The effect of minimum salaries on employment of teachers: a test of the monopsony model.

• Author: Boal, William M.

1. Introduction

   The market for schoolteachers has long been cited as an example of labor monopsony, where employers--that is, school districts--enjoy market power (Ehrenberg and Smith 2000; Hyclak, Johnes, and Thornton 2005). The reasons offered are plausible. By definition, school districts enjoy exclusive territories. Teachers have specialized training that might not be interesting to nearby nonschool employers. Many teachers are second earners in their families and might be unwilling to relocate in response to distant job offers. There is some evidence that teachers have strong personal geographic preferences (Boyd et al. 2005). It would appear that the set of potential employers available to a certified teacher is limited to the set of school districts within commuting distance of current residence. For these reasons, it is often argued that the greatest monopsony power is probably held by rural school districts because of their large geographic size.

   An empirical literature dating back to Landon and Baird (1971) has tried to document monopsony in this market by regressing teacher salaries on measures of geographic concentration of school districts. These studies often appear to find a negative effect of geographic concentration on teacher salaries (see Luizer and Thornton [1986] for a survey). A major difficulty with the salary-concentration research strategy is that concentration is inversely related to urbanization--because urban areas tend to have many school districts in close proximity--and salaries for all workers tend to be higher in urban areas. The apparent negative estimated effect of concentration may disappear when sufficient measures of urbanization are included (Ransom, Boal, and Beck 1998). Moreover, the urban-rural difference in teacher salaries appears similar to the urban-rural difference for other professionals (Hirsch and Nottage 1998). (1)

   A second difficulty with the salary-concentration research strategy is the increasing presence of teachers' unions. (2) A monopsonist faces, or at least perceives, an upward-sloping supply of labor. This upward slope raises marginal labor cost above the current wage, causing the monopsonist to reduce employment. Equilibrium occurs on the labor supply curve but below the monopsonist's labor demand curve. By contrast, a union tries to raise the wage by moving the equilibrium above the supply curve. Estimates based on 1970s data show that unionized teachers enjoyed an average wage differential of roughly 10%. (3) In some cases, a union might even move the equilibrium above the demand curve--this is the prediction of the so-called contract curve model, for which Eberts and Stone (1984, 1986) found some evidence among New York State school districts. Any test for monopsony ought to exclude unionized districts from the sample or control for unionism in some way. This has not generally been done. (4)

   A recent, seemingly unrelated literature has investigated the effects of legal minimum wages on employment in fast-food restaurants (Katz and Krueger 1992; Card and Krueger 1994). This literature has apparently documented slight increases in employment following increases in minimum wages. The authors note that this result is incompatible with competitive labor markets and may be evidence for employer monopsony. A modest increase in a minimum wage may increase employment in a monopsonized market because it flattens the employer's perceived labor supply curve and thereby lowers the employer's marginal labor cost curve. (5) These results hold whether the monopsony follows the old textbook model of an isolated employer or the "new monopsony" model of equilibrium search, proposed by Burdett and Mortensen (1998) and analyzed at length by Manning (2003). The new monopsony model assumes that market frictions rather than employer concentration are the source of employer monopsony. Thus, the new monopsony suggests that monopsony power could be held even by urban employers in unconcentrated markets. While the econometric results for fast-food restaurants have been challenged by other researchers (Neumark and Wascher 2000), the minimum-wage method offers a promising alternative research strategy for evaluating employer monopsony power.

   Apparently unnoticed in the literature on teacher labor markets is that teachers in many states are subject to their own "minimum wages." (6) Many states set minimum salaries for public schoolteachers; although, local districts are free to set salaries above the legal minima. In some states these minimum salaries take the form of an elaborate schedule, varying by educational attainment and experience, so that they are effectively binding on senior teachers as well as new hires. Thus, a change in the minimum salary schedule can directly affect every teacher in a district. By contrast, a change in the U.S. federal minimum-wage law directly affects only the least skilled and least experienced workers.

   This study measures the employment effects of increases in state minimum salaries in two nonunion states with different minimum-salary schemes: South Carolina and Texas. (7) The specification used here is similar to those used in the studies of fast-food restaurants previously cited, so the results may be directly compared. In fact, the results prove to be quite different. Increases in state minimum salaries decrease the number of teachers employed, even when (as in Texas) school districts are given additional state funding to pay for the minimum salary increases. This result is clearly incompatible with movement along a supply curve, so the monopsony model is rejected. Assuming that this result represents movement along a demand curve, the short-run elasticity of teacher demand is estimated to be between -0.2 and -0.4, holding constant districts' enrollment and tax base.

   The paper is organized as follows: Section 2 presents alternative models of employment determination by school districts, contrasting the responses to minimum salaries by competitive and monopsonistic school districts. Section 3 analyzes a panel data set of South Carolina school districts. Section 4 analyzes a panel data set of Texas school districts. Section 5 concludes.

2. Models of Competitive and Monopsonistic Employment Determination

   This section presents a comparative-static analysis of the effects of state minimum salaries on the employment of teachers. The standard textbook analysis of supply and marginal labor cost is extended to develop budget constraints with and without a corresponding change in state aid to assist the transition to the minimum salary. Throughout the discussion, the effects on competitor and monopsonist districts are contrasted.

   Assume that the representative school district maximizes output of school services subject to a budget constraint. Denote the production function for school services by U(L, K), where L denotes teachers, and K denotes all other inputs. Assume this function is characterized by diminishing marginal rates of substitution, and that all inputs are normal.

   Simple Minimum Salary

   Suppose the district is a competitor in the market for teachers. Its perceived "labor supply curve" is therefore a horizontal line at the going salary level (Figure la). Denote this going salary level [W.sub.0]. Let B denote the district's budget, assumed given, and let the price of other inputs equal one dollar. Then the district's budget constraint is simply

   B [greater than or equal to] K + [W.sub.0] L. (1)

   When a state minimum salary level, [W.sub.min] > [W.sub.0], is imposed, the district's "labor supply curve" rises but remains horizontal, and the competitor's new budget constraint becomes

   B [greater than or equal to] K+ [W.sub.min] L. (2)

   [FIGURE 1a OMITTED]

   [FIGURE 1b OMITTED]

   Budget constraints without and with a state minimum salary are depicted in Figure 2a. Both budget constraints have the same intercept on the vertical (K) axis. However, the budget constraint with a state minimum salary has a steeper slope, reflecting the higher but still constant salary level. Clearly, the minimum salary forces the district to a lower isoquant, and it will produce fewer educational services than before. Let [L.sub.0] denote the initial level of teacher employment before the minimum salary. Substitution and income effects of the new minimum salary will both be negative, so that under the state minimum salary, teacher employment will decline to something less than [L.sub.0].

   Alternatively, suppose the district is a monopsonist in the market for teachers. Its labor supply curve, denoted f(L), is upward sloping, so that f'(L) > 0 (Figure lb). For an unregulated monopsonist, marginal labor cost is given by

   d / dL (f(L) x L) = f(L) + f' (L) x L, (3)

   which is necessarily greater than W = f(L). Let [L.sub.0] denote the initial level of teacher employment, and [W.sub.0] denote the initial salary. When a state minimum salary level, [W.sub.min] > [W.sub.0], is imposed, the district's marginal labor cost acquires a discontinuity. For employment levels below [L.sub.1], defined by f([L.sub.1] = [W.sub.min], it becomes a horizontal line with height [W.sub.min]. For employment levels above [L.sub.1], the district's marginal labor cost is the same as before the minimum salary.

   [FIGURE 2a OMITTED]

   [FIGURE 2b OMITTED]

   Budget constraints without and with a state minimum salary are depicted in Figure 2b. Without a state minimum salary, the monopsonist's budget constraint is given by

   B [greater than or equal to] K + f(L) L, (4)

   a curve concave to the origin because f'(L) > 0. With a state minimum salary, the monopsonist's budget constraint acquires a kink at [L.sub.1] as follows:

   B [greater than or equal to] K + [W.sub.min] L, for L [less than or equal to] [L.sub.1] (5a)

   B [greater than or equal to] K + f(L) L, for L [greater than or equal to] [L.sub.l]. (5b)

   Clearly, the minimum salary forces the district to a lower isoquant, and it will produce fewer educational...