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I am looking for a theoretically rigorous textbook on Bayesian econometrics, assuming a solid understanding of frequentist econometrics.

I would like to suggest one work per answer, so that recommendations can be voted up or down individually.

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Bayesian Econometrics, by Gary Koop (2003) is a modern rigorous coverage of the field that I recommend. It is in addition completed by a book of exercises: Bayesian Econometric Methods (Econometrics Exercises) by Gary Koop, Dale J. Poirier and Justin L. Tobias (2007).

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    $\begingroup$ Both of these books come with accompanying MATLAB programs, too, so they're also useful for people doing applied work. $\endgroup$ – Graeme Walsh Dec 30 '14 at 18:25
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I suggest "Bayesian Data Analysis" by Gelman et al.:

Gelman, A., Carlin, J., Stern, H., Dunson, D., Vehtari, A., Rubin, D. (2013). Bayesian Data Analysis, Third Edition. New York: Chapman and Hall/CRC.

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    $\begingroup$ Bayesian Analysis is a terrific book. However, it hardly classifies as an econometrics textbook. $\endgroup$ – Xi'an Dec 30 '14 at 18:13
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An Introduction to Bayesian Inference in Econometrics

by Arnold Zellner (1971)

From the cover:

"This is the first book in econometrics to look at models and problems from the Bayesian point of view. [M]any comparisons of Bayesian and non-Bayesian results are presented. [...] An Introduction to Bayesian Inference in Econometrics will be of value as a guide to Bayesian Econometrics for graduate-level students and as a reference volume for researchers."

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    $\begingroup$ Great reference, slightly (?) outdated for a textbook as it was written in the pre-computational era. $\endgroup$ – Xi'an Dec 30 '14 at 18:14
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    $\begingroup$ Agreed; the book is old and does not cover more modern computationally intensive techniques like, say, Bayesian Model Averaging. That said, out of all of the Bayesian Econometrics books that I own, I learned the guts of what I know from this classic piece of work by Zellner. Interestingly, a couple of FORTRAN programs for numerical integration are included in the appendix. $\endgroup$ – Graeme Walsh Dec 30 '14 at 18:31
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    $\begingroup$ thanks. I am not certain FORTRAN programs are a plus nowadays...! $\endgroup$ – Xi'an Dec 30 '14 at 19:26
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    $\begingroup$ Ha! Well, that's arguable, so I won't go there. $\endgroup$ – Graeme Walsh Dec 30 '14 at 19:44
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While it's made for marketing, I'd suggest Bayesian Statistics and Marketing by Rossi, Allenby & McCulloch for Bayesian inference in economic models.

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  • $\begingroup$ Very dense but usefull text for people interested in modeling choice and demand. Since the authors acknowledge Seymour Geisser, Dennis Lindley, and Arnold Zellner as their influential teachers one might get an idea of what to expect. What makes this book very usefull is a set of 5 case studies complete with all data and R code for all models. $\endgroup$ – gwr Jul 3 '18 at 17:29
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I might consider Contemporary Bayesian Econometrics and Statistics by John Geweke. It is relatively brief. The first three chapters cover the sort of foundational stuff you find in any Bayesian analysis book. The next chapter is the linear model with a tad of non-linear regression, followed by latent variables and missing data, then time-series and closed with model comparison and evaluation. There's not very much on panel data or semi/nonparametric estimation.

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