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

Chau, Tak Wai (2015): Identification through Heteroscedasticity: What If We Have the Wrong Form of Heteroscedasticity?

Abstract

Recent literature propose estimators that utilize heteroscedasticity of the error terms to identify the coefficient of the endogenous regressor without using excluded instruments. The assumed forms of heteroscedasticity differ across estimators. This study investigates the robustness of the two most popular estimators under different forms of heteroscedasticity through simulations. The results show that both estimators can be substantially biased under the wrong form of heteroscedasticity. Moreover, the overidentification test proposed for one estimator can have low power against the wrong form of heteroscedasticity. This study also explores the use of the maximum likelihood framework and the Alkaline Information Criteria (AIC) to distinguish these two models. The simulation results show that it has good performance.

• Item Type: MPRA Paper
• Language: English
• Keywords: Instrumental Variable Estimation, Endogeneity, Heteroscedasticity, Misspecification, Maximum Likelihood
• Subjects: C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C13 - Estimation: General; C - Mathematical and Quantitative Methods > C3 - Multiple or Simultaneous Equation Models ; Multiple Variables > C31 - Cross-Sectional Models ; Spatial Models ; Treatment Effect Models ; Quantile Regressions ; Social Interaction Models; C - Mathematical and Quantitative Methods > C3 - Multiple or Simultaneous Equation Models ; Multiple Variables > C36 - Instrumental Variables (IV) Estimation

References

Baum, C.F and Schaffer, M. E., (2012) "IVREG2H: Stata module to perform instrumental variables estimation using heteroskedasticity-based instruments," Statistical Software Components S457555, Boston College Department of Economics, revised 02 Apr 2015.

References Breusch, T. and Pagan A. (1979) “A Simple Test for Heteroscedasticity and Random Coefficient Variation,” Econometrica, 47, 1287-1294.

References Emran, M. and Shilpi, S. (2012) “The Extent of the Market and Stages of Agricultural Specialization,” Canadian Journal of Economics, 12, 1125-1153.

References Farre, L. Klein, R. and Vella, F. (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, 44, 111-133.

References Fernihough, A. (2014). “ivlewbel: Uses heteroscedasticity to estimate mismeasured and endogenous regressor models.” R package version 1.1. http://CRAN.R-project.org/package=ivlewbel

References Hansen, L (1982) “Large Sample Properties of Generalized Method of Moments Estimators,” Econometrica, 50,1029-1054.

References Klein, R. and Vella, F. (2009) “Estimating the Return to Endogenous Schooling Decisions via Conditional Second Moments,” Journal of Human Resources, 44(4), 1047-1065.

References Klein, R. and Vella, F. (2010) “Estimating a class of triangular simultaneous equations models without exclusion restrictions,” Journal of Econometrics, 154, 154-164.

References Lewbel, A. (2012) “Using Heteroscedasticity to Identify and Estimate Mismeasured and Endogenous Regressor Models,” Journal of Business and Economic Statistics, 30(1), 67-80.

References Millimet, D. and Roy, J. (2015) “Empirical Tests of the Pollution Haven Hypothesis When Environmental Regulation is Endogenous,” Journal of Applied Econometrics, forthcoming.