Tractable Bayesian Inference For An Unidentified Simple Linear Regression Model

Robert Calvert Jump

The American Statistician, 2024, vol. 78, issue 4, 465-470

Abstract: In this article, I propose a tractable approach to Bayesian inference in a simple linear regression model for which the standard exogeneity assumption does not hold. By specifying a beta prior for the squared correlation between an error term and regressor, I demonstrate that the implied prior for a bias parameter is t-distributed. If the posterior distribution for the identified regression coefficient is normal, this implies that the posterior distribution for the unidentified treatment effect is the convolution of a normal distribution and a t-distribution. This result is closely related to the literatures on unidentified regression models, imperfect instrumental variables, and sensitivity analysis.

Date: 2024
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DOI: 10.1080/00031305.2024.2333864

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