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Model averaging, asymptotic risk, and regressor groups

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  • Bruce E. Hansen

Abstract

This paper examines the asymptotic risk of nested least‐squares averaging estimators when the averaging weights are selected to minimize a penalized least‐squares criterion. We find conditions under which the asymptotic risk of the averaging estimator is globally smaller than the unrestricted least‐squares estimator. For the Mallows averaging estimator under homoskedastic errors, the condition takes the simple form that the regressors have been grouped into sets of four or larger. This condition is a direct extension of the classic theory of James–Stein shrinkage. This discovery suggests the practical rule that implementation of averaging estimators be restricted to models in which the regressors have been grouped in this manner. Our simulations show that this new recommendation results in substantial reduction in mean‐squared error relative to averaging over all nested submodels. We illustrate the method with an application to the regression estimates of Fryer and Levitt (2013).

Suggested Citation

  • Bruce E. Hansen, 2014. "Model averaging, asymptotic risk, and regressor groups," Quantitative Economics, Econometric Society, vol. 5(3), pages 495-530, November.
  • Handle: RePEc:wly:quante:v:5:y:2014:i:3:p:495-530
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    Cited by:

    1. Rockey, James & Temple, Jonathan, 2016. "Growth econometrics for agnostics and true believers," European Economic Review, Elsevier, vol. 81(C), pages 86-102.
    2. Zhang, Xinyu, 2015. "Consistency of model averaging estimators," Economics Letters, Elsevier, vol. 130(C), pages 120-123.
    3. Kitagawa, Toru & Muris, Chris, 2016. "Model averaging in semiparametric estimation of treatment effects," Journal of Econometrics, Elsevier, vol. 193(1), pages 271-289.
    4. repec:taf:jnlasa:v:111:y:2016:i:516:p:1775-1790 is not listed on IDEAS
    5. McCloskey, Adam, 2017. "Bonferroni-based size-correction for nonstandard testing problems," Journal of Econometrics, Elsevier, vol. 200(1), pages 17-35.
    6. De Luca, Giuseppe & Magnus, Jan R. & Peracchi, Franco, 2018. "Weighted-average least squares estimation of generalized linear models," Journal of Econometrics, Elsevier, vol. 204(1), pages 1-17.
    7. Shangwei Zhao & Aman Ullah & Xinyu Zhang, 2018. "A Class of Model Averaging Estimators," Working Paper series 18-11, Rimini Centre for Economic Analysis.
    8. Shangwei Zhao, 2014. "Model averaging based on James–Stein estimators," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 77(8), pages 1013-1022, November.
    9. repec:eee:ecolet:v:162:y:2018:i:c:p:101-106 is not listed on IDEAS
    10. repec:eee:econom:v:203:y:2018:i:1:p:1-18 is not listed on IDEAS
    11. Zhang, Xinyu & Ullah, Aman & Zhao, Shangwei, 2016. "On the dominance of Mallows model averaging estimator over ordinary least squares estimator," Economics Letters, Elsevier, vol. 142(C), pages 69-73.

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