Stay at school or start working? - Optimal timing of leaving school under uncertainty and irreversibility

At any moment a student may decide to leave school and enter the labor market, or stay in the education system. The time of departure from school determines their level of academic achievement and formal qualification. Therefore, the major purpose of this paper is to derive a timing rule for leaving school and thus answer the question: How long should I go to school? To solve this problem we apply the real option approach. Real option theory offers a different perspective of the human capital investment decision under uncertainty and irreversibility. As future income is uncertain, we model future earnings as a continuous stochastic process. We use dynamic programming techniques to derive an income threshold at which a student should leave school irreversibly, and we determine the expected optimal duration of education. Unlike other approaches using real option theory we are able to provide a full analytical discussion of various determinants affecting the timing of the decision to start work. Among other things, we find that a rising income risk increases the duration of education. With a faster growth of expected individual income during working life the duration of schooling will decrease leading to less education. An increase in the no-education wage level will reduce human capital investments. Rising marginal rewards for a year of schooling (in terms of a rising differential in income level) will encourage more investment in human capital. Increasing education costs may also increase human capital investment as long as the marginal reward for a year of schooling is sufficiently high. However, allowing for discontinuities due to various cost and income profiles of formal qualification levels, high costs of schooling may lead to an achievable maximum net wealth of human capital even for lower qualification.