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In order to assess causality between binary economic outcomes, we consider the estimation of a bivariate dynamic probit model on panel data that has the particulary to account the initial conditions of the dynamic process. Due to the untractable form of the likelihood function that is a two dimensions integral, we use an approximation method: the adaptative Gauss-Hermite quadrature method as proposed by Liu and Pierce (1994). For the accuracy of the method and to reduce computing time, we derive the gradient of the log-likelihood and the hessian of the integrand. The estimation method has been implemented using the d1 method of Stata software. We made an empirical validation of our estimation method by applying on simulated data set. We also analyze the impact of the number of quadrature points on the estimations and on the estimation process duration. We then conclude that when exceeding 16 quadrature points on our simulated data set, the relative differences in the estimated coeffcients are around 0.01% but the computing time grows up exponentially.

On the Estimation of Causality in a Bivariate Dynamic Probit Model on Panel Data with Stata Software: A Technical Review