Accounting for Business Cycles
Summary (4 min read)
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.
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Cites result from "Accounting for Business Cycles"
...We report our benchmark calibration in table 3 and notice that our parameter values are broadly consistent with those reported in empirical studies of the Euro Area (among others, see Smets and Wouters 2003, Gerali et al. 2010, and Brinca et al. 2016)....
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Cites background or methods or result from "Accounting for Business Cycles"
...Great Recession can be found in Brinca et al. (2016). The basic idea of this approach is to decompose and attribute movements in the data to changes in wedges that appear in the equilibrium conditions of a representative economy....
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...This contrasts with the finding for the United States, where the data suggest a sizable role for labor market frictions (Brinca et al., 2016)....
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...Equivalent figures for the U.S. economy may be found in Brinca et al. (2016)....
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...economy may be found in Brinca et al. (2016). Figure 3 shows U.K. output alongside the efficiency wedge, At; labor wedge, 1– τnt ; and investment wedge, 1/[1+ τit]. The wedges alone do not tell us their impact on macroeconomic variables but do provide insight into the magnitudes of their distortion. The efficiency wedge and labor wedge show the greatest distortion during this period. In contrast, the investment wedge declines, recovers a little, and then stays at a fairly constant level, at around 99 percent of its steady-state value, for the full period. This pattern does not coincide with the Bernanke, Gerler, and Gilchrist (1999) style financial accelerator models, which affect the economy via an investment wedge....
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...economy may be found in Brinca et al. (2016). Figure 3 shows U....
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1 citations
References
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"Accounting for Business Cycles" refers background in this paper
...We then consider an economy that blends elements of Kiyotaki and Moore (1997) with that of Gertler and Kiyotaki (2009)....
[...]
...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....
[...]