Econometrica: Nov, 1989, Volume 57, Issue 6

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

https://doi.org/0012-9682(198911)57:6<1299:PPFIPF>2.0.CO;2-F
p. 1299-1316

Timothy Erickson

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.