Zellner (1971) An Introduction to Bayesian Inference in Econometrics

Summary

Arnold Zellner's foundational textbook on Bayesian inference in econometrics. Covers prior distributions, posterior analysis, prediction, and hypothesis testing for the linear model, seemingly unrelated regression (SUR), and simultaneous equations systems. The classic reference for conjugate Normal-Gamma and diffuse-prior Bayesian regression, and the first systematic treatment of Bayesian SUR (Zellner 1962 extended).

Key Claims

• Bayesian regression with diffuse prior yields posterior $\beta \mid y \sim t(\hat\beta, s^2(X'X)^{-1}, T-K)$ — the classical confidence interval interpretation is recovered as a limiting posterior credible interval.
• Combines Jeffreys-invariance arguments for noninformative priors with proper conjugate analysis.
• Discusses SUR (introduced by Zellner 1962) from a Bayesian perspective.

Concepts Introduced or Extended

• Bayesian Linear Regression
• Seemingly Unrelated Regression

Entities Mentioned

• Arnold Zellner

Quotes

"The purpose of this book is to present some Bayesian methods that are useful in econometric analysis."

My Take

The textbook that established Bayesian econometrics as a coherent discipline. Griffiths (2001) cites it as the reference for inequality-restricted priors via truncation of the normal-gamma posterior. Remains useful for its systematic conjugate analysis even though Markov chain Monte Carlo (MCMC) methods have since made non-conjugate models tractable.