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I want to study seemingly unrelated regression using Gibbs sampling for many equations. Can someone suggest some books on Bayesian approach for seemingly unrelated regression (SUR) with R examples. I am a beginner in Bayesian statistics and learn well with lots of examples.

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Probably the best and most widespread book about the thematic:

  • APA (6. Ausg.) Wooldridge, J. M. (2002). Econometric analysis of cross section and panel data. Cambridge, Mass: MIT Press.

Note: This is the book many universities use for teaching SUR and equation systems. It is aimed to graduate student, so you should have a solid foundation of statistics, probability and econometrics. I recommend you to buy or rent the book and put a focus on lecture 8 and lecture 9.

Rather general books for the theoretical background:

  • Greene, William H. (2012). Econometric Analysis (Seventh ed.). Upper Saddle River: Pearson Prentice-Hall. pp. 332–344. ISBN 978-0-273-75356-8.
  • APA (6. Ausg.) Wooldridge, J. M. (2006). Introductory econometrics: A modern approach. Mason, OH: Thomson/South-Western.
  • Srivastava, Virendra K.; Giles, David E.A. (1987). Seemingly unrelated regression equations models: estimation and inference. New York: Marcel Dekker. ISBN 978-0-8247-7610-7.

Note: The second woolridge and Greene are rather intuitive and on a lower level than the book I recommended you. Srivastavas book however is more specialised as it only covers SUR and not other topics of econometrics.

A broad and theoretical overview over the topic of SUR and (bayesian regressions):

Rather specific journal articles:

  • Kmenta, Jan; Gilbert, Roy F. (1968). "Small sample properties of alternative estimators of seemingly unrelated regressions". Journal of the American Statistical Association. 63 (324): 1180–1200. doi:10.2307/2285876.
  • Zellner, Arnold (1962). "An efficient method of estimating seemingly unrelated regression equations and tests for aggregation bias". Journal of the American Statistical Association. 57: 348–368. doi:10.2307/2281644.
  • Zellner,A. & Ando, T. (2010).Bayesian and non-Bayesian analysis of the seemingly unrelated regression model with Student-t errors, and its application for forecasting International Journal of Forecasting, vol. 26, issue 2, pages 413-434
  • Gao, C. and Lahiri, K. (1999), “A Comparison of Some Recent Bayesian and Non-Bayesian Procedures for Limited Information Simultaneous Equation Models,” 39 pp., paper presented to American Statistical Association Meeting, Baltimore, Maryland, August,
  • Tsurumi, H. (1990), “Comparing Bayesian and Non-Bayesian Limited Information Estimators,” in Geisser, S., Hodges, S., Press, J. and Zellner, A. (eds.), Bayesian and Likelihood Methods in Statistics and Econometrics, Amsterdam: North-Holland, 179-207
  • van der Merwe, A. and Viljoen, C. (1998), “Bayesian Analysis of the Seemingly Unrelated Regression Model,” Dept. of Math. Statistics, U. of the Orange Free State U., presented to the South African Statistical Association Meeting, Nov. 1998

Note: This journal articles focus rather on theory than on implementation in R. If you are looking for a Journal articles including implementation in R you might have a look at the Journal of Statistical Software. The paper from Zellner & Ando(2010) is probably the most specific and precise answer to your question. As the topic of SUR has been a topic in research constantly since the early 1960s this paper which is from 2010 should also give you a broad range of references to other literature

Examples in R:

  • Kleiber, Christian; Zeileis, Achim (2008). Applied Econometrics with R. New York: Springer. pp. 89–90. ISBN 978-0-387-77318-6.
  • Vinod, Hrishikesh D. (2008). "Identification of Simultaneous Equation Models". Hands-on Intermediate Econometrics Using R. World Scientific. pp. 282–88. ISBN 978-981-281-885-0.
  • Package vignette "systemfit"
  • Ressources from UCLA

Note: You might browser through the webpage of statistical consulting at UCLA and you might find other useful examples of implementations in R. Also note that such specific microeconometric topics are often not yet implemented in R. In Microeconometrics (e.g. SUR) Stata is still a widespread language.

Software recommendation:

I recommend to use either the systemfit package in R or the sureg package in Stata both packages are fine. Henningsen and Hamann describe in their paper several advantages of the systemfit package.

Although systems of linear equations can be estimated with several other statistical and econometric software packages (e.g., SAS, EViews, TSP), systemfit has several advantages. First, all estimation procedures are publicly available in the source code. Second, the estimation algorithms can be easily modified to meet specific requirements. Third, the (advanced) user can control estimation details generally not available in other software packages by overriding reasonable defaults

Therefore I think both Stata and R are valid options for these topics. However as far as I know SUR is mainly applied in microeconometric research and among those researches Stata is the mainly used tool. It is also possible to use other statistical software such as limdep, SAS or Eviews, but I don't know of any advantages of these implementations.Personally as I am mainly using R I would also use R for SURs. ;-)

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    $\begingroup$ +1 for the comprehensiveness. Just to give prespective, I wanted to use a method like the first example (Estimation of Household Equivalence Scales) in fbe.unimelb.edu.au/__data/assets/pdf_file/0005/803174/912.pdf . I have 9 x (ivar) and 9 y (dvar) (so, 9 equations) for i firms in 3 different classes. Also what are the benefits of Bayesian SUR over SUR. $\endgroup$ – Mumbo.Jumbo Oct 18 '16 at 11:57
  • $\begingroup$ I included some more specific papers in the post. Fell free to accept my post if it answers your question. Also feel free to ask for additional information. $\endgroup$ – Ferdi Oct 18 '16 at 12:11
  • $\begingroup$ Thanks for the edit. I will go through your suggestions. What software you suggest for the easiest implementation of the idea in my referenced paper. Also kindly comment make a brief comment why Bayesian SUR is better for my case. Thank you so much $\endgroup$ – Mumbo.Jumbo Oct 18 '16 at 12:16
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    $\begingroup$ I added a software recommendation, If you are advanced R as open source software offers the most possibilities and building up new functions bayesian forecasting. $\endgroup$ – Ferdi Oct 18 '16 at 12:32
  • $\begingroup$ @Ferdi, this is unrelated to this post, but I want to contact you regarding editing. I lost track of whether it was you who proposed an edit to this question, but I think it was. The edit had to be rejected because DF stands for degrees of freedom rather than Dickey-Fuller. It was pretty clear from the context. I suggest you pay a little bit more attention to these kind of details in the future. Otherwise, a good job, your editing helps improve the quality of the site! $\endgroup$ – Richard Hardy Dec 22 '16 at 8:59
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@Ferdi (+1) has some good references on the SUR approach. Ed Greenberg, Introduction to Bayesian Econometrics has a specific Bayesian focus in Chapter 9.

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