Accounting for Business Cycles

TL;DR: In this article, the authors compare the business cycle accounting method proposed by Chari et al. (2006) and apply it to compare the Great Recession across OECD countries as well as to the recessions of the 1980s in these countries.

Abstract: We elaborate on the business cycle accounting method proposed by Chari et al. (2006) , clear up some misconceptions about the method, and then apply it to compare the Great Recession across OECD countries as well as to the recessions of the 1980s in these countries. We have four main findings. First, with the notable exception of the United States, Spain, Ireland, and Iceland, the Great Recession was driven primarily by the efficiency wedge. Second, in the Great Recession, the labor wedge plays a dominant role only in the United States, and the investment wedge plays a dominant role in Spain, Ireland, and Iceland. Third, in the recessions of the 1980s, the labor wedge played a dominant role only in France, the United Kingdom, and Belgium. Finally, overall in the Great Recession, the efficiency wedge played a more important role and the investment wedge played a less important role than they did in the recessions of the 1980s.

Summary

Introduction

• Second, in the Great Recession, the labor wedge plays a dominant role only in the United States, and the investment wedge plays a dominant role in Spain, Ireland, and Iceland.
• When the authors map this model into the new prototype model with two capital-like variables, then the prototype model has only labor wedges.
• The authors then briefly discuss what at first seems to be an intuitive way to proceed: the wedges are identified with the underlying event not only in the estimation but also in the thought experiment.

A. The Benchmark Prototype Economy

• The benchmark prototype economy that the authors use later in their accounting procedure is a stochastic growth model.
• The economy has four exogenous stochastic variables, all of which are functions of the underlying random variable st: the effi ciency wedge At(st), the labor wedge 1 − τ lt(st), the investment wedge 1/[1 + τxt(s t)], and the government consumption wedge gt(st).
• Capital income taxes induce a wedge between the intertemporal marginal rate of substitution and the marginal product of capital, which is only slightly different from the distortion induced by a tax on investment.
• Thus, their method identifies the overall wedge induced by both distortions and does not identify each separately.
• Likewise, liquidity constraints on consumers distort the consumer’s intertemporal Euler equation, whereas investment financing frictions on firms distort the firm’s intertemporal Euler equation.

B. The Mapping– From Frictions to Wedges

• Now the authors illustrate the mapping between detailed economies and prototype economies for several types of wedges.
• The authors then consider an economy with heterogeneous productivity and collateral constraints and show that it maps into a prototype economy with effi ciency, labor, and investment wedges.
• The four economies the authors use to illustrate this mapping are closed economies for which the associated government consumption wedge in the prototype economy is identically zero.
• Since many models map into the same configuration of wedges, identifying one particular configuration does not uniquely identify a model; rather, it identifies a whole class of models that are consistent with that configuration.
• Their method does not uniquely determine the model most promising to analyze business cycle fluctuations.

A Detailed Economy with Investment Specific Technical Change

• The timing is that the capital stock in use at period t is chosen at the end of period t− 1 given the shock history st−1, whereas at the beginning of each period, after the current shock st is realized, labor and capital are allocated between sectors.
• An Equivalence Result for an Economy with Bank Collateral Constraints.

A Detailed Economy with Bank Collateral Constraints

• Consider an infinite horizon economy that blends elements of Kiyotaki and Moore (1997) with that of Gertler and Kiyotaki (2009) and is composed of a household that works and operates financial intermediaries, referred to as banks, together with firms and a government.
• Households elastically supply labor and save by holding deposits in banks and government bonds and receive dividends.
• The authors assume that a bank that ceases to operate pays out its accumulated net worth as dividends.
• The aggregate allocations in the detailed economy with bank collateral constraints coincide with those of the prototype economy if the effi ciency wedge in the prototype economy At(st) =, also known as Proposition 2.
• A, the labor wedge is zero, and the investment wedge is given by (27).

An Equivalence Result for an Economy with Heterogeneous Productivity and Collateral Constraints

• That proposition showed how a detailed model with financial frictions modeled as input-financing frictions is equivalent to a prototype economy with a labor wedge, an investment wedge, and an effi ciency wedge.
• This formulation immediately implies the following result.

An Equivalence Result for an Economy with Effi cient Search

• Consider the effi cient outcomes from a standard search model.
• A Detailed Economy with Effi cient Search.
• In each period, measure nt of the population is employed and the rest are unemployed.
• Since the labor wedge in the prototype economy is given by the right side of (44), the authors have the following result.

C. Adjusting the Prototype Economy

• So far the authors have always established equivalence results between a given detailed economy and the prototype one-sector growth model.
• When using business cycle accounting logic, one can always do that.
• When the underlying economy is suffi ciently different from the one-sector growth model, however, it is often more instructive to adjust the prototype model so that the version of it without wedges is the planning problem for the class of models at hand.

An Equivalence Result for an Economy with Ineffi cient Search

• Here the authors illustrate what they mean by considering a version of the search model in which search is ineffi cient in that the equilibrium of the economy does not solve the planning problem just discussed.
• The first term gives the marginal increase in utility from the increased consumption due to having an additional worker earning wt.
• These considerations suggest a different notion of a wedge relative to that used in the one-sector model.
• Next the authors compare the aggregate outcomes of the prototype model and the equilibrium search model.

2. The Accounting Procedure

• Having established their equivalence result, the authors now describe their accounting procedure at a conceptual level, discuss a Markovian implementation of it, and distinguish their procedure from others.
• The authors procedure is designed to answer questions of the following kind:.
• Critically, their procedure ensures that agents’expectations of how the effi ciency wedge will evolve are the same as in the prototype economy.
• These comparisons, together with their equivalence results, allow us to identify promising classes of detailed economies.

A. The Accounting Procedure at a Conceptual Level

• Recall that the state st is the history of the underlying abstract events st.
• Recall that the prototype economy has one underlying (vector-valued) 29 random variable, the state st, which has a probability of πt(st).
• All of the other stochastic variables, including the four wedges– the effi ciency wedge At(st), the labor wedge 1− τ lt(st), the investment wedge 1/[1 + τxt(st)], and the government consumption wedge gt(st)– are simply functions of this random variable.
• Hence, when the state st is known, so are the wedges.
• The authors compute the decision rules for the effi ciency wedge alone economy, denoted ye(st), le(st), and xe(st).

B. A Markovian Implementation

• So far the authors have described their procedure assuming that they know the stochastic process πt(s t) and that they can observe the state st.
• The authors assume that the state st follows a Markov process π(st|st−1) and that the wedges in period t can be used to uniquely uncover the event st, in the sense that the mapping from the event st to the wedges (At, τ lt, τxt, gt) is one to one and onto.
• The authors compare these components to output, labor, and investment in the data.
• By distinguishing the events to which the wedges are indexed from the wedges them- selves, the authors can separate out the direct effect and the forecasting effect of fluctuations in wedges.

C. Distinguishing Our Procedure from Others

• Since this way of separating the direct and forecasting effects of wedges is critical to their procedure, here the authors describe an alternative procedure that might, at first, seem like the intuitive way to proceed but does not answer the question that interests us.
• That is, the authors choose the sequence {ε̂t+1} so that, in the event, the realized value of the effi ciency wedge coincides with that in the data and the labor wedge is constant at, say, its mean value τ̄ l.
• Hence, this procedure meets their first two conditions but not their third.
• Note that in some preliminary notes for Chari, Kehoe, and McGrattan (2007), while the authors were aware of the flaws in the second attempt, they followed a version of this second attempt as a quick approximation to get an initial set of answers.
• To see that the third, and more subtle, condition is met, note from (60) the probability distribution over st+1, and therefore At+1 is the same in both the prototype economy and the effi ciency wedge alone economy.

A. Details of the Application

• To apply their accounting procedure, the authors use functional forms and parameter values that are familiar from the business cycle literature.
• Based on this idea, the authors reallocate current expenditures of consumer durables from consumption to investment.
• This assumption leads us to subtract sales tax revenues from both consumption and measured output.
• For countries for which the authors only have quarterly data for a subsample, they regress consumer durables on investment and output and use the coeffi cients to construct estimates of the missing data.
• The authors then estimate separate sets of parameters for the stochastic process for wedges (60) for each of the OECD countries after removing country-specific trends in output, investment, and government consumption.

B. Findings

• Now the authors describe the results of applying their procedure to OECD countries for the Great Recession and the 1982 recession.
• In Figure 2, panels C, D, and E, the authors see that the labor and investment wedges play the most important role in accounting for the downturn in output and labor, while the investment wedge accounts for the bulk of 38 the downturn in investment.
• Overall, considering the period from 2008 until the end of 2011, these results imply that the Great Recession in the United States should be thought of as primarily a labor wedge recession, with an important secondary role for the investment wedge.
• In Tables 5B and 5C, the authors report similar statistics for labor and its components and for investment and its components.
• The φ statistic captures in one statistic how much the component due to a wedge moves, as well as how closely this component tracks the underlying variable.

4. Conclusion

• The authors have elaborated on the business cycle accounting method proposed by CKM, cleared up some misconceptions about the method, and applied it to compare the Great Recession across OECD countries as well as to the recessions of the 1980s in these countries.
• First, with the notable exception of the United States, Spain, Ireland, and Iceland, the Great Recession was driven primarily by the effi ciency wedge.
• Second, in the Great Recession, the labor wedge plays a dominant role only in the United States, and the investment wedge plays a dominant role in Spain, Ireland and Iceland.
• Third, 44 in the recessions of the 1980s, the labor wedge played a dominant role only in France, the United Kingdom, Belgium, and New Zealand.
• Finally, overall in the Great Recession the effi ciency wedge played a much more important role and the investment wedge played a less important role than they did in the recessions of the 1980s.

Figures

Figure 4A

Figure 7C

Table 2C

Figure 4A

Figure 6C

Table 5C

Table 1 φ-statisti s for Output, Labor, and Investment Components, Great Re ession

Table 4B

Table 4B

Figure 5A

Figure 5A

Figure 7C

Figure 6C

Table 5C

Table 2C

Figure 4A

Figure 7C

Table 3 φ-statisti s for Output, Labor, and Investment Components, 1982 Re ession

Table 2C

Table 4B

Figure 5A

Full text

NBER WORKING PAPER SERIES
ACCOUNTING FOR BUSINESS CYCLES
Pedro Brinca
V. V. Chari
Patrick J. Kehoe
Ellen McGrattan
Working Paper 22663
http://www.nber.org/papers/w22663
NATIONAL BUREAU OF ECONOMIC RESEARCH
1050 Massachusetts Avenue
Cambridge, MA 02138
September 2016
We thank Peter Klenow for useful comments and Francesca Loria for excellent research
assistance. Chari and Kehoe thank the National Science Foundation for financial support. Pedro
Brinca is grateful for financial support from the Portuguese Science and Technology Foundation,
grants number SFRH/BPD/99758/2014, UID/ECO/00124/2013, and UID/ECO/00145/2013. The
views expressed herein are those of the authors and not necessarily those of the Federal Reserve
Bank of Minneapolis, the Federal Reserve System, or the National Bureau of Economic Research.
NBER working papers are circulated for discussion and comment purposes. They have not been
peer-reviewed or been subject to the review by the NBER Board of Directors that accompanies
official NBER publications.
© 2016 by Pedro Brinca, V. V. Chari, Patrick J. Kehoe, and Ellen McGrattan. All rights reserved.
Short sections of text, not to exceed two paragraphs, may be quoted without explicit permission
provided that full credit, including © notice, is given to the source.

Accounting for Business Cycles
Pedro Brinca, V. V. Chari, Patrick J. Kehoe, and Ellen McGrattan
NBER Working Paper No. 22663
September 2016
JEL No. E00,E12,E13,E22,E24,E44
ABSTRACT
We elaborate on the business cycle accounting method proposed by Chari, Kehoe, and McGrattan
(2007), clear up some misconceptions about the method, and then apply it to compare the Great
Recession across OECD countries as well as to the recessions of the 1980s in these countries. We
have four main findings. First, with the notable exception of the United States, Spain, Ireland, and
Iceland, the Great Recession was driven primarily by the efficiency wedge. Second, in the Great
Recession, the labor wedge plays a dominant role only in the United States, and the investment
wedge plays a dominant role in Spain, Ireland, and Iceland. Third, in the recessions of the 1980s,
the labor wedge played a dominant role only in France, the United Kingdom, Belgium, and New
Zealand. Finally, overall in the Great Recession the efficiency wedge played a more important
role and the investment wedge played a less important role than they did in the recessions of the
1980s.
Pedro Brinca
Robert Schuman Centre for Advanced Studies
San Domenico di Fiesole
Italy
pedro.ms.brinca@gmail.com
V. V. Chari
Department of Economics
University of Minnesota
1035 Heller Hall
271 - 19th Avenue South
Minneapolis, MN 55455
and NBER
varadarajanvchari@gmail.com
Patrick J. Kehoe
Department of Economics
Stanford University
579 Serra Mall
Stanford, CA 94305
and NBER
patrickjameskehoe@gmail.com
Ellen McGrattan
Department of Economics
University of Minnesota
4-101 Hanson Hall
1925 4th St S
Minneapolis, MN 55455
and NBER
erm@umn.edu

In this paper we elaborate on the business cycle accounting method proposed by Chari,
Kehoe, and McGrattan (2007), henceforth CKM, clear up some misconceptions about the
method, and then apply it to compare the Great Recession across OECD countries as well
as to the recessions of the 1980s in these countries. The goal of the method is to help guide
researchers’choices about where to introduce frictions into their detailed quantitative models
in order to allow the models to generate business cycle ‡uctuations similar to those in the
data.
The method has two components: an equivalence result and an accounting procedure.
The equivalence result is that a large class of models, including models with various types of
frictions, is equivalent to a prototype model with various types of time-varying wedges that
distort the equilibrium decisions of agents operating in otherwise competitive markets. At
face value, these wedges look like time-varying productivity, labor income taxes, investment
taxes, and government consumption. We labeled these wedges e¢ ciency wedges, labor wedges,
investment wedges, and government consumption wedges.
The accounting procedure also has two components. It begins by measuring the wedges,
using data together with the equilibrium conditions of a prototype model. The measured
wedge values are then fed back into the prototype model, one at a time and in combinations,
in order to assess how much of the observed movements of output, labor, and investment can
be attributed to each wedge, separately and in combinations.
Here we use this method to study the Great Recession in OECD countries. We also
compare this recession with the recessions of the early 1980s. While the exact timing of
the recessions of the early 1980s di¤ers across countries in our OECD sample, most of the
countries had a recession between 1980 and 1984. Throughout we refer to the recessions of
the early 1980s as the 1982 recession. We have four main …ndings. First, with the notable
exception of the United States, Spain, Ireland, and Iceland, the Great Recession was driven
primarily by the e¢ ciency wedge. Second, in the Great Recession, the labor wedge plays a
dominant role only in the United States, and the investment wedge plays a dominant role in
Spain, Ireland, and Iceland. Third, in the recessions of the 1980s, the labor wedge played
a dominant role only in France, the United Kingdom, Belgium, and New Zealand. Finally,
overall in the Great Recession the e¢ ciency wedge played a more important role and the

investment wedge played a less important role than they did in the recessions of the 1980s.
We now turn to elaborating on the equivalence results in CKM that link the four
wedges to detailed models. We begin by showing that a detailed economy with ‡uctuations
in investment-speci…c technological change similar to that in Greenwood, Hercowitz, and
Krusell (1997) maps into a prototype economy with investment wedges. This result makes
clear that investment wedges are by no means synonymous with …nancial frictions, a point
stressed by CKM.
We then consider an economy that blends elements of Kiyotaki and Moore (1997)
with that of Gertler and Kiyotaki (2009). The economy has a representative household
and heterogeneous banks that face collateral constraints. We show that such an economy
is equivalent to a prototype economy with investment wedges. This result makes clear that
some ways of modeling …nancial frictions do indeed show up as investment wedges.
Finally, we turn to an economy studied by Buera and Moll (2015) consisting of workers
and entrepreneurs. The entrepreneurs have access to heterogeneous production technologies
that are subject to shocks to collateral constraints. We follow Buera and Moll (2015) in
showing that this detailed economy is equivalent to a prototype model with a labor wedge,
an investment wedge, and an e¢ ciency wedge. This equivalence makes the same point as does
the input-…nancing friction economy in CKM, namely, that other ways of modeling …nancial
frictions can show up as e¢ ciency wedges and labor wedges.
The point of the three examples just discussed is to help clarify how the pattern of
wedges in the data can help researchers narrow down the class of models they are considering.
If, for example, most of the ‡uctuations are driven by the e¢ ciency and labor wedges in the
data, then of the three models just considered, the third one is more promising than the …rst
two.
We then turn to models with search frictions. We use these models to make an
important point. Researchers should choose the baseline prototype economy that provides
the most insights for the research program of interest. In particular, when the detailed
economies of interest are su¢ ciently di¤erent from the one-sector growth model, it is often
more instructive to adjust the prototype model so that the version of it without wedges
corresponds to the planning problem for the class of models at hand. For example, when we
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map the model with e¢ cient search into the one-sector model, that model does have e¢ ciency
and labor wedges, but if we map it into a new prototype model with two capital-like variables,
physical capital and the stock of employed workers, the new prototype model has no wedges.
We then consider a search model with an ine¢ cient equilibrium. When we map this
model into the new prototype model with two capital-like variables, then the prototype model
has only labor wedges. But if we map it into the original prototype model, it has e¢ ciency
wedges and (complicated) labor wedges. These …ndings reinforce the point that it is often
more instructive to adjust the prototype model so that the version of it without wedges
corresponds to the planning problem for the class of models at hand.
Taken together, these equivalence results help clear up some common misconceptions.
The …rst misconception is that e¢ ciency wedges in a prototype model can only come from
technology sho cks in a detailed model. In our judgment, by far the least interesting inter-
pretation of e¢ ciency wedges is as narrowly interpreted shocks to the blueprints governing
individual …rm production functions. More interesting interpretations rest on frictions that
deliver such high-frequency movements in this wedge. For example, the input-…nancing fric-
tion model in CKM shows how …nancial frictions in a detailed model can manifest themselves
as e¢ ciency wedges. Indeed, we think that exploring detailed models in which the sudden
drops in e¢ ciency wedges experienced in recessions come from frictions such as input-…nancing
frictions is more promising than blaming these drops on abrupt negative shocks to blueprints
for technologies. The second misconception is that labor wedges in a prototype model arise
solely from frictions in labor markets in detailed economies. The Buera-Moll economy makes
clear that this view is incorrect. The third misconception is that investment wedges arise
solely due to …nancial frictions. Clearly, the detailed model with investment-speci…c techni-
cal change shows that this view is also incorrect.
We turn now to describing our procedure. This procedure is designed to answer
questions of the following kind: How much would output ‡uctuate if the only wedge that
‡uctuated is the e¢ ciency wedge and the probability distribution of the e¢ ciency wedge is
the same as in the prototype economy? If the wedges were independent at all leads and
lags, the procedure can be implemented in a straightforward manner by letting only, say, the
e¢ ciency wedge ‡uctuate and setting all other wedges to constants. In the data, the wedges
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