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

Author

Listed:
  • 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.

Suggested Citation

  • De Luca, G. & Magnus, J.R., 2011. "Bayesian Model Averaging and Weighted Average Least Squares : Equivariance, Stability, and Numerical Issues," Discussion Paper 2011-082, Tilburg University, Center for Economic Research.
  • Handle: RePEc:tiu:tiucen:3aa66f2e-55c5-4ddb-8acf-710e61072f9a
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    File URL: https://pure.uvt.nl/portal/files/1341117/2011-082.pdf
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    References listed on IDEAS

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    1. Dardanoni, Valentino & Modica, Salvatore & Peracchi, Franco, 2011. "Regression with imputed covariates: A generalized missing-indicator approach," Journal of Econometrics, Elsevier, vol. 162(2), pages 362-368, June.
    2. 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.
    3. Danilov, D.L. & Magnus, J.R., 2002. "Estimation of the Mean of a Univariate Normal Distribution When the Variance is not Known," Discussion Paper 2002-77, Tilburg University, Center for Economic Research.
    4. Dardanoni, Valentino & De Luca, Giuseppe & Modica, Salvatore & Peracchi, Franco, 2012. "A generalized missing-indicator approach to regression with imputed covariates," Stata Journal, StataCorp LP, vol. 0(Number 4), pages 1-32.
    5. 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.
    6. Dmitry Danilov, 2005. "Estimation of the mean of a univariate normal distribution when the variance is not known," Econometrics Journal, Royal Economic Society, vol. 8(3), pages 277-291, December.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
    12. 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.
    13. repec:hal:journl:peer-00815561 is not listed on IDEAS
    14. 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.
    15. 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.
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    More about this item

    Keywords

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

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

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