Calvert Jump, Robert ORCID: 0000-0002-2967-512X (2024) Tractable Bayesian inference for an unidentified simple linear regression model. The American Statistician. ISSN 0003-1305 (Print), 1537-2731 (Online) (In Press)

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Abstract

In this paper, 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.

Item Type:	Article
Uncontrolled Keywords:	identification; unidentified models; sensitivity analysis; Bayesian statistics; omitted variable bias; linear regression
Subjects:	H Social Sciences > H Social Sciences (General) H Social Sciences > HA Statistics Q Science > QA Mathematics
Faculty / School / Research Centre / Research Group:	Faculty of Business
Last Modified:	18 Mar 2024 12:05
URI:	http://gala.gre.ac.uk/id/eprint/46413

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