# A Mathematical Model of Pay-for-Performance for a Higher Education Institution

## Article excerpt

ABSTRACT

This paper develops a mathematical model of the proposed pay-for-performance award system for an institution of higher education. Two constraints are imposed to ensure the fairness of the system. The model is general enough so that the payouts for the three performance levels (excellent, exceptional, and extraordinary) are clearly distinguished. Thus, the greater effort and performance that is required to achieve the highest level is rewarded with significantly higher monetary benefits. This outcome reinforces outstanding performance and should motivate faculty to perform at high levels in the future.

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INTRODUCTION

The payoff for exceptional productivity must be substantial to make the increased effort of the performance, as well as the evaluation of this productivity, worthwhile (Baker, Jensen, & Murphy, 1988). Pay-for-performance (PFP) is a program that offers such an incentive in that it has been designed to improve the productivity of individuals by offering financial incentives for exemplary outcomes. That is, it is a one-off bonus associated with exceptional work.

The Board of Trustees of a college of two of the authors set aside an annual PFP budget line item equal to eight percent of the total faculty compensation, both salary and benefits, to reward those who perform at an exemplary level.

This paper develops a mathematical model of the PFP awards system and introduces two constraints to ensure the fairness of the proposed system. After the literature review the paper discusses a numerical example, develops the mathematical model and then discusses it before offering a conclusion in the final section.

BRIEF LITERATURE REVIEW

Despite the findings of a meta-analysis of 39 studies over 30 years that showed that there is a positive correlation between performance and financial incentives (Jenkins, Mitra, Gupta, & Shaw, 1998), not all studies have supported PFP. Some researchers have found little evidence of the effectiveness of PFP in, for example, health care settings (Rosenthal & Frank, 2006). The lack of evidence in this sector, however, has done nothing to stem the enthusiasm for the program as more than half of a sample of health management organizations (HMOs) use PFP (Rosenthal, Landon, Normand, Frank, & Epstein, 2006). It is important to note that one of the reasons given for the lack of effectiveness in health care PFP systems was attributed to a low bonus size (Rosenthal & Frank, 2006). In business, the demand for PFP continues to be very strong, despite a weak economy, according to Mercer's 2010 U.S. Executive Compensation and Performance Survey (2010).

For the purpose of this paper, PFP is distinguished from other types of incentives such as reinforcement on a ratio scale (e.g., piece work) and merit pay increase. It has been wellestablished that piece work increases productivity over reinforcement on an interval scale (e.g., fixed salary) in a number of domains (Skinner, 1974). For example, a ratio reinforcement strategy has been found to increase productivity in tree planters (Shearer, 2004) and logging (Haley, 2003). Ratio scale reinforcement is obviously out of place in all areas of higher education beyond the experimental laboratories. Merit pay increase is a system that is used by some colleges in which faculty receive a percentage increase of their current salaries when they meet or exceed minimum outcomes. This percentage is then added to their base salaries.

PFP is an alternative mechanism that has been proposed as a method of providing a oneoff reward for exceptional work by faculty. However, evaluation and implementation can lead to disastrous outcomes (Terpstra & Honoree, 2008). Hence, it is necessary to present PFP in a tightly constrained mathematical model that gives structure to the implementation and consequent reinforcement process.

A mathematical model of a complex concept provides an objective abstract representation of that concept. …