TITLE:
On the Estimation of Causality in a Bivariate Dynamic Probit Model on Panel Data with Stata Software: A Technical Review
AUTHORS:
Richard Moussa, Eric Delattre
KEYWORDS:
Causality, Bivariate Dynamic Probit, Gauss-Hermite Quadrature, Simulated Likelihood, Gradient, Hessian
JOURNAL NAME:
Theoretical Economics Letters,
Vol.8 No.6,
April
24,
2018
ABSTRACT: 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 particularity to account the initial conditions of the
dynamic process. Due to the intractable form of the likelihood function that is
a two dimensions integral, we use an approximation method: The adaptative
Gauss-Hermite quadrature method. 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 coefficients are around 0.01%
but the computing time grows up exponentially.