# Resources for Bayesian Econometrics

Although the use of the Bayesian approach to statistical inference in applied research has been increasing over the last few decades, the classical/frequentist approach still dominates the landscape, at least in the field of econometrics. Most published scientific articles which involve some form of data analysis are based on classical methods. Similarly, textbooks on statistical inference are overwhelmingly frequentist and, usually, cover Bayesian methods only within a single chapter or section. Nevertheless, there are quite a few general statistics textbooks available, which concentrate on the Bayesian approach and a few specifically covering Bayesian econometrics.

Likewise, most of the statistical software packages used by econometricians are designed exclusively for frequentist analyses and Bayesian econometricians most often have to code the estimators themselves, using some programming language. This is changing fast, with some econometric packages, nowadays, offering Bayesian estimators as part of their procedures, or with the introduction of easy to use general-purpose statistical packages, which are becoming popular among econometricians.

This section of the website provides references to some of the textbooks which cover Bayesian econometrics, either extensively or exclusively. It also has a brief overview of Bayesian statistical software packages which are popular among econometricians. The emphasis is on econometrics and not general statistics, because the notation and terminology used therein should be familiar to the users of BayES.

# Textbooks on Bayesian Inference and Bayesian Econometrics

The following is a non-exhaustive list of Bayesian econometrics textbooks. Some of them place emphasis on the theoretical justification of the Bayesian approach to statistical inference, others on simulation methods and some on model setup and interpretation of the results. User need or preferences are important in making a choice among them.

- Zellner, A. (1971). An Introduction to Bayesian Inference in Econometrics. John Wiley & Sons, NY.
This is a classic reference and the first textbook to be dedicated to Bayesian econometrics. It contains a complete theoretical discussion of the Bayesian approach, but, because it predates the revolution that occurred in the application of Bayesian methods with the introduction of MCMC techniques, the models presented therein are constructed such that analytical results become available. Nevertheless, this textbook covers many of the most popular econometric models.

- Koop, G. (2003). Bayesian Econometrics. John Wiley & Sons, Chichester.
This is a very accessible textbook that concentrates on the setup of econometric models and the interpretation of their results, rather than estimation techniques and algorithms. It provides extensive coverage of a wide range of popular econometric models. However, the notation used is different from the documents in this site and, at times, it may become cumbersome.

- Lancaster, T. (2004). An Introduction to Modern Bayesian Econometrics. Wiley-Blackwell, UK.
This is another very accessible textbook, which can be viewed as a handbook for the applied Bayesian econometrician. It covers the theory behind the Bayesian approach to statistical inference and has an extensive discussion of simulation methods. It presents many popular econometric models and it contains multiple examples, complete with WinBUGS code.

- Geweke, J. (2005). Contemporary Bayesian Econometrics and Statistics. John Wiley & Sons, Iowa City.
This is a very rigorous textbook and about half of it is devoted to setting the stage for Bayesian statistical analysis. As such, it contains extensive treatments of the fundamentals of Bayesian inference, as well as of simulation methods, both Markov-chain based and otherwise. In terms of applications, it tends to concentrate on cross-sectional and time-series models, with minimal coverage of models for panel data. The notation used in this textbook is similar to Koop (2003).

- Greenberg, E. (2013). Introduction to Bayesian Econometrics (2
^{nd}Edition). Cambridge University Press, NY.This more recent textbook starts from the basics of probability theory and contains extensive discussions of the fundamental concepts in Bayesian inference. It covers simulation methods quite formally, but tends to move rather fast through the application of these methods to econometric models. Because of this, prior exposure to econometrics is essential.

# Software for Bayesian Econometrics

The following is, again, a non-exhaustive list of software packages that are either designed exclusively for Bayesian analysis or that incorporate some procedures for estimating complex models using the Bayesian approach. There are many software packages that can be used to conduct Bayesian inference, but this list contains only those that are considerably easy to use (i.e. do not require the user to code the samplers) and enjoy some degree of popularity among econometricians.

WinBUGS, OpenBUGS and JAGS are three very similar packages designed to conduct Bayesian inference in general problems, but which have become quite popular among econometricians. All three of them require a specification of the model using dialects of the BUGS language and, after data are provided to them, use expert systems for deciding the optimal way of sampling from the full conditionals of each parameter block. Development of WinBUGS has officially halted and OpenBUGS seems to be updated very infrequently. Development of JAGS, on the other hand, still appears to be very active.

Stan is another package similar in spirit to the three mentioned above, with two important differences: the language it uses is slightly more complex and its emphasis is on hierarchical models. It uses specialized sampling algorithms that circumvent the computational problems that appear in these complex models. On the other hand, Stan may be rather slow when estimating simple models, but it is being very actively developed, so these issues are likely to be overcome in the near future.

Stata

^{®}is a software package which is very popular among econometricians. It is primarily designed for classical inference, but since version 14, it contains procedures for Bayesian analysis. Using these procedures still requires some knowledge of the inner workings of the MCMC algorithms, but there is no need on the part of the researcher to derive full conditionals and code the samplers to perform the analysis. In version 15 the interface to the Bayesian estimators became much more user friendly.SAS

^{®}is another software package built primarily for statistical analysis using the frequentist approach, which however incorporates a few procedures for Bayesian estimation of some complex models. Although it is a general-purpose statistical package, it is quite popular among econometricians.

# Bayesian Econometrics using BayES^{™}

Bayesian Econometrics using BayES^{™}
is a textbook that aims to serve as an introduction to Bayesian econometrics for readers with limited prior
knowledge of econometrics. It covers the fundamentals of Bayesian inference and computation early on, but in
later chapters it concentrates mostly on the setup of econometric models and the interpretation of their
results. It contains many examples, complete with code written in BayES' language and the results are
presented as they are provided by BayES.

At its current state, this document is very incomplete and it covers only a handful of models. However, its development will follow the development of BayES and, as procedures for estimating particular models are added to BayES, these models will also be covered in the textbook.

The book is made available under a creative commons license and can be used for any purpose for free, as long as the copyright notices are maintained in any derivative work and derivative works are also made available under the same license.

The following two subsections provide links to the datasets used in the examples contained within the book and the code used in these examples.

#### Datasets used within the book

The following list contains links to the datasets used in the example boxes within the textbook
Bayesian Econometrics using BayES^{™}.
Some datasets are used multiple times in the textbook, but are listed here in the order they first appear
in the textbook.

#### Code used in the book's examples

The following list contains links to the code used in the example boxes within the textbook
Bayesian Econometrics using BayES^{™},
organized by chapter.

- Chapter 1
- Chapter 2
- Chapter 3
- Chapter 4
- Chapter 5
- Chapter 6
- Chapter 7
- Chapter 8