Kobayashi-sensei's Economic Research Picks

Part Five: 'Indivisible Labor' and the Great Depression

Faculty Fellow

Econo-kun is in his second year of the master's program at a private university, studying hard to become an economist.

Kobayashi Keiichiro's photoKOBAYASHI Keiichiro: This time, in addition to works of other economists, I would like to introduce my own research, or more precisely, the results of my trial-and-error attempts.

When we examine Japan's decade-long recession of the 1990s and the United States' Great Depression of the 1930s, we encounter a puzzling phenomenon described as "labor wedge deterioration" (Kobayashi and Inaba, 2005, "Business Cycle Accounting for the Japanese Economy"). Labor wedge (1-τl) refers to the ratio between the consumption-leisure marginal rate of substitution and the marginal product of labor. This ratio is 1 when no distortion is present in the economic system. When there is a distortion, which causes labor input inefficiency, the ratio falls below 1; the greater the distortion and labor inefficiency, the smaller the ratio. In both 1990s Japan and 1930s U.S. the labor wedge was found to deteriorate (1-τl became smaller) over time, indicating that labor input became inefficient.

Econo-kun's photoEcono-kun: How can this phenomenon be explained by economic theory?

Kobayashi Keiichiro's photoKOBAYASHI Keiichiro: Chari et al., who originated business cycle accounting (BCA), theoretically showed that the labor wedge deteriorates when a contractionary monetary shock occurs in an economy with sticky wages (wages set in a sticky manner under monopolistic competition by powerful unions). In the case of Japan's recession, however, this shock is believed to have occurred as early as the first half of the 1990s whereas the labor wedge deteriorated sharply in the latter part of the decade. This led me to believe that sticky wages and monetary (deflationary) shocks do not adequately explain what happened. I inferred and argued in my paper that financial factors - collateral constraints and declines in the value of collateralized assets - might play a role.

This time around, let's think about whether labor wedge deterioration can be explained by the labor market structure. More precisely, this is in order to examine whether this deterioration can be induced solely by changes in total factor productivity (TFP) when some sort of structure exists in the labor market. If this can be done, both the Great Depression and Japan's deflationary recession can be explained solely by productivity shocks, even in the absence of financial problems and monetary shocks.

First, let me identify the factors causing labor wedge deterioration, using data from Japan. The variables constituting the labor wedge are consumption, hours worked (per worker), employment rate (percentage of employed among the total working-age population), capital stock, and TFP. By allowing only one of these variables to change to represent the actual data while setting all the others to their initial values, I calculated hypothetical values for the labor wedge, thereby examining whether the changes in that variable can explain labor wedge deterioration.

Econo-kun's photoEcono-kun: What results did you obtain?

Kobayashi Keiichiro's photoKOBAYASHI Keiichiro: What I found is that a decrease in hours worked causes labor wedge deterioration while the other variables show little or no causal effect. Thus, the key question is whether an (excessive) decrease in hours worked (resulting from declining productivity) can be explained by the following model.

In the world of real business cycle (RBC) models, the "indivisible labor model" developed by Hansen* is widely used to model friction in the labor market.

*Hansen, G. D. (1985), "Indivisible Labor and the Business Cycle," Journal of Monetary Economics 16:309-27.

In Hansen's model, the number of working hours per worker is assumed to be fixed at a certain level by the employer. Workers determine the "employment rate," or the probability of being employed. Under this assumption, individuals optimize the trade-off between consumption and employment probability (in contrast to the trade-off between consumption and hours worked under the conventional RBC model). Individuals' expected utility has been shown to be given by a linear function of the employment rate under Hansen's model; more closely matching observed data than under the conventional RBC model. The indivisible labor assumption under Hansen's model has come to be used as a standard assumption under RBC models.

In order to explain labor wedge deterioration as observed in the Great Depression, I attempted to expand Hansen's model by positing the following assumption: the employment rate (employment probability) for individuals is determined by the employer while the number of hours worked is determined by each employee. The employer is also assumed to consider the desired number of working hours of each employee as a given factor in determining the employment rate, and individuals consider their employment rate determined by the employer as a given factor in deciding their desired number of working hours (see note).

Econo-kun's photoEcono-kun: How do you define wages?

Kobayashi Keiichiro's photoKOBAYASHI Keiichiro: I considered two different cases. In the first case, wage is assumed to be proportional to the aggregate number of hours worked. In the second, wage is assumed to be equal to the sum of the fixed cost per employee and a segment proportional to the aggregate number of hours worked. In the first case, the employer's total wage payment is defined as weh, in which w, e, h respectively represent "wage rate," "employment rate," and "hours worked," whereas the total wage payment in the second case is defined as we+ξweh=(1+ξh)we, in which ξ is a positive constant. It is immediately shown that w equals the marginal productivity of labor (w = MPL), as the employer works to maximize its profit. The question is what happens when we calculate the labor wedge using this model but introduce a new definition for the labor wedge and assign the Japanese data. If the deterioration trend of the labor wedge disappears, we are then able to conclude that the result obtained through the conventional BCA models - the finding that labor wedge deterioration occurs in recessions - is attributable to an error in the formulation of the model. This means that recessions can be almost fully accounted for by changes in TFP under the new model with the indivisible labor assumption.

However, the deterioration trend of the labor wedge did not disappear when I calculated Japan's labor wedge using the new model. (The same result was obtained in each of the above two cases assumed for the total wage payment.) Thus, labor wedge deterioration cannot be explained (by changes in TFP alone) under the new model with the indivisible labor assumption. This implies that some sort of change in the market structure - such as worsening financial problems, structural changes in the labor market, and/or severer monetary shocks - is needed in addition to the productivity change in order to explain labor wedge deterioration. So, I would say that this reconfirms that the standard RBC model (with the indivisible labor assumption) cannot sufficiently describe the actual state of recessions.

July 14, 2006
  1. ^ Under the new model, there are two choices of variable, - e for the employment rate and h for the number of hours worked. Thus, the model cannot be solved solely on the basis of optimization by worker and employer (i.e. the solution of the equation is indeterminable because the number of variables is larger than the number of conditional equations). Hence, in order to solve the model equation, it is necessary to apply additional conditions such as the value of w at equilibrium being constrained by a social convention that, for instance, calls for keeping the wage level constant. I believe that using a social norm as criteria for selecting equilibrium out of numerous equilibrium candidates - which has been employed by Robert E. Hall (2005) "Employment Fluctuations with Equilibrium Wage Stickiness," American Economic Review 95 (1): 50 - 65 - should not be considered as unusual in modeling frictions in the labor market.

July 14, 2006

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