## Abstract

We saw in Chap. 1 that the percentage of students going to college has greatly changed over time. How can we explain these changes? This chapter will answer this question. Applying the internal-rate-of-return method yields the simple answer that the changes are due to those in the (expected) private internal rate of return to investment in higher education. However, computing private rates of return over some period and comparing them with the percentages of students who went to college reveal that the question is not so simple.

## Keywords

High Education Family Income Application Rate Enrollment Rate Wage Growth
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## Notes

- 1.A large portion of this chapter is based on Arai (1990b).Google Scholar
- 3.Whitfield and Wilson (1991) have undertaken a regression analysis for the United Kingdom by introducing the internal rate of return as an independent variable and have found its effect significant. Their analysis uses other independent variables such as the unemployment rate, social class, and so on.Google Scholar
- 4.This is from the
*Monthly Labor Statistics Abstract*by the Ministry of Labor. This data is also used in the analysis by Fujino (1986), which will be quoted below.Google Scholar - 5.Mattila (1982) also estimates regression models which introduce the independent variable for family income and other independent variables. The results indicate that not only the internal rate of return but also family income can have a positive and significant effect on the enrollment rate.Google Scholar
- 6.Other studies include Handa and Skolnik (1972,1975), Pissarides (1981), and McPherson and Schapiro (1991).Google Scholar
- 8.Kaneko (1986) provides another study. His regression analysis explains the rate of logit change in the enrollment rate
*P*, i.e.,*1PIP(1 —*P), by the average expected returns ratio (which is defined as the ratio of the returns to higher education to its costs, and thus is similar to the internal rate of return), family income, and the cohort size (the number of students in the third year of senior high-school education). It was found by the analysis that these three independent variables have respectively positive, positive, and negative significant effects on male enrollment rate. This regression model differs from others in that it deals with changes in the enrollment rate. It may be said that this is a kind of internal-rate-of-return analysis because it uses a concept close to the internal rate of return.Google Scholar - 10.The fact that the effect of forgone earnings is smaller than that of tuition is also confirmed in the results of cross-sectional analyses by Bishop (1977) who has used micro-data from the United States and by Tannen (1978) who has used state-grouped data from the United States. Kodde and Ritzen (1984) have developed a theoretical model which indicates that forgone earnings and tuition have different effects on the demand for education when education has consumption benefits and when the capital market is perfect.Google Scholar
- 12.U. Other studies which have analyzed the relationship between unemployment and college-going decisions include Handa and Skolnik (1975) and Whitfield and Wilson ( 1991 ). According to the former, the effect of the number of unemployed workers on the number of students advancing to colleges in Ontario, Canada is significant but very small. Its effect on the number of students advancing to graduate schools was also analyzed, but is found to be insignificant. According to the latter study of the United Kingdom, the unemployment rate has a positive and significant effect on enrollment in higher education.Google Scholar
- 13.Firms, specially those in the manufacturing industries, tend to regard graduates from professional schools as lower specialists than those from colleges, and require them to quickly exhibit their abilities in limited fields without providing additional training for them (Kosugi, 1993).Google Scholar
- 14.The service industry is not included in the data prior to 1976 but is included afterwards. For the three years from 1976 through 1978 both kinds of data are available, and we can find that the difference in the proportion is slightly larger when the service industry is excluded. For this reason, adjustments have been made by multiplying the difference in the proportion prior to 1976 by 0.94, where 0.94 is the ratio obtained by comparing the data from 1976 through 1978. The essence of the argument would be the same even if such adjustments were not made.Google Scholar
- 16.When
*P*is the application rate, its logit transformation is expressed as ln[P/(1 —*P)]*,where In is the natural logarithm. When a rate (or a probability) is directly used as the dependent variable, the value of the regression equation will not necessarily be confined to between 0 and 1 depending on the values substituted into the independent variables. The logit transformation avoids such inconveniences. When the values of a rate (application or enrollment rate here) which actually matter are not close to 0 or 1, similar regression results will be obtained whether the rate is directly used or whether its logit transformation is used as the dependent variable. The former approach is often adopted, because it is simpler and also because it can provide direct information about the effect of a unit increase in the value of an independent variable on the dependent variable. The enrollment rate was directly used as the dependent variable in our regression analysis above and in that by Nakata and Mosk (1987).Google Scholar - 17.The simulation analysis by Ogura and Wakai (1991) also uses the application rate as the dependent variable. In their model, the application rate of new high-school graduates depends on the ratio of the total education cost (tuition + food costs + “daily costs”) to the wage index, the proportion of parents with college degrees, and the wage differential between college and high-school graduates.Google Scholar
- 18.Kaneko (1986) points out that institutions requiring relatively low minimum academic ability have considerable excess capacity and that this plays the role of a buffer in the adjustment of demand for and supply of higher education. To see the effect of a supply constraint, he has introduced into his empirical analysis an independent variable for cohort size. The result of this analysis suggests that the stagnation in the enrollment rate after the mid-1970s was due mainly to family income and not to cohort size. Because the cohort size in about ten years after the mid-1970s was smaller than before (see the
*Abstract of Education Statistics*by the Ministry of Education), it cannot be maintained that the cohort size or supply constraint generated the stagnation.Google Scholar

## Copyright information

© Kazuhiro Arai 1998