The trade-off between supervision and wages: evidence of efficiency wages from the NLSY.

• Author: Ewing, Bradley T.
• Position: National Longitudinal Surveys of Youth

1. Introduction

   The classical competitive theories of wage determination predict that workers will be paid the value of their marginal product. These theories suggest that, after accounting for differences in working conditions, there should be no variation in wages among homogeneous workers. Recent findings that industry affiliation and firm size affect wages suggest that part of the explanation of wage structure is missing.(1) These results call into "question the view that industry wage differentials can plausibly be rationalized with textbook competitive models" (Krueger and Summers 1988, p. 280).

   This paper follows the efficiency wage literature by assuming that one important determinant of wage differences is variation in employers' ability to monitor workers' efforts.(2) This paper provides new empirical evidence in support of efficiency wage theory using data from the National Longitudinal Surveys of Youth (NLSY), a data set that is noticeably absent from the efficiency wage literature.

   Efficiency wage models attempt to complete the explanation of wage structure by focusing on the idea that, over some range, profits may increase with the wage.(3) There are several reasons why this might be the case, such as to raise workers' effort level, reduce employee turnover, increase workers' feelings of loyalty to their employer, and attract a better pool of workers. Focusing on the effect of wages on effort, ti (1983, 1987, 1990) suggests that employer size is one measure of monitoring technology. In particular, it is more difficult (costly) to detect shirking in larger firms, ceteris paribus.4 The notion that a trade-off exists between wages paid and supervisory intensity has been examined in several papers. Kruse (1992) finds evidence using the 1980 Survey of Job Characteristics that supervisory intensity, as measured by the number of times a worker's supervisor checks up on his/her work, is negatively correlated to pay but makes no difference on the size effect. His findings are consistent with the shirking model. Leonard (1987) considers the trade-off between self-supervision and external supervision based on the premise that variation in monitoring costs for homogeneous workers may account for variations in wages across firms, provided supervisor intensity and wage bonuses are substitutes in production. Leonard (1987) predicts that firms employing more supervisors per worker will pay lower wages, although he finds little evidence to support this claim. Using the 1977 wave of the Panel Study of Income Dynamics, Neal (1993) finds no evidence in support of the idea that interindustry differences in monitoring contribute to interindustry wage differentials. Rebitzer (1995) examined the trade-off between wages and supervision in the petrochemical business and found support for the efficiency wage hypothesis.(5)

   A common feature of efficiency wage models is the attempt to explain why variables not associated with worker productivity should affect the structure of wages. The next section outlines a simple efficiency wage model that provides motivation for the empirical tests. The third section presents tests of this efficiency wage model. The final section contains concluding remarks.

2. Efficiency Wage Model

   In this section, we outline a typical efficiency wage model where employers differ in the degree to which workers can be monitored. Let p denote the probability that a worker who shirks in her position at the firm is caught.(6) Let us assume that the direct contribution to output produced by a worker at the firm who does not shirk is given by y, with y [greater than or equal to] 0. If a worker shirks, his y = 0. Further, we assume that the output good price is normalized to one. Letting q denote the probability that a worker at the firm does not shirk in her job, we thus have the following expression for the expected profit from a worker at the firm:

   [Pi] = qy - w(1 - q)p), (1)

   where w is the wage paid by the employer to a worker who is not caught shirking. Note that a worker caught shirking receives a zero wage.(7) The probability that a worker will not shirk is denoted by q. In the traditional efficiency wage literature, this probability is either one or zero, and there is a unique wage below which no worker provides any effort and above which no worker shirks.(8)

   For simplicity, assume that workers differ in some variable such as a distaste for effort. A standard feature of efficiency wage models is that the probability a worker at the firm does not shirk, q, depends directly on the wage offered by the firm (w), inversely on the alternative wage ([w.sub.a]), and directly on the probability a worker is caught shirking (p). Thus, drawing on the work of Shapiro and Stiglitz (1984), we have the following Equation 2, which is essentially a reduced form:

   q - q(D), where D [equivalent to] p(w - [w.sub.a]). (2)

   D represents the expected lost earnings from shirking. We assume there are diminishing returns to increasing D in terms of increasing the probability the worker does not shirk such that q[prime] [greater than] 0 and q[double prime] [less than] 0.

   Maximizing the profit function (Eqn. 1), we obtain the following first-order and second-order conditions, respectively:

   (y - wp)pq[prime] - [1 - (1 - q)p] = 0 (3)

   (y - wp)[p.sup.2]q[double prime] - 2[p.sup.2]q[prime] [less than] 0. (4)

   Clearly, the second-order condition holds and y [less than] wp for the first-order condition to hold.

   There are two parameters of the model of particular interest, the alternative wage [w.sub.a] and the probability of being caught shirking p. Totally differentiating Equation 3 with respect to w, [w.sub.a], y, and p, one obtains

   Adw + pq[prime]dy + Bdp + [Cdw.sub.a] = 0, (5)

   where, in Equation 5,

   A [equivalent to] [Delta][[Pi].sup.2]/[Delta][w.sup.2] (the second order condition),

   B [equivalent to] [(1/p) + (y - wp)(w - [w.sub.a])pq[double prime] - (w - [w.sub.a])pq[prime] - wpq[prime]],

   and

   C [equivalent to] [p.sup.2][q[prime] - q[double prime](y - wp)].

   Now A [less than] 0 (it is the second-order condition), C [greater than] 0, and B [less than], [greater than], or = 0. The last three terms in B are negative and the first term...