# Appendix 6: Value per Credit Hour Equivalent and the Mincer Function

Two key components in the analysis are 1) the value of the students’ educational achievements, and 2) the change in that value over the students’ working careers. Both of these components are described in detail in this appendix.

### Value per CHE

Typically, the educational achievements of students are marked by the credentials they earn. However, not all students who attended UHV in the 2018-19 analysis year obtained a degree or certificate. Some returned the following year to complete their education goals, while others took a few courses and entered the workforce without graduating. As such, the only way to measure the value of the students’ achievement is through their credit hour equivalents, or CHEs. This approach allows us to see the benefits to all students who attended the university, not just those who earned a credential.

To calculate the value per CHE, we first determine how many CHEs are required to complete each education level. For example, assuming that there are 30 CHEs in an academic year, a student generally completes 120 CHEs in order to move from a high school diploma to a bachelor’s degree, another 60 CHEs to move from a bachelor’s degree to a master’s degree, and so on. This progression of CHEs generates an education ladder beginning at the less than high school level and ending with the completion of a doctoral degree, with each level of education representing a separate stage in the progression.

The second step is to assign a unique value to the CHEs in the education ladder based on the wage differentials presented in Table 1.4. For example, the difference in regional earnings between a high school diploma and a bachelor’s degree is $29,500. We spread this $29,500 wage differential across the 60 CHEs that occur between a high school diploma and a bachelor’s degree, applying a ceremonial “boost” to the last CHE in the stage to mark the achievement of the degree.^{22} We repeat this process for each education level in the ladder.

^{22}Economic theory holds that workers that acquire education credentials send a signal to employers about their ability level. This phenomenon is commonly known as the sheepskin effect or signaling effect. The ceremonial boosts applied to the achievement of degrees in the Emsi impact model are derived from Jaeger and Page (1996).

Next we map the CHE production of the FY 2018-19 student population to the education ladder. Table 1.2 provides information on the CHE production of students attending UHV, broken out by educational achievement. In total, students completed 91,737 CHEs during the analysis year. We map each of these CHEs to the education ladder depending on the students’ education level and the average number of CHEs they completed during the year. For example, bachelor’s degree graduates are allocated to the stage between the associate degree and the bachelor’s degree, and the average number of CHEs they completed informs the shape of the distribution curve used to spread out their total CHE production within that stage of the progression.

The sum product of the CHEs earned at each step within the education ladder and their corresponding value yields the students’ aggregate annual increase in income (∆E), as shown in the following equation:

and n is the number of steps in the education ladder, ei is the marginal earnings gain at step i, and hi is the number of CHEs completed at step i.

Table A6.1 displays the result for the students’ aggregate annual increase in income (∆E), a total of $22.3 million. By dividing this value by the students’ total production of 91,737 CHEs during the analysis year, we derive an overall value of $243 per CHE.

TABLE A6.1: AGGREGATE ANNUAL INCREASE IN INCOME OF STUDENTS AND VALUE PER CHE

Aggregate annual increase in income | $22,254,804 |
---|---|

Total credit hour equivalents (CHEs) in FY 2018-19 | 91,737 |

Value per CHE | $243 |

### Mincer Function

The $243 value per CHE in Table A6.1 only tells part of the story, however. Human capital theory holds that earnings levels do not remain constant; rather, they start relatively low and gradually increase as the worker gains more experience. Research also shows that the earnings increment between educated and non- educated workers grows through time. These basic patterns in earnings over time were originally identified by Jacob Mincer, who viewed the lifecycle earnings distribution as a function with the key elements being earnings, years of education, and work experience, with age serving as a proxy for experience.^{23} While some have criticized Mincer’s earnings function, it is still upheld in recent data and has served as the foundation for a variety of research pertaining to labor economics. Those critical of the Mincer function point to several unobserved factors such as ability, socioeconomic status, and family background that also help explain higher earnings. Failure to account for these factors results in what is known as an “ability bias.” Research by Card (1999 and 2001) suggests that the benefits estimated using Mincer’s function are biased upwards by 10% or less. As such, we reduce the estimated benefits by 10%. We use state-specific and education level-specific Mincer coefficients.

^{23}See Mincer (1958 and 1974).

Figure A6.1 illustrates several important points about the Mincer function. First, as demonstrated by the shape of the curves, an individual’s earnings initially increase at an increasing rate, then increase at a decreasing rate, reach a maximum somewhere well after the midpoint of the working career, and then decline in later years. Second, individuals with higher levels of education reach their maximum earnings at an older age compared to individuals with lower levels of education (recall that age serves as a proxy for years of experience). And third, the benefits of education, as measured by the difference in earnings between education levels, increase with age.

FIGURE A6.1: LIFECYCLE CHANGE IN EARNINGS

In calculating the alumni impact in Chapter 2, we use the slope of the curve in Mincer’s earnings function to condition the $243 value per CHE to the students’ age and work experience. To the students just starting their career during the analysis year, we apply a lower value per CHE; to the students in the latter half or approaching the end of their careers we apply a higher value per CHE. The original $243 value per CHE applies only to the CHE production of students precisely at the midpoint of their careers during the analysis year.