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


  • Joshua C.C. Chan


  • Justin L. Tobias



Estimation in models with endogeneity concerns typically begins by searching for instruments. This search is inherently subjective and identification is generally achieved upon imposing the researcher's strong prior belief that such variables have no conditional impacts on the outcome. Results obtained from such analyses are necessarily conditioned upon the untestable opinions of the researcher, and such beliefs may not be widely shared. 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 requires 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 (BMI) on earnings.

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  • Joshua C.C. Chan & Justin L. Tobias, 2012. "Priors and Posterior Computation in Linear Endogenous Variable Models with Imperfect Instruments," ANU Working Papers in Economics and Econometrics 2012-580, Australian National University, College of Business and Economics, School of Economics.
  • Handle: RePEc:acb:cbeeco:2012-580

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    References listed on IDEAS

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    Cited by:

    1. Jiti Gao & Bin Peng & Zhao Ren & Xiaohui Zhang, 2015. "Variable Selection for a Categorical Varying-Coefficient Model with Identifications for Determinants of Body Mass Index," Monash Econometrics and Business Statistics Working Papers 21/15, Monash University, Department of Econometrics and Business Statistics.

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    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • I10 - Health, Education, and Welfare - - Health - - - General
    • J11 - Labor and Demographic Economics - - Demographic Economics - - - Demographic Trends, Macroeconomic Effects, and Forecasts

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