Structural estimation of real options models

We propose a numerical approach for structural estimation of a class of discrete (Markov) decision processes emerging in real options applications. The approach is specifically designed to account for two typical features of aggregate data sets in real options: the endogeneity of firms' decisions; the unobserved heterogeneity of firms. The approach extends the nested fixed point algorithm by Rust [1987. Optimal replacement of GMC bus engines: an empirical model of Harold Zurcher. Econometrica 55(5), 999-1033; 1988. Maximum likelihood estimation of discrete control processes. SIAM Journal of Control and Optimization 26(5), 1006-1024] because both the nested optimization algorithm and the integration over the distribution of the unobserved heterogeneity are accommodated using a simulation method based on a polynomial approximation of the value function and on recursive least squares estimation of the coefficients. The Monte Carlo study shows that omitting unobserved heterogeneity produces a significant estimation bias because the model can be highly non-linear with respect to the parameters.