Finite sample properties of nonstationary binary response models: A monte carlo analysis

This paper investigates the finite sample distributions of maximum likelihood estimators for nonstationary probit models. This model relates an I (1) variable x_t to a latent I (1) variable y_t^\ast . The binary variable, y_t , is coded as a one if y_t^\ast exceeds some threshold, \alpha , and as a zero otherwise. We find that, analogous to standard OLS models, commonly used tests statistics almost always reject the null hypothesis of no relationship between x_t , and a latent y_t , even when they are, in fact, generated by independent random walks. However, if x_t and y_t^\ast are cointegrated, the sampling distributions of the parameter estimates are better behaved and standard Z and Wald test statistics are consistent.

Keywords:

• Binary Choice
• Probit Models
• Nonstationary Processes