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Efficient estimation of regression models with user-specified parametric model for heteroskedasticty

Author

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  • Chaudhuri, Saraswata

    (Department of Economics, McGill University & Cireq, Montreal)

  • Renault, Eric

    (Department of Economics, University of Warwick)

Abstract

Several modern textbooks report that, thanks to the availability of heteroskedasticity robust standard errors, one observes the near-death of Weighted Least Squares (WLS) in cross-sectional applied work. We argue in this paper that it is actually possible to estimate regression parameters at least as precisely as Ordinary Least Squares (OLS) and WLS, even when using a misspeci ed parametric model for conditional heteroskedasticity. Our analysis is valid for a general regression framework (including Instrumental Variables and Nonlinear Regression) as long as the regression is de ned by a conditional expectation condition. The key is to acknowledge, as first pointed out by Cragg (1992) that, when the user-specific heteroskedasticity model is misspecified, WLS has to be modified depending on a choice of some univariate target for estimation. Moreover, targeted WLS can be improved by properly combining moment equations for OLS and WLS respectively. Efficient GMM must be regularized to take into account the possible multicollinearity of estimating equations when errors terms are actually nearly homoscedastic.

Suggested Citation

  • Chaudhuri, Saraswata & Renault, Eric, 2023. "Efficient estimation of regression models with user-specified parametric model for heteroskedasticty," The Warwick Economics Research Paper Series (TWERPS) 1473, University of Warwick, Department of Economics.
    • Handle: RePEc:wrk:warwec:1473
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    References listed on IDEAS

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    More about this item

    Keywords

    asymptotic optimality ; misspecification ; nuisance parameters ; weighted least squares JEL Codes: C12 ; C13 ; C21;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models

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