Tractable Bayesian Inference for Unidentified Linear Regression Models

6 Pages Posted: 30 Sep 2022

See all articles by Robert Calvert Jump

Robert Calvert Jump

University of Greenwich - Business School

Date Written: September 28, 2022

Abstract

In this paper, I propose a tractable approach to Bayesian inference in linear regression models 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 and partially identified regression models, imperfect instrumental variables, and sensitivity analysis.

Keywords: Partial identification, set identification, sensitivity analysis, Bayesian statistics, omitted variable bias, linear regression.

JEL Classification: C10, C11, C52.

Suggested Citation

Calvert Jump, Robert, Tractable Bayesian Inference for Unidentified Linear Regression Models (September 28, 2022). Available at SSRN: https://ssrn.com/abstract=4232133 or http://dx.doi.org/10.2139/ssrn.4232133

Robert Calvert Jump (Contact Author)

University of Greenwich - Business School ( email )

United Kingdom

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