Discussion over “Chari, Kehoe & McGrattan 2007 Business Cycle Accounting” WU Yaping Hector PIFARRE Andrea MATRANGA

This essay discusses Chari, Kehoe & McGrattan‘s paper “Business Cycle Accounting”2007. Their methodology and main contribution are highlighted while some potential problematical issues are discussed next. The plan of the essay is as follows: 1. A brief synthesis of the paper and its main contribution 2. Potential problems i)

Sensitivity to the identifying assumptions for wedges

ii)

Sensitivity to the different sets of data and estimation methodsLack of robustness checks on the stochastic process.

iii)

Lack of robustness checks on the Stochastic Process.

iv)

Data selection strategy (the estimation uses periods that may be heterogenous relative to the episodes studies).

v)

Inductive/empirical issues: dangerous to perform empirical investigation in the absence of an underlying theory.

3. Conclusion

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1. A brief synthesis of the paper and its main contribution In this paper, Chari, Kehoe & McGrattan proposed a “dual” method with respect to the standard method in Real Business Cycle literature and applied it to the analysis of Great Depression. In the dual method, economy is described as a prototype growth model with time-varying wedges, named efficiency, labor, investment and government consumption wedges, which distort the Euler equations from the maximization. The idea is the following: they don’t identify the primitive shocks in the economy, neither the propagation mechanism which leads to the face value of the wedges, they intended to show which wedges are most crucial in actual business fluctuations, then, models with distortions and shocks showing up as these crucial wedges are the promising ones for the future research. They have done it in two steps: first, they proved that a large class of quantitative models can be mapped into the prototype growth model with wedges. A model with input financing frictions can be mapped into a model with efficiency wedges; a model with labor-unions is equivalent to a model with a labor tax; a model with financial frictions is equivalent to a model with a tax on investment. Then, the equivalence results propose an accounting procedure in which, they use the decision rules of a parameterized model, law of motion of capital and the data to measure the realized wedge series, with an estimated stochastic process used in measuring investment wedge. By construction, the four wedges account for all of the movement in output, labor, investment and government consumption. Then, the wedges are fed back into the model each at a time or in combinations to assess which proportion of output movement can be attributed to each wedge or a certain combination. The result show that, the efficiency and labor wedges play a central role for fluctuations of all variables considered, while the government consumption wedge plays no role. The most important result is that investment wedge accounts almost none during the depression, it has even an expansionary effect on output.

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The most important contribution of this paper is having identified the broad class of models which present the most fruitful avenues for future research : models with distortions manifesting themselves as efficiency wedge and labor wedge. Models with distortions manifesting as investment wedges are not promising ones. It also has contribution to the focus of policy analysis, which should be on the most relevant wedges, for instance, the BCA approach has been used by international Monetary Fund to investigate the sources of economic fluctuations in Chile during 1998-2007, as well as studies on many Latin American countries like Argentina, Brazil and Mexico. It has even been extended by Roman · Sustek to develop the Monetary Business Cycle Accounting to investigates the quantitative importance of various types of real and nominal frictions for inflation and nominal interest rate dynamics.

2. Potential Problems i) Sensitivity to the identifying assumptions for wedges The results of the paper are based on the crucial identifying assumption for wedges, among which, the most controversial issue focuses on the investment wedge, as well as its insignificant role in depression. In the paper, financial frictions is assumed to manifest themselves as investment wedge. This is proved in the Appendix A and is stated through Proposition 6. Examining the proof, we found that the associated prototype economy with investment wedge is the same as their benchmark prototype economy except that in the new prototype economy they use a tax on capital income rather that a tax on investment. This approximation was also used in the previous section to prove the result of input financing frictions manifesting themselves as efficiency wedge. The capital wedge was proposed before in 2002 by Mulligan instead of investment wedge, consisting of an imaginary capital income tax on individual. It is established in the literature that, with only a slight difference, the capital wedge is equivalent to what 3

is induced by a tax on investment. If it is true, including a capital wedge instead of an investment wedge in the parameterized model to estimate then feed them back when assessing the role of individual wedge should yield the same result as the model with investment wedge. However, in the paper by Keiichiro Kobayashi and Masaru Inaba “Business cycle accounting for the Japanese economy”, they found contradictory result when including capital wedge instead of investment wedge. They have done the same accounting exercise for the Great Depression during the 1929—1939 period in the United States using respectively investment wedge and capital wedge.

Their four

figures are presented in the following two pages. The first two figures present the decomposition with investment wedge: the individual effect and combined effect of efficiency, labor and government consumption; the next two figures show the corresponding results with capital wedge. The result for the investment wedge is consistent with the results by Chari, Kehoe, and McGrattan, the investment wedge had a positive effect on the economy throughout the target period, which implies that investment friction is not a promising explanation for the Great Depression. However, the capital wedge had a severe depressing effect on output, and it continued to have a negative effect in 1935—39. In the last figure, the discrepancy between real data and the combined effect of the other three wedges indeed indicates the role of capital wedge in depression. This result contradict the BCA result of Chari, Kehoe, and McGrattan, because the capital wedge is equivalent to the investment wedge in the literature, and this has been used by Chari, Kehoe, and McGrattan to prove their equivalence results. The previous discussion putting the contradictory results against each other has pointed out somehow the sensitivity of BCA to the identifying assumptions of wedges. This may come from the measurement issue of wedges, or, perhaps, we have not completely found the right wedges representing financial frictions. The remaining problem as mentioned in Keiichiro Kobayashi and Masaru Inaba’ paper is how to reliably measure the wedge that represents the financial frictions.

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ii) Sensitivity to the different sets of data and estimation methods In this section, we will put Chari, Kehoe, and McGrattan’s result, Keiichiro Kobayashi and Masaru Inaba’ result and another economist Suparna Chakraborty’s results together against each other, to show the sensitivity of BCA to the different sets of data and estimation methods. We all knows that, Japanese economy performs poorly during the 1990s, In Chakraborty’s paper “Accounting for the ‘Lost Decade’ in Japan” , she applied the Business Cycle Accounting procedure of Chari, McGrattan and Kehoe to the Japanese depression. Her result is the following:

Her decomposition for the detrended output show that the investment wedge alone play a significant role in explaining per capita output increase and drop. Especially, it explains 19.82% of the drop in output per capita during 1991 to 1995, and 39.57% of the fall during 1997 to 2001. The efficiency wedge is still important in explaining the poor

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performance of the Japanese economy during the 1990s but labor wedge is not very important. She has also done the exercise for the other macro variables, like investment per working population:

Her result shows that Investment wedge alone suggests a 61.67% increase in investment per capita during 1980 to 1991; 20.5% drop in investment during 1991 to 1995; 7.65% increase in investment per capita during 1995 to 1997; and a 12.1% drop during 1997 to 2001. What is strange is that at some period, what is suggested by the efficiency wedge alone and by the labor wedge alone is quite the opposite against what is suggested by the data. Her result contradicts the general result of Chari, Kehoe, and McGrattan, which showed that investment wedge plays no role in economy depression. This contradictory results show that applying the BCA to different countries with different data sets may yield different results in assessing the relative role of four wedges. 8

Interestingly, let’s see the result of Keiichiro Kobayashi and Masaru Inaba, who have applied the BCA also to the Japanese economy, his result contradicts that of Chakraborty’s. They did the BCA exercise for Japan after Chakraborty, and their result is consistent at this point with Chari, Kehoe, and McGrattan’ general result : the investment wedge did not have a crucial effect. They explained the difference between Chakraborty’s result by a combination of differences in data constructions, data sources, and simulation methods: For example, government investment and net exports are categorized differently ; and Chakraborty simulates a log-linearlized model, while they simulate a full nonlinear model without linearizing it.

iii) Lack of robustness checks on the stochastic process. As the authors themselves freely acknowledge, the calculation of the investment wedge is the part of the model which is most dependant on the specification of the assumed underlying stochastic process. Since the agents are using the specified process to form their expectation of what will happen in the future, it is clear that the results are only as good as the underlying assumptions on the dynamic properties of the model. Specifically, the authors assume that all variable are linked to each other through a simple AR(1) process, for which they estimate the coefficient matrix. Their reported findings are based on this, and none more so than the magnitude of the effect due to the investment wedge. Realizing their potential exposed flank, the authors conduct a sensitivity analysis by artificially assuming that the coefficient on investment is large enough to explain the whole of the observed variation, obtaining essentially equivalent results. They argue that nonparameteric estimation methods would have been to computationally intensive, but they do not address the possible middle ground of more complicated parameteric methods. There is no discussion of how the results might be

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different if recalculated for different specifications of the stochastic process (ARMA(1,1), AR(2), etc ). Since they use quarterly data in their estimation, and investment is often budgeted at least on a yearly basis, there seems to be a mismatch between the likely inertias involved in the nature of the process, and the three-month memory they allow their agents to have. Whether relaxing this assumption would lead to different results would require further analysis.

iv) Data homogeneity issues The authors use data from 1901 to 1940 to obtain their results for the Great Depression, and from 1959 to 2004 for their 1979-82 event, which provide adequate sample sizes from a statistical standpoint. However, the implicit assumption is that throughout this period the US economy was a fundamentally static entity, where movement in variables did occur, but according to fixed rules. Alternatively, it could be that the the economy actually did change in fundamental ways, but the progression of these shifts was such that the effects cancelled out, and the estimated coefficients from the sample would be close enough to how the economy was actually working around the time of the episodes analyzed.

If neither of these two scenarios is true, then there is no reason to consider the analysis performed in the paper reliable. It might have been interesting to take narrower samples around the dates of interest, to see if the estimates are consistent.

v) Methodological issues Most science progresses from a clearly defined theory to the derivation of empirical assumptions, which are then tested experimentally or empirically. In the case of this paper, that order appears to be somewhat reversed. It is true that a broad class of pre-existing models is discussed and synthesized, but the exercise cannot be reasonably constructed as a test of either or all of them. 10

Rather, the authors in effect compute what result a fairly non-specific empirical test tests is likely to give about a given model from the target class. And thus hopefully guide researchers towards promising model classes. This raises some methodological issues, which while far from insurmountable are not adequately discussed.

We will illustrate by example.

At a crime scene in New York City, a blood drop from the killer is found to be of blood group AB-, which only 0.6% of the population has. Two different scenarios: a) The police already have suspicions on the boyfriend of the victim, with a history of violent behavior, no alibi, and a large insurance policy in his favor apparently signed by the victim in shaky handwriting shortly before the time of death. It turns out he has blood group AB-.

b) The police go to a blood bank and ask for the record of the first person in alphabetical order to have blood group AB-. Clearly, in the first case the police should arrest the boyfriend for further questioning, while in the second case the likelihood of the “suspect” being the killer should be somewhere around one in 120,000 (there’s 20 million people in NYC).

This is an admittedly extreme example, but shows the problem that may arise when empirical testing is done without an explicit model to test.

It is true that this paper only seeks to point researchers in the right direction, but it should be remarked upon that clearly if a model is then selected for further analysis based on this, its verification strategy cannot rely on the same methodologies used here (since that would bring no new information and would in fact be rather tautological.

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3. Conclusion The contribution of Chari, Kehoe & McGrattan‘s paper of “BCA” is that they have shown the precise mapping between the wedges and general equilibrium models with frictions and identified the promising class of models for future research, which have distortions showing up as efficient wedge and labor wedge. However, the BCA has also been showed to be very sensitive to identifying assumptions for wedges, especially the wedges representing the financial frictions. It is also sensitive to changes in data sets, and estimation methods. Further, both the dataset employed for the estimation, and the type of stochastic process employed raise cause for concern. A more fundamental problem is that the authors suggest employing the methodology for selecting promising models to analyze, without adequately covering the epistemological issues raised by their advice. How to improve and further develop the Business Cycle Accounting Approach is an important task for future research.

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References Chari, Kehoe & McGrattan, “Business Cycle Accounting”2006 Chakraborty,S. (2004).“Accounting for the ‘lost decade’ in Japan.” Mimeo. University Of Minnesota Keiichiro Kobayashi & Masaru Inaba.” Business cycle accounting for the Japanese economy” Sustek,Roman.”Monetary Business Cycle Accounting” 25.September2009 Ina Simonovska & Ludvig Söderling “Business Cycle Accounting For Chile” 2008 International Monetary Fund Lawrence J. Christiano & Joshua M. Davis. “Two Flaws in Business Cycle Accounting” Suparna.Chakraborty “Business Cycle Accounting of the Indian Economy” Dept.of Economics and Finance, Baruch College, CUNY. September10,2006

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