Arnold Zellner

Arnold Zellner (1927–2010) was one of the most important figures in the development of Bayesian econometrics. A professor at the University of Chicago's Booth School of Business for nearly five decades, he demonstrated that Bayesian methods could provide practical, principled, and computationally tractable solutions to core problems in economic modeling. His introduction of the g-prior for regression and his development of the seemingly unrelated regressions model were foundational contributions that continue to influence both statistics and economics.

Early Life and Education

Zellner was born in Brooklyn, New York, and earned his PhD in economics from the University of California, Berkeley, in 1957. He was influenced by the work of Savage and Jeffreys, and became convinced early in his career that Bayesian methods offered a superior framework for economic inference. He joined the University of Chicago in 1966, where he spent the remainder of his career.

Seemingly Unrelated Regressions

In his 1962 paper, Zellner introduced the seemingly unrelated regressions (SUR) model, which accounts for correlation between the error terms of different regression equations. Although the original formulation was frequentist (using generalized least squares), Zellner later developed fully Bayesian treatments. The SUR model became a standard tool in econometrics for analyzing systems of equations where the dependent variables are related through their error structure.

The g-Prior

Zellner's most widely used contribution to Bayesian statistics is the g-prior for regression coefficients, introduced in 1986. The g-prior specifies that the prior covariance matrix of the regression coefficients is proportional to the inverse of the information in the design matrix, scaled by a single parameter g. This elegant construction has several advantages: it automatically adapts to the scale of the data, produces analytically tractable posteriors, and reduces the prior specification problem for a high-dimensional parameter to the choice of a single scalar.

“It is my experience that simple models and methods usually work well, particularly when they are based on sound principles such as those of Bayesian analysis.”— Arnold Zellner

Bayesian Econometrics

Zellner's 1971 textbook An Introduction to Bayesian Inference in Econometrics was a landmark work that showed how Bayesian methods could be applied to the major models and problems of econometrics: regression, simultaneous equations, distributed lags, and time series. The book was both a technical manual and a philosophical argument, demonstrating that the Bayesian approach was not just theoretically attractive but practically superior for many common econometric problems.

H. G. B. Alexander Chair and Legacy

Zellner held the H. G. B. Alexander Distinguished Service Professorship at the University of Chicago and directed the H. G. B. Alexander Research Foundation. He trained many leading Bayesian econometricians and organized major conferences that brought together statisticians and economists. He received the American Statistical Association's Outstanding Statistical Application Award and was a fellow of numerous professional societies.