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

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 services than before, but it will likely employ more teachers. If the minimum salary, [W.sub.min], is only slightly higher than the original salary, [W.sub.0], both the minimum salary constraint, Equation 5a, and the labor-supply constraint, Equation 5b, will bind, and the district will now employ [L.sub.1] > [L.sub.0] teachers at the kink in its budget constraint. If the minimum salary, [W.sub.min], is slightly larger than this but still less than its original marginal labor cost, [W.sup.*.sub.0] = [W.sub.0] + f'([L.sub.0]), only the minimum salary constraint, Equation 5b, will bind, but the monopsonist will still employ more teachers than [L.sub.0]. Only if the minimum salary [W.sub.min] is greater than [W.sup.*.sub.0] will the district hire fewer teachers than [L.sub.0].

[FIGURE 3a OMITTED]

[FIGURE 3b OMITTED]

Minimum Salary with Salary Transition Aid

In Texas, beginning in the 1995-1996 school year, increases in the state minimum salary were accompanied by "salary transition aid" (STA), calculated to cover the difference between old salaries and the new minimum at the old level of employment. (8) Thus, STA increased the school district's budget by

[DELTA]n = ([W.sub..min] - [W.sub.0]) x [L.sub.0]. (6)

Consider the effect of a minimum salary with compensating STA.

Suppose again that a district is a competitor in the market for teachers. When a state minimum salary level, [W.sub.min] > [W.sub.0], is imposed, the district's "labor supply curve" rises but remains horizontal, as shown in Figure la, and the district's budget constraint becomes steeper. The competitor's new budget constraint, depicted in Figure 3a, becomes

[DELTA] B + B [greater than or equal to] K + [W.min] L. (7)

Note that STA ensures by definition that the old input combination is still feasible for the district. Clearly, the minimum salary with STA will permit the district to reach a higher isoquant, and it will produce more educational services than before, but it will employ fewer teachers. The substitution effect of the minimum salary with transition aid is negative, and there is no income effect.

Alternatively, suppose that the district is a monopsonist in the market for teachers. With a state minimum salary, the monopsonist's budget constraint acquires a kink at [L.sub.1] as follows:

[DELTA] B + B [greater than or equal to] K + [W.sub.min] L, for L [less than or equal to] [L.sub.1] , (8a)

[DELTA] B + B [greater than or equal to] K + f(L) L, for L [greater than or equal to] [L.sub.1]. (8b)

Again, STA ensures that the old input combination is still feasible for the district, as depicted in Figure 3b. If the new minimum salary, [W.sub.min], is less than [W.sup.*.sub.0] = [W.sub.0] + f'([L.sub.0]), the new budget constraint will be linear through the old input combination until it reaches a kink to the right of it, at [L.sub.1]. In that case, the minimum salary with STA will permit the district to reach a higher isoquant, and it will produce more educational services than before and employ more teachers. The district may choose the kink point [L.sub.1], where both the minimum salary constraint, Equation 8a, and the labor-supply constraint, Equation 8b, bind, or it may choose an interior solution between [L.sub.0] and [L.sub.1], where only the minimum salary constraint, Equation 8a, binds. In any case, a revealed preference argument ensures that in no case will the district reduce employment of teachers in response to the minimum salary with STA.

Summary

The effect of minimum salaries on employment of teachers depends critically on whether the school district is a competitor or a monopsonist. If the district is a competitor, a rise in the state minimum salary will cause it to employ fewer teachers. STA will attenuate but not reverse this effect. By contrast, if the school district is a monopsonist, a rise in the state minimum salary will cause it to employ more teachers, provided that the state minimum salary is not too large. STA will augment this effect.

3. Results for South Carolina

This section presents estimates based on a fairly long panel data set of South Carolina school districts. South Carolina provides a good setting for testing monopsony because public education is nonunion. The state has no statute regulating collective bargaining by teachers (Lund and Maranto 1996), and unionism is extremely low. Only 0.1% of school district employees were represented by bargaining units in 1987, while the U.S. average was 44.1%. (9) This reflects the nonunion character of the state as a whole. In 2000, only 13% of South Carolina public-sector workers were covered by union contracts, while the U.S. average was 42%, and only 3.4% of its private-sector workers were covered by union contracts, while the U.S. average was 9.8%. (10) South Carolina is a right-to-work state.

School District Data

School district data were taken from Rankings of the Counties and School Districts of South Carolina, published annually by the South Carolina State Department of Education. South Carolina currently has 86 school districts. Data were obtained for all districts in the school years 1985-1986 through 1998-1999, the last year for which complete data could be obtained at the time the analysis was conducted. Several mergers of school districts took place during the sample period, and a few observations were therefore excluded to ensure that mergers did not distort the results. (11) The available data include enrollment, number of teachers employed, total assessed value per pupil (a measure of school district wealth), and teacher salaries. Summary statistics are shown in Table 1.

Salaries of public schoolteachers in the United States are usually defined by local school districts according to a grid, whose dimensions are teaching experience and educational attainment. The Rankings publication reports salaries for four cells from each district's grid: a bachelor's degree with zero years of experience, a master's degree with zero years of experience, a bachelor's degree with 18 hours of graduate course work and 10 years of experience, and a master's degree with 17 years of experience. "Experience" means total teaching experience in any school district in South Carolina or elsewhere. (12)

South Carolina's state minimum salaries are defined using a similar grid. These minimum salaries are not reported in earlier issues of the Rankings publication and were obtained directly from the State Department of Education. Minimum salaries were increased in all but two years of the sample. (No increases were legislated for the years 1991-1992 and 1993-1994.) Whenever minimum salaries increased, they were always increased by the same percentage for all cells in the grid.

A reasonable way to measure the force of minimum salaries is by the "gap," or percent difference, between state minimum salaries in a particular year and actual salaries for the previous year. This is the definition used by Katz and Krueger (1992) and Card and Krueger (1994). Accordingly, define

[GAP.sub.i,t] = max {[WMIN.sub.t] - [W.sub.i,t-1] / [W.sub.i,t-1], 0}, (9)

where [W.sub.i,t-1] denotes the salary paid by district i to teachers with a bachelor's degree with zero years of experience in year t-1, and [WMIN.sub.t] denotes the state minimum wage for such teachers in year t. A positive sign for GAP indicates that a district must raise salaries to remain in compliance with state law. The size of GAP indicates the size of the required salary increase. By contrast, the value of GAP is zero for districts whose old salary is greater than the new state minimum. Figure 4a shows that, even though increases in the state minimum salaries were small, roughly half of South Carolina districts faced positive salary gaps whenever minimum salaries were increased (Figure 4b). South Carolina school districts were not given any STA to cope with these gaps. (13)

Rural school districts are more likely to hold monopsony power, according to the traditional monopsony model. Slightly more than half of South Carolina's school districts lie outside metropolitan statistical areas (MSAs). Table 2 shows summary statistics separately for districts inside and outside MSAs. On average, rural school districts in South Carolina are less than half as large as urban districts and pay slightly lower salaries.

Econometric Estimates

The econometric analysis seeks to determine whether state minimum salaries had a negative or positive effect on teacher employment. The basic equation to be estimated is

[DELTA] ln([L.sub.i,t]) = [[beta].sub.1] + [[beta].sub.2] [GAP.sub.it]. (10)

Here, [L.sub.i,t] denotes the number of (full-time equivalent) teachers employed in district i in school year t. [GAP.sub.i,t] is the percent difference between state minimum salaries for year t and actual salaries for year t-1 in district i, as defined in Equation 9.

The key parameter is [[beta].sub.2], the coefficient of GAP. Under the monopsony model, [[beta].sub.2] is positive, reflecting a movement along the district's labor supply curve. Formally, [[beta].sub.2] equals the short-run elasticity of labor supply to the individual school district, provided that the increase in the minimum salary is small.

[FIGURE 4a OMITTED]

[FIGURE 4b OMITTED]

By contrast, under the competitive model, [[beta].sub.2] is negative, reflecting a movement along the district's labor demand curve. Formally, without STA, [[beta].sub.2] equals the short-run gross or uncompensated elasticity of teacher demand by the individual school district, assuming that other determinants of teacher demand are held constant. Since these other determinants of teacher demand, such as enrollment or district wealth, might in fact be correlated with GAP, an expanded equation was also estimated as follows:

[DELTA] ln([L.sub.i,t]) = [[beta].sub.1] + [[beta].sub.2] [GAP.sub.i,t] + [[beta].sub.3] [DELTA] 1n([E.sub.i,t]) + [[beta].sub.4] [DELTA] ln ([V.sub.i,t]. (11)

Here, [E.sub.i,t] denotes district enrollment and [V.sub.i,t] total assessed valuation per pupil, a measure of district wealth.

These equations were estimated by ordinary least squares, with the results reported in Table 3. Estimates of Equation 10 are given in columns 1 and 3, and estimates of Equation 11 are given in columns 2 and 4. Fixed effects for years are included in all columns. Column 1 shows that for Equation 10, the coefficient of GAP is about -0.37 and easily less than zero at conventional levels of significance. Column 2 shows that when enrollment and assessed valuation are introduced as covariates, the coefficient of GAP drops to -0.26 but remains significant. Columns 3 and 4 show that when fixed effects for districts are introduced, the coefficient of GAP drops even further and is no longer statistically different from zero at conventional levels of significance. District fixed effects are intended to control for unobserved characteristics of districts, constant through time, that might be correlated with GAP.(14) However, those district fixed effects are themselves insignificant for the specifications with covariates, according to simple F-tests. (15) There appears to be a negative effect of minimum salaries on employment of teachers for South Carolina as a whole.

To investigate the traditional argument that monopsony power is stronger in rural areas, the same equations were estimated separately on urban and rural subsamples, with the results reported in Table 4. Columns 1 through 4 report estimates using only urban districts--that is, districts in MSAs. Estimates of Equation 10 are given in columns 1 and 3, and estimates of Equation 11 are given in columns 2 and 4. Estimates of the coefficient of GAP without district fixed effects for this subsample are roughly similar to estimates for the entire sample in Table 3, but the standard errors are nearly twice as large. Introduction of district fixed effects causes the estimates of the coefficient of GAP to become small and positive and raises the standard errors further. According to simple F-tests, the fixed effects are jointly significant for this subsample, so one must conclude that there is no evidence of a negative effect of minimum salaries on teacher employment in urban South Carolina. However, there is little evidence of a positive effect, either, because the estimated coefficients of GAP are only about half as large as their standard errors.

Columns 5 through 8 of the same table report estimates using only rural districts--that is, districts outside MSAs. Estimates of Equation 10 are given in columns 5 and 7, and estimates of Equation 11 are given in columns 6 and 8. Estimates of the coefficient of GAP without district fixed effects are roughly -0.2 and about twice their standard errors for this subsample, with p-values of 0.035 and 0.061, respectively. Introduction of district fixed effects does not change the coefficient estimates much but raises their standard errors substantially. However, the fixed effects are themselves not significantly different from zero. There is weak evidence for a negative effect of minimum salaries on teacher employment in rural districts, with a short-run elasticity of teacher demand of about -0.2.

Similar results were found when quadratic terms in enrollment (E) and assessed valuation (V) were introduced, or when Equations 10 and 11 were estimated separately on subsamples of large and small districts (see Appendix). In particular, estimates of the coefficient of GAP for "large" districts (observations with more than 4000 students) were close to zero. Estimates of the coefficient of GAP for "small" districts (fewer than 4000 students) were slightly larger than those for rural districts.

In summary, there is weak evidence in South Carolina of a negative effect of minimum salaries on teacher employment but--in contrast to the traditional argument--only for rural school districts.

4. Results for Texas

This section presents estimates based on a short panel data set of Texas school districts. As in South Carolina, public education in Texas is nonunion. The state has no statute regulating collective bargaining by teachers (Lund and Maranto 1996), and unionism is very low. Only 0.9% of school district employees were represented by bargaining units in 1987. (16) This reflects the nonunion character of the state as a whole. In 2000, only 21.6% of Texas public-sector workers were covered by union contracts, while the U.S. average was 42%, and only 4.7% of its private-sector workers were covered by union contracts, while the U.S. average was 9.8%. (17) Texas is also a right-to-work state.

Despite the absence of state legal protection, teachers in a few Texas school districts have achieved informal agreements for "exclusive consultation." These districts were excluded from the sample. (15)

School District Data

School district data for Texas were taken from Snapshot: School District Profiles, published annually by the Texas Education Agency. Texas has many more school districts than South Carolina--over 1000 total--but their average size is smaller and their size range greater. Data were obtained for the school years 1994-1995 though 1998-1999. These years were chosen because minimum salaries were not changed for many years before 1995 1996 and because a change in the state aid formula makes it impossible to calculate the GAP variable after 19981999. The available data include enrollment, number of teachers employed, total assessed value per pupil, and average teacher salaries. (Salaries for particular cells in the experience-education grid are never reported.) Texas has 1042 public school districts, but the actual number of districts available varies from year to year because of missing data. Summary statistics are shown in Table 5. (19)

Texas's state minimum salaries are defined using a simpler grid than South Carolina's grid. Since the 1995-1996 school year, Texas minimum salaries have varied only with experience, not educational attainment. ("Experience" means total teaching experience in any school district in Texas or elsewhere.) Unfortunately, the state minimum salary grid is difficult to compare with individual district average salaries reported in Snapshot.

Fortunately, an alternative measure of state minimum salaries is available in STA. From 1995-1996 through 1998-1999, Texas offered additional aid to local school districts to cover the difference between old salaries and the new minimum salaries at the old level of employment. Thus, the amount of STA received by a district in any given year, divided by the salary bill in the base year, equals the average gap between the year's state minimum salaries and the base year's actual salaries. The salary bill may be computed by multiplying average salary by employment, giving the following tentative definition for GAP:

[GAP.sub.i,t] = [STA.sub.i,t] / [L.sub.i,t]-1] x [WAVG.sub.i,t-1]. (12)

STA is not reported in the Snapshot publication--these data were obtained directly from the Texas Education Agency. (20)

In computing the GAP for Texas school districts, two complications require attention. The first is spurious correlation between the GAP variable and the dependent variable (i.e., the change in log employment). Note that the denominator of GAP as defined previously will be negatively correlated with the dependent variable because the base level of employment ([L.sub.i.t-1]) appears in the formulas for both variables. Using current employment ([L.sub.i,t]) in Equation 12 is no better--it will cause GAP to be positively correlated with the dependent variable for the same reason. To minimize spurious negative or positive correlation, the average of employment in the base and current years will be used to compute the GAP.

The second complication is the way Texas calculated STA. Texas operates on a fiscal biennium. Although minimum salaries were increased every year of the sample, the base year for calculating STA remained fixed for two years at a time. In particular, 1994-1995 served as the base year for computing STA in both the 1995-1996 and the 1996-1997 school years. Similarly, the 1996-1997 school year served as the base year for computing STA in both the 1997-1998 and the 1998-1999 school years. Thus, for the years 1995-1996 and 1997-1998, STA reflects a one-year increase in minimum salaries; whereas, for the years 1996-1997 and 19981999, STA reflects a two-year increase in minimum salaries.

[FIGURE 5a OMITTED]

[FIGURE 5b OMITTED]

To address these complications, the final definition of GAP becomes

[GAP.sub.i,t] = [STA.sub.i,t[ / (L.sub.i,base] + [L.sub.i,t] / 2) x [WAVG.sub.i,base], (13)

where [STA.sub.i,t] denotes STA received by district i in year t and [WAVG.sub.i,base] denotes the average teacher salary paid by district i in the base year. To accommodate the fiscal biennium, "base" is defined as the immediately prior school year when t = 1995-1996 or 1997-1998 and defined as the year before that when t = 1996-1997 or 1998-1999.

Figure 5a shows that, even though increases in the state minimum salaries were fairly small, a large and increasing number of districts had positive salary gaps (Figure 5b). By the end of the sample period, nearly all districts had positive gaps.

About 60% of Texas's school districts lie outside MSAs. Summary statistics are shown separately for districts inside and outside MSAs in Table 6. On average, rural school districts in Texas are only about a fifth as large as urban districts, and they pay slightly lower salaries.

Econometric Estimates

Equations 10 and 11 were estimated by ordinary least squares on the panel data set of all Texas school districts, with the results reported in Table 7. Again, estimates of Equation l0 are given in columns 1 and 3, and estimates of Equation 11 are given in columns 2 and 4. Fixed effects for years are included in all four columns. Columns 1 and 2 show that, without district fixed effects, estimates of the coefficient of GAP for Texas are negative and slightly larger than corresponding estimates for South Carolina. They are moreover statistically different from zero at conventional levels of significance. Introduction of district fixed effects raises the standard errors but also raises the coefficient estimates slightly, and the estimates remain statistically significant with p-values well below 0.01. The district fixed effects are themselves significant for every specification, according to simple F-tests. There is a clear negative effect of minimum salaries on employment of teachers for Texas as a whole.

Table 8 reports separate estimates for urban and rural subsamples. As in Table 4, columns 1 through 4 report estimates using only urban districts, while columns 5 through 8 report estimates using only rural districts. Estimates of Equation 10 are given in colunms 1, 3, 5, and 7, and estimates of Equation 11 are given in columns 2, 4, 6, and 8. In contrast to the results for South Carolina, the Texas results show virtually no difference between urban and rural school districts in the estimates of the coefficient of GAP. Introduction of district fixed effects, which are always significant in Texas, raises the estimates of the coefficient of GAP to between -0.35 and -0.39. P-values for the estimated coefficient of GAP are below 0.05 in every column but one. Similar results were obtained when quadratic terms in enrollment (E) and assessed valuation (V) were introduced (see Appendix). There is strong evidence for a negative effect of minimum salaries on teacher employment in both urban and rural districts, with a short-run elasticity of teacher demand of nearly -0.40.

Equations 10 and 11 were also estimated separately on subsamples of large and small districts (see Appendix). Estimates of the coefficient of GAP for "large" districts (observations with more than 1000 students) were smaller than those for urban districts and not statistically significant at conventional levels when district fixed effects were included. Estimates of GAP for "small" districts (fewer than 1000 students) were much larger--about -0.56, with p-values less than 0.02--when district fixed effects were included.

It is curious that the estimates of the coefficient of GAP for Texas are larger than the corresponding estimates for South Carolina. Recall that the South Carolina coefficients estimate the short-run gross, or uncompensated demand elasticity, while the Texas coefficients estimate the short-run net, or compensated demand elasticity, because districts received STA as minimum salaries were raised. One might have expected the Texas estimates to be closer to zero because they do not include an income effect. Note, however, that the South Carolina estimates are based on one-year differences, while the Texas estimates are based on a mixture of one- and two-year differences. If districts take time to adjust to salary changes, one would expect a larger change in employment in two years than in one year. Moreover, demand for teachers can differ across states for a variety of factors, including local preferences and state regulations.

One possible source of bias in the Texas data should be addressed. In principle, Texas's STA program could have created an incentive for school districts to inflate employment in the base year to maximize STA in subsequent years. The strength of this incentive would have depended on the size of the anticipated salary gap, therefore potentially causing negative bias in the estimated coefficient of GAP and obliterating evidence of monopsony power. (Bias of this type is not an issue in South Carolina, which provides no STA.) In practice, however, minimum salary increases are typically set by the Texas state legislature only at the end of the base year (Walt 1995, 1999), so school administrators would have required excellent foresight to exploit this incentive.

Nevertheless, to investigate the possibility of negative bias, Equations 10 and 11 were reestimated using only the two-year differences from the years 1994-1995 to 1996-1997 and from the years 1996-1997 to 1998-1999. Note that all these years were base years, so that if employment was inflated equally in all base years, the employment data after differencing should be less subject to bias. Results for the two-year differences subsample are shown in Table 9, with district fixed effects included in all specifications. All the coefficients of GAP for this subsample are more negative than the estimates in previous tables. In particular, the coefficients estimated on the entire sample and on the rural subsample are significantly different from zero, with p-values well below 0.01. There is no evidence of bias due to any incentive for districts to inflate initial employment and thereby maximize subsequent STA. (21)

In summary, there is strong evidence in Texas of a negative effect of increases in minimum salaries on employment of teachers. The effect is more negative and statistically stronger in rural and small school districts. The short-run elasticity of demand for teachers for all districts in Texas is probably about -0.4.

5. Conclusion

The effect of state minimum salaries on employment of teachers is definitely negative in Texas and probably negative in South Carolina. The evidence is strongest for school districts in rural areas. The simplest interpretation of these results is a rejection of the monopsony model--whether the traditional isolated employer model or the "new monopsony" model based on market frictions--for the market for schoolteachers. Teacher employment and salaries in these data sets appear to lie on downward-sloping teacher demand curves with short-run elasticities between -0.2 and -0.4. (22)

It might be argued in defense of the monopsony model that state minimum salaries for teachers are so high in these samples that the supply curve is no longer binding--that is, the minimum salary is above [W.sup.*.sub.0] in Figure la. If this interpretation is correct, the monopsony model is not rejected, strictly speaking, but simply irrelevant: State legislatures in South Carolina and Texas have taken away whatever market power school districts may have once possessed by raising minimum salaries into the demand-constrained range. But are minimum salaries in fact above [W.sup.*.sub.0] in Figure 1a? Figures 4 and 5 suggest otherwise because increases in minimum salaries in both states were modest and many districts were above the minimum, at least at the beginning of the samples.

Alternatively, it might be argued that some districts are supply-constrained monopsonists, exhibiting a positive relationship between minimum salaries and employment, while other districts are demand-constrained competitors, exhibiting a negative relationship. Econometric estimates in a study like this one measure only the average relationship. (23) Nevertheless, if this interpretation is correct, the preponderance of school districts in South Carolina and especially Texas have been shown to be demand-constrained.

However interpreted, the negative employment effects found in this paper stand in sharp contrast to the positive employment effects found by previous researchers (Katz and Krueger 1992; Card and Krueger 1994) for the fast-food industry using similar econometric specifications. Of course, the employers and workers in these two industries are quite different. Moreover, the structure of minimum salaries is different. In the fast-food industry, a single minimum salary directly affects only the lowest-paid and least experienced workers; whereas, in public education, a grid of minimum salaries directly affects even the most experienced teachers. From this perspective, one might expect changes in minimum salaries for teachers to have a greater effect on employment of teachers than changes in the minimum wage would have on employment of fast-food workers. On the other hand, the actual increases in minimum salaries analyzed in this study were quite modest--barely greater than contemporaneous increases in the consumer price index, on average--whereas the increases in the minimum wage analyzed by previous researchers were on the order of 15-20%. From this perspective, it is perhaps remarkable that an effect of minimum salaries on employment of teachers could be detected at all.

Appendix

This appendix reports alternative estimates for South Carolina and Texas when the samples were divided into large and small districts and when quadratic terms were added to Equation 11.

Equations 10 and 11 were estimated separately on subsamples of large and small districts. In South Carolina, median district enrollment was 3827, so to create roughly equal-sized subsamples, "large" districts were defined as all observations having enrollment greater than 4000 students and "small" districts as all observations having enrollment less than 4000 students. (Some districts that changed size are represented in both subsamples.) Results are presented in Table A1. They are similar to those for urban and rural districts in South Carolina. Estimates of the coefficient of GAP are of the same magnitude and statistical significance, and the district fixed effects are not significant when enrollment and assessed valuation are included as covariates, according to simple F-tests.

In Texas, median district enrollment was 868, so to create roughly equal-sized subsamples, "large" districts were defined as all observations having enrollment greater than 1000 students and "small" districts as all observations having enrollment less than 1000 students. (Again, some districts that changed size are represented in both subsamples.) Results are presented in Table A2. These results differ from those for urban and rural districts in Texas. Estimates of the coefficient of GAP for "large" districts are smaller than those for urban districts and not statistically significant at conventional levels regardless of whether district fixed effects are included. The fixed effects themselves are jointly significant. Estimates of the coefficient of GAP for "small" districts are larger in magnitude than those for rural districts, with p-values less than 0.02, regardless of whether district fixed effects are included. The fixed effects themselves are jointly significant, according to simple F-tests.

Equation 11 was reestimated with quadratic terms in the covariates:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (A1)

Results are reported in Tables A3 and A4. The coefficients of the quadratic terms were sometimes significant, but the estimates of the coefficient of GAP were usually very similar to the estimates for the linear Equation 11.
Table A1. Ordinary Least Squares Results for South
Carolina School Districts by District Enrollment Size

Regressor                      1          2          3           4

Sample definition            Large      Large      Large       Large
Salary gap                   -0.4041    -0.2147     0.1095      0.0141
                             (0.1218)   (0.1192)   (0.1422)    (0.1493)
Change in log enrollment                 0.6995                 0.3681
                                        (0.0563)               (0.0780)
Change in log total                      0.0419                 0.0345
  assessed value per pupil              (0.0147)               (0.0145)
Fixed effects for              No         No        Yes         Yes
  districts?
Adjusted [R.sup.2]            0.1913     0.3807     0.3714      0.3962
Number of districts          47         47         47          47
Number of observations      559        559        559         559
F-statistic for district                            4.3941      1.3038
  fixed effects
p-value                                             3.04E-17    0.0933

Regressor                      5          6          7          8

Sample definition            Small      Small      Small      Small
Salary gap                   -0.2790    -0.2146    -0.2384    -0.2551
                             (0.1025)   (0.0940)   (0.1661)   (0.1674)
Change in log enrollment                 0.3517                0.1866
                                        (0.0776)              (0.0843)
Change in log total                      0.0101                0.0060
  assessed value per pupil              (0.0095)              (0.0098)
Fixed effects for              No         No        Yes        Yes
  districts?
Adjusted [R.sup.2]            0.0881     0.1334     0.1179     0.1262
Number of districts          51         51         51         51
Number of observations      603        603        603        603
F-statistic for district                            1.3985     0.9034
  fixed effects
p-value                                             0.0413     0.6629

Dependent variable is change in log full-time equivalent teacher
employment. Standard errors (in parentheses) are computed using
formulas robust to heteroskedasticity and second- order serial
correlation. Year dummies included for all years (coefficient
estimates not shown to save space). "Large" subsample contains all
observations with more than 4000 students. "Small" subsample
contains all observations with fewer than 4000 students.

Table A2. Ordinary Least Squares Results for Texas
School Districts by District Enrollment Size

Regressor                     1            2

Sample definition             Large        Large
Salary gap                   -0.4114      -0.1438
                             (0.0874)     (0.0737)
Change in log enrollment                   0.7273
                                          (0.0411)
Change in log total                        0.0678
  assessed value per                      (0.0185)
  pupil
Fixed effects for             No           No
  districts?
Adjusted [R.sup.2]            0.0774       0.4779
Number of districts         488          488
Number of observations     1894         1894
F-statistic for district
  fixed effects
p-value

Regressor                     3            4

Sample definition           Large        Large
Salary gap                 -0.1787      -0.1532
                           (0.0959)     (0.0929)
Change in log enrollment                 0.4560
                                        (0.0568)
Change in log total                      0.0549
  assessed value per                    (0.0219)
  pupil
Fixed effects for            Yes          Yes
  districts?
Adjusted [R.sup.2]            0.5582       0.6123
Number of districts         488          488
Number of observations     1894         1894
F-statistic for district      5.2209       2.3434
  fixed effects
p-value                       8.2E-130     3.63E-34

Regressor                     5            6

Sample definition             Small        Small
Salary gap                   -0.3390      -0.3133
                             (0.1294)     (0.1223)
Change in log enrollment                   0.3925
                                          (0.0809)
Change in log total                        0.0674
  assessed value per                      (0.0230)
  pupil
Fixed effects for             No           No
  districts?
Adjusted [R.sup.2]            0.0133       0.1160
Number of districts         572          572
Number of observations     2233         2233
F-statistic for district
  fixed effects
p-value

Regressor                     7            8

Sample definition             Small        Small
Salary gap                   -0.5955      -0.5562
                             (0.2198)     (0.2231)
Change in log enrollment                   0.2495
                                          (0.1043)
Change in log total                        0.0682
  assessed value per                      (0.0337)
  pupil
Fixed effects for            Yes          Yes
  districts?
Adjusted [R.sup.2]            0.2551       0.2814
Number of districts         572          572
Number of observations     2233         2233
F-statistic for district      2.2662       1.8972
  fixed effects
p-value                       8.37E-37     7.05E-23

Dependent variable is change in log full-time equivalent teacher
employment. Standard errors (in parentheses) are computed using
formulas robust to heteroskedasticity and second order serial
correlation. Year dummies included for all years (coefficient
estimates not shown to save space). Data for the years 1995-1996
and 1997-1998 are one-year differences, while data for the years
1996-1997 and 1998-1999 are two-year differences. "Large" subsample
contains all observations with more than 1000 students. "Small"
subsample contains all observations with fewer than 1000 students.

Table A3. Ordinary Least Squares Results for South Carolina School
Districts with Quadratic Terms in Enrollment and Assessed Valuation

Regressor                         1            2            3

Sample definition                 All          All          Metro
Salary gap                       -0.2764      -0.1760      -0.2376
                                 (0.0718)     (0.1137)     (0.1255)
Change in log enrollment          0.4370       0.2115       0.5691
                                 (0.0598)     (0.0739)     (0.0746)
Change in log total               0.0212       0.0182       0.0706
  assessed value per pupil       (0.0083)     (0.0080)     (0.0191)
Change in log enrollment          0.9684       0.9058       1.4805
  squared                        (0.6825)     (0.6970)     (0.9150)
Change in log total assessed     -0.0097      -0.0134      -0.0359
value per pupil squared          (0.0031)     (0.0034)     (0.0114)
Fixed effects for districts?      No          Yes           No
Adjusted [R.sup.2]                0.2087       0.2175       0.3307
Number of districts              91           91           40
Number of observations         1163         1163          516
F-statistic for district                       1.1419
  fixed effects
p-value                                      0.1805

Regressor                         4            5            6

Sample definition               Metro       Nonmetro     Nonmetro
Salary gap                       0.0690      -0.1865      -0.2413
                                (0.1603)     (0.0938)     (0.1663)
Change in log enrollment         0.2809       0.3111       0.1711
                                (0.0837)     (0.0891)     (0.1074)
Change in log total              0.0719       0.0019       0.0024
  assessed value per pupil      (0.0167)     (0.0124)     (0.0121)
Change in log enrollment         0.6693       0.7587       0.9880
  squared                       (0.8926)     (0.8568)     (0.9086)
Change in log total assessed    -0.0467      -0.0106      -0.0099
value per pupil squared         (0.0104)     (0.0045)     (0.0047)
Fixed effects for districts?     Yes           No          Yes
Adjusted [R.sup.2]               0.3863       0.1353       0.1095
Number of districts             40           51           51
Number of observations         516          647          647
F-statistic for district         2.1570                    0.6350
  fixed effects
p-value                          0.0001                    0.9764

Regressor                         7            8

Sample definition                Large        Large
Salary gap                      -0.2187       0.0135
                                (0.1183)     (0.1495)
Change in log enrollment         0.6604       0.3680
                                (0.0616)     (0.0868)
Change in log total              0.0380       0.0281
  assessed value per pupil      (0.0224)     (0.0246)
Change in log enrollment         1.1626      -0.0330
  squared                       (1.1481)     (0.9475)
Change in log total assessed     0.0149       0.0315
value per pupil squared         (0.0766)     (0.0838)
Fixed effects for districts?      No          Yes
Adjusted [R.sup.2]               0.3799       0.3939
Number of districts             47           47
Number of observations         559          559
F-statistic for district                     1.2722
  fixed effects
p-value                                      0.1150

Regressor                         9            10

Sample definition                Small        Small
Salary gap                      -0.2344      -0.2804
                                (0.0963)     (0.1677)
Change in log enrollment         0.3275       0.1676
                                (0.0813)     (0.0908)
Change in log total              0.0137       0.0135
  assessed value per pupil      (0.0104)     (0.0094)
Change in log enrollment         0.9120       0.8397
  squared                       (0.8061)     (0.8323)
Change in log total assessed    -0.0067      -0.0151
value per pupil squared         (0.0047)     (0.0040)
Fixed effects for districts?      No          Yes
Adjusted [R.sup.2]               0.1329       0.1275
Number of districts             51           51
Number of observations         603          603
F-statistic for district                      0.9278
  fixed effects
p-value                                       0.6164

Dependent variable is change in log full-time equivalent teacher
employment. Standard errors (in parentheses) are computed using
formulas robust to heteroskedasticity and second- order serial
correlation. Year dummies included for all years (coefficient
estimates not shown to save space). "Large" subsample includes
observations with more than 4000 students. "Small" subsample
includes observations with fewer than 4000 students.

Table A4. Ordinary Least Squares Results for Texas School
Districts with Quadratic Terms in Enrollment and Assessed Valuation

Regressor                          1             2             3

Sample definition                 All           All           Metro
Salary gap                       -0.2792       -0.4093       -0.2414
                                 (0.0804)      (0.1367)      (0.1492)
Change in log enrollment          0.5058        0.2954        0.5734
                                 (0.0669)      (0.0936)      (0.0826)
Change in log total               0.0910        0.0743        0.0941
  assessed value per pupil       (0.0191)      (0.0212)      (0.0299)
Change in log enrollment         -0.6533       -0.4720        0.4575
  squared                        (0.4380)      (0.4972)      (0.4330)
Change in log total assessed      0.0059        0.0011       -0.0171
value per pupil squared          (0.0554)      (0.0488)      (0.0755)
Fixed effects for districts?      No            Yes           No
Adjusted [R.sup.2]                0.2006        0.3577        0.3387
Number of districts            1033          1033           402
Number of observations         4127          4127          1606
F-statistic for district                        1.9699
  fixed effects
p-value                                         6.76E-45

Regressor                          4             5             6

Sample definition                 Metro        Nonmetro      Nonmetro
Salary gap                       -0.3645       -0.2088       -0.3951
                                 (0.1536)      (0.1029)      (0.1843)
Change in log enrollment          0.1151        0.4025        0.2816
                                 (0.0681)      (0.0811)      (0.1034)
Change in log total               0.0622        0.0548        0.0673
  assessed value per pupil       (0.0326)      (0.0248)       (0.0263
Change in log enrollment          1.2631       -0.9108       -0.7220
  squared                        (0.3500)      (0.4794)      (0.5422)
Change in log total assessed     -0.0528        0.0548        0.0320
value per pupil squared          (0.0637)      (0.0667)      (0.0612)
Fixed effects for districts?      Yes           No            Yes
Adjusted [R.sup.2]                0.4986        0.1513        0.2958
Number of districts             402           631           631
Number of observations         1606          2521          2521
F-statistic for district          2.2536                      1.8092
  fixed effects
p-value                           2.79E-26                    8.56E-22

Regressor                          7             8

Sample definition                 Large         Large
Salary gap                       -0.1430       -0.1554
                                 (0.0717)      (0.0920)
Change in log enrollment          0.7250        0.4262
                                 (0.0381)      (0.0593)
Change in log total               0.0791        0.0631
  assessed value per pupil       (0.0246)      (0.0304)
Change in log enrollment          0.0272        0.3016
  squared                        (0.4979)      (0.4242)
Change in log total assessed     -0.0956       -0.0767
value per pupil squared          (0.0726       (0.0804)
Fixed effects for districts?      No            Yes
Adjusted [R.sup.2]                0.4792        0.6132
Number of districts             488           488
Number of observations         1894          1894
F-statistic for district                      2.3254
  fixed effects
p-value                                      1.81E-33

Regressor                          9            10

Sample definition                 Small         Small
Salary gap                       -0.3038       -0.5697
                                 (0.1210)      (0.2159)
Change in log enrollment          0.4217        0.2712
                                 (0.0777)      (0.1058)
Change in log total               0.0634        0.0708
  assessed value per pupil       (0.0266)      (0.0300)
Change in log enrollment         -0.8164       -0.5573
  squared                        (0.4624)      (0.5189)
Change in log total assessed      0.0446        0.0164
value per pupil squared          (0.0629)      (0.0533)
Fixed effects for districts?      No            Yes
Adjusted [R.sup.2]                0.1487        0.2916
Number of districts             572           572
Number of observations         2233          2233
F-statistic for district                        1.7761
  fixed effects
p-value                                         1.33E-18

Dependent variable is change in log full-time equivalent teacher
employment. Standard errors (in parentheses) are computed using
formulas robust to heteroskedasticity and second order serial
correlation. Year dummies included for all years (coefficient
estimates not shown to save space). Data for the years 1995-1996
and 1997-1998 are one-year differences, while data for 1996-1997
and 1998-1999 are two-year differences. "Large" subsample includes
observations with more than 1000 students. "Small" subsample
includes observations with fewer than 1000 students.


This paper has benefited from helpful comments on earlier drafts by David Harrington and Ronald Oaxaca, by seminar participants at Drake University and Iowa State University, and by anonymous referees.

Received November 2006: accepted February 2008.

References

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William M. Boal, College of Business and Public Administration, Drake University, Des Moines, Iowa 50311, USA; E-mail william.boal@drake.edu.

(1) A related literature examines nursing labor markets, regressing nursing salaries against measures of hospital concentration. Recent contributions include Currie, Farsi, and Macleod (2005) and Hirsch and Schumacher (2005).

(2) About 44% of school district employees in the United States were represented by bargaining units in 1987, and the proportion has likely risen since then (U.S. Bureau of the Census 1991, table 3). More recent editions of the Census of Governments do not tabulate collective bargaining by public employees.

(3) See survey in Freeman (1986, table 6).

(4) Luizer and Thornton (1986) estimate the concentration-salary relationship using data on Pennsylvania school districts in 1981, notwithstanding that more than half of Pennsylvania's school employees were covered by collective bargaining agreements (U.S. Bureau of the Census 1984, table 3). Landon and Baird (1971) estimate the concentration-salary relationship using data on 136 school districts in the United States in 1967, notwithstanding that, in 1972, more than one-quarter of U.S. school districts engaged in collective bargaining (U.S. Bureau of the Census 1975, table 3).

(5) This peculiar effect was apparently first noted by Stigler (1946). Of course, a very high minimum wage causes a decrease in employment in a monopsonized labor market, just as it does in a competitive labor market (see section 2).

(6) Among southeastern states, Alabama, Arkansas, Delaware, Georgia, Kentucky, Louisiana, Mississippi, North Carolina, Oklahoma, South Carolina, Tennessee, Texas, and West Virginia have state minimum salary schedules, but Florida, Maryland, and Virginia do not (Gale F. Gaines, Southern Regional Education Board, personal communication, June 9, 2000).

(7) Despite the absence of unions, teacher salaries in these states are not especially low compared to other states. South Carolina ranked 28th and Texas ranked 31st by average teacher salaries in 2004 (U.S. Bureau of the Census 2007, table 240).

(8) Section 1.09 of Texas House Bill 4, part (a). See also Walker and Casey (1996).

(9) U.S. Bureau of the Census (1991, table 3).

(10) Hirsch and Macpherson (2003).

(11) The following mergers took place during the sample period. In the summer of 1986, Dorchester 1 and Dorchester 3 merged to form Dorchester 4. Premerger observations on Dorchester 1 and 3 were dropped from the sample. In the summer of 1997, three mergers took place. Orangeburg 3 and Orangeburg 7 merged to form a new Orangeburg 3. Orangeburg 1, Orangeburg 4, and Orangeburg 8 merged to form a new Orangeburg 4. Orangeburg 2, Orangeburg 5, and Orangeburg 6 merged to form a new Orangeburg 5. Postmerger observations on Orangeburg 3, 4, and 5 were dropped from the sample. Enrollment data for the 1999-2000 school year are now available from the state department of education, but the number of teachers and teacher salary schedules are not available.

(12) South Carolina teachers participate in a statewide retirement plan, South Carolina Retirement Systems (http://www.retirement.sc.gov), so pension vesting does not pose a drag on mobility.

(13) South Carolina does offer across-the-board aid when minimum salaries are increased, but the amount awarded to each district is unrelated to the district's existing salaries. See Tetreault and Chandler (2001).

(14) Unobserved time-varying district characteristics might still be correlated with GAP, of course.

(15) Strictly speaking, these F-tests are invalid in the presence of heteroskedasticity or serial correlation.

(16) U.S. Bureau of the Census (1991, table 3).

(17) Hirsch and Macpherson (2003).

(18) Texas school districts with "exclusive consultation" include Corpus Christi, North Forest, San Antonio, South San Antonio, and Austin (Patricia Olshefski, American Federation of Teachers, personal communication, October 18, 1993).

(19) Texas teachers participate in a statewide retirement plan, the Teacher Retirement System of Texas (http://www.trs.state.tx.us), so pension vesting does not pose a drag on mobility.

(20) STA was not awarded after the 1998-1999 school year. Instead, teacher minimum salaries are now tied to overall state aid. See Clark (2001).

(21) Note that the coefficients in Table 9 estimate two-year elasticities; whereas, the coefficients in Tables 7 and 8 estimate an average of one-year and two-year elasticities. Thus, it is not surprising that the coefficients in Table 9 are larger than those in Tables 7 and 8.

(22) Because South Carolina school districts are substantially larger than Texas school districts, one might argue that the evidence for South Carolina may be more relevant to the traditional monopsony model.

(23) This framework is used by Dickens, Machin, and Manning (1999) in their analysis of British Wages Councils.
Table 1. Descriptive Statistics of Raw
Data for South Carolina School Districts

                                           Standard
Variable                           Mean    Deviation   Minimum

Teachers (full-time equivalent)      416         514        33
Salary, bachelor's degree,
  no experience                  $20,120      $2,143   $16,062
Salary, master's degree,
  no experience                  $23,020      $2,453   $18,391
Salary, bachelor's degree,
  10 years' experience           $26,482      $2,827   $21,202
Salary, master's degree,
  17 years' experience           $33,183      $3,549   $26,583
Salary gap                         0.90%       1.53%     0.00%
Enrollment                          7056        8702       467
Total assessed value per pupil   $11,548      $8,381    $2,947
Number of observations = 1163

Variable                         Maximum     Median

Teachers (full-time equivalent)     3728         227
Salary, bachelor's degree,
  no experience                  $25,277     $19,985
Salary, master's degree,
  no experience                  $28,944     $22,860
Salary, bachelor's degree,
  10 years' experience           $33,366     $26,276
Salary, master's degree,
  17 years' experience           $41,835     $32,879
Salary gap                         6.41%       0.00%
Enrollment                        59,135        3827
Total assessed value per pupil   $90,421      $9,690
Number of observations = 1163

Includes a maximum of 91 school districts from the years 1986-1987
through 1998-1999. Some observations were lost because of mergers
of school districts. "Salary gap" is defined as the maximum of zero
and the percent difference between this year's state minimum salary
and last year's actual salary for a teacher with a bachelor's
degree and zero teaching experience.

Source: South Carolina Department of Education (1985-1999),
Rankings of the Counties and School Districts of South Carolina,
various issues.

Table 2. Descriptive Statistics for South Carolina School
Districts by Metropolitan/Nonmetropolitan Location

                                                   Standard
Variable                                   Mean    Deviation   Minimum

School districts in metropolitan
  statistical areas (number of
  observations = 516)
Teachers (full-time equivalent)              630         678        66
Salary, bachelor's degree,
  no experience                          $20,484      $2,192   $16,062
Salary, master's degree, no experience   $23,463      $2,507   $18,391
Salary, bachelor's degree, 10 years'
  experience                             $26,985      $2,893   $21,202
Salary, master's degree, 17 years'
  experience                             $33,865      $3,624   $26,583
Salary gap                                 0.47%       1.13%     0.00%
Enrollment                                10,801      11,455     1,151
Total assessed value per pupil           $13,671     $10,293    $4,312

School districts outside metropolitan
  statistical areas (number of
  observations = 647)
Teachers (full-time equivalent)              245         205        33
Salary, bachelor's degree,
  no experience                          $19,830      $2,059   $16,062
Salary, master's degree, no experience   $22,667      $2,351   $18,391
Salary, bachelor's degree, 10 years'
  experience                             $26,081      $2,709   $21,202
Salary, master's degree, 17 years'
  experience                             $32,638      $3,393   $26,583
Salary gap                                 1.24%       1.71%     0.00%
Enrollment                                  4069        3385       467
Total assessed value per pupil            $9,856      $5,952    $2,947

Variable                                 Maximum     Median

School districts in metropolitan
  statistical areas (number of
  observations = 516)
Teachers (full-time equivalent)             3728         402
Salary, bachelor's degree,
  no experience                          $24,894     $20,464
Salary, master's degree, no experience   $28,505     $23,432
Salary, bachelor's degree, 10 years'
  experience                             $32,861     $26,995
Salary, master's degree, 17 years'
  experience                             $41,201     $33,867
Salary gap                                 6.41%       0.00%
Enrollment                                59,135       7,278
Total assessed value per pupil           $90,421     $11,439

School districts outside metropolitan
  statistical areas (number of
  observations = 647)
Teachers (full-time equivalent)             1019         172
Salary, bachelor's degree,
  no experience                          $25,277     $19,720
Salary, master's degree, no experience   $28,944     $22,531
Salary, bachelor's degree, 10 years'
  experience                             $33,366     $25,905
Salary, master's degree, 17 years'
  experience                             $41,835     $32,383
Salary gap                                 6.41%       0.00%
Enrollment                                 16597        2918
Total assessed value per pupil           $46,103      $8,042

Includes school districts from the years 1986-1987 through
1998-1999. "Salary gap" is defined as the maximum of zero and the
percent difference between this year's state minimum salary and
last year's actual salary for a teacher with a bachelor's degree
and zero teaching experience.

Source: South Carolina Department of Education (1985-1999),
Rankings of the Counties and School Districts of South Carolina,
various issues.

Table 3. Ordinary Least Squares Results for All South Carolina School
Districts

Regressor                            1               2

Salary gap                       -0.3674         -0.2566
                                 (0.0778)        (0.0701)
Change in log enrollment                          0.4633
                                                 (0.0567)
Change in log total assessed                      0.0166
  value per pupil                                (0.0079)
Fixed effects for districts?      No              No
Adjusted [R.sup.2]                0.1241          0.2074
Number of districts              91              91
Number of observations         1163            1163
F-statistic for district
  fixed effects
p-value

Regressor                            3               4

Salary gap                       -0.1224         -0.1640
                                 (0.1116)        (0.1138)
Change in log enrollment                          0.2349
                                                 (0.0687)
Change in log total assessed                      0.0121
  value per pupil                                (0.0082)
Fixed effects for districts?      Yes             Yes
Adjusted [R.sup.2]                0.2010          0.2157
Number of districts              91              91
Number of observations         1163            1163
F-statistic for district
  fixed effects                   2.2280          1.1339
p-value                           2.95E-09        0.1931

Dependent variable is change in log full-time equivalent teacher
employment. Standard errors (in parentheses) are  computed using
formulas robust to heteroskedasticity and second-order serial
correlation. Year dummies included for all years (coefficient
estimates are not shown to save space).

Table 4. Ordinary Least Squares Results for South Carolina
School Districts by Metropolitan/Nonmetropolitan Location

Regressor                      1          2          3           4

Sample definition             Metro      Metro     Metro        Metro
Salary gap                   -0.4186    -0.2278    0.0834       0.0729
                             (0.1328)   (0.1241)   (0.1561)    (0.1590)
Change in log enrollment                 0.5940                 0.2710
                                        (0.0740)               (0.0815)
Change in log total                      0.0368                 0.0296
  assessed value per pupil              (0.0144)               (0.0156)
Fixed effects for              No         No        Yes         Yes
  districts?
Adjusted [R.sup.2]            0.1606     0.3213     0.3485      0.3732
Number of districts          40         40         40          40
Number of observations      516        516        516         516
F-statistic for district                            4.7124      2.0613
 fixed effects
p-value                                             1.02E-16    0.0003

Regressor                      5          6           7          8

Sample definition            Nonmetro   Nonmetro    Nonmetro   Nonmetro
Salary gap                   -0.2050     -0.1708    -0.2044    -0.2316
                             (0.0970)    (0.0913)   (0.1671)   (0.1665)
Change in log enrollment                 0.3315                 0.1968
                                        (0.0827)               (0.1003)
Change in log total                      0.0006                 0.0011
  assessed value per pupil              (0.0131)               (0.0126)
Fixed effects for              No         No         Yes        Yes
  districts?
Adjusted [R.sup.2]            0.1005     0.1357      0.1018     0.1097
Number of districts          51         51          51         51
Number of observations      647        647         647        647
F-statistic for district                             1.0177     0.6311
 fixed effects
p-value                                              0.4432     0.9778

Dependent variable is change in log full-time equivalent teacher
employment. Standard errors (in parentheses) are computed using
formulas robust to heteroskedasticity and second- order serial
correlation. Year dummies included for all years (coefficient
estimates are not shown to save space).

Table 5. Descriptive Statistics for Texas School Districts

                                                Standard
Variable                               Mean    Deviation      Minimum

Teachers (full-time equivalent)          231          645            2
Average salary                       $31,181       $2,617      $18,932
Salary gap                             1.65%        2.04%        0.00%
Enrollment                              3539       10,863           16
Total assessed value per pupil      $217,530     $328,768       $9,801
Number of observations = 4127

Variable                            Maximum       Median

Teachers (full-time equivalent)       11,935           68
Average salary                       $49,187      $31,221
Salary gap                            14.16%        0.78%
Enrollment                           210,988          868
Total assessed value per pupil    $5,398,362     $136,559
Number of observations = 4127

Includes a maximum of 1033 school districts from the years
1995-1996 through 1998-1999. "Salary gap" is defined as salary
transition aid per teacher, as a percent of the average of this
year's average salary and last year's average salary.

Source: Texas Education Agency (1994-1999), various issues.

Table 6. Descriptive Statistics for Texas School
Districts by Metropolitan/ Nonmetropolitan Status

                                               Standard
Variable                              Mean     Deviation   Minimum

School districts in metropolitan
  statistical areas (number of
  observations = 1606)
Teachers (full-time equivalent)           456        979          5
Average salary                        $31,465     $2,440    $22,470
Salary gap                              1.14%      1.63%      0.00%
Enrollment                               7199     16,565         58
Total assessed value per pupil       $168,467   $151,857     $9,801

School districts outside
  metropolitan statistical areas
  (number of observations = 2521)
Teachers (full-time equivalent)            87        134          2
Average salary                        $31,000     $2,709    $18,932
Salary gap                              1.98%      2.20%      0.00%
Enrollment                               1206       2097         16
Total assessed value per pupil       $248,810   $399,768    $19,827

Variable                            Maximum     Median

School districts in metropolitan
  statistical areas (number of
  observations = 1606)
Teachers (full-time equivalent)        11,935        150
Average salary                        $41,319    $31,494
Salary gap                             12.77%      0.36%
Enrollment                            210,988       2247
Total assessed value per pupil     $2,737,836   $131,176

School districts outside
  metropolitan statistical areas
  (number of observations = 2521)
Teachers (full-time equivalent)          1427         46
Average salary                        $49,187    $31,020
Salary gap                             14.16%      1.25%
Enrollment                             21,830        549
Total assessed value per pupil     $5,398,362   $141,454

Includes school districts from the years 1995-1996 through
1998-1999. "Salary gap" is defined as salary transition aid per
teacher, as a percent of the average of this year's average salary
and last year's average salary.

Source: Texas Education Agency (1994-1999), various issues.

Table 7. Ordinary Least Squares Results for All Texas School Districts

Regressor                                           1           2

Salary gap                                       -0.4153     -0.3098
                                                 (0.0841)    (0.0778)
Change in log enrollment                                      0.4693
                                                             (0.0605)
Change in log total assessed value per pupil                  0.0864
                                                             (0.0165)
Fixed effects for districts?                       No          No
Adjusted [R.sup.2]                                0.0287      0.1807
Number of districts                            1033        1033
Number of observations                         4127        4127
F-statistic for district fixed effects
p-value

Regressor                                           3            4

Salary gap                                       -0.4410      -0.4095
                                                 (0.1381)     (0.1394)
Change in log enrollment                                       0.2713
                                                              (0.0849)
Change in log total assessed value per pupil                   0.0696
                                                              (0.0235)
Fixed effects for districts?                       Yes          Yes
Adjusted [R.sup.2]                                0.3206       0.3511
Number of districts                            1033         1033
Number of observations                         4127         4127
F-statistic for district fixed effects            2.7159       2.0483
p-value                                           1.71E-98     2.93E-50

Dependent variable is change in log full-time equivalent teacher
employment. Standard errors (in parentheses) are computed using
formulas robust to heteroskedasticity and second-order serial
correlation. Year dummies included for all years (coefficient
estimates not shown to save space). Data for the years 1995-1996
and 1997-1998 are one-year differences, while data for the years
1996-1997 and 1998-1999 are two-year differences.

Table 8. Ordinary Least Squares Results for Texas School
Districts by Metropolitan/Nonmetropolitan Location

Regressor                          1            2            3

Sample definition                 Metro        Metro        Metro
Salary gap                       -0.2985      -0.2293      -0.3939
                                 (0.1475)     (0.1478)     (0.1405)
Change in log enrollment                       0.6266
                                              (0.0506)
Change in log total assessed                   0.0941
value per pupil                               (0.0263)
Fixed effects for districts?       No           No           Yes
Adjusted [R.sup.2]                0.0635       0.3357       0.4590
Number of districts             402          402          402
Number of observations         1606         1606         1606
F-statistic for district                                    3.9186
  fixed effects
p-value                                                     2.8E-74

Regressor                          4            5            6

Sample definition                 Metro       Nonmetro     Nonmetro
Salary gap                       -0.3459      -0.2377      -0.2419
                                 (0.1485)     (0.1086)     (0.1018)
Change in log enrollment          0.2662                    0.3760
                                 (0.0613)                  (0.0884)
Change in log total assessed      0.0610                    0.0614
value per pupil                  (0.0250)                  (0.0216)
Fixed effects for districts?       Yes          No           No
Adjusted [R.sup.2]                0.4812       0.0120       0.1079
Number of districts             402          631          631
Number of observations         1606         2521         2521
F-statistic for district          2.1188
  fixed effects
p-value                           1.19E-22

Regressor                          7            8

Sample definition                Nonmetro     Nonmetro
Salary gap                       -0.3887      -0.3938
                                 (0.1913)     (0.1895)
Change in log enrollment                       0.2634
                                              (0.1098)
Change in log total assessed                   0.0687
value per pupil                               (0.0321)
Fixed effects for districts?     Yes          Yes
Adjusted [R.sup.2]                0.2467       0.2778
Number of districts             631          631
Number of observations         2521         2521
F-statistic for district          2.2441       1.9389
  fixed effects
p-value                           7.09E-40     5.73E-27

Dependent variable is change in log full-time equivalent teacher
employment. Standard errors (in parentheses) are computed using
formulas robust to heteroskedasticity and second order serial
correlation. Year dummies included for all years (coefficient
estimates not shown to save space). Data for the years 1995-1996
and 1997-1998 are one-year differences, while data for the years
1996-1997 and 1998-1999 are two-year differences.

Table 9. Ordinary Least Squares Results for All
Texas School Districts: Two-Year Differences Only

Regressor                            1               2            3

Sample definition              All districts   All districts    Metro
Salary gap                       -0.5331         -0.5266       -0.3826
                                 (0.1519)        (0.1524)      (0.2142)
Change in log enrollment                          0.2277
                                                 (0.0950)
Change in log total                               0.0666
  assessed value per pupil                       (0.0308)
Fixed effects for districts?        Yes             Yes          Yes
Adjusted [R.sup.2]                0.1364          0.1616        0.3548
Number of districts            1032            1032           402
Number of observations         2063            2063           803

Regressor                            4               5            6

Sample definition                  Metro         Nonmetro      Nonmetro
Salary gap                       -0.3759         -0.6058       -0.6030
                                 (0.2291)        (0.1927)      (0.1909)
Change in log enrollment          0.1500                        0.2505
                                 (0.0788)                      (0.1182)
Change in log total               0.0456                        0.0785
  assessed value per pupil       (0.0304)                      (0.0398)
Fixed effects for districts?        Yes             Yes          Yes
Adjusted [R.sup.2]                0.3600         -0.0069        0.0279
Number of districts             402             630           630
Number of observations          803            1260          1260

Dependent variable is change in log full-time equivalent teacher
employment. Standard errors (in parentheses) are computed using
formulas robust to heteroskedasticity. Year dummy included
(coefficient estimate not shown to save space). Data for the years
1996-1997 and 1998-1999 only: two-year differences.
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Comment:The effect of minimum salaries on employment of teachers: a test of the monopsony model.
Author:Boal, William M.
Publication:Southern Economic Journal
Geographic Code:1USA
Date:Jan 1, 2009
Words:12114
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