Are wages too low? Empirical implications of efficiency wage models.

• Author: Carter, Thomas J.

1. Introduction

   In efficiency wage models, firms choose to pay high wages to reduce turnover, eliminate shirking, increase morale, or in other ways enhance productivity. If wages exceed the market-clearing rates, unemployment results. Any further increase in wages, caused by some government policy, would likely worsen the unemployment problem but also further enhance productivity. Combining the two effects, would the wage increase raise or lower output and welfare? In other words, are efficiency wages too high or too low? That is the question this paper seeks to answer.

   Economists typically assume that the efficiency wage is too high and so leads to unemployment that is also too high. Regarding a model of costly labor turnover, Stiglitz (1974, pp. 210-11) writes,

   . . . firms are likely to pay too high wages. But it should be emphasized that it is possible that the competitive wage is too low. In the ensuing analysis, we shall follow the conventional presumption in calling the case where [the competitive wage exceeds the optimum wage] the normal case.

   This conventional presumption has been followed in most of the efficiency wage literature ever since.

   A well-known example is in the Handbook of Labor Economics; Johnson and Layard (1986) use efficiency wage models to argue for employment subsidies financed by wage rate taxes. These policies cause employment to rise and wages to fall. Johnson and Layard emphasize the gain from increased employment but do not consider any negative effects of lowered wages. Pisauro (1991) also follows convention by explicitly assuming that employment effects outweigh other effects. This ensures that low-wage/high-employment policies raise output.

   Of course, many other policies exist with effects similar to or even identical to the Johnson and Layard tax cum subsidy. Progressive income taxes (as in Johnson and Layard 1986) and the tax-based incomes policies of Jackman and Layard (1990) are two examples.(1) Similar policies include other incomes policies that increase the cost of raising wages and policies that change the relative bargaining power of firms and unions, such as right-to-work laws.

   The conventional presumption is that in efficiency wage models, these low-wage policies raise employment and output. Yet recently, several authors have found theoretical results that contradict this presumption. In some efficiency wage models, minimum-wage laws may raise employment. In Rebitzer and Taylor (1995), the more workers a firm employs, the more difficult it is to monitor those workers, and so the higher is the efficiency wage the firm must pay to deter shirking. This positive relation between firm employment and wages causes the firm to act like a monopsonist regarding minimum wages; a binding minimum wage raises employment. In Carter (1998), a minimum wage reduces the workers' quit rates. With less turnover, fewer job openings exist, lessening the need for unemployment as a worker discipline device. Therefore, in this model, unemployment may fall with the minimum wage. These models suggest that the market wage may be too low to be optimal. If so, the low-wage policies discussed previously may be harmful in that they move the wage further from its optimum.

   Other authors have found a complementary result: Even if employment falls, high-wage policies still raise output and welfare. Drazen (1986) and Perri (1990) show that in their models, laws mandating a wage increase raise output and welfare even as they lower employment. Carter (1995) finds that in a version of the Shapiro and Stiglitz (1984) model, any policy that raises welfare must raise wages and unemployment. The high wages can raise welfare because they lower turnover or shirking and so raise the workers' productivity. Even the higher unemployment can be output increasing if it further reduces turnover or shirking and so further raises productivity. Shapiro and Stiglitz (1984) find this result; in one version of their model, unemployment is too low to be optimal. The title of their paper, "Equilibrium Unemployment as a Worker Discipline Device," points out one way unemployment raises productivity.

   These results go against the conventional presumption. They support the use of high-wage policies such as minimum-wage laws.(2) But, how relevant are these results empirically? Are wages too low, as suggested by these results, or too high, as in the conventional presumption?

   To answer these questions, section 2 uses a simple efficiency wage model to find a necessary and sufficient condition for high-wage policies to raise output. The condition is a simple comparison of two elasticities, both of which have been estimated several times in published articles. Section 3 looks at these empirical results and finds substantial support for the condition.

2. The Model

   The model used in this paper is a simple general equilibrium efficiency wage model. It is consistent with many motivations for efficiency wages, such as shirking and turnover. However, it is not consistent with all models. Importantly, in this model policies that cause firms to raise wages also unambiguously lower employment.(3) Therefore, it is more similar to the model of Shapiro and Stiglitz (1984) than to that of Rebitzer and Taylor (1995). Although general in its motivation for efficiency wages, the model is specific enough to allow for a simple, empirically verifiable condition for a wage increase to raise output.

   Assume that some fixed number of identical, perfectly competitive firms pay efficiency wages and that all workers are identical. The following equations show three basic relationships of the model:

   [[Pi].sub.i] = Q([e.sub.i][N.sub.i]) - [w.sub.i][N.sub.i] (1)

   [e.sub.i] = [e.sub.i]([w.sub.i], [w.sub.A], N) (2)

   [Q.sub.N] = [Q.sub.N](eN). (3)

   Equation 1 shows a standard efficiency wage profit function. Labor is the only input. The good's price is the numeraire. Q is output, [w.sub.i] is the wage, [N.sub.i] is labor employed in the firm, and [e.sub.i] is the efficiency of that labor. The efficiency of labor is the effective labor input per worker.(4) The i subscripts refer to the firm; these are dropped in the following when it can be done without confusion. Equation 2 shows [e.sub.i] to be a function of the wage at the firm, the wage in other firms ([w.sub.A]), and the economy-wide employment rate (N). N equals one minus the unemployment rate. Let the total labor force equal one, so that N also equals total employment, the sum of all the firm's [N.sub.i]'s. All the identical firms act identically in their setting of e and w; w = [w.sub.A] in equilibrium. Equation 3 notes that the marginal product of an efficiency unit of labor, [Q.sub.N], identical for all the firms, is a function of the effective labor employed in the economy. With nonincreasing returns, [Delta][Q.sub.N]/[Delta][eN] [less than or equal to] 0.

   Equation 2 is consistent with many...