Predicting the Annual Salaries of Construction Educators using Multiple Regression

Introduction

How much should I be earning?  It is a question that most of us ask, but very few of us receive a satisfactory answer, particularly those of us who teach in institutions of higher learning. Studies on salary compensation are of interest to both academicians and administrators. There exists a wide body of literature on faculty salary levels in institutions of higher learning. One of the basic tenets of market economy is that income should be distributed according to contribution, and none takes greater pride in rewarding people for merit alone then academicians. Some studies seek to explain the difference in salary levels in terms of performance and contributions. The purpose of this study is to identify whether there are other factors that affect faculty compensation, particularly those engaged in teaching in the member schools of the Associated Schools of Construction.

Literature indicates that apart from scholarly productivity, longevity makes a substantial contribution to faculty salaries (Ferber, 1974; Monks & Robinson, 2001). Studies suggest that when adequate measures of past mobility are controlled for, the evidence of a positive correlation between income and seniority of academic faculty is overwhelming.

There is great dissatisfaction with the salary equity of women faculty in some universities.  Findings by Bellas et al. (2001) show that a sizable gap between men and women’s salaries exists after controlling for academic qualifications. The study indicates that women’s scarcity in higher-level faculty positions contribute to their slower promotion rates, which in turn depress their salary growth rates.

Faculty salaries also differ across the disciplines. A study by Cox (2001) shows that average earnings by law professors, at both public and private universities, are the highest among all disciplines. Similar findings are reported by an earlier study by Schneider (1999). Construction science is taught in schools ranging from architecture to business to technology in different universities. It is likely that the school in which they are employed may affect the salaries of the faculty in the department of construction.

Most of the studies on faculty salary include academic rank as an endogenous factor for prediction of salaries. Webster (1995) reports that while salary of a full professor differs from that of faculty in other ranks, the associate and assistant professor ranks have no statistically significant relationship with salary. He suggests that the outcome may be due to the effect of salary compression.

In view of the evidence provided by the results of the studies conducted in other disciplines, it is hypothesized that faculty salary in schools of construction that are members of the Associated Schools of Construction are affected by the following factors:

Method

Study Population

The study population consists of all Faculty that teach at institutions that are members of the Associated Schools of Construction (ASC).  The ASC web site identifies that there are 585 ASC Faculty.

Data Collection

During the fall of 2001 ASC faculty were sent email messages inviting them to take part in the survey.  The initial invitation was sent out on the 11 October and follow up messages were sent on 18 and 28 October.  The messages invited faculty members to visit the ASC web site and complete an on-line survey.  A screen capture from the web site showing the on-line survey form is shown in Figure 1.  By November 16, 2001, 200 of the 585 ASC Faculty had responded, a response rate of 34.2 percent.  From the 200 respondents, 21 selected not to participate leaving 181 Faculty completing the survey.  Of the 181 Faculty completing the survey, 5 Faculty did not supply a full-time annual salary figure and these responses therefore were not used in constructing the statistical model.  Permission was sought and obtained from the ASC to use the database for the purposes of this study.  The ASC board had previously voted to allow any program or faculty to have access to data within the ASC Database.  The data provided has been cleaned so that it is not proprietary and does not identify any particular individual.

Variables of Interest

The dependent variable of interest is the annual contract salary of ASC faculty for a period of 9 months (ASC_9MO).  Respondents submitted their annual contract salary and the annual contract period in months.  Multiplying the annual contract salary by 9 and dividing it by the number of months of the annual contract calculated the dependent variable.  The predictor or independent variables are of two types: quantitative and qualitative.  The quantitative predictor variables are:

The qualitative or dummy variables are used to represent further information about the faculty.  The dummy variables cover the qualifications, rank, geographical region, college and gender of the faculty.  A value of 1 is assigned if a faculty is a member of a particular qualification, rank, geographical region, college or gender group and a 0 if they are not.  The qualitative or dummy variables are:

The names within parentheses are the names assigned to the variables for use in the statistical software used for the analysis, SAS^® for Windows^® version 8.

Hypothesis

The hypothesis is that the 9-month annual salary of ASC Faculty can be predicted using the following multiple regression model:

The regression model shows that the dependent variable ASC_9MO is a function of an intercept value (β₀) and a series of independent variables numbered from 1 to 30 and an error value.  The “β” values are the parameter estimates and are calculated using the statistical software.  These are multiplied by the setting of the independent variable to arrive at a value for the dependent variable.

Analysis & Interpretation

Development of the Statistical Model

A multiple regression model was developed to express the relationship between the dependent variable and the independent variables.  The regression model was developed using the three-step approach set down by Ott (1993) namely; selecting the independent variables, forming a suitable model and checking the model assumptions.  The selection process identified those independent variables that caused the greatest variation in the dependent variable.  The stepwise selection method was used to select the variables in the model.  The significance level (P-value) for an independent variable to enter and remain in the model was set at 0.10. 

Results of the Stepwise Selection Method

The results of the multiple regression analysis are set out in Table 1.  The F value is used to test whether there is a regression relation between the dependent variable and the independent variables.  The high F value and low P value (<0.0001) show that there is a regression relation.  This in itself however does not mean that the model is suitable for predicting annual salaries.  The R-Square value is the coefficient of determination and measures how well the regression fits.  The R-Square value of 0.5140 shows that approximately 51 percent of the variation in the 9-month annual salary is explained by the variation in the selected independent variables.

The independent variables selected by the multiple regression process and their parameter estimates are set out in Table 2.  All variables selected for the model have a significance level of P < 0.10.  All the variables selected were qualitative or dummy variables, therefore the parameter estimate is the amount in dollars that is added to or subtracted from the intercept value.

Figure 2 is a chart showing predicted 9-month salary values with 95 percent confidence and prediction intervals and actual 9-month salary values for all 176 observations.  The values for predicted and 95 percent confidence and prediction intervals were calculated using the statistical software.  For example, the author is an Assistant Professor at a University in the South-central region in a College of Architecture and has a Ph.D.  To predict his 9-month salary the following equation is used: 

The values for the independent variables PHD and S_CENTRAL are 1.  The settings for all other independent variables are 0.  The prediction therefore is:

The predicted 9-month salary is therefore $51605.  This is considerably more than the author’s actual salary of $46,800.  The author’s salary does however fit within the 95 percent lower and upper prediction intervals that were calculated by the statistical software to be $31,798 and $71,374 respectively.

In light of the independent variables selected using the stepwise procedure, the salary prediction model can be rewritten as follows:

Discussion

The results show that faculty salary is correlated with one academic qualification variable, three of the faculty rank variables, two geographical region variables, and one college type variable. The regression model explains approximately 51 percent of the variation in the 9-month salary.  This means that the predictive efficacy of the model is not very high.  This can be seen in Figure 2.  The model appears to predict 9-month salaries between the values of $45,000 and $80,000 quite well, as most of the actual 9-month salary values lie within the 95 percent confidence intervals.  At the extreme ends of the salary scale the model is not so good at predicting salaries, although the actual 9-month salary values lie within the 95 percent prediction intervals.  There is some concern that some of the lower salary values may not be for full-time faculty members.  If this were the case then it would be prudent to change the ASC Faculty Salary Survey Update form to allow a faculty member to enter the percentage of a full-time salary they receive. In fact, the literature indicates that studies on faculty salary are usually conducted using full-time effort criterion (Monk & Robinson, 2001;Webster; 1995). The Information Management and Testing Services (1996) at Baylor University defines a full-time faculty as a member of the instructional staff who is employed full-time and whose regular assignment is instruction, including those with released time for research.

The model only selected PHD from the qualification dummy variables and suggests that the possession of a PHD adds approximately $ 4927 to a faculty member’s 9-month salary. Evidence in the literature provides support for this finding (Lamb & Moates, 1999; Webster, 1995).

Three faculty rank dummy variables were selected; this was expected as most promotions in academia result in salary increases. The model indicates the rank of Associate Professor would increase the 9-month salary by $ 7191, the rank of Full Professor by $ 20092, and the rank of Department Head by $ 22322. It will be interesting to see in future studies whether these differences remain significant if a productivity measure is introduced in the model.

Only two of the seven geographical region dummy variables were selected.  The model indicates that Faculty in the North Central and South Central regions would have their 9-month salaries reduced by $ 4765 and $ 5927 respectively. It will, however, be interesting to see whether these differences remain significant after adjusting for variations in taxes and cost of living across geographical locations.

The only college dummy variable selected was Technology.  The model indicates that being a faculty member in a College of Technology would decrease their 9-month salary by $ 4561. There is some evidence in the literature to support this finding. Schneider (1999) studied differences in salaries of university professors by disciplines in four-year institutions. The findings suggest that the average faculty salary in colleges of technology is significantly lower than that in colleges of architecture, business, and engineering.

The variables that were not selected are also of interest. Neither of the two quantitative independent variables, age and years in rank, was found to be statistically significant. Even though the general body of literature suggests that a correlation exists between salary compensation and these two variables, a study by Moore et al. (1998) provides evidence contrary to this belief. The researchers did not find any positive relationship between either longevity or seniority with faculty salary when the model took into account only these two independent variables. The variables, however, became significant when a quality-adjusted measure of research publications was introduced in the model. It will be worthwhile to introduce such a variable for future studies on ASC faculty salary.

The study did not provide any evidence of gender differences in salary, even though the literature indicates that women faculty earn less on average than their male counterparts (Bellas, et. al. 2001; Hamton, et. al. 2000). Bellas, et al. (2001), however, indicated in their study that this gap maybe partially attributed to the concentration of women faculty in relatively low-paying disciplines. It might be a reason for gender not being a predictor of salaries for the faculty in construction schools.

References

Bellas, M. L., Ritchey, P. N., & Permer, P. (2001). Gender differences in the salaries and salary growth rate of university faculty: An exploratory study. Sociological Perspectives, 44(2), 163.

Cox, A. M. (2001). Law professors top list in study comparing salaries across disciplines. Chronicle of Higher Education, 47(46), A10.

Ferber, M. A. (1974). Professors, performance, and rewards. Industrial Relations, 13(1), 69-77.

Hampton, M. & Oyster, C. (2000). Gender inequity in faculty pay. Compensation and Benefits Review, 32(6), 54-59.

Information Management & Testing Services (1996). http://www.baylor.edu/IMTS/Vol967/IR96714.htm: Faculty Salary Comparisons 1991-92 through 1995-1996. IRT Series, 96-97(14). Waco, TX: Baylor University.

Lamb, S. W. & Moates, W. H. (1999). A model to address compression inequities in faculty salaries. Public Personnel Management, 28(4), 689-700.

Monks, J. & Robinson, M. (2001). The returns to seniority in academic labor market. Journal of Labor Research, 22(2), 415-430.

Moore, J. M., Newman, R. J., & Turnbull, G. K. (1998). Do academic salaries decline with seniority? Journal of Labor Economics, 16(2), 352-364.

Ott, R. L. (1993).  An introduction to statistical methods and data analysis, (4^th ed.) Belmont, CA. Wadsworth Publishing Company.

Schneider, A. (1999). Law and finance professors are top earners in Academe survey finds. Chronicle of Higher Education, 45(38), 14-19.

Webster, A. L. (1995). Demographic factors affecting faculty salary. Educational and Psychological Measurement, 55, 728-35.