A benefit/cost model to evaluate educational programs

Essentially, a benefit/cost model provides a procedure to evaluate a project in terms of its economic objectives. The analytic task is to determine the present value of all benefits less the present value of all costs, so that the projects which maximise this difference can be selected. There are private benefits (those appropriated by the persons directly involved in the project), and social benefits (those derived by others because of the project) that should also be taken into account when public policy is involved. Limitations of data preclude us from considering all the benefits, but in the present study of the benefits of an educational program, the following have been incorporated: (1) increases in earnings due to attaining higher levels of education; (2) benefits that accrue to the offspring of the present generation resulting from the influence of the educational attainment of parents on that of their children; and (3) the reduction in juvenile crime.

The model that is used to estimate these benefits includes thirteen separate equations. A major ingredient of all of these equations is represented by equation 4 in the model:

According to this equation, the private benefits of additional education are calculated as the difference between the expected economic returns with the program (designated T) and the expected economic returns without the program. Expected economic returns are estimated by the product of lifetime earnings for each level of education (V_i) times the probability distribution of obtaining the various levels of education (P_i), where i designates a level of education. These benefits will be different for individuals with different characteristics, designated ε.

The parameters of the model have been estimated by the use of Census data for earnings, and various special survey data for the probabilities of educational attainment and committing juvenile crimes. Essentially an educational program changes the probabilities of educational attainment, increasing the probability of graduating from high school and going on to college.

In this study, we applied the model to a Title I ESEA, program in San Francisco, California, during 1966–1967. Since the program was implemented in the elementary grades, we used the mathematics of Markov Chains to estimate the probabilities of eventual grade level attainment. We found that prior to the program, about half of the disadvantaged non-Negro males and considerably more than half of the Negro males could be expected to be dropouts. The model showed, however, that a Title I program in San Francisco costing $220 per child sufficiently raised test scores in elementary grades so that the expected dropout rates were reduced about 3 per cent for non-Negro and 2 per cent for Negro male pupils.