ماندن در مدرسه و یا آغاز به کار ؟ تصمیم سرمایه گذاری در سرمایه انسانی تحت عدم قطعیت و برگشت ناپذیری

At any moment a student may decide to leave school and enter the labor market, or to stay in the education system. The timing of their departure determines their level of academic achievement and formal qualification. Education is a multi-stage process of investing in an accumulative human capital stock. How long can I expect to go to school? How much will I invest in my education? To answer these questions we apply the real option approach. We depart from recent literature by (1) adding accumulated education costs and determining the expected time of market entry, (2) considering complete earnings profiles including entry-level wages, sheepskin effects and earning dynamics, and (3) discussing the option value of schooling while introducing potential career opportunities or threats of unemployment modeled as major uncertain events connected with particular formal education achievements.

Education is obtained during a long process of personal maturation and the accumulation of knowledge and abilities. Hence, formal schooling is a learning and investment process that often lasts into one's mid‐twenties. When a young person makes plans for the future one of the biggest problems is uncertainty.1 The success of a long education is as uncertain as the process of earning income during a long working life. As time goes on, students repeatedly consider whether to continue their education or enter the labor market. During this sequential process of decision making each moment's conditions determine the eventual attainment level. Recent literature shows that real option theory can be applied to take into account uncertain time processes and irreversibility in schooling and human capital accumulation decisions. While Weisbrod (1962) and more formally Comay et al. (1973) suggested this way of thinking more than 30 years ago, a transfer of formal option theory – as established by Dixit and Pindyck (1994) – was suggested only recently. Hogan and Walker (2007) apply real option theory to human capital decisions. In their model, at any time a student has the option to leave school to work for wages that reflect the years spent in school. The decision to leave school is irreversible, so once the student has finished education they cannot return. They conclude that high returns on education and increasing risk will cause students to stay in school longer. They also analyze how progressive taxation and education subsidies affect schooling decisions and show that progressive taxes tend to reduce educational attainment. Jacobs (2007) uses the real option approach as well. However, unlike Hogan and Walker (2007) he uses a discrete time approach and states that the decision to start learning is irreversible. The option value stems from the fact that an individual could wait to enroll and would only do so once the returns are sufficiently large to compensate for the lost option value. The sunk cost of the investment consists of tuition costs and foregone labor earnings. More recent empirical literature on human capital investments suggests that the functional form of the Mincer model no longer adequately describes labor earnings for U.S. workers.2Heckman et al., 2003 and Heckman et al., 2006 test and reject the assumptions for using the Mincer model to estimate the internal rate of return. Heckman et al. (2008) emphasize that estimates should account for non-linearity and non-separabilities in earnings functions, income taxes, and tuition. In line with these findings is the idea of introducing risk and other non-pecuniary elements into the empirical model.3 In addition, Heckman et al. (2006) explain why option values should be included in the decision, and show how option values invalidate the internal rate of return as an investment choice criterion. “Our analysis points to a need for more empirical studies that incorporate the sequential nature of individual schooling decisions and uncertainty about education costs and future earnings to help determine their importance. We report evidence on estimated option values from the recent empirical literature using rich panel data sources that enable analysts to answer questions that could not be answered with the cross section data available to Mincer in the 1960s.” (Heckman et al. (2006) p. 6). However, all these findings encourage a closer look at the impact of real option theory on human capital investment decision under uncertainty and generate a more comprehensive theoretical framework. Departing from the model suggested by Hogan and Walker (2007) we discuss how uncertain time processes determine the duration of schooling and – with the timing decision to leave school – the accumulation of human capital. We extend their framework by 1) adding accumulated education costs during schooling, 2) considering complete earnings profiles including entry level wage, sheepskin effects and earning dynamics, and 3) discussing the option value of schooling introducing potential career opportunities or threats of unemployment modeled as major uncertain events connected with particular education achievements. In order to discuss these problems we proceed as follows. In Section 2 we introduce the real option base model to determine the expected time of leaving school for a continuous process of schooling. In Section 3 we solve the base model, and discuss comparative statics. In Section 4 we extend the model by introducing different levels of formal qualification and discuss the implications for option values with respect to sheepskin effects and major random events connected with particular formal education achievements. In Section 5 we conclude.

Education is a multi-stage investment and the realization of the various stages takes time. We consider two phases, a pure investment phase followed by a second earning phase. While in the investment phase each period's investment improves the outcome of the project, it is uncertain how long a student will have to invest and how much they will have to accumulate in order to maximize the education value. Hence, the question we answer is, how long (first passage time) and how much we can expect to invest during this kind of multi-stage sequential education process. Recent literature shows that real option theory can be applied to these questions in order to take into account uncertain time processes and irreversibility in human capital accumulation decisions. Based on the modeling suggested by Hogan and Walker (2007) we extend their framework by (1) adding accumulated education costs and determining the expected duration of schooling, (2) considering complete earnings profiles including entry-level wage, sheepskin effects and earning dynamics, and (3) discussing the option value of schooling introducing potential career opportunities or threats of unemployment modeled as major uncertain events connected with a particular education achievement. Marginal risk covers marginal fluctuations in income growth, usually depicted by the variance. Stochastic shocks are strong (more than marginal) upward or downward shifts in income. As these kinds of large sudden events are an important ingredient of income profiles connected to qualification levels we account for this phenomenon by extending the standard version of the model by an Ito–Lévy Jump Diffusion process. From comparative statics we obtain: (i) With an increase in education costs the student may stay in the system as long as the increasing costs of schooling is compensated sufficiently by the market. (ii) A sheepskin effect may produce an extra income premium, and completion of a formal education is often a necessary precondition for moving to the next level. Both facts describe a discontinuous jump in rewards once a student achieves a formal qualification. This leap increases the option value of additional education and hence the value of staying in school. Sheepskin effects, even of future levels of qualification and even if the time to completion is long, remain an encouraging component in the decision to remain in school longer. (iii) With respect to the effects of stochastic major events that we analyze, staying at school becomes less attractive if the frequency of such uncertain events offered by the market increases and if there are more opportunities overall than threats. In this case the uncertainty in the market is positive and students will want to seize these positive opportunities. However, if fewer threats and increasing opportunities go along with an increasing formal level of qualification the option value of achieving higher levels of education increases.