Priors and Posterior Computation in Linear Endogenous Variable Models with Imperfect Instruments


  • Joshua C. C. Chan,

    1. Research School of Economics, Australian National University, Canberra, ACT, Australia
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  • Justin L. Tobias

    Corresponding author
    1. Department of Economics, Purdue University, West Lafayette, IN, USA
    • Correspondence to: Justin L. Tobias, Department of Economics Krannert School of Management, Purdue University403 W. State StreetWest Lafayette, Indiana 47907-2056 USA. E-mail:

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In this paper we, like several studies in the recent literature, employ a Bayesian approach to estimation and inference in models with endogeneity concerns by imposing weaker prior assumptions than complete excludability. When allowing for instrument imperfection of this type, the model is only partially identified, and as a consequence standard estimates obtained from the Gibbs simulations can be unacceptably imprecise. We thus describe a substantially improved ‘semi-analytic’ method for calculating parameter marginal posteriors of interest that only require use of the well-mixing simulations associated with the identifiable model parameters and the form of the conditional prior. Our methods are also applied in an illustrative application involving the impact of body mass index on earnings. Copyright © 2014 John Wiley & Sons, Ltd.