992 1993 1994 1995 1996
1990 1991 1992 1993 1994 1995 1996
ROTATION DECOMPOSITION
BASELINE DECOMPOSITION
Note: (1) wedge - fraction of fall in raw data at the minimum for output accounted for by the intertemporal wedge; (2) R2 - R-square in regression of raw
data on wedge component throughout recession episode; (3) E - slope coefficient in preceding regression

0.98

1

1.02

0.98

1

1.02

0.9

1990

1

1
0.95

1.05

1.05

0.95

1.1

1.1

1991 1992 1993 1994 1995 1996
Wedge=1.1321 R2=0.74797 E=1.4334

1.02

0.99

1990

1.04

1

Wedge=0.5078 R2=0.77707 E=1.9646

Figure A7: Raw Data ('all wedges') and Three Counterfactual Simulations, Tobin's q = 1, Measurement Error = 0

GDP

INVESTMENT

HOURS

CONSUMPTION

2001
2002
2003
BASELINE DECOMPOSITION

2004

2001
2002
2003
2004
Wedge=-3.5841 R2=0.26094 E=-0.17036

2001
2002
2003
2004
Wedge=0.50247 R2=0.42252 E=1.2694

2001
2002
2003
2004
Wedge=1.6583 R2=0.78116 E=0.79426

0.99
2000

1

1.01

1.02

0.94
2000

0.96

0.98

1

1.02

2000

0.92

0.94

0.96

0.98

1

1.02

2000

0.96

0.98

1

1.02

2001
2002
2003
ROTATION DECOMPOSITION

2004

2001
2002
2003
2004
Wedge=-0.48362 R2=0.048874 E=0.086548

2001
2002
2003
2004
Wedge=0.066889 R2=0.046817 E=-0.42223

2001
2002
2003
2004
Wedge=0.89117 R2=0.86491 E=1.0505

Wedge=0.35676 R2=0.30753 E=0.56268

All Wedges
Intertemporal Wedge
Baseline

Note: (1) wedge - fraction of fall in raw data at the minimum for output accounted for by the intertemporal wedge; (2) R2 - R-square in regression of raw
data on wedge component throughout recession episode; (3) E - slope coefficient in preceding regression

0.99
2000

1

1.01

1.02

1.03

0.94
2000

0.96

0.98

1

2000

0.9

0.95

1

0.95
2000

0.96

0.97

0.98

0.99

Wedge=0.50177 R2=0.87454 E=1.6538

Figure A8: Raw Data ('all wedges') and Three Counterfactual Simulations, Tobin's q = 1, Measurement Error = 0

GDP

INVESTMENT

HOURS

CONSUMPTION

1940

1932
1934
1936
1938
Wedge=0.72082 R2=0.81247 E=1.0121

1930

1930

1932
1934
1936
1938
ROTATION DECOMPOSITION

1932
1934
1936
1938
Wedge=0.54379 R2=0.90475 E=1.0033

1930
1932
1934
1936
1938
Wedge=0.75138 R2=0.74424 E=0.99076

1930

Wedge=0.61871 R2=0.79552 E=0.98869

1940

1940

1940

1940

Note: (1) wedge - fraction of fall in raw data at the maximum for output accounted for by the intertemporal wedge; (2) R2 - R-square in regression of raw
data on wedge component throughout recession episode; (3) E - slope coefficient in preceding regression.

0.8

0.8

1930
1932
1934
1936
1938
BASELINE NONLINEAR DECOMPOSITION

0.9

1

0.9

1

0.8

0.8
1940

0.9

0.9

1930
1932
1934
1936
1938
Wedge=-0.00033565 R2=0.10101 E=1.3485

1

1

0.4

0.4

1930
1932
1934
1936
1938
1940
Wedge=0.00029434 R2=0.034298 E=0.68977

0.6

0.8

0.6

0.8

1

0.7

0.7

1

0.8

0.8

1940

0.9

0.9

1930
1932
1934
1936
1938
Wedge=0.00064992 R2=0.23846 E=0.95332

1

1

Wedge=0.00014874 R2=0.020206 E=0.91685

All Wedges
Intertemporal Wedge
Baseline

Figure A9: Wedges, US Great Depression Based on Second Order Approximation to Model, no Measurement Error, Tobin's q Elasticit y = 1

GDP

INVESTMENT

HOURS

CONSUMPTION

Working Paper Series
A series of research studies on regional economic issues relating to the Seventh Federal
Reserve District, and on financial and economic topics.
A Proposal for Efficiently Resolving Out-of-the-Money Swap Positions
at Large Insolvent Banks
George G. Kaufman

WP-03-01

Depositor Liquidity and Loss-Sharing in Bank Failure Resolutions
George G. Kaufman

WP-03-02

Subordinated Debt and Prompt Corrective Regulatory Action
Douglas D. Evanoff and Larry D. Wall

WP-03-03

When is Inter-Transaction Time Informative?
Craig Furfine

WP-03-04

Tenure Choice with Location Selection: The Case of Hispanic Neighborhoods
in Chicago
Maude Toussaint-Comeau and Sherrie L.W. Rhine

WP-03-05

Distinguishing Limited Commitment from Moral Hazard in Models of
Growth with Inequality*
Anna L. Paulson and Robert Townsend

WP-03-06

Resolving Large Complex Financial Organizations
Robert R. Bliss

WP-03-07

The Case of the Missing Productivity Growth:
Or, Does information technology explain why productivity accelerated in the United States
but not the United Kingdom?
Susanto Basu, John G. Fernald, Nicholas Oulton and Sylaja Srinivasan

WP-03-08

Inside-Outside Money Competition
Ramon Marimon, Juan Pablo Nicolini and Pedro Teles

WP-03-09

The Importance of Check-Cashing Businesses to the Unbanked: Racial/Ethnic Differences
William H. Greene, Sherrie L.W. Rhine and Maude Toussaint-Comeau

WP-03-10

A Firm’s First Year
Jaap H. Abbring and Jeffrey R. Campbell

WP-03-11

Market Size Matters
Jeffrey R. Campbell and Hugo A. Hopenhayn

WP-03-12

The Cost of Business Cycles under Endogenous Growth
Gadi Barlevy

WP-03-13

The Past, Present, and Probable Future for Community Banks
Robert DeYoung, William C. Hunter and Gregory F. Udell

WP-03-14

1

Working Paper Series (continued)
Measuring Productivity Growth in Asia: Do Market Imperfections Matter?
John Fernald and Brent Neiman

WP-03-15

Revised Estimates of Intergenerational Income Mobility in the United States
Bhashkar Mazumder

WP-03-16

Product Market Evidence on the Employment Effects of the Minimum Wage
Daniel Aaronson and Eric French

WP-03-17

Estimating Models of On-the-Job Search using Record Statistics
Gadi Barlevy

WP-03-18

Banking Market Conditions and Deposit Interest Rates
Richard J. Rosen

WP-03-19

Creating a National State Rainy Day Fund: A Modest Proposal to Improve Future
State Fiscal Performance
Richard Mattoon

WP-03-20

Managerial Incentive and Financial Contagion
Sujit Chakravorti and Subir Lall

WP-03-21

Women and the Phillips Curve: Do Women’s and Men’s Labor Market Outcomes
Differentially Affect Real Wage Growth and Inflation?
Katharine Anderson, Lisa Barrow and Kristin F. Butcher

WP-03-22

Evaluating the Calvo Model of Sticky Prices
Martin Eichenbaum and Jonas D.M. Fisher

WP-03-23

The Growing Importance of Family and Community: An Analysis of Changes in the
Sibling Correlation in Earnings
Bhashkar Mazumder and David I. Levine

WP-03-24

Should We Teach Old Dogs New Tricks? The Impact of Community College Retraining
on Older Displaced Workers
Louis Jacobson, Robert J. LaLonde and Daniel Sullivan

WP-03-25

Trade Deflection and Trade Depression
Chad P. Brown and Meredith A. Crowley

WP-03-26

China and Emerging Asia: Comrades or Competitors?
Alan G. Ahearne, John G. Fernald, Prakash Loungani and John W. Schindler

WP-03-27

International Business Cycles Under Fixed and Flexible Exchange Rate Regimes
Michael A. Kouparitsas

WP-03-28

Firing Costs and Business Cycle Fluctuations
Marcelo Veracierto

WP-03-29

Spatial Organization of Firms
Yukako Ono

WP-03-30

Government Equity and Money: John Law’s System in 1720 France
François R. Velde

WP-03-31

2

Working Paper Series (continued)
Deregulation and the Relationship Between Bank CEO
Compensation and Risk-Taking
Elijah Brewer III, William Curt Hunter and William E. Jackson III

WP-03-32

Compatibility and Pricing with Indirect Network Effects: Evidence from ATMs
Christopher R. Knittel and Victor Stango

WP-03-33

Self-Employment as an Alternative to Unemployment
Ellen R. Rissman

WP-03-34

Where the Headquarters are – Evidence from Large Public Companies 1990-2000
Tyler Diacon and Thomas H. Klier

WP-03-35

Standing Facilities and Interbank Borrowing: Evidence from the Federal Reserve’s
New Discount Window
Craig Furfine

WP-04-01

Netting, Financial Contracts, and Banks: The Economic Implications
William J. Bergman, Robert R. Bliss, Christian A. Johnson and George G. Kaufman

WP-04-02

Real Effects of Bank Competition
Nicola Cetorelli

WP-04-03

Finance as a Barrier To Entry: Bank Competition and Industry Structure in
Local U.S. Markets?
Nicola Cetorelli and Philip E. Strahan

WP-04-04

The Dynamics of Work and Debt
Jeffrey R. Campbell and Zvi Hercowitz

WP-04-05

Fiscal Policy in the Aftermath of 9/11
Jonas Fisher and Martin Eichenbaum

WP-04-06

Merger Momentum and Investor Sentiment: The Stock Market Reaction
To Merger Announcements
Richard J. Rosen

WP-04-07

Earnings Inequality and the Business Cycle
Gadi Barlevy and Daniel Tsiddon

WP-04-08

Platform Competition in Two-Sided Markets: The Case of Payment Networks
Sujit Chakravorti and Roberto Roson

WP-04-09

Nominal Debt as a Burden on Monetary Policy
Javier Díaz-Giménez, Giorgia Giovannetti, Ramon Marimon, and Pedro Teles

WP-04-10

On the Timing of Innovation in Stochastic Schumpeterian Growth Models
Gadi Barlevy

WP-04-11

Policy Externalities: How US Antidumping Affects Japanese Exports to the EU
Chad P. Bown and Meredith A. Crowley

WP-04-12

Sibling Similarities, Differences and Economic Inequality
Bhashkar Mazumder

WP-04-13

3

Working Paper Series (continued)
Determinants of Business Cycle Comovement: A Robust Analysis
Marianne Baxter and Michael A. Kouparitsas

WP-04-14

The Occupational Assimilation of Hispanics in the U.S.: Evidence from Panel Data
Maude Toussaint-Comeau

WP-04-15

Reading, Writing, and Raisinets1: Are School Finances Contributing to Children’s Obesity?
Patricia M. Anderson and Kristin F. Butcher

WP-04-16

Learning by Observing: Information Spillovers in the Execution and Valuation
of Commercial Bank M&As
Gayle DeLong and Robert DeYoung

WP-04-17

Prospects for Immigrant-Native Wealth Assimilation:
Evidence from Financial Market Participation
Una Okonkwo Osili and Anna Paulson

WP-04-18

Individuals and Institutions: Evidence from International Migrants in the U.S.
Una Okonkwo Osili and Anna Paulson

WP-04-19

Are Technology Improvements Contractionary?
Susanto Basu, John Fernald and Miles Kimball

WP-04-20

The Minimum Wage, Restaurant Prices and Labor Market Structure
Daniel Aaronson, Eric French and James MacDonald

WP-04-21

Betcha can’t acquire just one: merger programs and compensation
Richard J. Rosen

WP-04-22

Not Working: Demographic Changes, Policy Changes,
and the Distribution of Weeks (Not) Worked
Lisa Barrow and Kristin F. Butcher

WP-04-23

The Role of Collateralized Household Debt in Macroeconomic Stabilization
Jeffrey R. Campbell and Zvi Hercowitz

WP-04-24

Advertising and Pricing at Multiple-Output Firms: Evidence from U.S. Thrift Institutions
Robert DeYoung and Evren Örs

WP-04-25

Monetary Policy with State Contingent Interest Rates
Bernardino Adão, Isabel Correia and Pedro Teles

WP-04-26

Comparing location decisions of domestic and foreign auto supplier plants
Thomas Klier, Paul Ma and Daniel P. McMillen

WP-04-27

China’s export growth and US trade policy
Chad P. Bown and Meredith A. Crowley

WP-04-28

Where do manufacturing firms locate their Headquarters?
J. Vernon Henderson and Yukako Ono

WP-04-29

Monetary Policy with Single Instrument Feedback Rules
Bernardino Adão, Isabel Correia and Pedro Teles

WP-04-30

4

Working Paper Series (continued)
Firm-Specific Capital, Nominal Rigidities and the Business Cycle
David Altig, Lawrence J. Christiano, Martin Eichenbaum and Jesper Linde

WP-05-01

Do Returns to Schooling Differ by Race and Ethnicity?
Lisa Barrow and Cecilia Elena Rouse

WP-05-02

Derivatives and Systemic Risk: Netting, Collateral, and Closeout
Robert R. Bliss and George G. Kaufman

WP-05-03

Risk Overhang and Loan Portfolio Decisions
Robert DeYoung, Anne Gron and Andrew Winton

WP-05-04

Characterizations in a random record model with a non-identically distributed initial record
Gadi Barlevy and H. N. Nagaraja

WP-05-05

Price discovery in a market under stress: the U.S. Treasury market in fall 1998
Craig H. Furfine and Eli M. Remolona

WP-05-06

Politics and Efficiency of Separating Capital and Ordinary Government Budgets
Marco Bassetto with Thomas J. Sargent

WP-05-07

Rigid Prices: Evidence from U.S. Scanner Data
Jeffrey R. Campbell and Benjamin Eden

WP-05-08

Entrepreneurship, Frictions, and Wealth
Marco Cagetti and Mariacristina De Nardi

WP-05-09

Wealth inequality: data and models
Marco Cagetti and Mariacristina De Nardi

WP-05-10

What Determines Bilateral Trade Flows?
Marianne Baxter and Michael A. Kouparitsas

WP-05-11

Intergenerational Economic Mobility in the U.S., 1940 to 2000
Daniel Aaronson and Bhashkar Mazumder

WP-05-12

Differential Mortality, Uncertain Medical Expenses, and the Saving of Elderly Singles
Mariacristina De Nardi, Eric French, and John Bailey Jones

WP-05-13

Fixed Term Employment Contracts in an Equilibrium Search Model
Fernando Alvarez and Marcelo Veracierto

WP-05-14

Causality, Causality, Causality: The View of Education Inputs and Outputs from Economics
Lisa Barrow and Cecilia Elena Rouse

WP-05-15

5

Working Paper Series (continued)
Competition in Large Markets
Jeffrey R. Campbell

WP-05-16

Why Do Firms Go Public? Evidence from the Banking Industry
Richard J. Rosen, Scott B. Smart and Chad J. Zutter

WP-05-17

Clustering of Auto Supplier Plants in the U.S.: GMM Spatial Logit for Large Samples
Thomas Klier and Daniel P. McMillen

WP-05-18

Why are Immigrants’ Incarceration Rates So Low?
Evidence on Selective Immigration, Deterrence, and Deportation
Kristin F. Butcher and Anne Morrison Piehl

WP-05-19

The Incidence of Inflation: Inflation Experiences by Demographic Group: 1981-2004
Leslie McGranahan and Anna Paulson

WP-05-20

Universal Access, Cost Recovery, and Payment Services
Sujit Chakravorti, Jeffery W. Gunther, and Robert R. Moore

WP-05-21

Supplier Switching and Outsourcing
Yukako Ono and Victor Stango

WP-05-22

Do Enclaves Matter in Immigrants’ Self-Employment Decision?
Maude Toussaint-Comeau

WP-05-23

The Changing Pattern of Wage Growth for Low Skilled Workers
Eric French, Bhashkar Mazumder and Christopher Taber

WP-05-24

U.S. Corporate and Bank Insolvency Regimes: An Economic Comparison and Evaluation
Robert R. Bliss and George G. Kaufman

WP-06-01

Redistribution, Taxes, and the Median Voter
Marco Bassetto and Jess Benhabib

WP-06-02

Identification of Search Models with Initial Condition Problems
Gadi Barlevy and H. N. Nagaraja

WP-06-03

Tax Riots
Marco Bassetto and Christopher Phelan

WP-06-04

The Tradeoff between Mortgage Prepayments and Tax-Deferred Retirement Savings
Gene Amromin, Jennifer Huang,and Clemens Sialm

WP-06-05

Why are safeguards needed in a trade agreement?
Meredith A. Crowley

WP-06-06

6

Working Paper Series (continued)
Taxation, Entrepreneurship, and Wealth
Marco Cagetti and Mariacristina De Nardi

WP-06-07

A New Social Compact: How University Engagement Can Fuel Innovation
Laura Melle, Larry Isaak, and Richard Mattoon

WP-06-08

Mergers and Risk
Craig H. Furfine and Richard J. Rosen

WP-06-09

Two Flaws in Business Cycle Accounting
Lawrence J. Christiano and Joshua M. Davis

WP-06-10

7