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Identification through Heteroscedasticity: What If We Have the Wrong Form of Heteroscedasticity?

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  • Chau, Tak Wai

Abstract

Klein and Vella (2010) and Lewbel (2012) respectively propose estimators that utilize the heteroscedasticity of the error terms to identify the coefficient of the endogenous regressor in a standard linear model, even when there are no exogenous excluded instruments. The assumptions on the form of heteroscedasticity are different for these two estimators, and whether they are robust to misspecification is an important issue because it is not straightforward how to justify which form of heteroscedasticity is true. This paper presents some simulation results for the finite-sample performance of the two estimators under various forms of heteroscedasticity. The results reveal that both estimators can be substantially biased when the form of heteroscedasticity is of the wrong type, meaning that they lack robustness to misspecification of the form of heteroscedasticity. Moreover, the J statistics of the over-identification test for the Lewbel (2012) estimator has low power under the wrong form of heteroscedasticity in the cases considered. The results suggest that it is not enough for researchers to justify only the existence of heteroscedasticity when using the proposed estimators.

Suggested Citation

  • Chau, Tak Wai, 2015. "Identification through Heteroscedasticity: What If We Have the Wrong Form of Heteroscedasticity?," MPRA Paper 65888, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:65888
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    References listed on IDEAS

    as
    1. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-1054, July.
    2. Denny, Kevin & Oppedisano, Veruska, 2013. "The surprising effect of larger class sizes: Evidence using two identification strategies," Labour Economics, Elsevier, vol. 23(C), pages 57-65.
    3. Roger Klein & Francis Vella, 2009. "A semiparametric model for binary response and continuous outcomes under index heteroscedasticity," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 24(5), pages 735-762.
    4. Lídia Farré & Roger Klein & Francis Vella, 2013. "A parametric control function approach to estimating the returns to schooling in the absence of exclusion restrictions: an application to the NLSY," Empirical Economics, Springer, vol. 44(1), pages 111-133, February.
    5. Breusch, T S & Pagan, A R, 1979. "A Simple Test for Heteroscedasticity and Random Coefficient Variation," Econometrica, Econometric Society, vol. 47(5), pages 1287-1294, September.
    6. Arthur Lewbel, 2012. "Using Heteroscedasticity to Identify and Estimate Mismeasured and Endogenous Regressor Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 30(1), pages 67-80.
    7. Christopher F Baum, 2013. "Implementing new econometric tools in Stata," Mexican Stata Users' Group Meetings 2013 09, Stata Users Group.
    8. Roger Klein & Francis Vella, 2009. "Estimating the Return to Endogenous Schooling Decisions via Conditional Second Moments," Journal of Human Resources, University of Wisconsin Press, vol. 44(4).
    9. Christopher F Baum & Arthur Lewbel & Mark E Schaffer & Oleksander Talavera, 2012. "Instrumental variables estimation using heteroskedasticity-based instruments," United Kingdom Stata Users' Group Meetings 2012 07, Stata Users Group.
    10. Chowdhury, Mohammad Tarequl H. & Bhattacharya, Prasad Sankar & Mallick, Debdulal & Ulubaşoğlu, Mehmet Ali, 2014. "An empirical inquiry into the role of sectoral diversification in exchange rate regime choice," European Economic Review, Elsevier, vol. 67(C), pages 210-227.
    11. James Banks & Richard Blundell & Arthur Lewbel, 1997. "Quadratic Engel Curves And Consumer Demand," The Review of Economics and Statistics, MIT Press, vol. 79(4), pages 527-539, November.
    12. M. Shahe Emran & Zhaoyang Hou, 2013. "Access to Markets and Rural Poverty: Evidence from Household Consumption in China," The Review of Economics and Statistics, MIT Press, vol. 95(2), pages 682-697, May.
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    Cited by:

    1. Courtemanche, Charles & Pinkston, Joshua C. & Stewart, Jay, 2021. "Time spent exercising and obesity: An application of Lewbel’s instrumental variables method," Economics & Human Biology, Elsevier, vol. 41(C).

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    More about this item

    Keywords

    Instrumental Variable Estimation; Endogeneity; Heteroscedasticity;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C31 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models; Quantile Regressions; Social Interaction Models
    • C36 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Instrumental Variables (IV) Estimation

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