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Bayesian Versus Maximum Likelihood Estimation of Treatment Effects in Bivariate Probit Instrumental Variable Models

  • Florian M. Hollenbach, Jacob M. Montgomery and Adriana Crespo-Tenorio

Bivariate probit models are a common choice for scholars wishing to estimate causal effects in instrumental variable models where both the treatment and outcome are binary. However, standard maximum likelihood approaches for estimating bivariate probit models are problematic. Numerical routines in popular software suites frequently generate inaccurate parameter estimates and even estimated correctly, maximum likelihood routines provide no straightforward way to produce estimates of uncertainty for causal quantities of interest. In this note, we show that adopting a Bayesian approach provides more accurate estimates of key parameters and facilitates the direct calculation of causal quantities along with their attendant measures of uncertainty.

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Florian M. Hollenbach is an Assistant Professor in the Department of Political Science, Texas A&M University, 2010 Allen Building, 4348 TAMU, College Station, TX 77843-4348 ( Jacob M. Montgomery, Associate Professor, Department of Political Science, Washington University in St. Louis, Campus Box 1063, One Brookings Drive, St. Louis, MO 63130 ( Adriana Crespo-Tenorio, Lead Researcher, Facebook, 1 Hacker Way, Menlo Park, CA 94025 ( Previous versions of this paper were presented at the 2013 Annual Meeting of the Midwest Political Science Association in Chicago, the 2013 Summer Meeting of the Society of Political Methodology at the University of Virginia, and the 2016 Annual Meeting of the Southern Political Science Association in San Juan, Puerto Rico. Portions of this research were conducted with high performance research computing resources provided by Texas A&M University ( The authors are grateful for helpful comments from Kosuke Imai, Kevin Quinn, Marc Ratkovic, Justin Esarey, and a helpful audience at Washington University in St. Louis. To view supplementary material for this article, please visit

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Political Science Research and Methods
  • ISSN: 2049-8470
  • EISSN: 2049-8489
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