(Note: on this topic, see also “Jonathan Meer and Jeremy West: Effects of the Minimum Wage on Employment Dynamics.”)

In light of the current debate about raising the minimum wage, I wanted to bring to your attention University of Michigan graduate student Isaac Sorkin’s work on the minimum wage. He begins his paper “Minimum Wages and the Dynamics of Labor Demand” by raising the issue of long-run versus short-run: 

Typical analyses of the employment effects of minimum wages find effects too small to easily reconcile with the short-run elasticities implied by the textbook approach. However, if many firms do not fully adjust their labor demand in the short run, then the short-run employment responses would be much smaller in magnitude than the textbook approach implies, and in line with empirical work.

Later in the introduction, Isaac explains:

The main contribution of this paper is that it revives, formalizes and quantifies an old argument about the employment response to minimum wage increases that has been curiously neglected in the modern literature. In the famous Lester (1946), Machlup (1946), and Stigler (1946) debate about minimum wages, … Lester’s argument is that in response to temporary changes in wages, employers are unlikely to make the fundamental changes in how they do business necessary to reduce labor demand simply because it is not worth it to them to pay the adjustment cost. Thus, this paper follows in that tradition by arguing that the presence of adjustment costs on labor demand provides a cohesive explanation for the small short and long-run employment effects found in the minimum wage literature. 

The relevant quotation from Lester is this:

Most industrial plants are designed and equipped for a certain output, requiring a certain work force. Often effective operation of the plant involves a work force of a given size…Under such circumstances, management does not and cannot think in terms of adding or subtracting increments of labor except perhaps when it is a question of expanding the plant and equipment, changing the equipment, or redesigning the plant…

From much of the literature the reader receives the impression that methods of manufacture readily adjust to changes in the relative cost of productive factors. But the decision to shift a manufacturing plant to a method of production requiring less or more labor per unit of output because of a variation in wages is not one that the management would make frequently or lightly.

Richard A. Lester (1946, pg. 72-73). 

If the long-run effect of minimum wages is substantial, why then don’t we see this effect? Isaac argues it is because there have been very few long-run changes in the minimum wage in the United States, so evidence on their effects is scant. The minimum wages is set in nominal terms, so it declines with inflation, is raised, declines with inflation, is raised, etc.  This yields a sawtooth pattern of the real (inflation-adjusted) minimum wage in which almost all changes in the real minimum wage are temporary. And Isaac argues that temporary changes in the minimum wage have muted effects. In Isaac’s words:

… if adjustment is slow (because it is costly), then labor demand today is a forward-looking decision and depends critically both on the realized path, and the expectations, of minimum wages. In the US, minimum wages are mostly set in nominal terms and so a given increase is not very persistent. As a result, labor demand would never fully adjust to a given minimum wage increase and the long-run consequences of a given minimum wage increase for employment might be quite small.

Isaac backs up his story about how machinery adapted to be used by a given number of workers can influence labor demand by discussing detailed micro-data of the reaction to an important set of minimum wage increases in 1938 and 1939 (pp. 4-6).  

The implementation of the Fair Labor Standards Act of 1938 in the case of the seamless hosiery industry provides a nice example of this mechanism since the Bureau of Labor Statistics collected data on both employment and the kind of capital in January of 1938 and August of 1940, which is tabulated in US Department of Labor (1941)….

The minimum wage was implemented in two stages: it was set to 25 cents an hour in October 1938 and then raised to 32.5 cents in September 1939. The minimum wage was binding in the seamless hosiery industry….

The fundamental technological choice facing the seamless hosiery industry was whether to use machines where the top of the stocking was knit on a different machine than the stocking itself, or machines where the top was knit on the same machine as the stocking. The most labor-intensive process used the hand-transfer machine, where the top of the stocking was knit on a separate machine and then carried by hand to the knitting machine. A converted hand-transfer machine included an attachment to the hand-transfer machine that “in effect converts transfer machines into automatic machines” (US Department of Labor (1941, pg. 75)), while an automatic machine performed both steps in an integrated fashion. The hand-transfer machines were roughly four times more labor-intensive than the automatic machines (Hinrichs (1940, pg. 25, n. 15))….

… five points. First, as Seltzer (1997) emphasizes, the earnings and employment numbers are consistent with the minimum wage decreasing employment. Average hourly earnings rose three times faster in the low-wage plants than the high-wage plants. And employment fell in the low- wage plants and not in the high-wage plants.

Second, the plants paying higher wages in 1938 had a significantly different mix of machines than plants paying lower wages. In particular, half of the machines in the low-wage plants were the most labor-intensive, while only a quarter of the machines in the high-wage plants were the most labor-intensive. This is consistent with long-run differences in wages leading to differences in technology choice.

Third, in the two and a half year window around the implementation of minimum wages, bothhigh and low-wage plants shifted toward more capital-intensive machines, with much stronger shifts at the lower wage plants.

Fourth, the sharp increases in usage of more capital-intensive machines implies that the quantity of capital in use adjusts at least somewhat in the short run.

Finally, the speed of substitution toward more capital-intensive machines was slow.Two years after the change in relative labor costs, the use of the most labor-intensive machines declined by less than a quarter. Even among the plants paying on average below the minimum wage before its implementation, the use of the most labor-intensive machines declined by less than a third.

This evidence is consistent with a model in which conditional on installation of a machine the capital-labor ratio is fixed. Because the capital cost is sunk, the machines that continue to function remain in use, even if they do not have the optimal capital-labor ratio. To allow for the fact that there was a reduction in use of these labor-intensive machines even two year after the wage increase, some machines have to stop working at any given point in time. To capture the rapid increase in the use of capital-intensive machines, the model has to feature free entry into operating machines. The next section develops such a model and analyzes its implications for labor demand.