大学中退の逐次意思決定モデルの構造推定[Structural estimation of a sequential decision model of college dropout]

Using the four-year academic records of 301 male students who enrolled in a specific department at a certain university in April 2016, this paper estimates the structural parameters of a sequential decision model of college dropout and conducts a counterfactual analysis. A well-known method for structural estimation of a dynamic discrete choice model is the Conditional Choice Probability (CCP) method, which recovers the integrated value function from a nonparametric estimate of the reduced-form dropout probability function (CCP function) and constructs a correction term to be added to a binary logit model of staying/dropout to ensure consistent estimation of the structural parameters. The CCP method is especially easy to apply to optimal stopping models, given the value of stopping (expected lifetime earnings after dropout). If dropouts are rare, however, ML estimation of the binary logit model may fail due to complete separation. To avoid this problem, this paper considers a modification of the CCP method, which uses a nonparametric estimate of the log odds ratio of staying/dropout as the dependent variable to apply the least squares method. Monte Carlo experiments show that precise estimation of the structural parameters requires precise estimation of the reduced-form CCP function, which requires a large sample since some states may rarely occur in optimal stopping models. Indeed, precise estimation of the structural parameters was difficult with our data. Nevertheless, given the discount factor and the scale parameter, certain counterfactual behaviors are identifiable independently from the remaining structural parameters. As an example, this paper estimates the effect of four-year tuition subsidies on the dropout probability of the male students in our data. The results show that a tuition subsidy of 100,000 yen per semester reduces the four-year cumulative dropout probability by approximately 2.2%. However, the lower cumulative dropout probability is due to later dropout decisions, and does not necessarily imply a higher graduation probability.