becker and toutkoushian - measuring gender bias in the salaries (1)

A sample selection statistical procedure is used to correctfor the effects on salary of gender bias in promotion fromassociate to full professor.

NEW DIRECTIONS FOR INSTITUTIONAL RESEARCH, no. 117, Spring 2003 © Wiley Periodicals, Inc. 5

1

Measuring Gender Bias in the Salariesof Tenured Faculty Members

William E. Becker and Robert K. Toutkoushian

Since the passage of the Equal Pay Act of 1963 and subsequent extension tothe academic labor market in the 1970s, numerous studies have attemptedto measure the level of pay disparity between male and female faculty mem-bers. A key feature of these studies is the need to identify nongender (ornonsex)-related covariates that affect faculty compensation and, when usedas explanatory variables, remove the effects of these factors in measuringmale and female pay disparity. Along with a one-zero variable for a person’sgender (or sex), most analysts agree that factors such as faculty member’sacademic experience, educational attainment, and field or discipline shouldbe included among the regressors used to explain individual salaries. Theuse of other factors has generated considerable controversy in courtroomsand journal articles. A list of twenty-four faculty salary studies and theextent to which they controlled for various factors is provided in Table 1.1.

Of all the factors typically considered for inclusion in a model of facultysalary determination, the most controversial is academic rank. Because salaryincreases usually accompany promotions, the argument for including rankin an explanation of salaries is clear; the rank of each faculty member appearsas a significant predictor of salaries. Even among tenured faculty members,however, if women are not promoted from the associate to full professorrank at a rate commensurate with their qualifications, then the resulting gen-der coefficient in a salary regression, which also includes the rank of eachfaculty member as an independent variable, would understate the total levelof gender-based salary disparity. Women who are not promoted to the fullprofessor rank because of their gender but who are still employed at the

6 UNRESOLVED ISSUES IN CONDUCTING SALARY-EQUITY STUDIES

university at the associate professor rank are paid less than men as a resultof having less endowment of rank than would be true in a nondiscrimina-tory environment. Yet, within rank there would appear to be no discrim-ination in salary determination. Because no one is terminated, there mayappear to be no reason for concern. To the extent there is concern, the typ-ical solution is to remove the rank variable from the salary model. Omittingthe tainted rank variable from a salary regression, however, yields a biasedgender coefficient estimator because the effects of the omitted rank variableare captured in the error term, which is then correlated with the includedgender variable.

As evidenced by Weiler (1990), Ransom and Megdal (1993), Balzer andothers (1996), Boudreau and others (1997), and Strathman (2000), thedebate persists over the inclusion of rank and the bias associated with usingrank in salary-equity studies. Discrimination in the granting of tenure along

Table 1.1. Overview of Factors Included in Salary Models Developedby Other Researchers

Study Seniority

Years incurrent

rank EducationResearch

productivityAdministrative

experience Field

Institution-specific studiesKatz (1973) ● ● ● ●Ferber (1974) ● ●Gordon, Morton, and

Braden (1974) ● ● ●Johnson and Stafford (1974) ● ●Hoffman (1976) ● ● ●Koch and Chizmar (1976) ● ● ●Ferber, Loeb, and Lowry (1978) ● ● ●Hirsch and Leppel (1982) ● ●Ervin, Thomas, and Zey-

Ferrell (1984) ● ● ● ●Megdal and Ransom (1985) ● ● ●Raymond, Sesnowitz, and

Williams (1988) ● ● ● ●Raymond, Sesnowitz,

and Williams (1990) ● ● ● ●Ransom (1993) ● ● ●Hallock (1995) ● ● ●Balzer and others (1996) ● ● ● ●McNabb and Wass (1997) ● ●Boudreau and others (1997) ● ● ● ●

National samples of facultyBarbezat (1987) ● ● ● ●Barbezat (1989) ● ● ● ●Weiler (1990) ● ● ● ●Barbezat (1991) ● ● ● ●Ransom and Megdal (1993) ● ● ● ●Ashraf (1996) ● ●Barbezat and Donihue (1998) ● ● ●

Note: ● � controls included in the salary model

MEASURING GENDER BIAS IN THE SALARIES OF TENURED FACULTY MEMBERS 7

with the promotion from assistant to associate professor has been studied,but the salary effects arising from discrimination in the associate-to-full-professor decision receives scant attention in the literature and empiricalstudies. Johnson (1999) examined the salary and tenure attainment of fac-ulty members in the National Science Foundation’s survey of doctoral recip-ients and lists among his conclusions: “To some extent tenure—higher rankin general—is a nonpecuniary attribute of an academic position and isdetermined jointly with salary” (p. 12). Although Johnson recognized thesimultaneity in salary and tenure determination, he lumps associate and fullprofessors together with those with tenure and of higher rank but ignoresthe influence of (or role played by) the associate and full professor ranks in the salary determination process.

Yet, a unique attribute is associated with the decision to promote fromassociate to full professor: the unsuccessful do not have to leave the uni-versity whereas those not promoted from assistant to associate professormust leave the university with no future personnel records maintained.Complete records are typically kept on both associate professors grantedand not granted full professor rank because both the successful and unsuc-cessful can continue to be employees of the university. We recognize, how-ever, that there are situations where tenure-track faculty who are deniedpromotion to the associate level may take another position at the institu-tion. Likewise, not all promotions to associate professor include the receiptof tenure, and some associate professors who are denied tenure will, as aresult, choose to leave their institution. At the same time, some female asso-ciate professors may face a related form of rank discrimination if they arenot brought up for tenure in a timely manner.

In this chapter, we show how a statistical procedure developed byHeckman (1976) known as the “Heckit estimator” can be used to adjust forthe bias in estimating the effect of gender on salary when a promotion afterthe granting of tenure is used to help explain salaries. We provide a modelof selection of associate professors into the rank of full professor and illus-trate how to simultaneously derive a consistent and efficient estimator ofthe gender coefficient in a salary model after taking account of gender dif-ferences in promotion. Unlike Heckman’s original selection process, inwhich a specific cohort is observed before selection but only those selectedare observed after, our Heckit estimator takes account of the fact that boththose who are and are not selected for full professor rank continue to be inthe data set. That is, in our application, there is no automatic attrition forindividuals who are not promoted because associate professors typicallyhave tenure and can thus remain at the institution in question.

Furthermore, although the Heckman procedures are usually used toobtain unbiased coefficients of the selection process and the related variableof interest (in our case, the effect of rank on earnings), we focus here onhow the procedure can be used to correct for bias when another indepen-dent variable such as gender has an influence on both the selection variable


(rank) and another outcome variable (salary). We demonstrate this proce-dure using data from 1,392 full and associate professors at the University ofMinnesota in the 1986–87 academic year. Our results show that male fac-ulty members are significantly more likely than comparable female facultyto hold the rank of full professor, but adjusting for this risk or hazard ofpromotion in the salary equation does not result in a great reduction in thegender coefficient in the institution’s salary equation.

What We Know from Other Studies

Many studies have been conducted at both the institutional and nationallevels of gender equity within and among faculties. Most regression modelspecifications are based at least in part on human capital theory, whichasserts that a worker’s level of compensation will be influenced by thoseattributes that contribute to his or her productivity. Potential human capi-tal measures for faculty members include educational attainment, academicexperience, and research output. In studies where all female faculty mem-bers are treated as a single group, it is common to add variables that con-trol for meaningful differences across academic positions. These factorsmight include the length of appointment, whether a faculty member hasheld an administrative position at the institution, and academic field or dis-cipline. Gender-equity studies often rely on a single-equation approach tomeasure gender disparity in pay, where a single dummy variable for genderis added to the salary equation to capture the approximate salary advantagefor male faculty over female faculty (when G = 1 for men and G = 0 forwomen) after taking into account the other independent variables in themodel.

Whether academic rank is an appropriate control variable in gender-equity studies requires a more detailed discussion. The argument againstusing rank in the salary model is that rank assignment may be genderbiased, hence controlling for current rank in the salary model would leadto an understatement of the level of pay disparity between men and women.The following quotes illustrate the magnitude of this concern:

Whether or not rank should be included in the earnings equation is debat-able since there are good reasons for supporting it to be endogenous, deter-mined by, amongst other things, gender. The inclusion of rank willconsequently introduce a downward bias in the estimated gender effect andhas therefore been omitted in a number of studies [McNabb and Wass, 1997,p. 334].

Although one regression model (in the study) controls for rank, the possibil-ity that women are discriminated against with respect to promotion is onecompelling reason for omitting rank from the regressions [Barbezat, 1991, p. 192].


The findings of the current study support the contention that the use of pre-dictors, such as rank that can be potentially biased, may mask the occurrenceof bias in salary. Even more crucial, it illustrates the importance of indepen-dently investigating predictor variables that can be subject to contamination[Riggs, Downey, McIntyre, and Hoyt, 1986, p. 373].

In their review of the literature, Ransom and Megdal (1993) highlightthose studies that controlled for academic rank and stress that the “[i]nclu-sion of rank as an explanatory variable will likely understate the ‘gendergap’” (p. 27). For this reason, the official “salary kit” produced by theAmerican Association of University Professors recommended against con-trolling for rank in faculty salary models (Scott, 1977). At the same time,advocates on the other side of the issue point to the fact that academic pro-motions typically involve increases in pay and that academic rank has beenfound to be a good predictor of faculty salaries (Raymond, Sesnowitz, andWilliams, 1988; Boudreau and others, 1997).

In light of the debate, researchers have adopted two general approachesto the problem. The first approach is to conduct a statistical test to deter-mine if men and women with similar characteristics have an equal likeli-hood of attaining higher ranks. The results from this test are then used todecide whether to include rank as a variable in the salary model (Ervin,Thomas, and Zey-Ferrell, 1984; Riggs, Downey, McIntyre, and Hoyt, 1986;Weiler, 1990; Ransom and Megdal, 1993; Boudreau and others, 1997). Sucha test involves the use of discriminant analysis, or the estimation of a bivari-ate logit or probit selection model, followed by the estimation of a salaryequation with or without rank included, depending on the outcome of the selection model estimation. Implicit in such a two-step process is theassumption that the error terms in the two equations are independent,which as we demonstrate later need not be true.

In several studies in which such an examination of faculty rank attain-ment was performed, women were less likely than their male peers to attainhigher ranks within academia. Riggs, Downey, McIntyre, and Hoyt (1986)used discriminant analysis to show that female faculty at one institution in1983 often held ranks that were significantly below their predicted ranksfrom the model. Weiler (1990) found that for a national sample of facultyin 1968, after controlling for experience, race, educational attainment, typeof institution, field, and publications, female faculty were less likely thancomparable male faculty to hold higher ranks. In addition, Weiler showedthat the gender disparity in rank accounted for 15 to 20 percent of the over-all gender-based pay disparity in his sample. Ransom and Megdal (1993),using national samples of faculty from 1969, 1973, 1977, and 1984, foundthat after controlling for educational attainment, experience, seniority, andpublications, female faculty were significantly less likely than comparablemale faculty to hold the rank of full or associate professor. A similar genderdifference in rank attainment persisted for a sample of national faculty in


1993 at the full professor level (Toutkoushian, 1999), even after race, careerpublications, primary teaching field, educational attainment, type of insti-tution, experience, and seniority were taken into account. Similar genderdifferences in rank attainment have been observed by Ginther and Hayes(1999), Johnson (1999), and Long, Allison, and McGinnis (1993). Thisapproach of testing for gender bias in rank attainment has been supportedby researchers who typically favor including rank in the salary model. Forexample, whereas Boudreau and others (1997) and Balzer and others (1996)argue for including rank in studies of faculty salaries, they stress that con-cerns about discrimination in rank should also be addressed.

With the exceptions of those done by Weiler (1990) and Strathman(2000), these studies do not attempt to measure the degree to which genderbias in rank attainment contributes to the male-female salary difference.Weiler’s (1990) procedure involves an adjustment to the gender coefficientbased on differences between a person’s actual and predicted rank. One lim-itation of Weiler’s approach is that significance tests cannot be applied to theresulting gender salary difference because it is not a parameter obtained froma specific statistical procedure. Strathman (2000) recommends using a simul-taneous equation model to jointly estimate the rank and salary of individualfaculty. However, by including assistant, associate, and full professors in theanalysis, Strathman’s approach overlooks the unique nature of the decisionto promote from associate to full professor, where tenure ensures continuedemployment regardless of the promotion decision.

Rather than use information on gender bias in rank to determine ifrank should be included in a model of salary determination, a secondapproach advocates presenting results from a salary regression fit with andwithout a rank covariate. Authors of these types of studies do not argue infavor of one of the two salary model specifications, nor do they offerinformed opinions on how much of the change in the gender coefficientresulting from controlling for rank is “appropriate” versus “inappropriate.”Reporting both results is intended to allow readers to observe the sensitiv-ity of the unexplained wage gap to the use of rank, as seen in Ferber (1974),Hoffman (1976), Raymond, Sesnowitz, and Williams (1988), Barbezat(1987, 1989, 1991), and McNabb and Wass (1997). Studies of this typemake clear to readers that the inclusion of rank is an issue of contentionamong analysts, and authors provide regression results both with and with-out rank for the readers’ edification. As we show, both the salary regressionwith rank and the one without rank are likely misspecified and involvebiased estimators.

The specific details of how researchers have dealt with rank are pro-vided in Table 1.2. Note that only three of the twenty-four studies reviewedhere, and only one since 1976, controlled for rank without either testing forpossible gender bias in rank or showing the results from a similar salarymodel without rank. The most popular option has been to present findingsfrom two salary models, with and without controlling for rank, although in


the 1990s it also became common to conduct statistical tests for potentialgender bias in rank attainment. As we show, however, even after condi-tioning on only those with tenure, salary determination and rank assign-ment cannot be considered separate events.

Use of Gender and Rank in Faculty Salary Models

As stated, the terms of employment for tenured and nontenured facultymembers are materially different. The latter are temporary employees in thesense that they are typically dismissed if they are not promoted from assis-tant to associate professor in a fixed time. The former cannot be dismissedregardless of time in rank; that is, if tenured, an associate professor can beat an institution for life. The assignment of associate or full professor rank,therefore, represents a unique form of selection. Associate professors arenever required to achieve the higher rank of full professor to stay at theinstitution.

Table 1.2. Treatment of Faculty Rank in Salary Equity Studies

R No test conducted for gender bias r

StudyCurrent

rank usedCurrent rank

not used

Presentresults fromtwo models

Test forgender bias

in current rank

Institution-specific studiesKatz (1973) •Ferber (1974) •Gordon, Morton, and Braden (1974) •Johnson and Stafford (1974) •Hoffman (1976) •Koch and Chizmar (1976) •Ferber, Loeb, and Lowry (1978) •Hirsch and Leppel (1982) •Ervin, Thomas, and Zey-Ferrell (1984) •Megdal and Ransom (1985) •Raymond, Sesnowitz, and Williams (1988) •Raymond, Sesnowitz, and Williams (1990) •Ransom (1993) •Hallock (1995) •Balzer and others (1996) •McNabb and Wass (1997) •Boudreau and others (1997) •

National samples of facultyBarbezat (1987) •Barbezat (1989) •Weiler (1990) •Barbezat (1991) •Ransom and Megdal (1993) •Ashraf (1996) •Barbezat and Donihue (1998) •

Note: • � method used in the salary study


Because women (or men) can be unfairly held in the associate profes-sor rank and the promotion from associate to full professor leads to a sub-stantial jump in pay, the promotion of faculty from the rank of associate tofull professor can be a difficult-to-detect source of discrimination in salarydetermination. If a dummy one-zero variable is included in a salary regres-sion for the full or associate professor rank, then the gender variable willnot capture this discrimination because nonpromoted women will be at thehigher end of the (lower) salary distribution for associate professors. If nodummy variable for rank is included in the regression, a biased coefficientestimator for gender also results. Below, we show more formally how thesebiases arise and affect the estimated gender coefficient.

Problems When Excluding Rank from the Salary Model. To theextent that professorial status is determined by the same things that deter-mine pay but is also associated with an additional pay step, leaving it out ofan equation aimed at explaining salaries leads to omitted variable bias. Thecoefficient estimators of the explanatory variables—including the gendercoefficient—obtained by multiple regression (ordinary least squares) arebiased due to the correlation between these included variables and the errorterm that contains the omitted rank variable. Let’s begin with a simplemodel in which the ith person’s salary (measured as a natural logarithm, yi)is determined by only gender (Gi = 1 if male and 0 if female), rank (Pi = 1 iffull professor and 0 if associate), and a truly random error vi.

yi = �Gi + �Pi + vi (1)

where � and � are coefficients to be estimated.If the rank variable is left out of the regression model, we have an equa-

tion of the form

yi = �Gi + vi* (2)

where vi* = �Pi + vi. Let the ordinary least squares estimator of � be repre-

sented by a. Then it must be true that the expected value of the estimator(denoted E[a]) exceeds the true population parameter when gender is pos-itively correlated with the error term vi

* (meaning men are more likely thanwomen to hold the rank of full professor),

This shows mathematically how the use of multiple regression overesti-mates the effect of gender on salary if rank is omitted from the salary modeland thus would result in a biased estimate of the effect of gender on salary.

Problems When Including Rank in the Salary Model. When rankis used as an explanatory variable and it is correlated with gender, two

2E(a) � � � E G v* G � � (3)� i i � i� � �


statistical problems result. First, the correlation may lead to multi-collinearity. The true standard errors of the coefficients will be overlylarge, which lowers the z ratio and increases the likelihood of a Type IIerror in a hypothesis test of � equals 0 versus � is greater than 0. That is,even if there is discrimination against women in salary determination, thegreater the correlation between rank and gender, the harder it will be toreject the null hypothesis that gender does not affect salary in favor of thealternative hypothesis that being male raises salary. The effect of multi-collinearity on the estimated standard errors of coefficients also dependson the error sum of squares from the regression equation, which may belowered substantially as correlated regressors are brought into the model.

A second and perhaps more serious problem with the inclusion of rankin the salary model is that, to the extent that other factors are excluded fromthe regression that are correlated with gender and rank, the estimators of the gender and rank coefficients using multiple regression will be biased.This could arise when men and women with similar characteristics do nothave the same probability of achieving the rank of full professor.

Let’s assume that a tenured faculty member’s salary is determined bygender, rank, and a vector of personal characteristics (Xi), including suchthings as highest degree earned, experience, seniority, and citations to pub-lished works. The salary determination equation is now written as

yi = ��Xi + �Gi + �Pi + �i (4)

where the error term �i is distributed normally with mean zero and con-stant variance 2

� and � and � are the gender and rank coefficients to beestimated along with the other coefficients in vector �. The notation inEquation 4 differs from that in Equation 1 to call attention to the differ-ence in the models. To the extent that P, G, and � are related, the estima-tors for � and � obtained from multiple regression will be biased becauseof the correlation between the error term and the regressors in the salarymodel.

This regressor and error term correlation could be caused by differ-ences in the probability of like men and women being promoted. Anyattempt to estimate the influence of gender on salary must recognize andcontrol for the gender bias in promotion. To see this, let the rank of full ver-sus associate professor be assigned by the rule

Pi* = �Xi + �Gi + ui, (5)

where ui represents random error term with mean equals 0, Pi* equals an

unobservable likelihood of being assigned to the full professor rank, and Pi

equals 1 if Pi* is greater than 0, and Pi equals 0 if Pi

* is 0 or less. With somealgebraic manipulation, it can be shown that the probability of an individ-ual being assigned to the full professor rank can be expressed as


Prob(Pi = 1) = Prob(Pi* > 0) = � (�Xi + �Gi), (6)

where � represents a standard normal probability distribution function withdensity , which is a probit specification for selection. If full professors tendto be men with higher salaries, then �i and ui are related. Accordingly, weassume that �i and ui are correlated with correlation coefficient and there-fore follow a bivariate normal distribution.

With some additional algebraic manipulation, it can be shown that foreither full or associate professors, the expected difference between salariesfor a like man and woman is equal to � (that is, is unbiased) when the salarydetermination process is error free (�= 0), the processes in salary determi-nation and promotion are not related (� = 0), or gender has no effect in thepromotion process (� = 0).1 Even if none of these conditions hold, however,it would still be possible to get an unbiased estimate of � from those withextremely high or low X values where approaches zero. Neither of the firsttwo conditions is likely to occur; therefore, any bias in the gender coeffi-cient in the salary model would be largely attributed to whether there isgender bias in rank attainment. Furthermore, as long as the error terms inthe selection equation and salary equation are related (� ≠ 0), simultaneousestimation of both equations is warranted. An adjustment for the selectionbias will require the estimation of both � and �. The estimation of theseparameters cannot be done with many general statistical programs such asSPSS (Statistical Package for the Social Sciences) and currently requiresmore specialized programs such as LIMDEP (“limited dependent variable”).

Adjustment for Selection. The bias and inefficiency inherent in theleast-squares estimation of the gender coefficient when rank is or is notincluded as a regressor in the salary equation cannot be avoided. In this sit-uation, an alternative to the single-equation model and multiple regressionanalysis is required. The problem caused by this endogeneity of rank (P) issimilar to the treatment problem discussed in Greene (1997, pp. 981–982),where estimating separate regressions for those receiving different treat-ments yields inconsistent estimators because whether or not an observationhas been subject to treatment is itself affected by other factors. This certainlyholds true for faculty rank, which is not randomly assigned to individualsbut rather determined by many of the same factors that influence salary.

As Greene notes, the assessment of treatment effects in the light of sam-ple selection bias has received a lot of attention since the early work ofHeckman (1976). In the typical Heckit applications where analysts attemptto correct for sample selection bias, however, data are observed only forindividuals who have been selected into the category or treatment in ques-tion. Such is not the case for faculty at a particular institution, where dataare observed for associate professors who were not appropriately selectedfor inclusion in the full professor rank. In our case, adjustment for the selec-tion bias requires specifying an equation to explain the “rank treatment”that does not result in any change in sample size. This is accomplished by


adding a regressor to the salary equation (Equation 4) for the risk or haz-ard of a male or female faculty member being an associate professor. By theprobit specification of the selection equation (Equation 6), the vector ofcoefficients and gender coefficient � are simultaneously estimated withthe salary equation coefficient vector �, gender coefficient � , rank coeffi-cient �, and hazard coefficient ��.

An Application

To illustrate how the Heckit estimation method can be used in salary-equitystudies, we use data on 1,392 full and associate professors at the Universityof Minnesota in the 1986–87 academic year. The data set includes infor-mation on each faculty member’s monthly salary, experience level, educa-tional attainment, collegiate unit, academic rank, gender, and citationsreceived in 1985. Table 1.3 provides descriptive statistics for these factorsbroken down separately for men and women.

Of particular relevance to this study is that 85 percent of the tenuredfaculty were men, and more than two-thirds of those were full professors.Only 37 percent of the tenured female faculty were full professors. Thedescriptive statistics in Table 1.3 suggest that some portion of the rank dif-ference between the genders could be caused by differences in academicexperience, educational attainment, and research output or reputation, asrepresented by citations.

Table 1.4 contains the results from the estimation of four differentmodels. The first column of numbers shows the coefficient estimates froma probit model designed to explain whether a faculty member is a full or associate professor. The set of explanatory variables includes years of

Table 1.3. Descriptive Statistics for University of MinnesotaProfessors, 1986–87

Men only Women only

Variable Mean SD Mean SD

Highest degree master’s 0.08 0.27 0.17 0.38Highest degree doctorate 0.80 0.40 0.73 0.45Highest degree professional 0.03 0.18 0.03 0.18Years of experience 23.20 9.39 19.01 8.64Years of seniority 16.17 8.16 11.40 5.94Days of nonprofessional leave 32.87 199.70 94.11 329.49Citations in 1985 12.16 26.30 6.49 17.03Retention funding 0.10 0.30 0.10 0.30Nine-month appointment 0.66 0.48 0.68 0.47Full professor 0.68 0.47 0.37 0.48

Notes: Sample (n � 1,392) includes only faculty on the Twin Cities campus of the University ofMinnesota who were either full or associate professors in the 1986-87 academic year.


experience, three variables for highest degree, years of seniority, citationsto publications in 1985, days of nonprofessional leave, college affiliation(twenty-one categories), and gender. For brevity, the coefficient estimatesfor twenty-one college-unit dummy variables are not reported.

The second, third, and fourth columns of numbers are coefficient esti-mates for regressions on the natural logarithm of salary. The second col-umn shows the salary equation for faculty with the estimates of � and �

Table 1.4. Models Explaining Rank Status and Salaries of Faculty atthe University of Minnesota, 1986–87

Variable

Probit:1 if full

professor“Heckit”

model

Modelwithout

rankModel

with rank

Highest degree master’s �0.920** �0.040 �0.099** �0.036(0.200) (0.024) (0.026) (0.023)

Highest degree doctorate �0.314* 0.002 �0.013 0.003(0.152) (0.014) (0.019) (0.017)

Highest degree professional �0.266 0.022 0.014 0.024(0.333) (0.038) (0.042) (0.036)

Gender (1 � male) 0.459** 0.054** 0.085** 0.049**(0.124) (0.017) (0.017) (0.014)

Years of experience 0.039** �5.4e-04 �8.4e-04 �0.002(0.007) (0.002) (0.003) (0.003)

Years of experience squared � 6.4e-05 1.2e-04* 9.3e-05(3.9e-05) (5.8e-05) (5.0e-05)

Years of seniority 0.065** 0.013** �0.003 �0.012**(0.009) (0.003) (0.003) (0.003)

Years of seniority squared � 3.1e-04** 1.8e-04* 3.2e-04**(6.7e-05) (8.7e-05) (7.5e-05)

Days of nonprofessional leave 5.8e-05 �8.7e-05** �8.2e-05** �8.4e-05**(2.1e-04) (1.6e-05) (2.4e-05) (2.1e-05)

Total citations in 1985 0.023** 0.002** 0.003** 0.002**(0.003) (1.4e-04) (2.2e-04) (1.9e-04)

Full professor � 0.231** � 0.244**(0.013) (0.011)

Received retention funds � 0.126** 0.172** 0.129**(0.015) (0.018) (0.016)

Nine-month appointment � 0.034 0.040 0.033(0.023) (0.022) (0.019)

Selectivity parameters� � �0.377** � �

(0.064) � 0.169** � �

(0.003)R2 NA NA 0.41 0.56

Notes: *p � .05, **p � .01. Each model also contains an intercept and twenty variables for collegeaffiliation. The “Heckit” model is estimated using the maximum likelihood routine in LIMDEP.Standard errors are shown in parentheses. The sample includes only faculty at the full and associateprofessor ranks (n � 1,392). NA � not applicable.

as multiplicative factors forming the coefficient of the (hazard) adjustmentterm for selection into the full professor rank. The third and fourthcolumns represent the traditional multiple regression equation without andwith rank included as a regressor. The three salary equations use the sameset of regressors as in the probit model that explains rank, plus controls forsquared experience, squared seniority, length of appointment (nine versustwelve months), and whether the person had received special funds asso-ciated with an anticipated or actual outside offer (retention funding). Toestimate the coefficients in simultaneous equation models such as these, itis necessary that both equations are “identified,” meaning that algebraicsolutions exist for the coefficients. For the selection model, the fact thatthe rank equation uses a nonlinear form and the salary equation is linearserves to identify both equations.

The probit model shows that male faculty are significantly more likelythan their female counterparts to hold the rank of full professor, holdingconstant the other variables in the model. For example, setting experience,seniority, citations, and days of leave at their mean levels, the probabilitythat a woman doctorate holder in the base college unit is a full professor is.34, and the probability that a like man is a full professor is .52.

When the risk or hazard of holding the rank of full professor is used asa control variable in the salary equation, the gender coefficient of 0.054 isstill highly significant. To see how this gender coefficient estimate compareswith the two standard multiple regression equation alternatives, look atcolumns 3 and 4. When rank is excluded from the model (column 3), thegender coefficient 0.085 is larger. When a dummy variable for full profes-sor is added as a control (column 4), the gender coefficient drops to 0.049.Eighteen percent of all ranked faculty at the University of Minnesota in1986–87 were assistant professors. When the salary models shown in thelast two columns of Table 1.4 were estimated for all faculty, the gender coef-ficients were similar to those reported here. The adjustment for sex dis-crimination in the assignment of rank places the salary effect of genderbetween the multiple-regression estimates when rank is and is not includedas an explanatory variable. Because the unbiased gender effect in this exam-ple is relatively close to the gender coefficient when rank is included in themodel, it does not appear as though the gender bias in promotion to fullprofessor had a large effect on the estimated level of pay disparity betweenmen and women within these two ranks.

Summary and Discussion

Gender-equity studies of faculty salaries that use rank as an independent vari-able are criticized because the gender bias in rank attainment affects the esti-mated level of pay disparity between male and female faculty. We show howa Heckit estimation procedure can be used to correct salary equations for gen-der bias in promotion from associate to full professor. Unlike the typical


Heckit adjustment for sample selection bias (where those not selected areomitted), in the case of promotion from associate to full professor, everyonecontinues to be observed regardless of rank; those not promoted to full pro-fessor have continued employment as associate professors.

The Heckit procedure involves maximum likelihood estimation of theparameters in a two-equation simultaneous model: one equation toexplain rank and the other to explain salary, with an adjustment for therisk or hazard of holding a certain rank. When this approach is used toestimate the effect of gender in the salary determination process at theUniversity of Minnesota, we find that the estimated gender coefficient iscloser to the estimated gender coefficient obtained from a single-equationsalary model that included rank than to the estimated gender coefficientin a single-equation salary model without rank as a regressor. We alsofound evidence that rank assignment was biased in favor of men.Independent of the effects of rank assignment on salary, the results sug-gest that this problem should also be addressed because rank assignmentaffects faculty in ways other than salary, including morale, reputation, andmobility. Although these results cannot be applied to other institutions,the approach can certainly be adapted for other institutions and alsoapplied to questions of salary equity for nonfaculty or to academicemployees by race or ethnicity.

Although we argue that this approach to studying gender equity insalaries is useful, some practical constraints limit the extent to which itmight be adopted by analysts. First and foremost is that in many salary-equity studies, for political and other reasons it is necessary to include assis-tant professors in the analysis. The Heckit procedure as described herecannot be applied to assistant, associate, and full professors because of thedifferent selection processes for assistant (nontenured) versus associate orfull (tenured) professors. Nonetheless, when the vast majority of faculty inan institution are tenured, applying the Heckit model to only tenured fac-ulty will give the analyst some valuable information about the likely extentof bias in the gender coefficient when the salary model is estimated for thelarger data set. Likewise, the Heckit procedure is cumbersome to estimatefor those who currently rely on more general statistical packages that do nothave modules readily available for performing the necessary calculations.In time, however, the ease with which this procedure can be used will likelyincrease, making it a more feasible alternative for analysts interested inexploring questions of salary equity.

Note

1. The mathematical details behind this result are contained in an earlier version of thisarticle that was presented at the National Bureau of Economic Research (Becker andToutkoushian, 1999). The article is available from the authors on request.


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WILLIAM E. BECKER is professor of economics at Indiana University.

ROBERT K. TOUTKOUSHIAN is executive director of the Office of Policy Analysis,University System of New Hampshire.


becker and toutkoushian - measuring gender bias in the salaries (1)

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academic labor market

american economic review

female faculty members

tenured faculty members

female salary differentials

measuring gender bias

salary determination process

comparable male faculty