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Gender differences in salaries: an application to academe.

I. Introduction

There is a lengthy body of literature investigating differences between male and female salaries in academe. Most of these studies have two common characteristics: they examine salary levels but not raises, and they lack information about research productivity. Because of that, they tell us much about the differences between male and female salary levels but little about salary increments for research production. Yet the allocation of raises is an important element in the study of gender differences in compensation. Even if males and females have equal starting salaries, raises which do not fully reflect productivity would soon lead to salary differentials. The purpose of this study is to fill this void by analyzing longitudinal data, including research output, from the University of Alabama for the years 1981-1985.(1)

We do not find that females receive lower salaries or lower raises than males given differences in human capital, academic discipline, rank, and research productivity. On the contrary, there is some evidence that females receive higher salaries and raises than their human capital, academic discipline, rank, and research productivity would warrant. These interesting, yet controversial, findings are explored more fully in this paper.

This paper proceeds as follows. In section II, a short background of the problem is presented and the contradictory nature of the findings of various studies are discussed. Section III contains a description of the data set used in this paper and a discussion of the statistical methodology. Section IV and section V include discussions of the results and conclusions, respectively.

II. Background

Taken collectively, previous studies present a varied picture of the gender differences in academic salaries. There is still uncertainty as to whether the salary differences reflect discrimination by universities or reflect human capital differences, productivity, or choices on the part of the suppliers of labor.

Johnson and Stafford |21~ maintain that over one-half of the academic year salary differentials found between full-time female and male Ph.D. faculty members at American universities are due to gender. They attribute this difference to voluntary decisions by women to interrupt their careers. However, Strober and Quester |31~ show that only a small fraction of full-time female faculty interrupt their careers. Barbezat |2, 428~ also found that marital and parental variables have little affect on women's salaries.

There is no consensus on whether the differences occur at entry level or become evident with experience and rank. Hirsch and Leppel |17~ find women's salaries initially lower but steeper and more concave than men's salaries over time. That is, women faculty receive lower entry salaries but they are treated the same as their counterparts over time. Megdal and Ransom |25~ find a comparable situation at the University of Arizona for the years 1972, 1977, and 1982. They find women's initial salaries to be lower than men's but growing at a higher rate than men's.

Gordon, Morton, and Braden |14~ record a female-male differential which they say is explained by differences in individual characteristics such as age, seniority, education, rank, race, and discipline. Hoffman |18~ adjusts the Gordon, Morton, and Braden model by recognizing that "sex discrimination may occur through slower promotion rates for females in which case rank itself would reflect discrimination." Weiler |37~ suggests that rank and seniority are correlated for men, but not for women.

Raymond, Sesnowitz, and Williams |29~ in a study of 1983-1984 Kent State University data find raw salary differentials by sex. However, the differentials disappear after adjusting for experience, degrees, specialties, scholarly publications, and graduate faculty standing. Moreover, they find that, "reverse discrimination appears when the rank variables are added ..." |29, 48~.

While these studies provide insights |13~, their results have not been subjected to statistical tests of significance. By employing statistical tests omitted from previous studies, we can evaluate results with a higher degree of confidence. In addition, by analyzing raises across time we can gain new insights into how productivity affects salary differences between males and females.

III. Description of Data and the Model

Data Description

The data used in this study were collected from The University of Alabama administration, faculty, budget documents and directories. The data set contains all faculty who were employed at the university consecutively across the period 1981 through 1985. The difference in the logarithm of salary between 1981 and 1985 salaries constitutes the rate of salary increase.

Human capital variables include years of service at the university, administrative service, prior experience, and degree held. Academic discipline variables are included to take into account the variation in salaries between disciplines. Since distinguishing between disciplines a priori is somewhat subjective, the categories of disciplines used in this paper are similar to those used by Hirsch and Leppel |17~. Productivity variables include numbers of books, refereed articles, and exhibitions-performances.(2) No distinction is made between single authors and coauthors. Faculty teaching and service are not included. A problem inherent in using research productivity measures is the aspect of placing weights on publications. Weights have been used in studies which evaluated research output |4~; however, there is no consensus on an appropriate weighting scheme. In this paper, the number of books, refereed articles, and exhibitions-performances are not weighted.

The primary focus of this paper is on raises and research productivity. However, we also are interested in salary level differences between male and female faculty. Therefore, both salary level and raises are examined. In this study, a variation of the traditional human capital model employed in the previous work of Blinder |3~, Oaxaca |26~, Ferber, Loeb and Lowry |10~, Hirsch and Leppel |17~, and Jackson and Lindley |19~ is developed.

Model

Following the human capital view of wage determination, we posit a traditional behavioral model to analyze the determinants of 1985 salary levels:

|Mathematical Expression Omitted~

where y is an (n x 1) vector of observations on the natural logarithm of yearly (9 month) salary, X is an (n x k) matrix of observations taken by the k human capital, rank, and academic discipline variables discussed above, |beta~ is a (k x 1) vector of unknown coefficients measuring the response of the wage rate to these determinants, and e is a stochastic disturbance vector (n x 1). To aid in the discussion to follow, we rewrite equation (1) more explicitly:

|Mathematical Expression Omitted~

where H|C.sub.j~ (j = 1,...,5) are five human capital measures, A|D.sub.k~ (k = 1,...,11) are eleven academic discipline categories, and |R.sub.m~ (m = 1,...,3) represent three academic ranks. Within the context of equation (1), the variables in equation (2) are

|Mathematical Expression Omitted~

|Mathematical Expression Omitted~

|Mathematical Expression Omitted~

and

|Mathematical Expression Omitted~.

Thus k, the number of parameters to be estimated (including the constant term), in equation (1) is equal to 20 in the salary level analysis to follow.

While using Blinder's method to decompose a wage equation of the form of (1) or (2) is a traditional method of investigating gender differences in academic (or most other types of) salaries, employing a similar approach to investigate gender differences in salary changes over time, i.e., raises, is not so traditional. Ideally, if data were available on all variables for, say, the years 1981 and 1985, we would augment equation (1) with a gender dummy and a full set of gender-interaction variables. We would then pool the 1981 and 1985 samples, add a time dummy with a full set of time-interaction variables, and estimate this further-augmented model by OLS regression techniques. The resulting model would be a full four-way analysis of covariance model (male and female equations for 1981 and male and female equations for 1985) so that intertemporal gender differences in salary coefficients could be analyzed directly. While we have a full set of data for 1985, we have only salary data for 1981-1985 and data on changes in our productivity measures during that period.(3) However, this is precisely the data that we need to carry out an analysis of gender differences in raises that is equivalent to a full-scale intertemporal analysis of covariance and, perhaps, it is more informative.

To see this, first consider our traditional salary level model posited for 1985 and for 1981, respectively,

|Mathematical Expression Omitted~

and

|Mathematical Expression Omitted~

Assuming our model specifying salary levels is appropriate, the only way for salary (ys) to change over the four-year period is for the variables (Xs) or their coefficients (|beta~s) to change. Thus

|Mathematical Expression Omitted~

Now rewriting these differences in the form of equation (2), note that:

|Mathematical Expression Omitted~

The second, fourth, and sixth terms on the right in equation (6) represent intertemporal changes in "endowments" weighted by 1981 coefficients; the first, third, fifth, and seventh terms on the right in equation six represent intertemporal coefficient differences weighted by 1985 endowments. This is the form an intertemporal analysis of covariance, ignoring gender differences, would take.

At this point, it is important to take a realistic look at what could change over this four-year period. One change is that academic markets will value human capital characteristics, academic disciplines, and rank differently over time. For example, changes in demand for faculty in the business and liberal arts disciplines has been a fact of life over recent history. To the extent that the university incorporates these varying opportunity costs when determining raises, we would expect the salary coefficients of these characteristics to change over time. Hence, the first, third, fifth, and seventh terms in equation six are required components of any model attempting to explain raises. The same cannot be said for terms relating to changes in endowments: some endowments can be expected to change over the period while others, either because of the nature of the sample or the structure of academe, will not.

The construction of our sample results in many of the endowment variables remaining constant across the time period we measure. For example, our sample includes only faculty employed by the university for the entire 1981-1985 period. Consequently, years of service are incrementally increased by four years over the period for all faculty. Since the change in this variable is a constant four years, there can be no gender differences in this particular endowment change. For similar reasons, whether or not one was hired with experience will not change over the period of analysis. Additionally, even though faculty may move from one department to another within a given school or college from time to time, one almost never observes faculty moving from one school or college to another within a given university. Thus, the fourth term in equation (6) should vanish; one could reasonably expect A|D.sub.1~s not to change from the beginning to the end of the period for any of the i individuals in the sample.

We would expect some of the human capital and rank variables to change over the sample period. Faculty may have received Ph.D's or professional degrees, or they may have been promoted. Thus, there could be some intertemporal changes in endowments. These observations form our point of departure with the strict analysis-of-covariance approach. Capturing these intertemporal changes would require a full time-interaction and gender-interaction model. This would result in a 2k increase (over a simple gender-interaction model) in coefficients to be estimated which, in turn, would use an additional forty degrees of freedom. We elect to employ a more parsimonious approach but one which enriches the economic content of our model. The temporal changes that would be observed in a given faculty member's human capital and academic rank characteristics ought to be determined, at least in the main, by his or her academic productivity, e.g., articles and books written, over the period. Since we have data on some of these productivity measures, it would seem approximately equivalent and considerably more informative to include these variables in a model to analyze gender differences in raises rather than to try to infer such differences from intertemporal changes in dummy variables representing these characteristic-a la analysis of covariance techniques.

This discussion leads to the following model of raise determination:

|Mathematical Expression Omitted~

where |delta~|y.sub.i~ is the geometric mean growth rate of salary received by the ith individual over the 1981-1985 period; |Mathematical Expression Omitted~ are the 1985 values of our human capital, academic discipline, and rank variables; |P.sub.p~ (p = 1,...,3) are our productivity measures (refereed papers, books, and performances/exhibitions) computed over the 1981-1985 period; and u is a stochastic disturbance term. It is worth noting that, by equation (6), the coefficients e, |f.sub.j~ (j = 1,...,5), |g.sub.k~ (k = 1,...,11), and |h.sub.m~ (m = 1,...,3) can be interpreted as intertemporal differences in the corresponding coefficients of equation (2), i.e., a, |b.sub.j~, |c.sub.k~, and |d.sub.m~, respectively. It also is worth noting that in a fully interactive model of gender difference in raises, the coefficients on the gender-interaction variables corresponding to these terms indicate gender differences in the way salary responds to those variables over time (e.g., does an additional four years of services raise salary more for males than females).(4)

In summary, equations (2) and (7) form the basic models of salary levels and raises, respectively, that we analyze to detect genders differences. Our subsequent analysis employs a procedure suggested by Jackson and Lindley |19~ which modifies the decomposition technique recommended by Blinder |3~ and Oaxaca |26~. The modification has the advantage of providing a direct test of the residual effect and its components (the constant and coefficient effects). An additional advantage is that it provides for a test of either the constant or coefficient effect without restricting the others to zero.(5)

IV. Empirical Results

The results of the models are presented in Tables I and 11. Five regressions are presented in each table, (1) a male model, (2) a female model, (3) a pooled model, (4) a pooled model with a gender dummy variable, and (5) a pooled model with dummy and dummy interaction terms.(6) Five regressions are presented because at least some information from each model is useful for statistical testing. The mean values for the variables also appear in the tables. Salary level is examined first with equation (1) and the results are compared with those of other studies which use a similar model. Raises are then examined with equation (2).

Salary Level

Overall, the equations for log of the 1985 salary level predict well. The |R.sup.2~ is .74 or greater for all of the equations. However, there are marked differences as to which variables are significant in the male model relative to the female model

Administrative experience, associate and full professor rank, and the discipline of law lead to salaries for both sexes which exceed their respective mean salaries. Of more importance than a comparison to means is the comparison between sexes of the contribution of each category to salaries. For example, what is the difference between the two groups in terms of the contribution of administrative experience to salary determination. The interaction term for each category, the male coefficient minus the female coefficient, provides this information.

For administrative experience, the difference in the coefficients is not significant. Thus, administrative experience contributes approximately the same toward salary levels for both sexes. The same can be said for the rank of full professor. However, for the rank of associate professor or a position in law, the negative and significant interaction terms show that these categories contribute significantly more to female than to male salaries.

Males in humanities, social science, communication, education, home economics, library services, natural science and mathematics and social work, have salaries significantly lower than the mean male salary. Females in natural science and mathematics, social work, business, and engineering, as well as holding the rank of assistant professor, have salaries which exceed the mean female salary. In all cases, however, the interaction terms are negative and significant verifying that positions in these disciplines contribute more to female than male salaries.

These differences in contributions of variables between male and female salaries suggest that the factors which determine salaries differ between the two groups. At the same time, we cannot conclude that this difference results in average salaries which do not reflect human capital. The male and female models must be decomposed to determine the impact of human capital on salary differences.

Calculating the total effect reveals that male salaries are twenty-three percent greater than female salaries. This result is consistent with Johnson and Stafford |21~. The endowment effect is approximately eighteen percent. Female salaries are eighteen percent less than male salaries due to human capital, academic discipline, and rank. Male salaries exceed female salaries by approximately five percent due to the residual effect. That five percent difference is significant at the. 10 level. At this significance level, we reject that female salaries are equal to male salaries when account is taken of endowments. However, further decomposing the residual effect into the constant effect and coefficient effect and testing for significance reveals contrasting influences at work.

The constant effect (gender coefficient in equation (5), Table I) is significant and positive. The significant constant effect indicates that there are differences between the two models which are not explained by the differences in coefficients or endowments. Part of this unexplained difference reflects the impact of the base categories such as instructor rank or disciplines not explicitly listed. Part also reflects the influence of factors not captured by the traditional model.

A concern when evaluating results is model specification |20~. To test for model specification, a RESET test was conducted. Test results allowed us to reject the hypothesis of no specification TABULAR DATA OMITTED TABULAR DATA OMITTED error. However, changing the functional form of the equation to the square root of salary rather than the log of salary did not allow us to reject that the model is correctly specified.(7) From this we conclude that there is no evidence of omitted variables,

In contrast to the constant effect, the coefficient effect is negative and numerically large, although it is not significant. The negative sign implies that if females were rewarded for their human capital, academic discipline, and rank on the same basis as males, they would have received lower salaries. Two offsetting forces are at work. One, there is a numerically large negative coefficient effect due to females receiving salaries exceeding what would be paid males with the same attributes. Two, there is a positive constant effect due to male salaries exceeding female salaries as a result of, (1) factors which are not captured by the traditional model or (2) differences in reservation salaries for the base groups.

These contrasting results make it difficult to say with certainty that there is or is not discrimination in terms of salary levels. However, the results do demonstrate that discrimination is not apparent when considering the variables routinely used in addressing this problem. The only significant differences become evident in the constant effect.

Raises

Turning to Table II, it can be seen that specific disciplines have different impacts on the raises of males and females. A position in humanities or natural science and mathematics increases the percentage raise for females but not males, while being in communication, education, library services, and social work lowers the percentage raise for males but not females. The interaction terms reflect the same results as in the salary level analysis. These disciplines contribute significantly more to female raises than male raises. Rank also affects the two groups differently. The rank of full and associate professor leads to increased raises for females but not for males. However, the interaction terms are not significant indicating that rank contributes approximately the same to male and female raises.

The years-of-service variable is negative and significant for both male and females indicating that longevity, per se, is not rewarded for either males or females. Hired with experience is negative for both and significant for males. The negative sign indicates that previous experience does not translate into increased salaries after hire. This result, combined with the insignificance of this variable in the salary level equation, suggests that any differential which an experienced faculty member receives upon entry disappears over time. In terms of contribution to raises, the interaction terms do not show that these categories contribute significantly more to female raises than male raises.

Of particular interest are the measures of research productivity in determining raises. Of the three measures of research productivity, only refereed articles are significant. Books and exhibitions-performances do not have a significant impact on raises. Moreover, refereed articles lead to significantly higher than average raises for males but not for females. However, this result should be interpreted with caution. It reflects that, on average, female raises are not heavily influenced by refereed journal articles. It does not necessarily imply that individual female faculty are not rewarded for publishing refereed journal articles nor that females did not publish refereed journal articles. Nonetheless, as in many other studies,(8) the mean number of articles per female faculty is significantly lower than that of the male faculty.(9)

Recall that the gender interaction term for refereed articles measures the difference between the male coefficient and the female coefficient for refereed articles. Since the difference is not significant, we can conclude that an article would contribute as much toward a raise for a female as for a male. At the same time, we cannot rule out that females without refereed articles may be receiving raises comparable to females with refereed articles.

Calculating the total effect reveals that males receive seven percent higher raises than females. The endowment effect reflects that males receive more than six percent higher raises than females due to research productivity, rank, degree held, experience, and academic discipline. The residual effect is negative but less than one percent and insignificant. We cannot reject that male and female salaries are receiving raises at the same rate once human capital, discipline, rank, and productivity are taken into account.

As before, there is a negative residual effect suggesting contrasting influences at work. Indeed, the constant effect is positive and significant, although less so than for salary, and the coefficient effect is negative but not significant.(10) As previously pointed out, the constant effect differences may be reflecting base category differences and factors which the traditional model does not capture. There is no evidence that the model is misspecified. The F value for Ramsey's test is not significant using Leamer's F.

The large and negative coefficient effect suggests that if females were given raises based on their human capital, academic discipline, rank, and productivity in the same manner as males, they would receive lower raises than they actually received. This result is consistent with the result of the examination of the differential impact of refereed articles on male versus female salaries. As with salary level, raises for females appear to be determined by a set of factors which differ from those used to determine male raises.

V. Conclusions

By incorporating factors representing research productivity and employing additional statistical tests, added evidence on the differences in salaries between male and female faculty is provided. A longitudinal data set for The University of Alabama is used to analyze salary differences for males and females when human capital, academic discipline, rank, and productivity are taken into account.

There is strong evidence that salaries (raises) for females are determined by a set of factors which differ from those used to determine male salaries. It appears that the university pays higher salaries and gives higher raises to females than their human capital, academic discipline, rank, and research productivity would warrant but pay lower salaries and give lower raises based on factors whose effects show up in the constant (intercept) differences.

Similar to the conclusions of Raymond, Sesnowitz and Williams |29~ in the Kent State University study, any suggested discrimination is not occurring in response to human capital, rank, discipline, and research productivity at The University of Alabama. Indeed, female faculty members receive higher raises than male faculty members in response to these factors.

1. Many studies have ignored various factors which are important when considering discrimination |5; 7~. Some, for instance, have used human capital models including only inputs into the production function (education, experience, etc.) and not measurements of output (productivity of faculty) when comparing salary differences. Exceptions to this are Ferber and Green |9~, whose results were contradicted by Herberfield and Gerhart, |16~, who found no gender discrimination when replicating the 1984 study. Others include Ferber, Loeb, and Lowry |10~, and Tuckman, Gapinski, and Hagemann |34~. For related studies regarding faculty productivity, see Sauer |30~, Hamermesh, Johnson, and Weisbrod |15~, Katz |22~, and Tuckman and Leahey |33~.

Others have limited their analysis to a single point in time and ignored raises over time. An exception to this is the work by Father |8~. Farbet uses longitudinal data representing many institutions while the data used here are for one institution.

In addition, most of these studies have presented statistical measures of discrimination without sufficient statistical tests of significance. See Jackson and Lindley |19~ for discussion of this point.

2. The category "exhibitions-performances" includes those activities which do not involve written output, but nonetheless are important measures of productivity in the applicable disciplines. Examples are production of pieces of art, performance in theater or music, and recitations of work in literature.

3. Productivity variables can be considered change variables in that they reflect the incremental increase to a stock of research. Data for the stock of research prior to 1981 was not available. Thus, we were not able to create a relative change variable (incremental increase/base) or to determine the extent to which previous research affected raises.

4. The salary level model also was run with productivity variables to determine their impact. Productivity variables were significant in approximately the same manner as they were for the raise model.

5. A significant and positive residual effect can be interpreted as evidence that females receive salaries (raises) significantly less than males even after consideration is taken of endowments. The term endowment effect stems from its use in models employing only human capital variables. In this paper, explanatory variables include not only human capital variables, but employment variables (disciplines and rank) and productivity variables. Thus, the endowment effect includes the effect of human capital, discipline, rank, and research productivity. A positive and significant constant effect suggests discrimination against females since it reflects that there are significant differences in salaries (raises) which are not explained by the independent variables. A positive and significant coefficient effect can be interpreted as evidence that males receive higher salaries (raises) even when account is taken of the endowment variables (human capital, academic discipline, rank, and research productivity). A negative and significant coefficient effect can be interpreted as evidence that females receive higher salaries (raises) than their endowment variables would warrant. In essence, reverse discrimination against males would be implied. See Fishback and Terza |12~ for another possible approach to investigating this problem.

6. For discussions regarding tests using pooled data see Amemiya |1, 35-37~, Conefly and Mansfield |6~, Kmenta |23~, Toyoda |35~, and Weerahandi |36~.

7. A significant constant effect can be considered prima facie evidence of discrimination if the model is not misspecified. However, omitted variables, endogenous explanatory variables, errors in measurement, or an incorrect functional form could be leading to biased estimates of the constant and coefficient effects. A test for misspecification has been developed by Ramsey |27~ and modified by Ramsey and Schmidt |28~, and Thursby and Schmidt |32~. For the log of salary model, the F value (F = 7.17 for Ramsey's test is significant using Leamer's critical value for F for testing specification hypotheses |24, 114-15~. Leamer's F value is calculated as |Mathematical Expression Omitted~ where N = number of observations, K = number of variables, and R = number of restrictions. In this case, the critical F = 5.5. In an attempt to determine if an incorrect functional form was leading to misspecification, the regressions were run using the square root of salary as the dependent variable. The F value for Ramsey's test is 1.27 which is not significant at the .10 level leading us to reject that the model is misspecified. The results of this model are virtually identical to those of the log salary model. Because of the predominant use of log salary models in discrimination investigations, the log salary results are used in the paper.

8. Much evidence exists which suggests productivity differences. For example, Katz |22~, using a productivity index, found that men were significantly more productive than women. Ferber, Loeb and Lowry |10~ reported that men published significantly more articles than women; Ferber and Green |9~ report higher levels of research output for males than for females; and Fish and Gibbons |11~ found that female economists have a lower average number of publications. Lastly, Strober and Quester |31~ cite an unpublished paper which examined differences in salaries between males and females in terms of research and found lower productivity for women.

9. The maximum number of articles for males is 32 while the maximum number for females is 19. The mean number of articles for males is 2.76 and for females 1.39. The t value for the differences between the means is 3.67 which is significant at the .01 level.

10. The constant effect and the coefficient effect usually have the same sign and in that case a positive constant effect would lead to a positive residual effect.

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