Friday, June 29, 2012

SURE Models

In recent weeks I've had several people email to ask if I can recommend a book that goes into all of the details about the "Seemingly Unrelated Regression Equations" (SURE, or just SUR) model.

Any decent econometrics text discusses this model, of course. However, the treatment usually focuses on the asymptotic properties of the standard estimators - iterated feasible GLS, or MLE.

This is fine, but what about things like:
  • A comprehensive treatment of the finie-sample properties of these estimators.
  • A rigorous treatment of the "unbalanced sample" situation.
  • Extending the model to allow for heteroskedastic errors.
  • Stein-rule and ridge regression versions of the SURE model.
  • etc., etc.
To the best of my knowledge the only monograph that is devoted entirely to a comprehensive discussion of the SURE model is one that my late friend an colleague, Viren Srivastava, and I published in 1987.

That book is V. K Srivastava and D. E. A. Giles, Seemingly Unrelated Regression Equations Models: Estimation and Inference (Marcel Dekker, New York). Marcel Dekker subsequently became part of Chapman & Hall/CRC Press.

At the risk of unashamed self-promotion (!), it's a book that I still recommend quite frequently.

There's quite a story relating to the actual writing of this book with Viren - but more on that, perhaps, in a subsequent post.

© 2012, David E. Giles


  1. Dear Professor Giles,

    Thanks for the nice posts on your blog. I am a regular beneficiary of your blog. Would you please write me how I can test heteroskedasticity afted a 'sureg' estimation on STATA?


    1. Mac - thanks for the kind comment. I' afraid I'm not a STATA user. Perhaps another reader can offer advice?

  2. Dear Professor Giles,
    Today I discovered your bog and I wanted to congratulate you for your feedback. They really are very interesting.
    I would like to ask a question about SURE. Would you please tell me how I can test what form is best suited to estimate whether OLS or GLS ?


  3. Dear Prof. Guiles,

    What is the advantage of estimating a demand-supply model as a system in EViews using OLS, versus estimating it by SUR as a system in EViews also? Thanks.

    1. You use SUR, rather than OLS, if you have a group of equations whose error terms may be correlated. In general, this will then improve the asymptotic efficiency of your estimator. This assumes that all of the regressors are exogenous - otherwise both OLS and SUR will be inconsistent estimators, in general. In the case of a supply/demand system you have both quantity and price being endogenous, so neither OLS nor SUR are appropriate. They will be inconsistent. You need to estimate this simultaneous system either equation-by-equation using an I.V. estimator such as 2SLS; or to get more asymptotic efficiency you can use a full-information estimator such as 3SLS or FIML.

    2. Thank you for your easy to understand clarification. Actually, I conducted a regressor endogeneity test in EViews before asking the above question. The food price appears to be exogenous (probably because of strong government influence)so I thought that system estimation by OLS and SUR is sufficient. However, choosing the appropriate IV is difficult and if any readers have a suggestion on the common IV used in the literature for food price (aside from weather related), I appreciate them much.


    3. If the data are time-series, lagged values of the variables will generally provdie valid instruments, as long as the errors are serially independent.

  4. can you help me that how can i estimate SUR model for TODO and YAMAMOTO causality test??????????please i need your help......

    1. See my post :


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