OLS and IV estimation of regression models including endogenous interaction terms
AbstractWe analyze a class of linear regression models including interactions of endogenous regressors and exogenous covariates. We show that, under typical conditions regarding higher-order dependencies between endogenous and exogenous regressors, the OLS estimator of the coefficient of the interaction term is consistent and asymptotically normally distributed. Although not a necessary condition, we demonstrate that multivariate symmetrically distributed data are sufficient for OLS consistency. In general, we propose a Wald test to test for the validity of these higher-order moments. Applying heteroskedasticity-consistent covariance matrix estimators, we then show that standard inference based on OLS is valid for the coefficient of the interaction term. Furthermore, we analyze several IV estimators, and conclude that an implementation exploiting instruments interacted with the exogenous part of the interaction term is to be preferred. Using our theoretical results we confirm recent empirical findings on the nonlinear causal relation between financial development and economic growth.
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Bibliographic InfoPaper provided by Universiteit van Amsterdam, Dept. of Econometrics in its series UvA-Econometrics Working Papers with number 14-02.
Date of creation: 28 Jan 2014
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Postal: Dept. of Econometrics, Universiteit van Amsterdam, Valckenierstraat 65, NL - 1018 XE Amsterdam, The Netherlands
Web page: http://www.ase.uva.nl/uva-econometrics
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Other versions of this item:
- Bun, Maurice J.G. & Harrison, Teresa D., 2014. "OLS and IV estimation of regression models including endogenous interaction terms," School of Economics Working Paper Series 2014-3, LeBow College of Business, Drexel University.
- C01 - Mathematical and Quantitative Methods - - General - - - Econometrics
- 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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