Tractable Bayesian inference for an unidentified simple linear regression model
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) (doi:https://doi.org/10.1080/00031305.2024.2333864)
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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 |
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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: | 07 May 2024 12:01 |
URI: | http://gala.gre.ac.uk/id/eprint/46413 |
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