Abstract
This article, drawing on a rich panel of administrative data comprising all public school teachers employed in Kentucky from 1997 to 2005, utilizes methods developed in spatial econometrics to test for spatial interdependence in the teacher remuneration policies utilized by public school districts. The results of the best fitting model suggest that a 1 percentage point increase in the salary generosity of a particular district’s distance-weighted neighbors yields a 0.57 percentage point increase in the generosity of salaries within that district, even after controlling for relevant district characteristics and including time and district fixed effects. The results are discussed within the context of state education finance reforms, the school choice movement as well as the continued national focus on improving teacher quality as a primary mechanism to increase student achievement.
Much literature continues to document the difficulty of staffing traditionally disadvantaged schools—defined as those serving higher concentrations of minority students, those in areas demarcated by higher levels of poverty, and those with lower average achievement—with high-quality teachers. This literature has demonstrated that teachers, like other wage earners, balance pecuniary and nonpecuniary benefits when making employment decisions. Increasingly, a robust literature has demonstrated that teachers are sensitive to the availability of alternative labor market opportunities in private schools or in alternative occupations, due in part to the attractiveness of the salaries offered by these opportunities (Murnane and Olsen 1990; Loeb and Page 2000; Vedder and Hall 2000; Ballou 2001; Corcoran, Evans, and Schwab 2004; Eide, Goldhaber, and Brewer 2004). Further, a limited literature finds that higher salaries may function to retain high-quality teachers (Figlio 1997, 2001; Hanushek and Rivkin 2007; Clotfelter et al. 2008). In sum, there are many reasons to suspect that the compensation that a school district provides to its teachers may have important ramifications for the quality of the teachers that it employs and, ultimately, the quality of the education that it provides.
A sizable literature has examined the determinants of teacher salaries. However, very little of that work explicitly considers the influence of salaries paid in geographically proximate districts. Due to the geographic preferences of teachers and the segmented nature of teacher labor markets generally (Boyd et al. 2005; Fowles et al. 2014), it is reasonable to assume that school districts in geographic proximity to each other may influence each other’s salary structures through a number of mechanisms. Whether or not salaries in proximate districts (however defined) influence salaries paid in a particular district is an empirical question. However, the econometric difficulty of correctly specifying the interdependent nature of these effects in empirical models has meant that this is a topic that has received little attention in the literature. As states continue to grapple with redistributive policies designed to equalize educational opportunities across districts with heterogeneous wealth and preferences for education, filling this gap in knowledge is an important step toward achieving such critical goals.
Drawing on a rich panel of administrative data comprising all public school teachers in the state of Kentucky from 1997 to 2005, this article employs methods developed in spatial econometrics to search for spatial interdependence in teacher compensation across proximate school districts over time. Statistically significant evidence of positive spatial interdependence in compensation is uncovered, even after controlling for variables capturing the local socioeconomic and demographic characteristics of the population in a district as well as fixed characteristics of the districts themselves. These results are discussed within the context of Kentucky’s comprehensive education finance reform and the continued national focus on improving teacher quality as a primary mechanism to increase student achievement.
Spatial Dimensions of Teacher Compensation
A robust literature has looked at the determinants of public teacher salaries. This scholarly attention is not surprising, given the magnitude of the enterprise that is public education in the United States. In 2011, public schools across the United States collectively employed 3.3 million full-time equivalent (FTE) teachers, at an average salary of over US$56,000 (in 2011 dollars), an increase in real dollars of over 3 percent compared to a decade earlier (Snyder and Dillow 2012). Various factors have been considered by this literature, including alternative labor market opportunities beyond the classroom (Loeb and Page 2000); collective bargaining (Zwerling and Thomason 1995; Lemke 2004; Babcock, Engberg, and Greenbaum 2005; Cowen 2009; Winters 2011); as well as competition driven by private schools (Hoxby 1994; Vedder and Hall 2000), charter schools (Taylor 2010; Jackson 2012), or voucher programs (Hensvik 2012). However, the bulk of these studies ignore critical finding from the public finance literature, that is, the fact that the financial decisions made by a given jurisdiction are not only determined by the relevant conditions as they exist within that district but also likely influenced by the financial choices of neighboring jurisdictions. Brueckner (2003) terms this interdependence the spatial reaction function.
Brueckner’s (2003) review of the literature identifies two distinct processes through which these interdependencies function, namely, spillover models and resource flow models. Anselin (2002) provides a concise summary of Brueckner’s dichotomy, differentiating the two models by the nature of interjurisdictional effect. Spillover models are those in which a jurisdiction is directly affected by a decision variable chosen by another jurisdiction. A rich literature looking at public sector salaries argues for interjurisdictional wage spillovers, a process through which salaries in neighboring jurisdictions directly affect each other. Scholars have put forth several mechanisms through which these spillovers may plausibly occur. For instance, Babcock and coauthors in a series of articles posit that the collective bargaining strategies utilized by public sector labor unions induce spillovers as the negotiation strategy commonly employed by the union representatives relies on the salaries in comparable jurisdictions (Babcock, Wang, and Lowenstein 1996; Babcock, Engberg, and Greenbaum 2005). However, the unique characteristics of public sector labor markets (as compared to their private counterparts) may imply that these spillovers occur even in the absence of formal collective bargaining. More broadly, the lack of adequate and uniform performance metrics means that citizens face difficulty in evaluating the quality and efficiency of public services. As such, the so-called “yardstick competition” literature suggests that one source of information upon which citizens may rely in evaluating the performance of government is the performance of neighboring jurisdictions, thereby inducing spatial correlation in the service characteristics of spatially proximate governments. This axiom may be particularly true in the educational context as the difficulty of evaluating educational outcomes means that input-based measures may serve as proxy metrics for quality or government’s commitment to education. A rich literature in education and economics finds that teacher salaries often function in this exact role, despite the fact that much empirical work has found teacher salaries and student outcomes to be somewhat weak correlates in aggregate.
Conversely, in resource flow models, jurisdictions affect each other indirectly, that is, the availability of a resource in a particular jurisdiction is affected by the consumption choices made in other jurisdictions (Anselin 2002). In the current context, it is reasonable to suspect that the salaries set by a particular jurisdiction impact the teachers that it is able to employ. When a given district hires a teacher, that teacher is no longer in the potential hiring pool for other districts, making the pool a little more shallow for all other jurisdictions. The extent to which this actually affects other districts depends on the depth of the pool overall. The impact may be minimal if labor markets are large and robust but could be potentially profound if they are small and isolated. Given the literature that demonstrates the limited nature of public teacher labor markets, districts may be setting salaries strategically to secure the top choices out of the local pool of new teachers, to protect its teachers from being poached by other districts, or to poach teachers from other schools, choices that may generate significant external effects on a jurisdiction’s neighbors. As this review demonstrates, there are many reasons to posit spatial interdependence in teacher remuneration policies across neighboring school districts. Even so, this has received comparatively little attention in the empirical literature. The few studies that do exist have mainly relied upon cross sections of data (Wagner and Porter 2000; Ghosh 2010; Winters 2011) or panel data sets collapsed to cross sections by taking averages over time (Greenbaum 2002), thereby ignoring the rich and dynamic variation in district remuneration policies that has occurred over time. Babcock, Engberg, and Greenbaum (2005) present one of the few analyses that utilizes panel data. However, their data are drawn from a highly unionized state, leaving important questions unanswered about the nature of interjurisdictional interdependencies in the absence of collective bargaining.
Regardless of the nature of the data employed, a pragmatic difficulty in searching for spatial effects is determining how “neighbors” are defined and thereby how the spatial weighting matrix utilized in the empirical analysis is specified. Within the context of teacher labor markets, evidence consistently emphasizes the importance of geographic distance as a key driver of the individual employment decisions made by public school teachers (Boyd et al. 2005; Miller 2008; Fowles et al. 2014). These studies concur that public school teacher labor markets are highly regionalized and segmented and demonstrate that the geographic distance between alternative districts functions as the primary driver of such segmentation.
Relying on the common conceptualizations utilized in the extant literature, I therefore specify and empirically examine three alternative connectivity matrices that are defined in geographical terms. First, I use first-order queen contiguity, in which the salary generosity of each of Kentucky’s 175 individual school districts is assumed to be affected only by the jurisdictions with which it shares a border. Second, drawing on the comparative wage index (CWI) data set published by Taylor and Fowler (2006), I create an alternative weighting matrix that defines “neighbors” as districts located within a shared labor market. According to the CWI, Kentucky contains twenty-five such unique labor markets. Finally, I utilize the simple inverse of the geographic distance between districts. Specifically, I calculate this as the as-the-crow-flies distance between the geographic information system coordinates (latitude and longitude) of the school districts’ central offices as reported in the National Center for Education Statistics’ Common Core of Data (NCES CCD). This specification allows all districts to impact each other but presumes that such effects diminish smoothly as the distance between said districts grows. In so doing, I provide comparison of model fit and coefficient size across the three alternative specifications, allowing the results to speak to the relative ranges at which the spatial dynamics are strongest and the distance at which they persist (LeSage and Pace 2010). Given the growing body of work that has shown public teacher labor markets to be small, imperfect, and geographically isolated, one important ramification of the results presented here is to provide researchers with a straightforward, evidence-based strategy to gauge the size and position of such markets that is drawn from actual district wage data. These types of data are becoming increasingly available to scholars and policy makers alike across the various states.
Educational Funding in Kentucky: The Kentucky Education Reform Act (KERA) and Support Education Excellence in Kentucky (SEEK)
Of obvious importance to this study is the context in which it occurs. KERA was enacted by the Kentucky General Assembly in 1990. It introduced broad changes to Kentucky’s system of public education, including dramatic changes to curriculum, testing, and the governance of the schools and districts. It also fundamentally changed the funding mechanisms through which school districts in Kentucky are supported. SEEK is the funding formula that was developed under KERA. The explicit goals of SEEK were to: provide a minimum level of funding for each student regardless of the wealth of the student’s school district; require at least a minimum level of effort to provide funding from each school district; make spending per pupil more equal across Kentucky by basing the amount of state aid per pupil on the wealth of the local school district; and within the constraint of keeping funding per pupil relatively equal, encourage local school districts to increase education funding. (Jacovitch et al. 2002, xiii)
Further, the revenue equalization plan adopted as part of KERA was not accompanied by explicit restrictions or rules with respect to district expenditures. Despite an implicit goal of raising teacher salaries both across the state and especially in traditionally disadvantaged, poor, rural school districts as a mechanism for increasing student performance, boosting teacher salaries was nowhere codified in the reform itself beyond the establishment of a statewide minimum salary schedule. As such, research has demonstrated that dramatic differences remain in terms of district expenditure patterns after the reform and provides little evidence that SEEK funds had a lasting effect on the relative distributions of teacher salaries across districts throughout the state (Hoyt 1999; Streams et al. 2011). The tenacity of these differences, both across jurisdictions and over time, raises important questions about how district finance policies are determined as well as the equity of the education provided across districts of disparate wealth.
Measuring District Salary Generosity
The primary source of data for this analysis is a rich administrative data set made available by the Kentucky Educational Professional Standards Board (EPSB). This data set comprises a census of all certified staff employed in Kentucky public school districts at the individual level for the years 1997–2005; data are unavailable for academic year 1999, so the final analytical sample includes eight academic years. I supplement this data set with data on the individual districts drawn primarily from the U.S. Census Bureau and the NCES CCD. In Kentucky, like many other states, salaries of public school teachers are partially determined by a state law that establishes a statewide minimum salary schedule, which rewards teachers based on two characteristics: experience measured in years and rank, which is a function of educational attainment. The highest rank, rank I, requires a master’s degree and thirty hours of additional course work. Rank II requires a master’s degree. Rank III requires a bachelor’s degree. Ranks IV and V are used for emergency or temporary certification of teachers who are still pursuing a bachelor’s degree. Table 1 displays Kentucky’s statewide minimum salary schedule for public teachers in academic year 2005, the most recent year included in the data.
Kentucky’s Statewide Minimum Salary Schedule for Academic Year 2005
However, as discussed earlier, subject to the local preferences for spending on teachers and the availability of funds, local districts can set salaries higher than this minimum without restriction. There are a number of ways that these increases could be implemented. Most straightforwardly, some or all of the salaries listed in the individual cells in the state’s schedule could be increased. Additionally, districts could create additional categories for teacher rank (increasing the number of columns in the schedule), thereby rewarding progression toward higher ranks before those credentials are completed, or reward higher levels of educational attainment beyond rank I. Finally, districts could choose to increase salaries more frequently than the five-year increments listed in the state’s schedule or that provide salary increases for teachers beyond year twenty, thereby more generously rewarding experience as compared to the state’s minimum schedule (increasing the number of rows).
This complexity introduces some empirical difficulty in developing one metric that captures salary generosity. In surveying the literature, two common metrics utilized in studies of public school teacher salaries are the salary of a hypothetical “typical” teacher or teachers of illustrative characteristics (Greenbaum 2002; Wagner and Porter 2000; Winters 2011; Babcock, Engberg, and Greenbaum 2005) or the unadjusted average salary of all teachers employed in a district (Millimet and Rangaprasad 2007). Measuring the salary of a single hypothetical teacher, even if that teacher is chosen based on the average characteristics of teachers observed in the data or employed in the district, necessarily implies that potentially important salary differences may be overlooked if districts do not uniformly reward education and experience across the pay schedule. Similarly, looking at simple unadjusted average salaries, calculated by summing the salaries paid to all teachers in a district and dividing by the total number of teachers employed, is also limiting in that it inherently cannot distinguish between higher salaries driven by generosity (in the sense that teachers are paid above the state’s required minimums) and higher salaries driven by the characteristics of the individual teachers themselves that command higher salaries by law. Given the tenure process that protects mid- and late-career teachers from termination and the mandated salary increases associated with experience, this is a potentially nontrivial problem.
To avoid these issues, I calculate the generosity of a district’s remuneration policies by matching each teacher to a cell in the statewide minimum salary schedule in effect in that year based on the teacher’s reported rank and experience. I then compare this number to the actual base salary paid to that teacher in the administrative data provided by the EPSB. The ratio of these two numbers provides a measure of the relative generosity of each teacher’s salary. Certainly, base salary is only one part of the total compensation paid to teachers. Total compensation for teachers includes not only base salary but also extra duty pay and nonwage compensation such as health care and retirement benefits. However, there are reasons to suspect that base salary differences comprise the primary margin upon which districts differentially compensate teachers. In general, analysis of the administrative data reveals that extra duty pay is a very small portion of the average teacher’s salary. Preliminary analysis of these data indicates that extra duty pay is most commonly awarded to younger males teaching in high schools, suggesting that the most likely purpose of these funds is to compensate the coaches of athletic teams. Further, all Kentucky public school teachers receive standardized retirement and health benefits in a system managed by the state, so these are not margins on which districts may compete unlike corresponding private labor markets.
In order to generate a metric that captures the overall generosity of a district, I simply calculate the average salary generosity across all teachers employed in a given district in a given year, a number that functions as the dependent variable in the analysis that follows. Specifically, this is calculated as:
where Gjt is the measure of average generosity of district j in year t, Njt captures the number of teachers employed in district j in year t, and Aijt and Mijt capture the actual salary and state minimum required salary, respectively, for teacher i working in district j in year t. This approach circumvents some of the limitations of the measures observed in the extant literature by capturing generosity wherever it exists across the pay scale while simultaneously imposing no assumptions regarding the composition of the teaching workforce as it may exist across districts with respect to education and experience. Table 2 provides some descriptive statistics of this measure disaggregated by academic year and expressed as whole percentages. As the table demonstrates, the actual salaries paid to public school teachers in the state have well exceeded the state minimums for all academic years represented in the data set in even the least generous districts, although a large degree of heterogeneity exists in generosity both across districts and over time.
Descriptive Statistics for District Salary Generosity, Academic Years 1997–2005
Estimation Results
Note: Average direct effects are given within brackets. Standard errors are given within parentheses and are clustered at the district level. Dependent variable: district average salary generosity (percentage). AIC = Akaike’s information criterion; BIC = Bayesian information criterion.
*p < .1 **p < .05 ***p < .01.
Descriptive Spatial Patterns in the Distribution of Salaries
Before proceeding with the multivariate analysis, I first provide some descriptive evidence that corroborates my theoretical supposition regarding the existence of spatial interdependence in salaries across districts. First, figure 1 provides a visual representation of the relative salary generosity of the various districts, averaged over all years in the data set. The districts are grouped by quintile, with darker shades indicating higher relative salaries. As this map demonstrates, there appears to be some clustering of districts with higher relative salaries, evidence that is consistent with spatial interdependence. However, the sheer number of districts as well as the fact that the data employed in the figure are aggregated across all years represented in the data set makes identification of such patterns difficult and, taken in isolation, at best provides only suggestive evidence of spatial interdependence. Further, such descriptive evidence cannot differentiate between observed similarities in salaries driven by observable and unobservable district characteristics that are correlated spatially from similarities driven by underlying interdependencies between districts. These critical limitations motivate the multivariate analysis that follows.
Average district salary generosity by quintile, 1997–2005
Multivariate Model
In order to further test for strategic interdependence in district salaries, I estimate a model specified as:
where i indexes the individual districts, t indexes individual academic years, y is the estimated measure of salary generosity, W is a prespecified matrix of spatial weights defining the connectivity between districts as described earlier, X is a vector of district characteristics described in greater detail subsequently, u and v are sets of district and year indicator variables, respectively, and ∊ is the usual idiosyncratic error term. Aside from the econometric complications introduced by including the spatially lagged dependent variable as a covariate on the right-hand side of the equation, equation (2) is the typical two-way fixed effects model commonly employed in the analysis of panel data. The district fixed effects capture the impact of any time-invariant district characteristics, while the year fixed effects capture the effect of any common temporal shocks affecting all districts.
An econometric issue with estimating equation (2) via methods like ordinary least squares (OLS) is the potential bias introduced by the temporal simultaneity of the spatial lag term. In a shared labor market, salaries in district j affect those in district i in year t and salaries in district i simultaneously affect those in district j in that same year. This simultaneity, if not specifically accounted for in the estimation procedure, introduces bias and inconsistency into estimated coefficients. In general, if we presume positive spatial interdependence, estimating equation (2) via OLS “tends to overestimate the strength of spatial interdependence at the expense of unit-level and exogenous external explanatory factors … which will tend to be consequently underestimated in proportion to their relative correlation with the spatial lag” (Franzese and Hays 2006, 4–5). A common “remedy” to this problem temporally lags the entire spatial lag term by one or more periods, thereby utilizing the passage of time to purge the impact of simultaneity. In practice, this does indeed accomplish this task, but at the cost of introducing omitted variable bias if spatial dependence occurs within, rather than across, time periods. Accordingly, researchers have sought alternative estimators that produce consistent estimates of contemporaneous spatial effects.
One such consistent estimation approach is spatial maximum likelihood (S-ML). The original formulation of this model appears in Ord (1975). The likelihood function employed in S-ML models is built on those utilized for classic linear regression, extending them by specifying the joint likelihood of the dependent variable to incorporate explicitly the spatial interdependence between observations. While conceptually straightforward, this procedure requires the manipulation of N × N matrices at each iteration in the search for a maximum of the likelihood function. This is potentially quite computationally demanding, especially considering the matrix to be manipulated grows exponentially with the sample size.
A second approach observed in the literature is to utilize spatial instrumental variables or spatial generalized method of moments (S-IV/S-GMM). This approach treats the spatial lag as endogenously determined and instruments it using spatially weighted values of exogenously determined variables from other observations. Endogeneity in nonspatial models is a well-known and well-researched problem with a canon of relevant theoretical and empirical literature that is directly applicable to S-IV/S-GMM estimation. As this literature reveals, conditional on appropriate selection of instruments, IV (and, by extension, S-IV/GMM) also produces consistent parameter estimates.
The models presented subsequently are estimated using the S-ML method. This approach was chosen over the S-IV/S-GMM method for two primary reasons. First, as LeSage and Pace (2009) note, advances in modern computing power have rendered the criticism of S-ML models as prohibitively computationally expensive largely moot. Second, I rely on the work of Franzese and Hays (2007) who explore the properties of the two competing consistent estimators through simulation. They compare the relative bias and efficiency of S-ML to S-IV by calculating root mean squared errors of coefficient estimates across simulations that vary both in the strength of interdependence and in sample size, concluding straightforwardly that S-ML weakly dominates S-IV across all simulations. Further, they observe that S-ML has the additional desirable property of exhibiting downward small sample bias versus S-IV’s upward bias, thereby producing more conservative test statistics than S-IV when sample sizes are limited.
I include several relevant, time-varying observable characteristics of the individual districts as controls. First, I include the county-level social capital index created by Rupasingha and Goetz (2008), an index that was updated in 1997 and 2005; the 1997 values are carried forward for the years 1997–2004. This index captures several relevant features of the individual counties in which the school districts reside: the number of membership associations and not-for-profit organizations per 10,000 people, the Census response rate, and the voter turnout rate. This variable is included in order to capture relevant aspects of the local community that might influence teacher salaries. However, the expected effect of this variable is theoretically ambiguous, that is, on one hand, we may imagine that areas with high social capital might hold differing preferences for teacher remuneration, thereby resulting in a positive relationship between social capital and teacher salaries. On the other hand, areas with high social capital are also likely to have greater local amenities. If we assume that teachers value both the salary offered by a district and the availability of local amenities when making employment decisions, we might suppose that higher social capital would decrease the compensating differential necessary to attract and retain teachers (Miller 2008).
Second, I include two relevant characteristics of the local economy: the annualized unemployment rate in the county in which the district is located (drawn from the local area unemployment statistics collected by the US Department of Labor’s Bureau of Labor Statistics) and the county’s per capita income (in constant dollars, drawn from the data collected by the US Department of Commerce’s Bureau of Economic Analysis). Similar to the abovementioned social capital measure, the effects of these variables are theoretically ambiguous. They may imply that higher compensating differentials are required in order to attract teachers. However, it is also likely that these variables capture the general economic conditions of the local jurisdiction that would influence its ability to afford such expenditures. It is reasonable to suspect that the redistribution scheme utilized by the state should imply that the former effect would be stronger than the latter.
Third, I include several relevant characteristics of the school districts themselves that are drawn from the CCD produced by the NCES. I include a variable capturing the overall district size measured as the log of total student enrollments. It may be the case that economies of scale allow larger districts to pay teachers higher wages. Finally, I also include the minority student population, as measured by the total percentage of the district’s students that are black. I include two variables related to district finance, namely, total district revenue per pupil (in real dollars) and the percentage of revenue generated through local taxation, the latter of which, in conjunction with the county-level variables included earlier, is intended to roughly proxy community wealth (Cowen 2009). Note that the two district-level finance variables may be endogenously determined, that is, a district may first set teacher compensation and then adjust revenues to generate sufficient funds to cover salary obligations, resulting in reverse causality and biased coefficients on these variables. Accordingly, some caution is warranted in interpreting the estimated coefficients for these variables.
Results and Robustness Checks
Results
The results of estimating equation (2) utilizing the three alternative weighting matrices are presented in table 3. Reported standard errors for all models are clustered on the individual districts and are robust to arbitrary forms of heteroskedasticity. Additionally, I report both the Bayesian information criterion (BIC) and Akaike’s information criterion (AIC). These statistics provide a simple measure of the relative fit of the specified models. Given that the three estimated models differ only in the specification of the spatial weighting matrix, these statistics permit some evaluation of the various weighting schemes themselves (LeSage and Pace 2010). Both criteria consistently agree that the inverse distance specification is the best fitting model followed by the shared labor market specification, with the contiguous neighbor specification displaying the poorest fit.
ρ, the parameter from equation (2) that captures the effect of the spatially lagged dependent variable, is positively signed across all three models as expected. Focusing on the best fitting model, the natural interpretation of ρ implies that a 1 percentage point increase in the salary generosity of a particular jurisdiction’s distance-weighted neighbors yields a 0.57 percentage point increase in the generosity of a particular district’s base salaries, even after controlling for relevant observable district characteristics; unmeasured, time-invariant district characteristics; and common exogenous shocks. A smaller but still statistically significant relationship is found using the shared labor market specification, and no statistically significant spatial interdependence is found utilizing first-order queen contiguity as the criteria for defining a district’s neighbors. In order to ensure that the “contiguous neighbors” results are unaffected by the omission of salary data from districts in other states that border Kentucky, I estimated the “contiguous neighbors” specification including only those districts located in Kentucky counties that do not border other states. These results are not presented here but are substantively similar to the results presented in table 3.
Before discussing the effects of the other variables, readers should be cautioned that the estimated coefficients for the explanatory variables do not represent marginal effect sizes, as is the case with OLS. The sign and statistical significance of the individual variables are still interpretable in the usual way, but the magnitude of the effects cannot be inferred by coefficient size. This is due to the nature of the specification of the model: changes in an explanatory variable in one district affect the outcome observed not just in that district but in all other districts as well, which in turn affect the outcome in the original district. As such, in addition to reporting the estimated coefficients, I utilize the procedure outlined by LeSage and Pace (2009) and report average direct effects, calculations that align more closely with marginal effects.
Beyond ρ, few of the variables included in the model reach statistical significance at generally accepted levels. No significant relationship is identified between salary generosity and county social capital and unemployment rate. This is not wholly unexpected, given the largely incremental nature at which these variables change and the inclusion of district and year fixed effects in the models. Interestingly, no statistically significant relationship is found between per capita income and teacher salaries across all specifications. Per capita income serves in these models as a proxy measure for two interrelated factors. First, it measures local wealth. If we presume that educational spending, like other types of government spending, is a normal good, then individuals would prefer a higher level of spending on public education as incomes increase. Second, this variable, to some extent, proxies the alternative economic opportunities available to teachers. An increase in local incomes suggests that the local labor market might offer teachers more financial rewarding opportunities in alternative occupations. The two factors operate in an identical direction, suggesting that, as incomes increase, we might expect a corresponding uptick in teacher wages. As shown in table 3, per capita income is positively signed across all specifications but not statistically significant, a finding that contrasts with much of the extant literature. Although the results are not presented here, models estimated utilizing alternative metrics for local wealth and alternative economic opportunity including assessed value of property per capita and Taylor and Fowler’s (2006) CWI yield substantively identical results to those presented in table 3.
Although the exact reason for this departure from the extant literature is unknown, the fact that most articles in this literature employ nonspatial methods offers one possible explanation. If we presume positive underlying spatial interdependence in salaries and positive correlation between local wealth and the spatial lag (i.e., areas with greater local wealth are also areas where the salaries paid to teachers in neighboring districts are higher), then we might expect the estimated effect of local wealth to be upwardly biased due to the omission of the spatial lag as a covariate. While further empirical work is needed to test this explanation, it does in general speak to the importance of considering and explicitly modeling spatial interdependence if such effects are theoretically plausible.
Consistent with expectation, I do find that, all else held constant, as a district grows, it compensates its teachers more generously. Given the dramatic differences that exist in Kentucky (and many other states) in terms of district size, this is a finding that warrants further consideration. In Kentucky, it is the small, rural school districts that have been traditionally lower achieving, a fact that contrasts Kentucky’s context from other states where the primary focus has been on the education disparities between the large, urban districts and their suburban counterparts. Whether the higher salaries are driven by cost advantages associated with economies of scale or some other reason, this finding invariably reinforces long-standing concerns about the ability of the small, rural districts to attract and retain high-quality teachers.
Robustness Checks
In order to evaluate the robustness of the findings, I report the results of running several alternative specifications of equation (2). Because the AIC and BIC presented in table 3 support the inverse distance specification as the superior fit among the three alternatives evaluated, all results presented subsequently utilize that measure of spatial connectivity.
The first robustness check employs an alternative measure of district salary generosity. As discussed earlier, the salary schedules of the individual districts (and perhaps more importantly, the political and administrative processes through which changes to those schedules are made) are not directly observed. Accordingly, one might be concerned that the generosity measure used in the reported results are driven by the germane characteristics (education and experience) of a district’s teachers, rather than the intentional and strategic remuneration choices of the districts themselves. To ensure that the reported are not simply an artifact of the specification of the relative generosity variable, I substitute an alternative measure of salary generosity that does not rely on the salary schedules of the individual districts and reestimate equation (2) utilizing this alternative measure. To generate this measure, I first estimate the following equation:
In this equation, i indexes individual teachers and j the individual districts. The dependent variable, s, is the base salary of a particular teacher; r, e, and e2 are that teacher’s rank (coded as a series of dummy variables), experience in years, and experience squared, respectively; uj is a series of dummy variables indicating the individual districts; and εij is the usual idiosyncratic error term. I estimate this equation separately for each year in the data set, thereby allowing the impact of the covariates to differ over time. Further, I adjust the base salaries for cost-of-living differences across jurisdictions utilizing the Taylor and Fowler’s CWI in order to take into account the regional differences in labor markets.
After estimating these models, I employ the annual estimated coefficients of each of the district dummy variables as my relative measure of district salaries since these coefficients directly capture the average salary differences across districts, after controlling directly for the rank and experience of the teachers as well as local cost of living differences as captured by the CWI. In order to make these individual coefficients comparable across years—and simplify the interpretation of them by omitting the reliance on a base (omitted) district—I standardize each cross section utilizing percentile rankings. This process transforms the vector of individual coefficients into an easily interpretable variable that captures the relative salary generosity of a particular district, as compared to its peers in that year: a fifty indicates salary generosity at the 50th percentile, a ninety-five indicates salary generosity at the 95th percentile, and the like. This measure is employed as the dependent variable in equation (2). The results of estimating this model are presented in column (1) of table 4. Beyond the increase in the magnitude of the coefficients associated with the district size and per-pupil revenue variables, the results are not substantively different from those presented in table 3. Further, the estimated coefficient on the spatial lag term is nearly identical to that presented in the original results.
Robustness Checks
Note: Standard errors are given within parentheses and are clustered at the district level. Weighting matrix: inverse distance.
*p < .1 **p < .05 ***p < .01.
A second concern expressed about the analysis was whether the results are driven by the state’s two large, urban school districts in Lexington (Fayette County Public School District) and Louisville (Jefferson County Public School District). These two districts collectively employ nearly 20 percent of the state’s public teachers and are the only two in the state with student enrollments exceeding 20,000, so we may be concerned that their influence over state teacher labor market dynamics implies that the regression results do not well represent the conditions facing the “typical” district. To evaluate this supposition, column (2) of table 4 presents the results of reestimating equation (2), omitting from the analysis Fayette and Jefferson counties, thereby precluding the remuneration policies of these two districts from driving the results. As the estimates demonstrate, the empirical findings are insensitive to the inclusion or exclusion of these two large, urban districts, suggesting that the competitive dynamics of those areas are not substantively different from those operating in the rest of the state.
Finally, one might be concerned about whether or not equation (2) appropriately models the temporal aspect of spatial interdependence among districts. In the reported results, spatial interdependence is modeled as occurring exclusively within, rather than across, time periods. However, it not unreasonable to suspect that some interdependence could occur across years, implying that the remuneration decisions made in previous years by one’s neighbors impact one’s contemporaneous salary decisions. If so, this implies that equation (2) is misspecified and its estimated coefficients potentially biased. We can evaluate this supposition by reestimating equation (2), extending it by adding the temporal lag of the spatial lag directly as a regressor. Column (3) of table 4 presents the coefficients generated by estimating this model on the data. As these results show, including the time-lagged spatial lag term as a covariate yields a slightly smaller coefficient on the contemporaneous spatial lag term but does not meaningfully change any of the substantive results as presented earlier. Additionally, the estimated coefficient for the time-lagged spatial lag is not itself statistically significant, supporting the choice to model interdependence as occurring within, rather than across, time.
Concluding Remarks
This research uncovers statistically significant and substantively powerful jurisdictional interdependence with respect to teacher salaries across Kentucky public school districts. The fact that this study relies on data from only one state raises important questions about the generalizability of its findings to other contexts. To address this concern, we can look at certain conditions and features of Kentucky and compare them to other states, thereby offering some speculation on how these results may speak to school district behaviors in other areas.
Others in this literature have suggested that the explicit comparisons of salaries in proximate jurisdictions made at the bargaining table, or less officially through active political lobbying by union representatives, drive interdependence in remuneration policies across districts (Babcock, Engberg, and Greenbaum 2005). Although the Kentucky Education Association (the state affiliate of the National Education Association) does maintain a presence in each school district, Kentucky law does not require that districts recognize or engage in collective bargaining with the unions. Rather, the law permits collective bargaining over workplace conditions (including salary), only in the case where the district voluntarily decides to do so, with the caveat that the resultant negotiated contract is approved by all teachers including nonunion members. To date, only one district in Kentucky formally bargains with its teachers over salaries. Further, evidence suggests that the informal political influence of the unions is limited. A recent survey of both the presidents of the local union affiliates and school district administrators revealed that, beyond Jefferson County (the only district that bargains), the teacher associations do not exert a strong influence over school administration or engage in significant lobbying activity for the purpose of influencing district elections and policies (Seiler et al. 2010). As such, alternative mechanisms to explain the observed interdependence must be sought.
One such explanation is that the observed interdependence simply reflects interdistrict competition for teachers. Many states have enacted laws and created new policies and programs that are designed to change the behaviors of public educational agencies by introducing competition for resources. Although Kentucky has enacted limited regulations permitting students in lower-performing schools to enroll elsewhere within district, it has no voucher program and is one of only a handful of states that does not allow charter schools, standing it in marked contrast from many of the states and locales that are most frequently studied by scholars of education policy. Further, the lower population density in the rural areas of the state means that most districts operate very few actual schools, especially at the high school level, implying that competition within a given district for students and state funding is very limited. The confluence of these factors resulted in Kentucky being ranked forty-seventh out of the fifty states in the “Parent Power Index,” a metric created by the Center for Education Reform. It measures whether a state’s education policies “allow a maximum number of parents to actually make choices” with respect to their children’s education. In other words, compared to its peers, Kentucky relies much less on market mechanisms and competition for steering the behaviors of its public schools and districts. Further, Kentucky is comprised of a large number of rural and relatively isolated jurisdictions demarcated by low citizen mobility—the exact conditions that the extant literature argues are likely to give rise to district monopsony power over labor markets.
In summary, Kentucky appears to possess a unique combination of geographic, political, and administrative characteristics that collectively should, all else equal, function to dampen interjurisdictional competition, however defined. Despite this, the results presented here suggest that Kentucky’s school districts do face competitive pressures for labor and respond to that pressure strategically in setting teacher wages. Further, the results from testing the competing weighting matrices suggest that these effects, although primarily localized, do seem to extend beyond the very narrow geographic area in which a district is located. In states with more market-oriented approaches, strong labor unions, or more integrated geographies, it seems reasonable to suspect that these pressures may be more pronounced. As policy makers in many states continue to consider policies adopting a more market-oriented approach to school funding and management, the findings presented here speak to the importance of developing a more holistic understanding of the underlying baseline conditions in which schools and districts currently function. Such knowledge is required in order to gauge the likely impacts of such reforms on educational efficiency, quality, and equity.
Further, given that interjurisdictional differences in per-pupil revenues have shown resilience to the state’s explicit attempts to suppress them, we may be concerned about the distributional consequences of this competition. The ability of local districts to augment revenues means that the districts with the greatest ability to pay high salaries are likely to be those with citizens that already place a high value on education. These also may be the districts where the highest quality teachers are least needed (and potentially least effective, from a value-added perspective). The competitive pressure that wealthier districts exert on their neighbors may mean that districts with more restricted revenues are forced to augment teaching salaries to remain competitive, inducing budgetary shortfalls in other areas. Surveys conducted by the American Association of School Administrators demonstrate that many administrators across the United States have responded to the budgetary shortfalls associated with the recent recession by increasing class sizes, eliminating summer and nonacademic programs, cutting extracurricular activities, and reducing transportation availability, in addition to cutting noncertified staff (Ellerson 2012). If competitive pressure on teacher salaries yields similar trade-offs, the net effect may be an exacerbation of inequality among districts that is not accounted for (or intended by) current policy. As Kentucky and other states continue to struggle with improving the educational attainment of underserved areas, these are issues that deserve further attention.
Footnotes
Acknowledgments
The author would like to thank Eugenia Toma, Luke Miller, and the anonymous reviewers for their valuable comments and suggestions. Additionally, I extend my thanks to Terry Hibpshman and the staff of the Kentucky Educational Professional Standards Board for their willingness and assistance in making the administrative data available for research purposes, and to the Spencer Foundation for funding the collection of the administrative data under the project title Teaching Careers in Rural Schools (Grant no. 201000055).
Declaration of Conflicting Interests
The author declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.
Funding
The author disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This research received no specific grant from any funding agency in the public, commercial, or not-for-profit sectors.