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Bayesian Model Averaging and Weighted Average Least Squares: Equivariance, Stability, and Numerical Issues

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Author Info

  • De Luca, G.
  • Magnus, J.R.

    (Tilburg University, Center for Economic Research)

Abstract

This article is concerned with the estimation of linear regression models with uncertainty about the choice of the explanatory variables. We introduce the Stata commands bma and wals which implement, respectively, the exact Bayesian Model Averaging (BMA) estimator and the Weighted Average Least Squares (WALS) estimator developed by Magnus et al. (2010). Unlike standard pretest estimators which are based on some preliminary diagnostic test, these model averaging estimators provide a coherent way of making inference on the regression parameters of interest by taking into account the uncertainty due to both the estimation and the model selection steps. Special emphasis is given to a number practical issues that users are likely to face in applied work: equivariance to certain transformations of the explanatory variables, stability, accuracy, computing speed and out-of-memory problems. Performances of our bma and wals commands are illustrated using simulated data and empirical applications from the literature on model averaging estimation.

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Bibliographic Info

Paper provided by Tilburg University, Center for Economic Research in its series Discussion Paper with number 2011-082.

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Date of creation: 2011
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Handle: RePEc:dgr:kubcen:2011082

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Web page: http://center.uvt.nl

Related research

Keywords: Model uncertainty; Model averaging; Bayesian analysis; Exact computation;

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References

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  1. Magnus, Jan R. & Powell, Owen & Prüfer, Patricia, 2010. "A comparison of two model averaging techniques with an application to growth empirics," Journal of Econometrics, Elsevier, vol. 154(2), pages 139-153, February.
  2. Valentino Dardanoni & Salvatore Modica & Franco Peracchi, 2011. "Regression with imputed covariates: A generalized missing-indicator approach," Post-Print peer-00815561, HAL.
  3. Einmahl, J.H.J. & Magnus, J.R. & Kumar, K., 2011. "On the Choice of Prior in Bayesian Model Averaging," Discussion Paper 2011-003, Tilburg University, Center for Economic Research.
  4. Valentino Dardanoni & Giuseppe De Luca & Salvatore Modica & Franco Peracchi, 2012. "A generalized missing-indicator approach to regression with imputed covariates," Stata Journal, StataCorp LP, vol. 12(4), pages 575-604, December.
  5. Winford H. Masanjala & Chris Papageorgiou, 2008. "Rough and lonely road to prosperity: a reexamination of the sources of growth in Africa using Bayesian model averaging," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 23(5), pages 671-682.
  6. Magnus, Jan R. & Wan, Alan T.K. & Zhang, Xinyu, 2011. "Weighted average least squares estimation with nonspherical disturbances and an application to the Hong Kong housing market," Computational Statistics & Data Analysis, Elsevier, vol. 55(3), pages 1331-1341, March.
  7. Ley, Eduardo & Steel, Mark F.J., 2007. "Jointness in Bayesian variable selection with applications to growth regression," Journal of Macroeconomics, Elsevier, vol. 29(3), pages 476-493, September.
  8. Carmen Fernandez & Eduardo Ley & Mark F. J. Steel, 2001. "Model uncertainty in cross-country growth regressions," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 16(5), pages 563-576.
  9. Danilov, Dmitry & Magnus, J.R.Jan R., 2004. "On the harm that ignoring pretesting can cause," Journal of Econometrics, Elsevier, vol. 122(1), pages 27-46, September.
  10. Xavier Sala-I-Martin & Gernot Doppelhofer & Ronald I. Miller, 2004. "Determinants of Long-Term Growth: A Bayesian Averaging of Classical Estimates (BACE) Approach," American Economic Review, American Economic Association, vol. 94(4), pages 813-835, September.
  11. Jan R. Magnus, 2002. "Estimation of the mean of a univariate normal distribution with known variance," Econometrics Journal, Royal Economic Society, vol. 5(1), pages 225-236, June.
  12. Jan R. Magnus & J. Durbin, 1999. "Estimation of Regression Coefficients of Interest When Other Regression Coefficients Are of No Interest," Econometrica, Econometric Society, vol. 67(3), pages 639-644, May.
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Cited by:
  1. Hagen, Tobias, 2013. "Impact of national financial regulation on macroeconomic and fiscal performance after the 2007 financial shock: Econometric analyses based on cross-country data," Economics Discussion Papers 2013-26, Kiel Institute for the World Economy.
  2. Hagen, Tobias, 2013. "The impact of national financial regulation on macroeconomic and fiscal performance after the 2007 financial shock: Econometric analyses based on cross-country data," Economics - The Open-Access, Open-Assessment E-Journal, Kiel Institute for the World Economy, vol. 7(33), pages 1-44.
  3. Shekhar Aiyar & Romain A Duval & Damien Puy & Yiqun Wu & Longmei Zhang, 2013. "Growth Slowdowns and the Middle-Income Trap," IMF Working Papers 13/71, International Monetary Fund.
  4. Chiu Adrian & Wieladek Tomasz, 2013. "Is the “Great Recession” really so different from the past?," The B.E. Journal of Macroeconomics, De Gruyter, vol. 13(1), pages 48, October.
  5. Poghosyan, K., 2012. "Structural and reduced-form modeling and forecasting with application to Armenia," Open Access publications from Tilburg University urn:nbn:nl:ui:12-5590845, Tilburg University.
  6. repec:cam:camdae:1324 is not listed on IDEAS
  7. Hagen, Tobias & Waldeck, Stefanie, 2014. "Using panel econometric methods to estimate the effect of milk consumption on the mortality rate of prostate and ovarian cancer," Working Paper Series: Business and Law 03, Frankfurt University of Applied Sciences, Faculty of Business and Law.
  8. Mallick, Debdulal, 2012. "The role of the elasticity of substitution in economic growth: A cross-country investigation," Labour Economics, Elsevier, vol. 19(5), pages 682-694.
  9. Karen Poghosyan & Jan R. Magnus, 2012. "WALS Estimation and Forecasting in Factor-based Dynamic Models with an Application to Armenia," International Econometric Review (IER), Econometric Research Association, vol. 4(1), pages 40-58, April.
  10. Magnus, J.R. & Wang, W., 2012. "Concept-Based Bayesian Model Averaging and Growth Empirics," Discussion Paper 2012-017, Tilburg University, Center for Economic Research.
  11. Hagen, Tobias, 2013. "Impact of national financial regulation on macroeconomic and fiscal performance after the 2007 financial stock: Econometric analyses based on cross-country data," Working Paper Series: Business and Law 02, Frankfurt University of Applied Sciences, Faculty of Business and Law.

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