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Proper Posteriors from Improper Priors for an Unidentified Errors-in-Variables Model

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  • Erickson, Timothy

Abstract

The problem considered is inference in a simple errors-in-variables model where consistent estimation is impossible without introducing additional exact prior information. The probabilistic prior information required for Bayesian analysis is found to be surprisingly light: despite the model's lack of identification, a proper posterior is guaranteed for any bounded prior density, including those representing improper priors. This result is illustrated with the improper uniform prior, which implies marginal posterior densities obtainable by integrating the likelihood function; surprisingly, the posterior mode for the regression slope is the usual least squares estimate. Copyright 1989 by The Econometric Society.

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  • Erickson, Timothy, 1989. "Proper Posteriors from Improper Priors for an Unidentified Errors-in-Variables Model," Econometrica, Econometric Society, vol. 57(6), pages 1299-1316, November.
    • Handle: RePEc:ecm:emetrp:v:57:y:1989:i:6:p:1299-1316
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    Cited by:

    1. Hu, Yingyao, 2006. "Bounding parameters in a linear regression model with a mismeasured regressor using additional information," Journal of Econometrics, Elsevier, vol. 133(1), pages 51-70, July.
    2. Kishore Gawande & Alok K. Bohara, 2000. "Errors‐in‐Variables Bounds in a Tobit Model of Endogenous Protection," Southern Economic Journal, John Wiley & Sons, vol. 66(4), pages 881-905, April.
    3. Bollinger, Christopher R. & van Hasselt, Martijn, 2017. "Bayesian moment-based inference in a regression model with misclassification error," Journal of Econometrics, Elsevier, vol. 200(2), pages 282-294.

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