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The Bivariate Probit Model, Maximum Likelihood Estimation, Pseudo True Parameters and Partial Identification

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  • Chuhui Li
  • Donald S. Poskitt
  • Xueyan Zhao

Abstract

This paper presents an examination of the finite sample performance of likelihood based estimators derived from different functional forms. We evaluate the impact of functional form miss-specification on the performance of the maximum likelihood estimator derived from the bivariate probit model. We also investigate the practical importance of available instruments in both cases of correct and incorrect distributional specifications. We analyze the finite sample properties of the endogenous dummy variable and covariate coefficient estimates, and the correlation coefficient estimates, and we examine the existence of possible "compensating effects" between the latter and estimates of parametric functions such as the predicted probabilities and the average treatment effect. Finally, we provide a bridge between the literature on the bivariate probit model and that on partial identification by demonstrating how the properties of likelihood based estimators are explicable via a link between the notion of pseudo-true parameter values and the concepts of partial identification.

Suggested Citation

  • Chuhui Li & Donald S. Poskitt & Xueyan Zhao, 2016. "The Bivariate Probit Model, Maximum Likelihood Estimation, Pseudo True Parameters and Partial Identification," Monash Econometrics and Business Statistics Working Papers 16/16, Monash University, Department of Econometrics and Business Statistics.
    • Handle: RePEc:msh:ebswps:2016-16
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    More about this item

    Keywords

    partial identification; binary outcome models; mis-specification; average treatment effect;
    All these keywords.

    JEL classification:

    • C31 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models; Quantile Regressions; Social Interaction Models
    • C35 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions
    • C36 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Instrumental Variables (IV) Estimation

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