FACULTY SALARIES

A MODEL TO CALCULATE FAIR COMPENSATION

 

Amadeo J. Pesce

University of Cincinnati

Cincinnati, OH

 

    The University of Cincinnati faculty is represented by the American Association of University Professors (AAUP) in contract negotiations for salary and working conditions with the University Administration.  The result has been a traditional collective bargaining agreement often achieved by confrontational negotiations.  In an attempt to substitute more rational negotiations both the AAUP and the University agreed to use Mutual Gains Bargaining (MGB).  Both sides were trained by the MIT-Harvard Negotiation Project.1  Virtually all items in the contract were settled by this approach.  The most difficult one was wages.  The group discussed and created models of salary in order to estimate the impact of wage increases on the faculty and the cost to the University.  In terms of the MGB approach which uses interest statements, the faculty wanted wages which were competitive with that paid by other Universities of our type (Midwestern, public funded), with real wages increasing as a result of years of service.  The University had created a model of funding which was based on historical projections.  One parenthetical observation must be noted here.  One cannot do MGB without honest access to all databases.  Trust in these negotiations is built on the agreement of the database validity.

 

    We present here a mathematical model developed during these negotiations which shows some surprising aspects of faculty salaries and their costs in the case of a mature institution such as the University of Cincinnati.  Two seemingly contradictory observations were made.  First, individual faculty salaries historically increase at a rate greater than inflation.  Second, the cost to the institutions can be shown to be approximately that of the inflation rate. 

 

    We used a database of faculty salary and age distribution to create our model (Table 1).  There were 1296 faculty included in our database.  This did not include any medical school faculty.  Arbitrarily we chose those ages which included about 95% of the faculty; these were ages 31 to 65.  The data for individual years had significant fluctuations.  For example the wage at age 64 was $55,405 and at 65 was $47,205.  To obtain a better average, the data was analyzed by the regression statistic.  Best fit of the data was by conversion to a logarithmic function.  This analysis gave a best fit with a slope of 1.5% per year compounded annually.  This was interpreted to mean that wage increments of 1.5% above inflation are necessary to maintain the current wage structure.

 

    Using the database, a model for faculty salary may be generated by making the following assumptions:

  1. The average length of service is 30 years
  2. The difference between starting Assistant Professor and retiring Professor is 1.59 fold.
  3. Faculty are distributed in equal numbers in every year of service i.e. the institution is well established and there has been little expansion of faculty numbers.
  4. Replacement faculty are hired only at the assistant professor level

 

    The above model can be applied to the question of defining the actual cost.  Usually, in most negotiations the cost to the institution is calculated by multiplying the percent increase by the total current cost of salary.  However, in a system of faculty compensation in which members with the longest ser vice have the greatest salaries, and in which most replacement faculty are hired at the starting rate, this cost calculation does not hold. 

 

    Attrition must be factored into the wage system.  As we have shown above, the average wage of individuals in the system increases faster than inflation.  However, almost all of this increased wage is recovered by the difference between the higher wages of the faculty members who leave the system, and the lower wages of those newly hired.

 

    The consequences of this model are:

  1. An annual average increment of 1.5% above inflation (including promotional wages) is required for each individual faculty member to maintain the observed wage increments as a function of service years
  2. At retirement or if the faculty member leaves the institution (i.e. attrition), then an amount of money equal to (0.015)exp(service years) x (starting salary) x (inflation rate) is added back to the salary pool to accommodate the average annual 1.5% increments greater than inflation.
  3. The total cost of faculty salary and salary driven fringe will increase at a rate different (less) than that of the individual faculty member's rate of increase.

 

    A second set of historical data provided confirmation of this analysis and an opportunity to consider the long term effects of collective bargaining.  The University of Cincinnati considers itself comparable in many ways (except in football) to the 'Big Ten' schools.  They are all in the Midwest and similar in size and diversity.  Except for Northwestern they are funded by state legislatures.  The data for average salaries of assistant professors and professors for the years 1974-1975 and 1988-1989 for the Big Ten2 and Cincinnati are presented in Table 2.  The year 1974-1975 was chosen because it was the last year before collective bargaining at the University of Cincinnati.  The ratio of salary of professor to assistant professor at Cincinnati (1.68) is comparable to that of other, similar institutions (average 1.62).  This is consistent with the longevity factor of 1.59 calculated from Table 1.  The slightly lower ratio reflects that not all faculty achieve the rank of professor.  Table 2 shows that historically this ratio has not changed significantly over the 14 year period (1.68 vs 1.62).  This implies that market or other forces are responsible for the salary pattern.  The data also show that an approximation of the annual increase above inflation necessary to maintain the salary structure can be calculated from the data published in Academe.

 

    Although this analysis was not accepted as the rationale for the final settlement, the author believes it will be the basis for further discussion if MGB is used in future negotiations.  It offers both sides a rational approach to calculate the options to implement their interest statements.

 

References

 

  1. Fisher, R. and Ury, W.  Getting to Yes:  Negotiating Agreement Without Giving In, Viking Penguin Inc.  NY, NY  1988.

  2. Academe March-April 1989.

 

Table 1.

Salary and age distribution at the University of Cincinnati 1989

Age N Wage Age N Wage
26 3 32,304 51 48 48,494
27 4 31,458 52 31 49,042
28 3 27,719 53 26 49,254
29 7 34,843 54 33 50,074
30 17 32,623 55 32 50,005
31 26 32,455 56 28 50,332
32 17 35,934 57 41 51,666
33 27 32,609 58 35 49,982
34 36 34,811 59 19 47,764
35 37 31,540 60 26 56,793
36 38 34,631 61 19 52,119
37 32 35,442 62 7 54,740
38 39 34,524 63 18 50,076
39 48 38,695 64 15 55,405
40 51 39,822 65 7 47,205
41 51 38,947 66 10 54,913
42 51 40,957 67 5 54,361
43 39 40,462 68 9 58,628
44 52 41,439 69 6 56,985
45 64 44,870 70 2 57,162
46 67 44,938
47 44 47,706
48 37 50,570
49 41 48,360
50 47 45,405

 

Table 2

Historical Ratio of Professorial Salaries in the 'Big Ten' for the years 1988-1989 and (1974-1975)

School Professor Assist. Prof. Ratio
Illinois 57.2    (24.0) 36.4    (13.7) 1.57    (1.75)
Indiana 54.5    (22.5) 32.3    (13.7) 1.69    (1.64)
Iowa 55.7    (22.1) 35.8    (14.0) 1.56    (1.58)
Michigan 62.9    (25.6) 39.2    (15.1) 1.60    (1.70)
Michigan St. 53.5    (23.0) 33.4    (14.5) 1.60    (1.59)
Minnesota 54.5    (22.3) 34.4    (13.5) 1.58    (1.65)
Northwestern 64.6    (26.7) 38.9    (14.2) 1.66    (1.88)
Ohio State 60.8    (22.3) 36.8    (13.5) 1.65    (1.65)
Purdue 57.8    (23.4) 34.1    (13.4) 1.70    (1.75
Wisconsin 53.1    (22.8) 34.5    (14.1) 1.54    (1.62)
Average 1.62    (1.68)
Cincinnati 57.4    (22.4) 34.2    (12.8) 1.68    (1.75)

SALARIES