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Heckman, J.J. (1979) The Incidental Parameters Problem and the Problem of Initial Conditions in Estimating: A Discrete Time-Discrete Data Stochastic Process and Some Monte Carlo Evidence. Graduate School of Business and Department of Economics, University of Chicago, Chicago.

has been cited by the following article:

  • 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.