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Estimating the Firms Labor Supply Curve in a New Monopsony Framework: Schoolteachersin MissouriAuthor(s): Michael R Ransom and David P. SimsSource: Journal of Labor Economics, Vol. 28, No. 2, Modern Models of Monopsony in LaborMarkets: Tests and Estimates. Papers from a Conference Held in Sundance, Utah, November2008, Organized by Orley Ashenfelter, Henry Farber, and Michael Ransom. Alan Manning,Editor. Sponsored by Industrial Relations Section, Princeton University (April 2010), pp. 331-355Published by: The University of Chicago Press on behalf of the Society of Labor Economists and theNORC at the University of ChicagoStable URL: http://www.jstor.org/stable/10.1086/649904 .Accessed: 14/06/2011 08:48

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331

[Journal of Labor Economics, 2010, vol. 28, no. 2] 2010 by The University of Chicago. All rights reserved.0734-306X/2010/2802-0002$10.00

Estimating the Firms Labor SupplyCurve in a New Monopsony

Framework: Schoolteachersin Missouri

Michael R Ransom, Brigham Young University

David P. Sims, Brigham Young University

In the context of certain dynamic models, it is possible to infer theelasticity of labor supply to the firm from the elasticity of the quitrate with respect to the wage. Using this property, we estimate theaverage labor supply elasticity to public school districts in Missouri.We leverage the plausibly exogenous variation in prenegotiated dis-trict salary schedules to instrument for actual salary. These estimatesimply a labor supply elasticity of about 3.7, suggesting that school

districts possess significant market power. The presence of monop-sony power in this teacher labor market may be partially explainedby its institutional features.

I. Introduction

There have been few attempts to estimate the labor supply elasticity toindividual firms. In their survey of monopsony in the labor market, Boaland Ransom (1997) discussed only four studies that examine the question.

We acknowledge helpful comments on this paper by Peter Kuhn, Ted To, AlanManning, and other participants at the October 2008 Monopsony in the LaborMarket conference held at Sundance, Utah. We also are grateful for comments

on earlier versions of the paper by David Card and John Pencavel. Daniel Oakesand Brigham Wilson provided helpful research assistance. We express gratitudeto Bruce Moe of the Missouri State Teachers Association for providing data on

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332 Ransom/Sims

Mannings (2003) recent book mentions another three, more recent papers.This dearth of research is somewhat surprising, as the elasticity of thelabor supply curve has important implications for labor market policiessuch as the minimum wage.

Although this small pool of research partly reflects the technical dif-ficulty of estimating the firms labor supply curve (due in part to a lackof convincing natural experiments or instruments to solve the inherentendogeneity problem), a more likely explanation may lie in the skepticismabout the Robinsonian model of single-firm monopsony (Robinson 1969),which was thought to be of limited empirical relevance. However, recenttheoretical models of the labor market suggest that individual firms mayface upward-sloping labor supply curves even in markets with many com-peting firms. For example, Bhaskar and To (1999) propose a model of

monopsonistic competition. In a much different approach, Manning (2003)develops the implications of a search model that also yields upward-slopinglabor supply curves to a firm, even when there are many firms in the labormarket.

We posit a dynamic model of labor market monopsony. In a model ofthe sort that Manning proposes, the elasticity of labor supply to the firmcan be described in terms of the elasticity of quits to the wage, providinga convenient way to estimate the firms labor supply elasticity. We adoptthis approach to examine the labor supply elasticity for a well-definedskilled labor force, teachers in Missouri school districts during the 1980s.

This is a promising setting in which to examine labor supply to thefirm. First, it is clear that the work teachers do is very similar across

districts within a single state, as the state sets the curriculum and certifiesteacher skill level. Also, the labor market for schoolteachers has oftenbeen suggested as a likely place to observe monopsony power (see Beck[1993] for an example and a survey of the literature). Furthermore, thewidespread public collection of education data means we can control fora variety of pertinent worker and workplace characteristics. Finally, wehave salary schedule data for many Missouri districts that allow us toconstruct instruments to correct for measurement error in salaries, thepotential confounding effects of unobserved teacher characteristics, orother sources of endogeneity. In our analysis, we estimate much largerelasticities when we control for these sources of endogeneity. Such en-dogeneity may explain why Manning (2003, chap. 4) estimates such smalllabor supply elasticities in his analysis of large panel data sets, for whichthis sort of instrument is not available.

salary schedules and to Paul Beck of Graceland College, who provided his col-lection of data from the Missouri Department of Elementary and Secondary Ed-ucation. The Missouri State Census Data Center also provided U.S. Census dataaggregated to match school district boundaries.

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334 Ransom/Sims

It follows that, in a steady state,

s(w)N(w) p R(w)

or

N(w) p R(w)/s(w), (1)

which can be interpreted as the long-run labor supply function to thefirm, since it is based on a steady-state equilibrium. In elasticity terms,this dynamic labor supply function can be written as

p . (2)Nw Rw sw

This provides a basic framework from which the elasticity of labor

supply to the firm might be estimated. However, as Manning (2003, 97)points out, estimating the elasticity of recruits with respect to the wageis conceptually difficult. The Burdett-Mortensen-Manning model pro-vides a powerful insight into the relationship between the recruitmentand separation elasticities. In that model, the recruit to one firm is theseparation from another.1 The number of recruits that a firm might gainby increasing its offered wage is exactly the same magnitude as the numberof quits that would be deterred. Thus, the recruitment elasticity is simplythe negative of the separation elasticity (see Manning [2003, 97] for aformal derivation of the result). Therefore, the elasticity of labor supplyto the firm can be written as

p p 2 . (3)Nw Rw sw sw

This result makes it possible to estimate the firms labor supply elasticityonly from information on the firms separations, conceptually a straight-forward task if the necessary data are available.

Strictly, the simplification expressed in equation (3) derives from a verystylized model of the labor market. Many of the predictions of the Bur-dett-Mortensen model are clearly inconsistent with known facts aboutthe labor market, as Kuhn (2004) points out in his thoughtful critique.

While we recognize such criticism, we believe that there is at leastintuitive support for estimating the labor supply elasticity to the firm byequation (3). Essentially, our approach relies on two crucial results, bothof which we argue are likely to hold outside the strict Burdett-Mortensenframework. The first is that dynamic labor supply to the firm may be

upward sloping, a result consistent with much more general versions ofthe search model, such as Mortensen (2003) or Bontemps, Robin, and

1 Actually, the firm may also hire unemployed workers, but in the Burdett-Mortensen model, unemployed workers will accept any wage offered, so increas-ing the wage does not increase the number recruited from unemployment.

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Estimating a Firms Labor Supply Curve 335

van den Berg (1999), as well as alternative models of monopsony such asBhaskar and To (1999).

The second essential result is that recruitment and separation elasticitiesare equal in absolute value. The insight that one firms quit is anotherfirms recruit has strong intuitive appeal. Those who quit must (usually)end up working for another employer who provides a better job. It ishard to imagine how the size of one employers gain from offering ahigher wage can be much different than the size of the loss suffered byanother because it offers a lower wage. However, like many steady-stateresults, the equality between recruitment and separation elasticities mightbe better viewed as an approximation.

III. Data

The analysis makes use of data from several sources. The data aboutindividual schoolteachers as well as some district characteristics comefrom the Missouri Department of Elementary and Secondary Education(MSDESE) census of teachers. For the 198889 and 198990 school yearsthis provides the actual salary, fraction of time employed (full-time equiv-alent), years total teaching experience, years seniority in current district,and highest educational degree held, along with a unique identificationnumber for each teacher.

Most school districts in Missouri have established a salary schedulea guideline that defines the salary in terms of the teachers highest degreeand seniority and, in some cases, teaching experience in other districts.Each year the Missouri State Teachers Association (MSTA) surveys dis-

tricts in the state and collects salary schedules from those that respondto their survey. From this survey we obtain the salary point for a teacherwith a bachelors degree and no experience, referenced hereafter as thebase salary, and calculate the average pay increase from moving up onestep on the schedule (the salary increase that results from one additionalyear of seniority), which we refer to as the salary slope. Not all districtsrespond to the MSTA survey, and not all districts that do respond havea salary schedule in place, but most districts (451 of 540) provided basesalary information for the 198889 year (which will be the primary focusof this analysis), and all but 13 of those provide enough information tocalculate a slope measuring expected salary increases. Additional char-acteristics of Missouri school districts, such as student averages for race,ethnicity, IEP (special education) status, and free lunch eligibility as wellas per pupil spending data for the 198990 school year, come from theNational Center of Education Statistics Common Core of Data.

The final source for data is the 1990 Decennial Census of the UnitedStates, from which we have obtained variables that measure the urbanstatus and economic characteristics of residents who live within the dis-

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336 Ransom/Sims

Table 1Descriptive Statistics, Individual Teachers

Variable Mean (SD)

Separation (p1 if left 1988 job) .098 (.297)FTE Salary 25,856 (6,863.102)FTE .992 (.060)Female .749 (.434)BA/BS Degree .564 (.496)MA Degree .405 (.491)Specialist Degree .017 (.129)Doctorate Degree .004 (.062)Years Teaching Experience 13.525 (8.620)Years Tenure with District 10.627 (7.988)Number of Pupils in District 10,012 (13,151)Kansas City MSA .198 (.399)St. Louis MSA .318 (.466)

St. Joseph MSA .021 (.143)Springfield MSA .049 (.216)Columbia MSA .020 (.141)Joplin MSA .028 (.165)

Note.N p 49,357.

trict. These variables include the percentage of the population of a schooldistrict that lives in a rural area, population density, and the median house-hold income in each district. These data have been aggregated from censusgeographical units to match the school district boundaries by the Officeof Social and Education Data Analysis of the Missouri State Census DataCenter.

There were a total of 49,874 teachers in the MSDESE data for the198889 school year, of which 177 had a full-time equivalent (FTE) ofzero or missing. Of the remaining 49,697, there were 340 teachers workingat less than 50% FTE, and these have been excluded from the sample.This number represents less than 0.7% of the sample. Table 1 summarizesthis individual-level data.

A separation occurs if a teacher who was present in the 198889school year is not present in the 198990 school year, or if the teacherworks for a different district in the latter year. The overall separation rateis just less than 10%. Average full-time-equivalent salary is $25,856 for1988, although the data indicate a range from $505 to $91,692. Both theseextremes are likely the result of some sort of clerical error, as there areonly 23 recorded salaries below $5,000 and one above $65,000. The fol-lowing analysis includes all observations, but results are not sensitive toomitting these 24 outliers.

Slightly more than 50% of all teachers work for districts located in theSt. Louis or Kansas City metropolitan areas. The average teacher teachesin a district that contains about 10,000 students, although the number ofstudents in a district ranges in value from 14 to 46,128 and is highlyskewed in distribution.

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Table 2Descriptive Statistics, District Averages

VariableAll Districts

(1)Base Salary Districts

(2)

Separation Rate .143 (.114) .136 (.098)District Base Salary . . . 16,141.76 (1,966.18)Average Salary Slope . . . 322.78 (176.47)FTE Salary 21,125 (3,894) 21,627 (3,926)Log Salary 9.935 (.162) 9.958 (.160)Number of Pupils in District 1,485 (3,478.877) 1,599 (3,113)Number of Teachers 91.419 (227.009) 96.8 (189.7)District Population Density .257 (.912) .288 (.937)District Fraction Rural .796 (.337) .763 (.352)Log of Median Household Income 9.964 (.278) 9.977 (.281)Fraction Free Lunch Eligible .285 (.156) .273 (.152)Fraction IEP .122 (.054) .119 (.048)

Fraction Black Students .039 (.114) .043 (.118)Fraction Hispanic Students .003 (.009) .003 (.007)Per Pupil Expenditures 4,242.370 (1,120.514) 4,134.634 (1,046.272)Kansas City MSA .085 (.279) .093 (.291)St. Louis MSA .104 (.305) .118 (.322)St. Joseph MSA .015 (.121) .016 (.124)Springfield MSA .035 (.184) .033 (.180)Columbia MSA .022 (.148) .024 (.154)Joplin MSA .011 (.105) .011 (.105)N 540 451

Table 2 presents the district aggregate data. Column 1 considers alldistricts in the sample. The separation rate for the average district is about14%. This reflects the skewness of school district size. Smaller districtstend to have higher separation rates, and most districts are small. Similarpatterns are also visible in other variables, such as the number of pupilsin the district or the metropolitan area dummies. The average district hasonly about 1,500 students, while the average teacher is employed by adistrict that has about 10,000 students! All of these results reflect the factthat the majority of the districts in the state are small and rural, whilethere are a few very large districts. Column 2 considers the subsample ofdistricts for which base salary data are available. A comparison of thecolumns does not reveal any striking (or indeed statistically significant)differences in most characteristics, but it shows a number of small dif-ferences consistent with the fact that the smallest school districts, thosewith fewer than 25 teachers, are less likely to have a salary schedule.

Figure 1 displays the geographical boundaries of school districts inMissouri and shows the relative size in terms of number of studentsenrolled. The map also outlines the boundaries of the six MetropolitanStatistical Areas (MSAs) in Missouri. It is clear from the map that almostall districts in Missouri are quite small. The few large districts are typicallylocated in the principal cities of MSAs. Even the largest metropolitanareas of the state contain some small school districts.

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338 Ransom/Sims

Fig. 1.Enrollment levels by district

Figure 2 illustrates the geographical distribution of base salaries across

school districts. The blank areas represent districts for which we do nothave a base salary. There is no obvious geographical pattern of missingdata. Darker shading indicates higher salaries. Although districts withinthe Kansas City and St. Louis metro areas appear to have higher salaries,it is also apparent that there is a fairly large amount of geographicalvariation in base salaries, even in areas of the state that are clearly ruralin nature.

IV. Estimation Strategy

A. Background

The task at hand, essentially, is to estimate the elasticity of separationswith respect to the wage. There is already a large literature in labor eco-nomics that examines separations. Much of this literature concentrates onthe relationship between demographic characteristics and the likelihoodof quitting or being laid off, and although these issues are related to thisstudy, they are not particularly relevant to the analysis. This literature issurveyed, for example, in Farber (1999).

More germane are a number of studies that examine the sensitivity of

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Fig. 2.Base salary, 198889 by district

quits to wages, such as Pencavel (1972) and Parsons (1972). In fact, thePencavel model has some search-theoretic elements, including the mo-nopsonistic idea that the firm can influence the turnover rate by choosing

a high or low wage. However, most of this literature focuses on thequestion of specific human capital, since turnover is particularly costlyfor firms and workers in industries in which there is a large amount ofspecific training. District- or school-specific human capital is probablyrelatively unimportant in the market for public school teachers, as statesset the curriculum. What an instructor teaches in one school she could

just as well teach in another.Although these previous papers do not address the issue of the labor

supply to the firm directly, a few recent studies apply a similar approachto estimate labor supply to the firm. Mannings (2003) book containsextensive empirical analyses, some of which are comparable to the analysispresented here. Ransom and Oaxaca (2010, in this issue) and Hirsch,Schank, and Schnabel (2010, in this issue) estimate models that are similarto ours in order to explain differences in pay between men and women.

B. Identification Strategy

The primary obstacle to estimating a separation elasticity and, hence,an elasticity of labor supply to the firm is likely to be an identification

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340 Ransom/Sims

issue. To see this, consider estimating a regression of a dichotomous in-dicator for teacher separations on the natural logarithm of teacher salarywith the goal of converting the parameter estimate into a separation elas-ticity (through dividing by the average separation rate) as in the followingequation:

S p a b ln W , (4)i,d i,d i,d

where i indexes teacher and d district.The variation in observed salaries is likely attributable to a number of

factors, including teacher attributes, union rules, district attributes,districtdesire for a certain workforce size (as suggested in our model), and evenerrors in measuring true salary levels. As a result, the estimate of b pro-

duced by this regression is unlikely to capture the true relationship insofaras many of these unobservable correlates of teacher salary also affectseparation rates.

In particular, we are concerned that teachers may possess unobservableattributes that lead to both differential salaries and different separationrates. Indeed, prior research suggests that teacher attributes beyond ex-perience and possession of an advanced degree are correlated with theirpay levels (Ehrenberg and Brewer 1994; Figlio 1997) as well as withseparation rates (Murnane and Olsen 1989, 1990). Although we will runour regressions at a district level, these characteristics are unlikely to berandomly distributed across schools or districts (Lankford, Loeb, andWyckoff 2002). Also, these characteristics do not necessarily have to beproductive in the sense of improving student learning. For example, cer-

tain types of teacher personalities may be perceived as more accommo-dating to administrators, which may result in higher salaries as well asgreater stability of employment.2

Fortunately, our data allow us to address this potential problem throughthe use of an instrumental variables strategy with the district base salaryand the average slope of its salary increments from the salary schedule asinstruments for actual salary. Since both base salaries and salary incrementsare directly correlated with actual salary, and unlikely correlated with theunobservable characteristics of teachers, they may provide a method ofidentifying the separation elasticity. Such instrumental variables estimatesalso account for the potential attenuation bias due to errors in measuringactual salary.

However, even with this instrumental variables strategy, there are still

remaining threats to identification, most particularly from unobservable

2 Beyond this simple consideration, the salary of a particular individual mayalso represent some match-specific rents. This raises complicated issues that arebeyond the scope of this study but are discussed, for example, in Altonji andShakotko (1987).

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district characteristics. To illustrate this, consider a more generalized re-gression model:

WdS p a b ln X g (5)d d d( )Cd

p a b ln W b ln C X g ,d d d d

where Sd and remain as previously defined, while Cd is a district-ln Wdlevel cost of living index and Xd is a vector including other district char-acteristics that may affect teacher salaries. In this formulation, the firmselasticity of separations with respect to the wage may be calculated as

. An average elasticity is , where is the sample mean sepa- b/S b/S Sdration rate. Although the model does suggest the possibility of identifying

different elasticities for teachers or districts with particular characteristics,we initially confine our interest to estimating the average elasticity.

Equation (5) shows that a cost index is necessary because salary dif-ferentials likely reflect, in part, the higher cost of living in some areas.Furthermore, it is possible that our instruments, especially the base salary,preserve this variation due to cost of living, meaning our instrumentalvariables (IV) specification will fail to consistently estimate b withoutfurther controls. Although exact differences in the cost of living dependon the teachers housing locations, we will assume that housing locationsare closely proxied by job location. Thus, we include the census estimatedmedian household income of the school district in our regressions tocontrol for the salary differential due to locational factors. Recognizingthe limited nature of any single cost index, we also include a populationdensity index for the district and the fraction of the districts residentswho live in rural areas, since some who live in MSAs actually live inthe rural parts of counties. (MSA boundaries follow the boundaries ofcounties, not necessarily the boundaries of the urbanized area of the city.)

Urban economic models of location choice, such as the open citymodel in Mills and Hamilton (1989, 115), explain differences in wagesacross geographical areas as compensating differences for the higher costof housing and/or the longer commutes required of those who live inlarger cities. Since in locational equilibrium the cost of living is the samefor everyone living in the same city, and because all of those living outsideof metropolitan areas experience roughly the same cost of living, thesemodels suggest that another candidate index for the geographical variationin cost of living can be captured with a set of dummy variablesthat identifythe major cities of the state. In this spirit we also present regressions withdummy variable controls for census Metropolitan Statistical Areas of thestate (an approximation to these cities). Our results indicate that usingeither or both methods of accounting for cost of living differences pro-duces similar estimates of the labor supply elasticity.

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342 Ransom/Sims

Beyond the cost of living issues there are other potential district char-acteristic pitfalls. For example, Hanushek, Kain, and Rivkin (2001) showthat teacher separations depend on the race and socioeconomic charac-teristics of the students in the district. If there is some sort of bonuscombat pay attached to districts with those characteristics, this wouldrepresent another potential source of bias. Consequently, we will controlfor student characteristics in all of our regression estimates.

Although we are concerned about the potential effects of both unob-servable teacher and district characteristics on the identification of ourestimates, there is less cause for concern about union influence. Teachersunions in Missouri are prohibited by state law from formal collectivebargaining. The law requires districts to meet and confer with teachersor their representatives. This means that bargaining takes place at the

discretion of the local school district. Teachers are legally proscribed fromstriking and cannot enter into a binding collective bargaining contractwith local school districts. Nevertheless, a more or less formal bargainingprocess does take place in the large St. Louis and Kansas City districts.3

While it is possible that teachers unions exert some influence in the salarydetermination process, this is unlikely to be a source of much salaryvariation as we will show that excluding urban districts will not changeour estimates. Even if unions had a strong role in setting base salaries,our estimates would still be interpretable as the labor supply elasticity tothe firm, regardless of districts inability to exercise the full implied mo-nopsony power.

As our theory suggests that districts set wages to achieve a certain size(in employees) in steady state, an ideal instrument would encapsulate thatpart of teacher salary that reflects the predetermined wage-setting policyof an employer. While the variation in base salary may also reflect costof living and working conditions considerations, we believe we can suc-cessfully control for these undesirable sources of variation. Given a suc-cessful control strategy, the remaining variation in base salary is likely tobe due to differential district-level demand for teachers, exactly what werequire to identify a supply parameter. Estimation then proceeds via two-stage least squares on equation (5) with the natural logarithm of a districtsbase salary as the excluded instrument. The elimination of bias due tounmeasured teacher characteristics and measurement error should lead tosubstantial improvements over the ordinary least squares (OLS) estimatesthat could be produced using standard national data sources.

While the base salary instrument captures level differences betweendistrict compensation policies, the average slope of their schedule capturesdifferences in trajectory. Nevertheless, the variation in the salary slope

3 This information is based on a discussion with Michael Podgursky, professorof economics at the University of Missouri.

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instrument is likely to come from similar sources as the base instrumentsome combination of cross district variation in demand for retaining ex-perienced teachers and a set of district characteristics that affect the teach-ers willingness to supply labor. If we can control for the latter source ofvariation, we can also expect the salary slope instrument to yield consistentestimates, although the teachers for whom it induces variation might notbe representative of Missouri teachers as a whole.

V. Results

A. Estimation

As we will be using district-level variation in salary schedule instru-ments to identify our separation elasticity, working with district-level

observations seems sensible. However, we still wish to account for thefact that observable teacher-level characteristics such as experience arelikely to have an important role in explaining separations and salary levels.Consequently we begin by estimating:

S p a X l d h (6)i,d i,d d i,d

via a linear probability model. The term Si,d is a dummy variable equal toone if the teacher leaves his or her district after the 198889 school year;Xi,d is a vector of teacher characteristics, including experience, time withcurrent employer, sex, and education level; and dd is a district fixed effect.We then form district average residuals from this regression, for eachSddistrict. We use a similar methodology to produce a district-level re-gression adjusted log salary residual, . Regression coefficients forln Wdthese models are reported in table A1.

The regression adjustment allows us to easily see the relationship be-tween salaries and separations at a district level, presented asln W Sd dfigure 3. Note that the separation rate is declining with increases in salaryas expected, although the slope does not appear particularly steep. Also,it appears that several districts had very few separations during this yearand that one of the districts experienced a full turnover of 100% of theirteachers. (That district had only 30 students and three teachers in 1988.)

Figure 4 illustrates the positive bivariate first-stage relationship betweenlog base salary and our district regression adjusted average salary, .ln WdIt also suggests that the positive relationship between base and actualsalary is not confined to large districts. Table 3 provides the regressionestimates of the first-stage relationship and shows a strong positive cor-relation between both potential instruments and actual salaries. This re-lationship persists with the addition of numerous control covariates in-cluding standard metropolitan statistical area (SMSA) fixed effects. TheF-statistic on the null hypothesis that the two instruments jointly havezero effect the first stage is close to 60 in all cases, suggesting that the

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Fig. 3.Relationship of district separation rate and average salary. Size of the circle isproportional to the number of teachers in the district. Both variables are district averagedresiduals from individual level regressions on teacher characteristics.

analysis is unlikely to suffer from weak instrument issues. Also the in-struments and included controls do a good job of explaining cross district

salary differences, with a coefficient of variation of 0.90 in one specifi-cation.

As a benchmark, columns 13 of table 4 present OLS estimates of theelasticity of separations from equation (5), along with the implied elasticityof the labor supply curve to Missouri school districts. Column 1 includescontrols designed to capture differences in the cost of living across dis-tricts. The estimates here suggest that it would require almost a 10%increase in average teacher salary to reduce separations by a single per-centage point. These coefficient estimates are robust to the addition ofother district characteristics in column 2 and the addition of MSA fixedeffects in column 3.4

Because of the lack of sensitivity of separations to wage changes, these

OLS estimates generate a low implied elasticity of labor supply to thefirm, around 1.6. If true, these estimates suggest that Missouri school

4 The use of a Probit model produces similar estimated marginal effects of logsalary on separations, so we do not believe that model linearity is important inour results.

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Fig. 4.Relationship of district base salary and actual average salary. The size of thecircle is proportional to the number of teachers in the district. Adjusted District AverageLog Salary represents district averaged residuals from individual level regressions on teachercharacteristics.

districts have a great deal of power to set wages. A standard measure ofmonopsony power is Pigouvian exploitation:

(MRP w) 1E p p . (7)

w N,w

(See Boal and Ransom [1997, 87] for a discussion.) A profit-maximizingmonopsonist facing a labor supply elasticity of less than two would paya wage less than half of the marginal value of output! Of course, in thecontext of equilibrium search models, the comparison is not quite sostraightforward, as the monopsony power arises from imperfect infor-mation and other frictions in the labor market, and it is likely that labormarket institutions, such as unions, may limit the exercise of this power.Nevertheless, this is an extremely low elasticity of labor supply to thefirm. The OLS estimates here are robust to the choice of covariates.Additional robustness checks not reported in the table find that the onlyspecification that results in estimated elasticities that are much greater inmagnitude is one that eliminates all cost of living controls (includingSMSA fixed effects) from the regression.

In order to provide estimates that will be directly comparable to theinstrumental variable regressions, columns 46 repeat the previous analysis

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346 Ransom/Sims

Table 3First-Stage Estimates of the Total and Base Salary Relationship

(1) (2) (3) (4)

A. Instruments:Log Base Contract Salary .440** .363** .506** .491**

(.048) (.036) (.047) (.048)Average slope of salary schedule .203** .199**

(.035) (.032)Joint F-statistic instruments p 0 57.10 59.39

B. Other controls:District Population Density .002 .009 .000 .001

(.005) (.005) (.004) (.004)District Percent Rural .068** .100** .050** .049**

(.016) (.013) (.014) (.013)Log of Median Household Income .157** .052** .128** .092**

(.016) (.017) (.019) (.018)

Fraction Free Lunch Eligible .002 .028 .004 .008(.030) (.024) (.030) (.030)Fraction IEP .138 .241** .055 .149

(.097) (.081) (.096) (.090)Fraction Black Students .038 .026 .032 .013

(.027) (.030) (.028) (.025)Fraction Hispanic Students .221 .678 .501 .476

(.392) (.615) (.388) (.450)Per Pupil Expenditures (#1,000) .001 .007* .002 .001

(.003) (.003) (.003) (.003)Kansas City SMSA .039** .045**

(.012) (.013)St. Louis SMSA .058** .032*

(.016) (.014)St. Joseph SMSA .012 .032

(.013) (.018)Springfield SMSA .029 .013

(.017) (.012)

Joplin SMSA

.012

.019(.016) (.010)Columbia SMSA .046 .066**

(.025) (.020)R2 .78 .88 .89 .90N 451 451 438 438

Note.The dependent variable is district average of the natural logarithm of teacher salary. Allregressions weighted by the number of teachers in the district. Robust standard errors in parentheses.

* Significant at 5%.** Significant at 1%.

using only those districts that have base salary data available. Figure 2shows the districts for which the base salary data are not available, mostnotably the St. Louis school district, the largest in the state. The effectof salary on separations is not much different from the OLS coefficientobtained from the whole sample, so the IV results discussed below arenot driven by selecting a particular composition of districts. As furtherleast squares estimates using the 438 districts for which both instrumentsare available differ only marginally from those shown in columns 46,we do not report the coefficients.

These instrumental variables estimates are presented in table 5, whose

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Table 4OLS Estimates of the Labor Supply Elasticity to Missouri School Districts

All DistrictsDistricts with Base Salary

Data

(1) (2) (3) (4) (5) (6)

Log Salary .114** .119** .112** .116** .125** .118**(.027) (.027) (.031) (.030) (.030) (.033)

Implied Labor Supply 1.594 1.664 1.566 1.706 1.838 1.735District Population

Density .007** .003 .005 .008** .004 .005(.002) (.002) (.003) (.002) (.002) (.003)

District Percent Rural .009 .016 .018* .015 .020* .021*(.008) (.009) (.009) (.008) (.009) (.009)

Log of Median HouseholdIncome .015 .029* .034* .015 .028* .031*

(.009) (.011) (.014) (.009) (.012) (.014)Fraction Free Lunch

Eligible .023 .023 .018 .017(.023) (.023) (.025) (.025)

Fraction IEP .073 .072 .058 .057(.061) (.061) (.062) (.063)

Fraction Black Students .016 .016 .019 .020(.016) (.016) (.016) (.016)

Fraction Hispanic Students .405 .349 .172 .118(.250) (.281) (.240) (.258)

Per Pupil Expenditures(#1,000) .002 .002 .003 .003

(.002) (.002) (.002) (.002)SMSA fixed effects No No Yes No No YesR2 .30 .32 .33 .32 .34 .34N 540 540 540 451 451 451

Note.Dependent variable is a district separation rate that has been regression adjusted to reflectdifferences in individual level teacher characteristics. All regressions weighted by the number of FTE

teachers in the district. Robust standard errors in parentheses. Joint F-tests fail to reject the hypothesisthat the collective SMSA fixed effects equal zero.* Significant at 5%.** Significant at 1%.

columns contain specifications with control variables that match those ofthe corresponding column in the preceding table. The first three columnsuse the base salary from the salary schedule as the excluded instrument.Here the estimated coefficient on salary is much larger than that estimatedby OLSonly a 4%5% salary increase would be required to producea one percentage point decrease in separation rates. This difference is likelydue to bias in the OLS estimates from some combination of omittedvariables and measurement error. These results, in turn, imply a muchhigher elasticity of labor supply to the firm, although the implied elasticityis still only about 3.7. Furthermore, the parameter on which the elasticityestimate is based is estimated with relatively high precision, and it isevident that the elasticity of labor supply to the firm is much smaller thanthe infinity of the perfectly competitive model. Interestingly, the PigousE for this estimate is still around 27%, which seems rather large. These

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348 Ransom/Sims

Table 52SLS Estimates of the Labor Supply Elasticity to Missouri School Districts

Natural Log of Base SalaryNatural Log of Base Salary,

Salary Slope

Instruments (1) (2) (3) (4) (5) (6)

Log Salary .211** .243** .251** .226** .242** .248**(.064) (.069) (.079) (.050) (.053) (.063)

Implied Labor Supply 3.103 3.574 3.691 3.424 3.667 3.758District Population

Density .009** .003 .004 .009** .003 .003(.002) (.002) (.003) (.002) (.003) (.002)

District Percent Rural .005 .009 .010 .002 .009 .009(.010) (.011) (.011) (.010) (.010) (.010)

Log of Median HouseholdIncome .035* .051** .049** .039** .052** .048**

(.015) (.017) (.018) (.013) (.016) (.017)Fraction Free Lunch

Eligible .016 .012 .017 .013(.026) (.027) (.025) (.025)

Fraction IEP .025 .019 .010 .002(.067) (.070) (.066) (.069)

Fraction Black Students .029 .027 .027 .024(.017) (.017) (.017) (.017)

Fraction Hispanic Students .249 .257 .343 .354(.246) (.272) (.241) (.266)

Per Pupil Expenditures(#1,000) .003 .003 .003 .003

(.002) (.002) (.002) (.002)SMSA fixed effects No No Yes No No YesR2 .31 .32 .32 .30 .32 .32N 451 451 451 438 438 438

Note.Dependent variable is the district separation rate. All regressions weighted by the number ofFTE teachers in the district. Robust standard errors in parentheses. Elasticities are figured using the

relevant separation rate for that sample: .136 for cols. 13 and .132 for cols. 46.* Significant at 5%.** Significant at 1%.

results indicate that Missouri school districts have a meaningful level ofmarket power. The IV results are also quite robust to changes in includedcovariates.

Columns 46 of table 5 use both the base level and average slope ofthe salary schedule as dual excluded instruments. Although this does lowerthe standard errors on the log salary coefficient, it does not substantiallychange the coefficient estimates, which continue to imply a labor supplyelasticity to the firm in the range of 3.63.7 when district level controlsare fully considered. This might be taken as evidence that the salary scaleis set in a consistent manner to consider both new hiring and retention.

Although the primary identifying assumption of the instrumental var-iables model, the excludability of base salary from the reduced form re-gression, is not directly testable, there are a couple of plausible theoriesthat might lead us to question it. Both revolve around differences betweenrural and urban school districts. In the first, urban school districts might

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Table 6Labor Supply Elasticity, Rural Specification Checks

(1) (2) (3) (4)

Log Salary .243** .226* .231* .317*(.069) (.094) (.101) (.154)

Average separation rate .136 .150 .155 .167Implied Labor Supply 3.574 3.013 2.981 3.796Sample Baseline No KC or StL MSA Nonmetro Totally ruralN 451 356 318 283

Note,Dependent variable is the district separation rate. Regressions are analogous to table 5, col.2. Robust standard errors reported in parentheses. Column 2 omits all districts within the St. Louis andKansas City MSAs. Column 3 includes in the sample only districts outside metro areas, andcol. 4 includesdistricts located entirely in rural areas.


provide higher salaries in an attempt to compensate for poor workingconditions not captured by our included controls yet still suffer higherseparation rates due to these conditions. Alternatively, the higher salariesand quit rates might reflect cost of living differences or other factorsinherent to cities. Even if the exclusion restriction holds, urban and ruraldistricts might pick equilibrium points with different labor supply elas-ticities.

Table 6 investigates the possible divergence of urban and rural supplyelasticities by examining different cuts of the data. Using two-stage leastsquares regressions following the middle specification of the previoustable, column 2 contrasts a sample omitting all districts in the Kansas

City and St. Louis MSAs with the whole base salary sample results re-ported in column 1. Since those are the most urbanized areas and representmore than half of the teachers in Missouri, it is perhaps surprising to seea statistically insignificant change of less than 0.02 in the estimated co-efficient. Further examination of labor supply to rural districts also showsfew changes. Column 3 excludes from the sample all districts in metro-politan areas, and column 4 looks only at districts with entirely ruralpopulations. These specifications demonstrate that there are few differ-ences in labor supply elasticity to school districts in Missouri that arisefrom urban-rural differences, once we condition on included control var-iables. Indeed the implied labor supply elasticities remain in a 2.98 to 3.80range around our baseline estimate of 3.57.

B. DiscussionIs the estimated labor supply elasticity to firms too low to be plausibly

believed? Is the number really an indication of a shortcoming in theapplicability of a monopsony model to the teacher labor market? Whileboth of those conclusions are possible, there are some institutional features

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350 Ransom/Sims

of the labor market for teachers that suggest that a high degree of districtmarket power is plausible.

First, there is the Boyd et al. (2005) evidence on the strong locationalpreferences of teachers. They show that teachers have a strong preferenceto work in geographical areas near the high school they attended. In theirstudy of teachers in the state of New York, they found that new teacherswere four times more likely to accept a teaching position within 5 milesof their hometown than one more than 40 miles away. A second fact thatis consistent with district market power is that a substantial fraction ofteachers are also second earners within their families, which may limittheir mobility. An analysis of the 1990 public use microdata sample(PUMS) census data (Ruggles et al. 2004) reveals that almost two-thirdsof Missouri schoolteachers in 1990 were born in Missouri, a fact consistent

with strong locational preferences of teachers. If the sample is furtherrestricted to exclude the teachers in the large cities of St. Louis and KansasCity, the Missouri natality of teachers is 20 percentage points higher.

A strong preference for employment in a small geographical area iscertainly a potential factor in low responsiveness of quit rates to salarydifferentials. A further barrier to movement between districts is the natureof salary schedules for Missouri school districts. Salary level is typicallydetermined by years of seniority with the particular district (along witheducation level). While some districts may grant full credit for teachingexperience in another district, the most common practice is to credit nomore than 5 years of teaching experience toward seniority steps. Thus, ateacher with 10 years experience in district A might suffer a substantialpay cut if he were to move to district B.5

Another possible source of market power is the nature of teacher pen-sions. Many school districts, including those in Missouri in the late 1980s,offer defined benefit pension plans that vest after some term of employ-ment (5 years for almost all Missouri districts). However, these pensionsaccrue in a highly nonlinear way based on years of experience and age.Simulations in Podgursky and Ehlert (2007) show that pension wealthfor Missouri teachers accumulates very rapidly during certain years of ateachers career (sometimes exceeding annual salary in present value), andthis situation would clearly deter a teacher from moving to another em-ployer that did not share the same pension plan. On the other hand, withthe exceptions of the large districts of St. Louis and Kansas City thatoperate their own separate pension plans (see Podgursky and Ehlert 2007,2), all public school teachers in Missouri belong to the same pension plan.However, any salary penalty due to incomplete credit for teaching ex-

5 Of course, a teacher with high levels of experience at a very low pay districtmight receive a higher salary at a high pay district, even with the incompleteexperience credit.

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Table 7Labor Supply Elasticities by TeacherCharacteristic

A. Teacher tenure with district:Less than 10 years 4.771020 years 1.04

B. Teacher overall experience:Less than 10 years 4.221020 years 1.24

C. Teacher education:Bachelors only 3.44Advanced degree 3.17

D. Teacher sex:Male 4.45Female 3.02

Note.Each separation elasticity is computed usingthe results from an individual level regression (for those

teachers with the indicated characteristic) of a separationdummy on the teachers log salary, with salary schedulebase and slope as instruments. Individual characteristiccontrols as well as the district-level controls of table 5,col. 2, are included. A group specific elasticity can thenbe computed using that groups average separation rate.

perience could be magnified by the pension system, even for movementsbetween employers within the system, since benefits are based on somemeasure of average salary. Thus, changing to a different employer couldinduce a significant financial loss to a Missouri schoolteacher.

If pension lock or incomplete credit for experience play a role in thelow responsiveness of teachers to salary differentials, the responsivenessshould vary by teacher experience. Table 7, which examines supply elas-ticity heterogeneity across a few teacher characteristics, provides evidencethat this is indeed the case. Since the table is designed to explore differencesdue to individual teacher characteristics, it represents the results of a seriesof individual level two-stage least squares regressions of a separationdummy on the teachers actual salary as well as personal and districtcharacteristics. The base salary and salary slope are used as excluded in-struments. This methodology differs somewhat from our baseline, whichlooks at adjusted district averages and produces slightly smaller averagecoefficients for the whole sample. However, the coefficient estimates to-gether with specific separation rates for teachers with a particular char-acteristic allow us to produce supply elasticity estimates that may becomparable in a relative sense across groups.

The first panel of table 7 shows that teachers with less than 10 yearsof tenure in a district are four times more sensitive to wage differencesthan their colleagues with between 10 and 20 years of tenure. The disparityof results is somewhat smaller when overall experience is considered,suggesting that the tenure with the current district is likely the drivingforce behind this effect rather than age or general experience. To further

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352 Ransom/Sims

emphasize this point, panel C shows that there are comparatively smalldifferences in responsiveness between teachers with different degree levels,conditional on experience.

Panel D of table 7 looks at differences in wage responsiveness by teachersex. It finds that male teachers are approximately 50% more responsiveto wage changes in terms of separations. In our data sample we find thatmen teaching in Missouri school districts are paid slightly more than a6% premium relative to women with equivalent experience and education(see table A1). Manning (2003) and, more recently, Hirsch et al. (2010,in this issue) suggest that some of the observed pay differential betweenmen and women may be due to different labor supply elasticities to theemployer. Ransom and Oaxaca (2010, in this issue) show that the equalityof marginal costs across inputs for profit-maximizing firms implies a direct

relationship between the log wage gender gap and differing labor supplyelasticities to a firm:

1 1ln (w ) ln (w ) p ln 1 ln 1 . (8)m f m f( ) ( )

Nw Nw

While it is possible that school districts are not equating marginal costsacross various groups of teachers, if we proceed with the assumption thatthis approximates their behavior, the gender supply elasticites of table 7suggest that we should expect to see a log wage gap of 8% favoring menin the Missouri teacher labor market, remarkably close to the actual 6%gap. Thus, employer monopsony power provides a plausible explanationfor the magnitude of the observed gender wage differential for public

school teachers in Missouri.

VI. Conclusions

Newer models of many-firm monopsony help motivate the notion thatthe dynamic movement of labor markets may not be frictionless. Thisframework provides a potential new approach for estimating the elasticityof labor supply to the firm. In this study, we estimate the labor supplyelasticity to public school districts in Missouri. Because of the likely pres-ence of measurement error and bias due to unmeasured teacher charac-teristics, we adopt an instrumental variables strategy using published sal-ary schedules of the districts to create instruments. Although the IV andOLS results are quite different, both indicate that the process by whichteachers and districts are matched results in a substantial amount of wage-setting power for school districts.

In fact, our instrumental variables estimates imply a labor supply elas-ticity to the firm of about 3.7. This suggests that labor market frictionsgive employers enough power to reduce wages somewhere in the neigh-borhood of 27% when compared with a world of perfectly informed and

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mobile workers, in the absence of institutions or factors that might limita districts ability to exercise its monopsony power. Our results also sup-port the idea that certain institutional features of the teacher labor market,such as existing pension plans, serve to limit the mobility of teachers.Furthermore, our estimates suggest that the wage disparity between maleand female teachers in Missouri can be explained by differing elasticitiesto the firm.

This research shows that in one well-defined labor market, that ofschoolteachers in Missouri, employers enjoy a substantial amount of mo-nopsony power in spite of the presence of many competitors. Furtherresearch is needed to understand how these results apply to firms moregenerally.

Appendix

Table A1Individual Determinants of Teacher Outcomes

EmploymentSeparation

(1)

LogSalary

(2)

Teaching Experience .011** .020**(.001) (.000)

Experience2 (#100) .036** .037**(.002) (.001)

Tenure with District .010** .010**(.001) (.000)

Tenure2 (#100) .025** .012**(.003) (.001)

Female .015** .061**(.003) (.001)

MA Degree .017** .116**(.003) (.001)

Specialist Degree .019 .137**(.011) (.004)

Doctoral Degree .050* .193**(.021) (.008)

Number of district fixed effects 540 540R2 .03 .64

Note.Standard errors in parentheses. N p 49,357. All regressions alsoinclude district fixed effects.


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