Using Stochastic Dominance to Investigate Salary Inversion in Business Schools

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1 Using Stochastic Dominance to Investigate Salary Inversion in Business Schools Tom Arnold Raymond P. H. Fishe Robins School of Business University of Richmond Richmond, VA Adam Schwartz Williams School of Commerce, Economics and Politics Washington & Lee University Lexington, VA ABSTRACT The paper analyzes AACSB salary survey information from 1979 to The question addressed in this analysis is whether salary inversion is wide-spread across the business disciplines. We find limited evidence of mean level inversions, which is concentrated in recent years. Stochastic dominance methods confirm these results. We also develop a measure of salary dominance based on comparing the distribution of reported salaries. This statistic shows a significant trend towards salary inversion in most AACSB disciplines. Contact author: pfishe@richmond.edu Draft: September 2008 Comments Welcome Please do not cite or quote without permission of the authors Pat Fishe thanks the Robins School of Business for generous research support and assistance with purchases of AACSB data. The authors also wish to thank Eli Bauman and Neil Biller for very capable research assistance and data collection. Also, special thanks to Joseph Mondello (AACSB) for assembling copies of the early salary survey reports. All errors are our own responsibility.

2 Using Stochastic Dominance to Investigate Salary Inversion in Business Schools I. Introduction Every year academic department chairs and deans deliberate over salary adjustments from limited raise pools. Generally, business schools base a substantial portion of these raise adjustments on merit, as opposed to rank or length of service. Even so, considerations of equity are not lost in the process. In particular, the phenomenon of salary inversion may arise in some disciplines, which may task administrators to explain their decisions. Salary inversion occurs when a faculty member of higher rank receives a salary less than that of a faculty member of lower rank. 1 Salary inversion may also arise after the hiring of new junior faculty members and provides insight into the basic supply and demand conditions in the market. As merit considerations may be difficult to quantify and comparisons of records and experience equally difficult to develop objectively, those faculty affected by salary inversion may feel wronged or disadvantaged by the raise or hiring processes. In an effort to provide better information to all faculty and administrators, we investigate the extent of salary inversion in business schools accredited by the Association to Advance Collegiate Schools of Business (AACSB). We study eight disciplines: Accounting, Computer Information Systems (CIS), Economics, Finance, Management, Marketing, Organizational Behavior, and Operations Management. We use data collected by the AACSB in its annual salary survey. Our dataset covers the 1 Toutkoushian, (1998) uses level of experience instead of rank to define salary inversion. We will use the rank measure, as the level of experience is not available from the AACSB salary surveys.

3 years, 1979 to These are aggregate data, which reveal means, medians and other selected distributional information on academic salaries. We document mean levels of salary inversion between assistant and associate professor ranks for Finance and Accounting disciplines at both private and public business schools, and for Economics and Operations Management at private schools. Typically, these average level inversions arise first at private schools and then at public schools. All of these inversions begin in the late 1990s or early 2000s. We find little evidence of sustained inversions between assistant and associate professors or any years with average level inversions between associate and full professors in these business disciplines. We also analyze the distribution of salaries across disciplines and ranks over the AACSB data. We examine whether junior ranks dominate the more senior ranks in terms of first- and second-degree stochastic dominance. We use stochastic dominance methods because they offer information on all salaries within a rank, not just a summary comparison such as provided by mean or median statistics. First-degree stochastic dominance implies that salaries are uniformly higher across the entire distribution of all junior faculty members. Thus, first-degree dominance is a stronger statement about salary conditions between ranks than a comparison of means, and implies a greater burden on administrators to explain relative salary levels and adjustments. Note that if a junior rank is first-degree dominate over a more senior rank then the average salary of the junior rank will be greater than the average salary of the more senior rank. 2 Therefore, first-degree stochastic dominance implies average-level salary inversion, but not vice versa. 2 There is an extensive literature on the use of stochastic dominance in portfolio selection and decisionmaking under uncertainty. See Levy (2006) for comprehensive discussion of this literature and stochastic dominance theorems. 2

4 Evidence of first-degree stochastic dominance in any period is also likely to imply substantial salary changes in future periods when some junior faculty are promoted and move up through the ranks. LeClair (2004) makes a similar point while discussing the AACSB salary survey: most recent trends still hold. For instance, the inversion of salary rates where new hires earn as much or more than experienced faculty is still in place and will inevitably contribute to the escalation of salaries across all categories. We test for second-degree stochastic dominance when the salary distributions cross, which negates evidence of first-degree dominance. Second-degree stochastic dominance also implies that salaries show inversion at the mean. 3 However, when there is no first-degree dominance, second-degree dominance allows some salaries for faculty at senior ranks to exceed those of junior ranks when matched along the probability distribution of salaries. In effect, business schools exhibit a spectrum of faculty quality, which leads to both higher and lower relative salaries from rank comparisons. With second-degree dominance, we develop a summary statistic to define the incidence of dominance between two salary distributions. This statistic reveals the fraction of the junior rank distribution that dominates a more senior rank distribution. Our results show only a limited number of years with stochastic dominance in which a junior rank dominates a senior rank. We find no examples of either first- or second-degree dominance for associate and full professors, and only four years with second-degree dominance between assistant and associate professors. These are all recent years and arise in the disciplines of Finance and Operations Management. 3 Strictly speaking, if X is second-degree stochastically dominant over Y then E[X] E[Y]. 3

5 To address the issue of faculty quality with the AACSB data, we perform separate analyses for private and public business schools. We also re-calculate salary distributions after adjusting for non-overlapping observations. Specifically, many business schools may have senior faculty members who have substituted away from the school s mission or otherwise become less productive, and the salary of such faculty will be relatively low as a result. Alternatively, some schools may have recently hired outstanding senior scholars at salaries far above those at the same rank. These outliers may significantly affect our mean level and distributional comparisons. To eliminate this problem, we adjust the salary distributions such that only salaries that overlap between rank comparisons are included in the analysis. For example, assistant professors of finance had a salary range of $48,700 to $171,800 in the AACSB salary survey of private accredited schools, while associate professors of finance had a range of $43,400 to $195,400. At the mean, assistant professors earn $116,600 and associate professors earn $112,500, which indicates salary inversion. However, these data only overlap for the assistant professor range, so we recalculate the associate professor distribution to make mean and stochastic dominance comparisons only over this range. This has the effect of shifting the associate professor (conditional) mean to $117,006, which no longer shows salary inversion. In effect, by comparing faculty with overlapping salaries who arguably may have similar levels of productivity we introduce a control for quality differences that left uncontrolled may skew our results. Our research relates to recent work on salary compression in higher education (Toutkoushian (1998) and Barbezat (2004)). Salary inversion is closely associated with 4

6 salary compression, which occurs when salaries for different ranks approach each other over time. Toutkoushian (1998) suggests that salary compression (or inversion) arises in institutions that have hired several new junior faculty members, but failed to adjust compensation levels to existing faculty members. He develops a regression procedure to estimate what junior faculty would earn if they were compensated according to the mechanism used for more senior faculty. Barbezat (2004) applies this method to two national surveys of faculty salary and finds evidence of salary compression across a range of disciplines. By using the AACSB survey data, we also provide evidence for a national sample, although our methods are different because we do not observe individual faculty data. The outline of this paper is as follows. In section II, we discuss the development of the AACSB salary surveys and the extent of information provided about salary distributions. Section III investigates mean level salary inversion and documents inversion differences between private and public business schools. This section also provides a detailed discussion of the Finance discipline. Section IV introduces stochastic dominance methods and applies them to the AACSB data. We modify these methods to help control for quality differences among faculty and develop a statistic to measure the degree of dominance between faculty ranks. Section V offers our conclusions. II. Data The AACSB has conducted salary surveys from member business schools since The early salary surveys ( ) were more general data collection and reporting efforts. Beginning in 1972, member institutions reported detailed information 5

7 that included means and standard deviations. These detailed surveys reports distinguished salary information by discipline, degree-granting level, enrollment and regional categories. Beginning with the survey, the AACSB changed the method by which it reported salary distributions, providing data on salaries at specific percentiles. The percentile breakdown reported maximum and minimum salaries as well as salary cutoffs for the 10%, 25%, 50%, 75%, and 90% levels. The mean salaries continued to be reported, but the standard deviations were dropped after Throughout the years since 1978, the AACSB continued to modify what information they collected. In 1983, it introduced additional discipline distinctions particularly the Management discipline was further distinguished with Organizational Behavior and Operations Management distinctions. However, the basic format of the salary information means and percentiles remained the same, so these reports continued to provide a consistent series on annual academic compensation in business schools. As an accrediting body, the response rates to these surveys have always been high, typically above 90 percent for accredited schools and around 50 percent for nonaccredited schools. Table 1 shows that the majority of the overall response rates are between 70 to 80 percent and that the sample sizes are all large for the four institutional groupings: private versus public and accredited versus non-accredited. However, the lower response rates for non-accredited schools may introduce selectivity biases into our analysis. As such, we will only focus on salary structure in accredited business schools. These response rates exceed the sample size requirements necessary to make reliable statistical statements and leave little concern for selectivity bias, as the number of nonrespondents is unlikely to skew any results. 6

8 The data that we analyze consists of 16,698 entries from the AACSB annual surveys conducted between 1979 and The smallest unit of measurement in these surveys is the rank and hiring status of faculty. Specifically, the survey reports provide average and percentile information for existing instructors, assistant, associate and full professors, as well as new hires. These salary data are reported separately by discipline, institutional type (public or private) and accreditation status. Table 2 offers a picture of these data by summarizing of the mean, maximum and minimum salary averages across accredited schools for assistant, associate and full professors by discipline for the first, middle and last year of the AACSB sample data. Table 2 reports salary data in $1,000s, which are not inflation adjusted. These data show substantial nominal salary grow rates in most business disciplines. For the entire 26-year period, salaries over all disciplines grew at a compound average of 5.7% per year. As CPI inflation over this period averaged 3.8% per year, real wage growth was about 2.0% per year. Slightly less favorable conditions prevailed in the second half of our sample, between 1992 and Nominal salary growth averaged 3.9% per year and inflation averaged about 2.4% per year. Thus, real wage growth dipped to 1.5% per year. The minimum salary levels grew at 1.8% per year less than the average growth rate and the maximum levels grew at 1.5% more than the average, which suggests that the variance of accredited business school salaries has increased over time. III. Analysis of Averages Our focus is on relative salary comparisons between ranks within a given discipline. We begin the analysis by investigating sample averages across the AACSB 7

9 disciplines. The data in Table 2 provide our first look at salary inversion cases in AACSB business schools. This table shows that Assistant Professors on average earn more than Associate Professors in Finance during the academic year. This result also arises with a comparison of the median salaries in Finance. No other discipline shows an average level inversion during or in the two previous surveys. However, the disciplines of CIS, Marketing and Operations Management all show median level inversions and CIS shows an inversion at the maximum level. These data suggest that mean salary inversions are likely a limited phenomenon in business schools. To explore these results further, we examine the Finance discipline in more detail, and then use similar methods for the other disciplines. A. A Closer Look at Finance Salaries Figures 1 and 2 provide graphs of average and maximum salary levels for the Finance discipline over our sample period. The data in both figures are for accredited business schools. Figure 1 shows salary information for private schools and Figure 2 shows the same information for public schools. The two graphs in each figure pair up assistant and associate professors and associate and full professors, respectively. The pairing for assistants and associates at both public and private schools show that average level salary inversions began at different periods for these two types of institutions. For private schools, average salary inversions in finance began in 1999, but it was not until 2002 that it arose in public schools. There may be many possible reasons for this threeyear lag in competitiveness, such as budget constraints tied to state funding, a lack of 8

10 incentives to be competitive in public schools, and a selectivity preference among the more talented new or existing assistant professors toward private institutions. Unfortunately, the AACSB data do not provide an opportunity to examine these various possibilities in detail. However, we can investigate the extent of these differences across the various business school disciplines. Specifically, we can say that the differences in salaries between public and private institutions are statistically different from zero at the 1% level with private institutions paying more on average for all ranks in finance. A time-trend regression shows that that average salaries of assistant professors are increasing by approximately $78 per year (p-value = 0.07) more than average salaries of associate professors at private schools. 4 This estimate is $51 per year for public schools, but the time trend coefficient is not statistically significant for the public school sample. The data in Figures 1 and 2 also show that average salary inversions do not extend to a comparison between associate and full professors of finance. The average salary difference is $12,800 between associate and full professors in public schools versus $25,300 in private schools. The public/private gap is greatest in the 2005 survey, where the average associate-to-full salary difference is $28,000 for public schools and $46,300 for private schools. Figures 1 and 2 also confirm that associate/full professor salary gap is increasing over time. Similar to the results for assistant and associate professors, we estimated a time trend regression to determine the relative salary path for associate and full 4 This is the coefficient on the time trend variable in a regression adjusted for first-order serial correlation and estimated over the entire sample period. The p-value of this estimated coefficient is and the adjusted R-squared is The dependent variable is the difference in average salary between assistant and associate professors. 9

11 professors. This regression shows that the average salary of associate professors decreases $855 per year (p-value = 0.003) relative to the average salary of full professors in private business schools. This time trend coefficient shows a decrease of $311 per year (p-value = 0.011) for public business schools. These results also show that salary relationships differ between private and public business schools, with private schools maintaining increasingly higher salaries for full professors. The differences between average salaries for associate and full professors of finance suggest that the variance of these salary distributions may be increasing over time, which may also be true for assistant professors. The increasing levels of the maximum salaries in Figures 1 and 2 also support this view. B. Salary Inversion by Discipline Table 3 provides a summary of mean level salary inversions for all years in our sample. Four disciplines Accounting, Economics, Finance and Operations Management show evidence of salary inversion in private business schools, whereas only Accounting and Finance show this evidence in public business schools. Across these groups, the average size of such inversions range from $500 in Economics to $5,775 in Operations Management for private schools and from $300 in Accounting to $3,700 in Finance for public schools. Table 3 also shows that salary inversion is a recent phenomenon with the earliest case in Finance in Most instances, however, began in 2002 or 2003, which means that overall salary inversion has affected business schools for only a few years. Although deans and department chairs must rationalize salary decisions to other administrators and 10

12 possibly the faculty, these results show relatively small differences in compensation are in question, except for the discipline of Operations Management. Thus, the concern expressed by LeClair (2004) that salary inversion is widespread in business disciplines may be overstated. To determine whether these average salary differences are statistically significant, we conducted three tests: pairwise Student s t-test assuming unequal variances, Wilcoxon signed-rank test and the Mann-Whitney U-test, with the Mann-Whitney U-test focused on whether the distributions between two ranks were identical. Table 4 reports the results of these tests for all disciplines with AACSB-accredited private and public schools analyzed separately. Table 4 reports the p-values for each test. If deans and department chairs are treating the different ranks as increasing in value from junior to senior levels, then we would expect to find significant differences between these salary comparisons. This result arises most strongly for associate and full professor comparisons. In every discipline and for private and public schools, average salaries are statistically greater for full professors than associate professors. This result is not compelling for salary comparisons between assistant and associate professors. The Student s t-test and Mann- Whitney U-test show a lack of significance for every discipline except accounting in public business schools. The Wilcoxon signed-rank test shows a different set of results. With this test, only the Finance discipline in private business schools has no statistically significant difference between average salaries for assistant and associate professors. This test may lack power compared to the Student s t-test, particularly the assumption that the data are from two related samples may not be valid in these comparisons. The 11

13 general import of these results is that we will now focus our remaining analysis on the differences between assistant and associate professors because it appears that there are demonstrative differences between associate and full professor ranks. IV. Stochastic Dominance in Salaries The previous results show that there is some evidence of average-level salary inversion across certain AACSB disciplines for assistant and associate professor ranks, but none for associate and full professors. The significance tests, however, show more similarity between the junior ranks than indicated by average comparisons, particularly for private business schools. In this section, we examine the relationship between assistant and associate ranks using stochastic dominance methods. We also adapt these methods to control for quality differences and to develop a statistic that measures the extent of dominance between two salary distributions. A. Stochastic Dominance by Discipline We investigate the AACSB salary distributions for evidence of first- and seconddegree stochastic dominance. 5 First-degree dominance implies that the salary distribution of a junior rank everywhere dominates that of a senior rank. In effect, the cumulative distribution function of the junior rank lies beneath that of the senior rank as measured across salaries. Second-degree dominance is less restrictive and is a consideration when the two cumulative distributions cross, possibly multiple times. Second-degree dominance requires a comparison of the areas between the two distributions over the 5 We do not compute third-degree stochastic dominance results, although they may be derived from the AACSB data. 12

14 entire range of salaries. These areas are compared at each salary level, and the junior rank distribution must prevail in area for every comparison for second degree dominance to hold. We follow the methods in Levy (2006), who provides details on how such comparisons are made using asset return distributions to construct optimal portfolios. As both first- and second-degree stochastic dominance imply mean level salary inversion, there are only a few years and disciplines that present the opportunity for either type of dominance by junior ranks. However, we can reverse the analysis to ask whether the associate rank shows evidence in its salary distribution of dominating the assistant rank. One may expect to find such dominance given the lack of salary inversion in most years and most disciplines. Table 5 presents the results of this analysis. Table 5 reports all cases of dominance in either direction of rank. Panel A reports results for private business schools and Panel B reports results for public business schools. These panels show consistent dominance by associate professors over assistant professors in the early years of the AACSB salary surveys. For the six years, 1983 to 1988, 85% of the entries show first- or second-degree dominance by associate professors in private schools, and 95% of the entries show associate professor dominance in public schools. The six-year period at the end of our sample, 2000 to 2005, tells a different story. Now only 28% or the entries show dominance by associate professors for private schools and only 52% show this dominance for public schools. The trend is that first- and second-degree dominance is more difficult to identify because assistant and associate salary distributions show more ranges in which salaries overlap, which rules out firstdegree dominance. This trend holds for all disciplines except Economics in public schools and Organizational Behavior in both private and public schools. 13

15 B. Stochastic Dominance Adjusted for Overlapping Salaries The basic results on stochastic dominance offer no controls for faculty quality other than the distinction between private and public schools. However, the AACSB survey data offer an opportunity for an additional control on quality. Specifically, we can determine where salaries overlap on these distributions, and re-compute the stochastic dominance comparisons using only overlapping salary ranges. 6 To the extent that academic salaries are competitively determined, these overlapping ranges are expected to identify faculty who offer their institutions similar marginal revenue product. In which case, we would expect to find fewer examples of one rank consistently dominating another rank using these adjusted distributions. Table 6 presents our results on stochastic dominance for overlapping salary ranges. Now either first- of second-degree stochastic dominance arises in many fewer cases. In Table 5 using the entire salary distribution, 37% of the comparisons for private schools and 33% for public schools resulted in No dominance for either rank. These results change to 65.2% and 55%, respectively, in the overlapping salary results shown in Table 6. These percentage increases give support to the view that institutions may regard the assistant and associate ranks as having similar marginal revenue product. The results in Table 6 also continue to support the view that salaries for the assistant professor rank in selected disciplines are gaining on the associate professor rank. The fraction of cases in which associates dominate assistants decreased significantly between the early and late six-year intervals, and For private schools, this fraction decreased from 35.4% to 8.3% and for public schools in decreased even 6 After determining the overlapping salaries ranges, the distributions are re-scaled to proper density before computing stochastic dominance tests. 14

16 more notably from 61.4% to 11.4%. A look at Table 6 will also show many more cases in which assistant professors are first- or second-degree dominant over associate professors. The clearest cases of this trend occur in Finance and CIS at public schools and Management at private schools. C. Measuring the Degree of Dominance The stochastic dominance results suggest that there may be a trend towards greater salary inversion over time. Unfortunately, the discrete nature of the stochastic dominance method either first degree or second degree or not dominant provides little flexibility to understand how close these salary distributions are to being dominant in one form or another, and whether this closeness is changing over time. To address this problem, we develop a measure of the degree of first-degree dominance between two salary distributions. First-degree dominance between assistant and associate professors implies that the assistant professor distribution lies everywhere beneath the associate professor distribution over the range of salaries. If these distributions overlap, then first-degree dominance cannot hold. This means that these distributions may overlap for only a small salary range and first-degree dominance is invalidated. As first-degree dominance offers a clear picture of salary inversion, we extend the concept to measure the degree to which one distribution lies beneath another over the salary range. Specifically, we define the dominance fraction as the percent of the cumulative distribution function that lies beneath the comparison cumulative distribution. If the dominance fraction equals 100% then one distribution is first-degree dominant over the other distribution. If the dominance fraction 15

17 is 0%, then the second distribution actually dominates the first distribution. The dominance fraction provides a continuum of values between zero and one to use in judging how close two ranks are to first-degree stochastic dominance. Table 7 reports the dominance fraction for both private and public schools across the eight business disciplines. We compute the dominance fraction for two cases: the entire salary distribution (All) for assistant and associate professors and the overlapping distributions for these ranks (Overlap). The case in which the entire distribution is used shows an increasing dominance fraction in recent years. In private schools, only the discipline of Organizational Behavior is not participating in this trend, which appears to be strongest in Finance and Operations Management. The trend is also present in public schools but the dominance fraction is not as large as in private schools. The overlapping distributional data show even stronger results for dominance of assistant professor over associate professors. In Finance, the overlapping distribution of assistant professors is first-degree dominant for the last four years of the AACSB salary survey in public schools, and nearly as strong in private schools. The disciplines of Operations Management and Management also show a strong degree of dominance in recent years in private schools. Overall, these results indicate that salaries of assistant professors are converging (or exceeding) to those of associate professors across business school disciplines with only a few notable exceptions. V. Conclusion The issue of relative academic salaries is important to faculty and administrators for budgeting and provision of incentives within business schools. Using AACSB salary 16

18 survey data, we show that mean level salary inversion between assistant and associate professors is isolated to only a few disciplines, and found only in recent years. However, applying the method of stochastic dominance, we observe that there is a trend towards increasing salary inversions. We develop a dominance fraction to measure this trend and find that notable increases in the degree of dominance by assistant professors in both public and private business schools. 17

19 References Barbezat, Debra A., 2004, A Loyalty Tax? National Measures of Academic Salary Compression, Research in Higher Education 45 (7), Gomez-Mejia, Luis R. and David B. Balkin, 1987, Pay Compression in Business Schools; Causes and Consequences, Compensation and Benefits Review 19 (5), Glandon, Sid and Terry Ann Glandon, 2001, Faculty Turnover and Salary Compression in Business Schools: Comparing Teaching and Research Missions, Journal of Applied Business Research 17 (2), LeClair, Dan, 2004, The Professor s Paycheck, BizEd (March/April), Levy, Haim, 2006, Stochastic Dominance: Investment Decision Making Under Uncertainty, Studies in Risk and Uncertainty, Springer: New York. Toutkoushian, Robert K., 1998, Using Regression Analysis to Determine if Faculty Salaries are Overly Compressed, Research in Higher Education 39 (1),

20 Table 1 Response Rates to AACSB Salary Surveys, 1979 to 2005 This table reports response rates and counts of business school respondents to the AACSB salary surveys from 1979 to The total faculty included in these surveys is also shown. Note that ʺnrʺ indicates that this information is not available in the salary report. Responses Received From: Accredited Non accredited Year Response Rate Mailed to Private Public Private Public Sample Size Total Faculty % , % , % , % , % , % , % , % , % , % , % , % , % , % , % , % , % , % , % , % , % , % 628 nr nr nr nr , % 550 nr nr nr nr , % 571 nr nr nr nr , % 563 nr nr nr nr , % 548 nr nr nr nr , % 538 nr nr nr nr ,926

21 Table 2 AACSB Salary Comparisons for 1979, 1992 and 2005 This table reports salary data by discipline across all reporting AACSB member schools, combining accredited with non accredited and public and private institutions. Data are shown for the beginning, midpoint and ending periods in the AACSB sample. Panel A reports the salary averages, Panel B reports the salary medians and Panel C reports the salary maximums. For the survey years 1979 to 1982, the AASCB did not provide separate information for Computer Information Systems, Organizational Behavior and Operations Management disciplines, so a ʺnrʺ is reported. All amounts are in $1,000 without inflation adjustments. Discipline Survey Year Assistant Professor Associate Professor Full Professor Survey Year Survey Year Assistant Professor Associate Professor Full Professor Assistant Professor Associate Professor Full Professor Panel A: Average across All Business Schools Accounting Computer Information Systems nr nr nr Economics Finance Management Marketing Organizational Behavior nr nr nr Operations Manage me nt nr nr nr Panel B: Medians across All Business Schools Accounting Computer Information Systems nr nr nr Economics Finance Management Marketing Organizational Behavior nr nr nr Operations Manage me nt nr nr nr Panel C: Maximum across All Business Schools Accounting Computer Information Systems nr nr nr Economics Finance Management Marketing Organizational Behavior nr nr nr Operations Manage me nt nr nr nr

22 Table 3 Salary Inversions for Assistant versus Associate Professors by Discipline This table reports the years during which the average salary of assistant professors exceeded associate professors by discipline and by type of institution. The average difference in salaries is reported using only years where salaries are inverted. A positive number implies that assistant professorsʹ average salary exceeding associate professorsʹ average salary by that mean amount. Computer Information Organizational Operations Comparison Accounting Systems Economics Finance Management Marketing Behavior Management Panel A: Private AASCB Accredited Business Schools Inversion Years none none none none Average Salary Difference for Inversion Years $2,000 n.a. $500 $3,671 n.a. n.a. n.a. $5,775 Panel B: Public AACSB Accredited Business Schools Inversion Years none none none none none none Average Salary Difference for Inversion Years $300 n.a. n.a. $3,700 n.a. n.a. n.a. n.a.

23 Table 4 Comparison Tests for Average Salaries by Discipline This table reports the results of three statistical tests designed to determine if there are significant differences between salaries at lower and higher ranks. The Studentʹs t test compares means salaries assuming unequal variances; the Wilcoxon Signed Rank test compares paired differences of salary averages; and the Mann Whitney U test compares salary distributions. Data shown in the table are p values for one tail t tests and two tail tests for the remaining statistics. The data are divided by discipline and institutional type private versus public in Panels A and B. The results for Computer Informaton Systems, Organizational Behavior and Operations Management disciplines are for 1983 to Studentʹs t test Wilcoxon Signed Rank Mann Whitney U Assistant Assistant Assistant v. Associate v. Associate v. Associate Discipline Associate v. Full Associate v. Full Associate v. Full Panel A: Private AASCB Accredited Business Schools Accounting Computer Information Systems Economics Finance Management Marketing Organizational Behavior Operations Management Panel B: Public AACSB Accredited Business Schools Accounting Computer Information Systems Economics Finance Management Marketing Organizational Behavior Operations Management

24 Table 5 First and Second degree Stochastic Dominance for Assistant and Associate Professors The results of first and second degree dominance tests are presented for private business schools in Panel A and public business schools in Panel B. The distributions are compared for each survey year, 1979 to 2005 by discipline. All faculty are affiliated with AACSB accredited business schools. An ʺASSTʺ implies that Assistant professors are dominant over Associate professors; an ʺAssocʺ implies that Associate professors are dominant; and ʺNoʺ implies that a dominance relationship cannot be determined. Computer Information Systems Economics Finance Management Marketing Accounting Organizational Behavior Operations Management Year 1st deg 2nd deg 1st deg 2nd deg 1st deg 2nd deg 1st deg 2nd deg 1st deg 2nd deg 1st deg 2nd deg 1st deg 2nd deg 1st deg 2nd deg Panel A: Private AACSB accredited Business Schools 1979 Assoc Assoc Assoc Assoc Assoc Assoc Assoc Assoc Assoc Assoc 1980 Assoc Assoc Assoc Assoc Assoc Assoc No No Assoc Assoc 1981 Assoc Assoc Assoc Assoc Assoc Assoc Assoc Assoc Assoc Assoc 1982 Assoc Assoc Assoc Assoc Assoc Assoc Assoc Assoc Assoc Assoc 1983 Assoc Assoc Assoc Assoc Assoc Assoc Assoc Assoc Assoc Assoc Assoc Assoc Assoc Assoc Assoc Assoc 1984 Assoc Assoc Assoc Assoc Assoc Assoc Assoc Assoc Assoc Assoc No No Assoc Assoc Assoc Assoc 1985 Assoc Assoc Assoc Assoc Assoc Assoc No No No No No No No No No No 1986 Assoc Assoc Assoc Assoc Assoc Assoc Assoc Assoc Assoc Assoc Assoc Assoc Assoc Assoc Assoc Assoc 1987 Assoc Assoc Assoc Assoc Assoc Assoc Assoc Assoc Assoc Assoc Assoc Assoc Assoc Assoc Assoc Assoc 1988 Assoc Assoc Assoc Assoc Assoc Assoc Assoc Assoc Assoc Assoc No No Assoc Assoc Assoc Assoc 1989 No No Assoc Assoc Assoc Assoc Assoc Assoc Assoc Assoc No No Assoc Assoc No No 1990 Assoc Assoc Assoc Assoc No Assoc No No Assoc Assoc Assoc Assoc Assoc Assoc Assoc Assoc 1991 No No No No No No No Assoc Assoc Assoc No No Assoc Assoc Assoc Assoc 1992 No Assoc Assoc Assoc No No No Assoc No Assoc No No No No No Assoc 1993 No No No No Assoc Assoc Assoc Assoc No No No Assoc No No Assoc Assoc 1994 Assoc Assoc No Assoc Assoc Assoc No No No Assoc Assoc Assoc Assoc Assoc Assoc Assoc 1995 No No No No Assoc Assoc No No No Assoc Assoc Assoc Assoc Assoc Assoc Assoc 1996 Assoc Assoc No No Assoc Assoc No Assoc No Assoc No No Assoc Assoc No Assoc 1997 Assoc Assoc No No Assoc Assoc No Assoc Assoc Assoc No No Assoc Assoc Assoc Assoc 1998 Assoc Assoc Assoc Assoc Assoc Assoc No Assoc Assoc Assoc No No No No No Assoc 1999 No No No No Assoc Assoc No No Assoc Assoc No Assoc Assoc Assoc Assoc Assoc 2000 No No No Assoc No No No No No Assoc No No Assoc Assoc Assoc Assoc 2001 No No No No No No No No No No Assoc Assoc No No Assoc Assoc 2002 No No No No No No No No No Assoc No No Assoc Assoc No ASST 2003 No No No Assoc No Assoc No No Assoc Assoc No Assoc Assoc Assoc No No 2004 No No No No No No No No No Assoc No Assoc Assoc Assoc No ASST 2005 No No No No No No No ASST No No No Assoc Assoc Assoc No ASST

25 Table 5 (continued) First and Second degree Stochastic Dominance for Assistant and Associate Professors Computer Accounting Information Systems Economics Finance Management Marketing Organizational Behavior Operations Management Year 1st deg 2nd deg 1st deg 2nd deg 1st deg 2nd deg 1st deg 2nd deg 1st deg 2nd deg 1st deg 2nd deg 1st deg 2nd deg 1st deg 2nd deg Panel B: Public AACSB accredited Business Schools 1979 Assoc Assoc Assoc Assoc Assoc Assoc Assoc Assoc Assoc Assoc 1980 Assoc Assoc No Assoc Assoc Assoc Assoc Assoc Assoc Assoc 1981 Assoc Assoc Assoc Assoc Assoc Assoc Assoc Assoc Assoc Assoc 1982 No No No No No No Assoc Assoc Assoc Assoc 1983 Assoc Assoc Assoc Assoc No No Assoc Assoc Assoc Assoc Assoc Assoc Assoc Assoc Assoc Assoc 1984 Assoc Assoc Assoc Assoc Assoc Assoc Assoc Assoc Assoc Assoc Assoc Assoc No No Assoc Assoc 1985 Assoc Assoc Assoc Assoc Assoc Assoc Assoc Assoc Assoc Assoc Assoc Assoc Assoc Assoc Assoc Assoc 1986 Assoc Assoc Assoc Assoc Assoc Assoc Assoc Assoc Assoc Assoc Assoc Assoc No No Assoc Assoc 1987 Assoc Assoc Assoc Assoc Assoc Assoc Assoc Assoc Assoc Assoc Assoc Assoc Assoc Assoc Assoc Assoc 1988 Assoc Assoc Assoc Assoc Assoc Assoc Assoc Assoc Assoc Assoc Assoc Assoc Assoc Assoc Assoc Assoc 1989 Assoc Assoc Assoc Assoc No No No No No No Assoc Assoc Assoc Assoc Assoc Assoc 1990 Assoc Assoc Assoc Assoc No Assoc No No No No Assoc Assoc Assoc Assoc Assoc Assoc 1991 Assoc Assoc Assoc Assoc Assoc Assoc No No Assoc Assoc Assoc Assoc No No Assoc Assoc 1992 Assoc Assoc Assoc Assoc Assoc Assoc No Assoc No No No No No No No No 1993 No No Assoc Assoc No No No Assoc No No No No No No Assoc Assoc 1994 Assoc Assoc Assoc Assoc No No No Assoc No Assoc No No No No Assoc Assoc 1995 Assoc Assoc Assoc Assoc No No No Assoc Assoc Assoc Assoc Assoc Assoc Assoc No No 1996 Assoc Assoc Assoc Assoc No No Assoc Assoc No No No No Assoc Assoc No No 1997 Assoc Assoc Assoc Assoc No No Assoc Assoc No No Assoc Assoc Assoc Assoc No No 1998 Assoc Assoc No No No No No Assoc No No Assoc Assoc Assoc Assoc Assoc Assoc 1999 No No Assoc Assoc No Assoc No Assoc No No No No Assoc Assoc Assoc Assoc 2000 Assoc Assoc Assoc Assoc No No No No Assoc Assoc No No Assoc Assoc Assoc Assoc 2001 No Assoc Assoc Assoc Assoc Assoc No Assoc Assoc Assoc No No Assoc Assoc Assoc Assoc 2002 No Assoc No Assoc Assoc Assoc No No No Assoc No Assoc No No No No 2003 No Assoc No Assoc Assoc Assoc No No No Assoc No Assoc No Assoc No Assoc 2004 No No No Assoc Assoc Assoc No No No Assoc No No Assoc Assoc No Assoc 2005 No No No No Assoc Assoc No No No Assoc No Assoc Assoc Assoc No Assoc

26 Table 6 Stochastic Dominance for Overlapping Salary Ranges between Assistant and Associate Professors This table recomputes first and second degree stochastic dominance using only the overlapping salary ranges for Assistant and Associate professors. The results are presented for private business schools in Panel A and public business schools in Panel B. The distributions are compared for each survey year, 1979 to 2005 by discipline. All faculty are affiliated with AACSB accredited business schools. An ʺASSTʺ implies that Assistant professors are dominant over Associate professors; an ʺAssocʺ implies that Associate professors are dominant; and ʺNoʺ implies that a dominance relationship cannot be determined. Computer Information Systems Economics Finance Management Marketing Accounting Organizational Behavior Operations Management Year 1st deg 2nd deg 1st deg 2nd deg 1st deg 2nd deg 1st deg 2nd deg 1st deg 2nd deg 1st deg 2nd deg 1st deg 2nd deg 1st deg 2nd deg Panel A: Private AACSB accredited Business Schools 1979 Assoc Assoc Assoc Assoc No No No No Assoc Assoc 1980 Assoc Assoc No Assoc No No No Assoc Assoc Assoc 1981 Assoc Assoc No Assoc Assoc Assoc No No No No 1982 Assoc Assoc No No No No No No No No 1983 ASST ASST ASST ASST No ASST ASST ASST ASST ASST No No ASST ASST ASST ASST 1984 No No No No No Assoc Assoc Assoc No No No Assoc No No No Assoc 1985 Assoc Assoc No No Assoc Assoc Assoc Assoc Assoc Assoc Assoc Assoc Assoc Assoc No No 1986 No Assoc Assoc Assoc No Assoc No No Assoc Assoc No No No No No Assoc 1987 No Assoc Assoc Assoc No Assoc ASST ASST No No No No No No No No 1988 No ASST Assoc Assoc No Assoc ASST ASST No Assoc Assoc Assoc No No No ASST 1989 No No No Assoc No Assoc No No No No No Assoc No No ASST ASST 1990 No No No No Assoc Assoc No Assoc No No No No No No No No 1991 No No Assoc Assoc Assoc Assoc No No No No Assoc Assoc No Assoc No No 1992 No No No Assoc No Assoc No No No No No No No Assoc No No 1993 No No No Assoc No Assoc No ASST No No No No No Assoc No No 1994 No No No No No Assoc No No No No No No No No No No 1995 No Assoc Assoc Assoc No No No No No No No No No ASST No No 1996 No No Assoc Assoc No No No No No No Assoc Assoc Assoc Assoc No No 1997 No No Assoc Assoc No No No ASST No No Assoc Assoc No No No No 1998 No No No Assoc No No No ASST No No No Assoc No No Assoc Assoc 1999 No Assoc No Assoc No Assoc No No No No No No No No No No 2000 No Assoc No No No No No ASST No No No Assoc No No No No 2001 No No No No No No No No Assoc Assoc No No Assoc Assoc No No 2002 No No No ASST No No No ASST No No No Assoc No ASST No No 2003 No No ASST ASST No No No ASST ASST ASST No ASST No Assoc No No 2004 No No No No No No No No ASST ASST No ASST No No ASST ASST 2005 No No No No No No No No No ASST No ASST No ASST ASST ASST

27 Table 6 (continued) Stochastic Dominance for Overlapping Salary Ranges between Assistant and Associate Professors Computer Information Organizational Operations Accounting Systems Economics Finance Management Marketing Behavior Management Year 1st deg 2nd deg 1st deg 2nd deg 1st deg 2nd deg 1st deg 2nd deg 1st deg 2nd deg 1st deg 2nd deg 1st deg 2nd deg 1st deg 2nd deg Panel B: Public AACSB accredited Business Schools 1979 Assoc Assoc No No No Assoc No Assoc Assoc Assoc 1980 No No Assoc Assoc Assoc Assoc No Assoc Assoc Assoc 1981 No Assoc Assoc Assoc Assoc Assoc Assoc Assoc No No 1982 No Assoc Assoc Assoc No Assoc Assoc Assoc Assoc Assoc 1983 ASST ASST ASST ASST ASST ASST No No No No ASST ASST No ASST No No 1984 Assoc Assoc No Assoc No Assoc No Assoc Assoc Assoc Assoc Assoc Assoc Assoc No No 1985 Assoc Assoc Assoc Assoc Assoc Assoc Assoc Assoc Assoc Assoc Assoc Assoc Assoc Assoc No No 1986 Assoc Assoc Assoc Assoc Assoc Assoc No No Assoc Assoc Assoc Assoc Assoc Assoc Assoc Assoc 1987 Assoc Assoc No Assoc Assoc Assoc Assoc Assoc Assoc Assoc No Assoc Assoc Assoc No No 1988 Assoc Assoc Assoc Assoc Assoc Assoc No No Assoc Assoc No No No No No No 1989 No Assoc No No Assoc Assoc No Assoc No Assoc No No No No No No 1990 No No No No No No No Assoc No No No No No Assoc Assoc Assoc 1991 No No No No Assoc Assoc No ASST No No No No No Assoc No No 1992 No No No No No No No ASST Assoc Assoc No Assoc Assoc Assoc No Assoc 1993 No Assoc No No No Assoc No ASST No Assoc No No Assoc Assoc No No 1994 No Assoc No No No Assoc No ASST No No No Assoc Assoc Assoc No No 1995 No Assoc No No Assoc Assoc No ASST No No No No No Assoc Assoc Assoc 1996 No Assoc No No No Assoc No ASST No Assoc No Assoc No No Assoc Assoc 1997 No Assoc No Assoc No Assoc No No No Assoc No No No No No Assoc 1998 No Assoc No Assoc No Assoc No No No Assoc No No No Assoc No No 1999 No Assoc No No Assoc Assoc No No Assoc Assoc No Assoc No No No No 2000 No No No No Assoc Assoc No No No No No Assoc No No No No 2001 No No No No Assoc Assoc No No No No No Assoc No No No No 2002 No No No ASST No No ASST ASST No No No No Assoc Assoc No Assoc 2003 No No No ASST No No ASST ASST No No No No No No No No 2004 No No ASST ASST No Assoc ASST ASST No ASST No No No No No ASST 2005 No No No No No Assoc ASST ASST No No No No No No No ASST

28 Table 7 Measuring the Degree of First Order Dominance between Assistant and Associate Professors This table reports the degree to which the salary distribution of Assistant Professors is first order dominate over the salary distribution for Associate Professors. The degree of dominance is measured by computing the fraction of the Assistant Professor cumulative distribution function that lies beneath the corresponding Associate Professor cumulative distribution function. A fraction equal to 100% implies that Assistant Professors are first degree dominate over Associate Professors. Computer Information Systems Accounting Economics Finance Management Marketing Organizational Behavior Operations Management Year All Overlap All Overlap All Overlap All Overlap All Overlap All Overlap All Overlap All Overlap Panel A: Private AACSB accredited Business Schools % 0.0% 0.0% 0.0% 0.0% 2.2% 0.0% 4.0% 0.0% 0.0% % 0.0% 0.0% 4.1% 0.0% 6.4% 3.2% 1.3% 0.0% 0.0% % 0.0% 0.0% 2.6% 0.0% 0.0% 0.0% 2.5% 0.0% 1.3% % 0.0% 0.0% 1.7% 0.0% 0.8% 0.0% 6.4% 0.0% 8.9% % 100.0% 0.0% 100.0% 0.0% 74.4% 0.0% 100.0% 0.0% 100.0% 0.0% 89.3% 0.0% 100.0% 0.0% 100.0% % 2.7% 0.0% 11.8% 0.0% 2.8% 0.0% 0.0% 0.0% 7.5% 2.8% 0.7% 0.0% 9.7% 0.0% 8.7% % 0.0% 0.0% 10.0% 0.0% 0.0% 6.6% 0.0% 7.5% 0.0% 5.5% 0.0% 5.9% 0.0% 10.0% 92.7% % 40.5% 0.0% 0.0% 0.0% 3.1% 0.0% 53.8% 0.0% 0.0% 0.0% 14.1% 0.0% 3.6% 0.0% 13.8% % 28.6% 0.0% 0.0% 0.0% 2.6% 0.0% 100.0% 0.0% 9.0% 0.0% 5.5% 0.0% 7.2% 0.0% 42.3% % 77.4% 0.0% 0.0% 0.0% 35.2% 0.0% 100.0% 0.0% 2.5% 7.9% 0.0% 0.0% 31.8% 0.0% 46.5% % 18.1% 0.0% 7.5% 0.0% 7.8% 0.0% 24.4% 0.0% 10.1% 8.3% 3.4% 0.0% 23.2% 43.3% 100.0% % 43.8% 0.0% 14.5% 2.5% 0.0% 9.9% 8.7% 0.0% 10.7% 0.0% 8.5% 0.0% 10.1% 0.0% 36.0% % 52.8% 9.8% 0.0% 25.6% 0.0% 11.5% 29.9% 0.0% 7.2% 6.6% 0.0% 0.0% 3.8% 0.0% 5.4% % 52.7% 0.0% 8.0% 5.9% 13.8% 7.6% 28.7% 6.6% 30.8% 6.6% 11.0% 3.7% 3.3% 14.8% 35.0% % 46.0% 6.0% 3.5% 0.0% 19.7% 0.0% 60.3% 11.9% 21.8% 7.3% 23.3% 8.7% 8.5% 0.0% 5.5% % 41.7% 5.9% 6.8% 0.0% 5.4% 12.6% 39.3% 0.8% 9.3% 0.0% 15.6% 0.0% 9.5% 0.0% 18.4% % 8.6% 7.4% 0.0% 0.0% 10.6% 10.0% 22.4% 1.5% 9.0% 0.0% 11.2% 0.0% 54.9% 0.0% 12.7% % 21.3% 8.1% 0.0% 0.0% 12.5% 1.1% 51.2% 5.4% 7.9% 8.6% 0.0% 0.0% 0.0% 4.7% 6.2% % 17.6% 9.8% 0.0% 0.0% 11.4% 14.2% 61.4% 0.0% 11.0% 5.3% 0.0% 0.0% 77.7% 0.0% 6.9% % 32.9% 0.0% 4.4% 0.0% 29.4% 20.9% 99.3% 0.0% 40.0% 4.6% 20.7% 7.7% 59.3% 5.0% 0.0% % 39.0% 5.4% 7.6% 0.0% 13.7% 58.3% 88.9% 0.0% 25.7% 3.9% 51.3% 0.0% 52.2% 0.0% 40.3% % 38.5% 25.2% 54.0% 42.4% 58.1% 62.9% 98.1% 4.9% 53.2% 11.1% 35.8% 0.0% 14.2% 0.0% 60.6% % 48.0% 48.3% 55.4% 46.9% 70.8% 64.5% 73.7% 17.9% 0.0% 0.0% 51.5% 7.3% 0.0% 0.0% 43.6% % 48.8% 52.4% 91.7% 63.6% 58.9% 66.4% 92.9% 6.4% 58.4% 4.2% 38.2% 0.0% 89.1% 76.3% 86.6% % 48.5% 29.2% 100.0% 38.1% 69.6% 69.8% 99.1% 0.0% 100.0% 48.1% 90.8% 0.0% 31.7% 64.0% 83.6% % 61.9% 29.0% 56.0% 46.9% 78.5% 72.9% 84.8% 39.9% 100.0% 30.1% 86.5% 0.0% 50.4% 87.7% 100.0% % 78.4% 69.0% 77.7% 46.7% 67.4% 74.7% 82.3% 41.5% 96.5% 52.4% 95.4% 0.0% 59.5% 83.1% 100.0%