Accounting for the Great Depression

by V. V. Chari, Patrick J. Kehoe, Ellen R. McGrattan
Accounting for the Great Depression
V. V. Chari, Patrick J. Kehoe, Ellen R. McGrattan
The American Economic Review
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Accounting for the Great Depression


The Great Depression is not yet well under- stood. Economists have offered many theories for both the massive decline and the slow re- covery of output during 1929-1939, but no consensus has formed on the main forces behind this maior economic event. Here we describe and demonstrate a simple methodology for de- termining which types of theories are the most promising.

Several prominent theories blame the Great Depression on frictions in labor and capital mar- kets. The sticky-w,age theoy is that wage stick- iness together with a monetary contraction produces a downturn in output (see Michael Bordo et al., 2000). The cartelization theory is that an increase in cartelization and unioniza- tion leads to a slow recovery (see Harold Cole and Lee Ohanian, 2001). The investrnent

friction theory is that monetary contractions in- crease frictions in capital markets that produce investment-driven downturns in output (see Ben Bernanke and Mark Gertler, 1989; Charles Carlstrom and Timothy Fuerst, 1997). We think the critical feature of both the sticky-wage and cartelization theories is that their frictions lead to a wedge between the marginal rate of substi- tution between leisure and consumption and the marginal product of labor. The critical feature of the investment-friction theory is that capital- market frictions introduce a wedge between the intertemporal marginal rate of substitution in consumption and the marginal product of capital.

We show that the aggregate properties of a class of models with sticky wages and with cartels or unions are the same as those of a growth model with suitably constructed taxes

* Chari: University of Minnesota and Federal Reserve Bank of Minneapolis; Kehoe and McGrattan: Federal Reserve Bank of Minnea~olis. NBER. and University of Minnesota. We thank the NSF for tinancial support. The views expressed herein are those of the authors and not necessarily those of the Federal Resene Bank of Minneap- olis or the Federal Resene System. For a more detailed version of this paper, see (http:l/ researchlu~plwp619.html).


on labor. We also show that a class of models with investment frictions is equivalent in terms of aggregate properties to a growth model with suitably constructed taxes on investment. We then consider an input-friction theory in which frictions in financing inputs lead to a wedge between aggregate inputs and outputs. Such models have the same aggregate properties as a growth model with suitably constructed produc- tivity (see Raphael Bergoeing et al. [2002] for other frictions that show up as time-varying productivity). These observations lead us to conclude that a large class of business-cycle models are equivalent to a prototype growth model with time-varying wedges that, at least at face value, look like time-varying labor taxes, investment taxes, and productivity. We refer to these wedges as labor wedges, investment wedges, and ejjiciency wedges.

These equivalence results lead us to propose a method for accounting for economic fluctua- tions in general: business-cycle accounting. We first use a parameterized prototype growth model to measure in the data the wedges we have identified.' We then feed the lalues of these wedges back into the growth model to conduct our accounting exercise, namely, to assess what fraction of the output movements can be attributed to each wedge separately and in combination. (In a deterministic model. by construction, all three wedges account for all of the observed movements in output.)

The goal of this business-cycle accounting is to guide researchers to focus on developing detailed models with the kinds of frictions that can deliver the quantitatively relevant types of observed wedges in the prototype economy. For example, both the sticky-wage and cartelization theories are promising explanations of the ob-

served labor wedges, while the simplest models of capital-market frictions are not. Theorists

' Casey Mulligan (2000) measures the labor wedge in the Great Depression. as we do. and provides a variety of interpretations of this wedge, including the onec that ue do.


attempting to develop models of particular channels through which shocks cause large fluctuations in output will benefit from asking whether those channels are consistent with the fluctuations in wedges that we document.

Our accounting yields clear results for the Great Depression: Almost all of the decline in output from 1929 to 1933 is due to a combina- tion of efficiency wedges and labor wedges, while much of the slow recovery from 1933 to 1939 is due to labor wedges alone. Investment wedges play, at best, a minor role in the decline and recovery.

While numerous theories lead to labor wedges, relatively few lead to efficiency wedges. We find it uninteresting to view the efficiency wedge as emanating from a loss of knowledge or a decline in the quality of blueprints. Rather, we think the observed movements in measured productivity are the results of poor government policies interacting with shocks. These policies turn what otherwise would be modest down- turns into prolonged depressions. Developing models with these properties is the key to un- locking the mysteries of the Great Depression.

I. Equivalence Results

Here we show how various models with un- derlying distortions map into a prototype econ- omy with one or more wedges. We choose simple models to illustrate this mapping. Since many models map into the same configuration of wedges, identifying one particular configura- tion does not uniquely identify a model; rather, it identifies a whole class of models consistent with that configuration. In thls sense, our method does not uniquely determine the most promising model; rather it guides researchers to focus on the key margins that need to be distorted.

The prototype economy is a growth model with three stochastic variables (our "wedges"): A,, 1 -T~,, and 1 + T,,. Using standard notation, we say that consumers maximize E, 2, PtU(c,, e,) subject to

Firms maximizeA,F(k,, e,) -r,k, -w,t?,. The equilibrium is summarized by the resource con- straint, c, + k,, ,= y, + (1 -6)k,, together with

We call A, the eficiency wedge, 1 -TE, the labor wedge, and 1/(1 + T,,) the investment wedge.

A. Eficiency Wedges

Our input-friction theory has a simple deter- ministic economy with financing frictions that lead to distortions in the allocation of inputs across two types of firms. Before firms can produce, both types must borrow to pay for an input, say, labor. Firms of the first type, located in sector 1. are financiallv constrained in that they must p'ay a higher price for borrowing than do firms of the second type, located in sector 2. We think of these frictions as capturing the idea that some firms, which can be thought of as small, find borrowing harder than others do. One source of the higher price paid by the financially constrained firms is that moral-hazard problems are more severe for small firms. (While this theory is reminiscent of that of Bernanke and Gertler [1989], the margins that get distorted in our model and in theirs are quite different.)

In each period t, firms borrow at the begin- ning of the period to finance inputs and repay their loans at the end of the period. Final output y, is produced from the outputs of sectors 1 and 2, y,, and y2,, according to y, = y:,y~tY. The representative firm producing final output max-

imizes y~,Y~f- -pl,ylr -p2,y2,, where pi, is the price of the output of sector i. Firms in sector i hire labor ti,to produce output accord- ing to y,, = [: and maximize pi,[: -Ri,w,ti,, where w,is the wage rate and Ri, is the gross interest rate paid on loans by firms in sector i. We imagine that firms in sector 1 are more financially constrained than those in sector 2, so that R,, > R,,. Let Rit = R,(1 + rir),where R, is the rate savers earn and rir measures the wedge, induced by financing constraints, be- tween the rate paid to savers and the rate paid by borrowers in sector i. Since savers do not discount utility within the period, R, = 1. Consumers choose consumption c, and labor e, to maximize E7="=,P'U(c,, e,) subject to c, = w,e, + H,, where II, is the period t profits earned by firms. The resource constraints are

e, = t,,+ e,,andc, = y,.

We specialize our prototype economy to have a fixed capital stock normalized to 1 and con- sider any period. In Chari et al. (2002a),we prove the following.

PROPOSITION 1: The equilibrium allocations for an economy with input jinancing frictions coincide with those of the prototype economy with eficiency wedge A, and labor wedge r[,,


Suppose that the fluctuations in the underly- ing distortions rl, and r,, are such that the constructed 1 -ref is constant. That is, on average, financing frictions are unchanged, but relative frictions fluctuate. An outside observer using a one-sector growth model to fit the data generated by the economy with input financing frictions would identify the fluctuations in rel- ative distortions with fluctuations in technology and would see no fluctuations in the labor tax rate. In particular, periods in which the rela- tive distortions increase would be misinterpreted as periods of technological regress. We thus want a more neutral label than "technolo- gy" for A,. We call it the efficiency wedge since it is a simple measure of aggregate production efficiency.

More generally, fluctuations in the input fi- nancing wedges r,, and r,,, which lead to fluc- tuations in re,, show up in the prototype economy as fluctuations in both the efficiency wedge A, and the labor wedge 1 -re,.

B. Labor Wedges

Now consider two economies that give rise to labor wedges. In one, wages are sticky, so that fluctuations in monetary policy induce fluctua- tions in output. In the other, unions have monopoly power, so that fluctuations in the government's pro-competitive policies toward unions induce fluctuations in output.

Consider a sticky-wage economy with utility function U and production function F, and let -U:,/UT,F*,, be evaluated at the equilibrium of this economy. In Chari et al. (2002a),we prove the following.

PROPOSITION 2: The aggregate allocations in a prototype economy with taxes on labor income given by 1 -r,, = -U$,/U:,F$, coincide with those of the sticky-wage economy.

We call the constructed labor tax rate 1 -r,, the labor wedge. This wedge reflects the gap between the marginal product of labor and the marginal rate of substitution between leisure and consumption in the intratemporal first-order condition for labor. An outside observer using the prototype economy to fit the data of the sticky-wage economy would interpret output fluctuations that arise from fluctuations in mon- etary policy as arising from fluctuations in labor wedges.

An exactly analogous proposition holds for an economy with monopoly unions. An outside observer of a unionized economy would inter- pret output fluctuations arising from fluctuations in the government's pro-competitive policies as arising from fluctuations in labor wedges.

C. Investment Wedges

For investment frictions, the link between the original economy and a prototype economy is immediate. Many of the frictions discussed in the literature end up affecting the economy by raising the firms' cost of investment, from 1 to 1 + r.,,. These show up in the prototype econ- omy as an investment wedge, a gap between the intertemporal marginal rate of substitution in consumption and the marginal product of capi- tal in equation (3).

Bernanke and Gertler (1989)and others have pointed to agency costs as the source of invest-




ment distortions. Carlstrom and Fuerst (1997) embed the frictions studied by Bernanke and Gertler into a standard growth model. In Chari et al. (2002a), we find, as Carlstrom and Fuerst do, that the Carlstrom-Fuerst model is equiva- lent to the prototype growth model with in- vestment wedges and adjustment costs in investment. Most interesting, we think, is that the equivalent prototype model has neither ef- ficiency wedges nor labor wedges.

11. Business-Cycle Accounting

Now we try to measure our three wedges and determine how much of actual U.S. out- put fluctuations they can account for. (For details underlying this section, see Chari et al. [2002b].)

Given data on y,, kt, e,, and c,, we use equations (1)-(3) to construct series for effi- ciency and labor wedges. In Figure 1 we display real detrended output, the detrended efficiency wedge, and the labor wedge. All the series are normalized to equal 100 in 1929. As is clear in Figure 1, output is 35 percent below trend in 1933 and is still 20 percent below trend by 1939. In 1933, the efficiency wedge is 17 per- cent below trend, but by 1939 it has essentially recovered to trend. In 1933, the labor wedge is 28 percent lower than its 1929 level, and in 1939 it is still that low. Thus, the underlying distortions that manifested themselves as effi- ciency and labor wedges became substantially worse from 1929 to 1933. By 1939, the effi- ciency wedge had disappeared, but the labor wedge remained as large as it had been in 1933.

If we assume no uncertainty, we can use equation (3) to measure the investment wedge as well. With that assumption, however, we find that 1/(1 + T,,) is higher than its 1929 level throughout the 1930's: according to this measurement, the underlying distortions that manifested themselves as investment wedges actually diminished in the Great Depression. This conclusion is not plausible; hence, we will propose an alternative method for assess- ing investment wedges.

A. Tlze Prototype Economy with Eflciency and Labor Wedges

First, we ask: What fraction of output fluctu- ations can be accounted for by the efficiency and labor wedges? We answer this question by simulating our prototype economy with our measured wedges and comparing the result to actual U.S. data. We find that together these wedges can account for essentially all of the fluctuations in U.S. output between 1929 and 1939.

We start by independently inserting the se- ries for each of the two wedges into the pro- totype model and setting the other wedges to their 1929 levels. We assume that consumers believe that in each year from 1930 through 1932 it is equally likely that, in the following year, the wedges will stay at their current levels, revert to the 1929 levels, or take on the values in the data. From 1933 on, we assume perfect foresight.

With the efficiency wedge alone, the proto- type economy generates much of the observed downturn in output, but much too rapid a recov- ery. As can be seen in Figure 2, for example, by 1933 output falls about 26 percent in the model and about 35 percent in the data. By 1939, the efficiency-wedge model generates an output de- cline of only 6 percent rather than the observed 20 percent. As can also be seen in Figure 2, the reason for this rapid recovery is that the efficiency-wedge model completely misses the continued sluggishness in labor from 1933 on- ward. For investment, this model shows a sim- ilar fall as in the data from 1929 to 1933. but a


---Efficiency wedge -. . -..-Labor wedge


faster recovery. Here and throughout, labor is per capita man-hours, while investment is de- trended and normalized by output in 1929.

In our model with only labor wedges, out- put falls only about half as much by 1933 as output actually fell: 17 percent vs. 35 percent. By 1939, output in both this model and the data have fallen about 20 percent. The labor- wedge model misses the sharp decline in in- vestment from 1929 to 1933, but it does generate the sluggishness in labor input after 1933.

These observations suggest investigating a prototype economy with^ both efficiency and labor wedges. We thus simulate an economy with our constructed series for these two wedges with the investment wedge set to its 1929 level. Figure 3 shows that the result- ing model captures both the downturn in output and the slow recovery remarkably well. It also generates the sluggishness in labor after 1933 and does reasonably well on investment.



B. The Prototype Economy with Investment Wedges

What fraction of outuut fluctuations can be accounted for by the investment wedge? Our difficulties in inferring a reasonable level of that wedge from the U.S. data make us wary of trying to answer this question by simply putting in the wedge 1/(1 + T,,) inferred from a deterministic version of equa- tion (3). Instead, we consider a prototype economy with the efficiency and labor wedges set to their 1929 levels and let the invest- ment wedge be whatever it must be in order for the model to generate the actual invest- ment series. In a sense, by attributing all movements in investment to this wedge, we are overstating its contribution to output fluctuations.

In Figure 4, we see that the prototype econ- omy with an investment wedge generates only a modest fall in output from 1929 to 1933 and does not generate the recovery after 1933.


While this economy does generate a recovery in labor, the effect on output is offset because the capital stock is lower due to the cumula- tive effect of the decade-long investment slump.

111. Conclusion

Our business-cycle accounting suggests that research on the Great Depression should focus on building detailed models with underlying distortions that produce efficiency and labor wedges. Building models of investment wedges is not likely to yield a high payoff.


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Bordo, Michael D.; Erceg, Christopher J. and Evans, Charles L. "Money, Sticky Wages, and the Great Depression." American Eco- nomic Review, December 2000, 90(5), pp. 1447-63.

Carlstrom, Charles T. and Fuerst, Timothy S. "Agency Costs, Net Worth, and Business Fluctuations: A Computable General Equi- librium Analysis." American Economic Re- view, December 1997, 87(5), pp. 893-910.

Chari, V. V.; Kehoe, Patrick J. and McGrattan, Ellen R. "Business Cycle Accounting." Un- published manuscript, Research Department, Federal Reserve Bank of Minneapolis, 2002a.

. "Accounting for the Great Depression." Federal Reserve Bank of Minneapolis Research Department Working Paper No. 619, 2002b.

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