Federal Reserve Bank of Minneapolis Research Department Staff Report 328 Business Cycle Accounting * A. a Detailed Economy with Input-financing Frictions 2. Applying the Accounting Procedure

We propose and demonstrate a simple method for guiding researchers in developing quantitative models of economic fluctuations. We show that a large class of models are equivalent to a prototype growth model with time-varying wedges that resemble time-varying productivity, labor taxes, and capital income taxes. We use data to measure these wedges, called efficiency, labor, and investment wedges, and then feed their measured values back into the model. We assess the fraction of fluctuations in output, employment, and investment accounted for by these wedges during the Great Depression and the 1982 recession. For the Depression, the efficiency and labor wedges together account for essentially all of the fluctuations; investment wedges play no role. For the recession, the efficiency wedge plays the most important role; the other two, minor roles. These results are not sensitive to alternative measures of capital utilization or alternative labor supply elasticities. ∗The authors thank the National Science Foundation for support. The views expressed herein are those of the authors and not necessarily those of the Federal Reserve Bank of Minneapolis or the Federal Reserve System. We propose and demonstrate the use of a simple method for guiding researchers in developing quantitative models of economic fluctuations. Our 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 frictions, are equivalent to a prototype growth model with time-varying wedges which, at least at face value, look like time-varying productivity, labor taxes, and capital income taxes. For example, we show that an economy in which the technology is constant but input-financing frictions vary over time is equivalent to a growth model with time-varying productivity. We show that models with sticky wages andmonetary shocks or unions and antitrust policy shocks are equivalent to a growth model with time-varying labor taxes, and a model with investmentfinancing frictions and wealth redistribution shocks is equivalent to a growth model with time-varying capital income taxes. These examples lead us to label the time-varying wedges efficiency wedges, labor wedges, and investment wedges. Our accounting procedure begins by using data together with the equilibrium conditions of a prototype growth model to measure the wedges. We then feed the values of these wedges back into the growth model, one at a time and in combinations, to assess what fraction of the output movements can be attributed to each wedge separately and in combinations. By construction, all three wedges account for all of the observed movements in output. In this sense, our method is an accounting procedure. We demonstrate the usefulness of our method by applying it to two actual U.S. business cycle episodes: the most extreme in U.S. history–the Great Depression–and a downturn less severe and more like those seen often since World War II—the 1982 recession. During the Great Depression, output, labor, and investment declined dramatically in the early 1930s. The ensuing recovery was slow, so that even by 1939, output was well below trend. The slowness of the recovery was especially marked for labor, which in 1939 was still at its 1933 level. Our accounting shows that the efficiency wedge alone accounts for roughly two-thirds of the decline in output and about one-third of the decline in labor from 1929 to 1933, but this wedge cannot account for the sluggish recovery in either output or labor. The labor wedge alone accounts for much of the fall in labor but can only account for about one-half of the fall in output from 1929 to 1933. In terms of the recovery, the labor wedge accounts for essentially all the sluggishness in labor and the failure of output to return to trend. In combination, the efficiency and labor wedges account for all of the fall in output, labor, and investment from 1929 to 1933 and the behavior of these variables in the recovery. The investment wedge actually drives output the wrong way, that is, it leads to an increase in output during much of the 1930s. Thus, this wedge cannot account for either the downturn or the slow recovery. For the more typical U.S. recession in 1982, we find that the efficiency wedge alone accounts for most of the decline and recovery in output, but misses some of the downturn in labor. The labor wedge alone produces hardly any fluctuations in output, but captures some of the downturn in labor. Together these two wedges capture the downturn in output well, though they produce a sharper recovery than in the data. The investment wedge is unchanged early in this episode and then steadily worsens, even through the recovery. Relative to the Great Depression, we find that the labor wedge plays a much smaller role in the 1982 recession, and the worsening of the investment wedge helps account for the modest nature of the recovery. The investment wedge plays only a bit larger role here than in the Depression. We ask whether our results are sensitive to our assumptions about capital utilization rates and labor supply elasticities. In our benchmark model, we assume that the capital utilization rate is fixed, and we use labor supply elasticities similar to those in the business cycle literature. We then investigate what happens when we allow for either variable capital utilization or less elastic labor supply. We find that the size of our measured wedges changes substantially, but not the equilibrium responses to the wedges. The lesson we draw from this finding is that focusing on the size of the measured wedges rather than the equilibrium responses can mislead researchers about the quantitative importance of competing mechanisms of business cycles.