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OLS and IV estimation of regression models including endogenous interaction terms

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  • Maurice J.G. Bun
  • Teresa D. Harrison

Abstract

We 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 Info

Paper provided by Universiteit van Amsterdam, Dept. of Econometrics in its series UvA-Econometrics Working Papers with number 14-02.

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Date of creation: 28 Jan 2014
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Handle: RePEc:ame:wpaper:1402

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Postal: Dept. of Econometrics, Universiteit van Amsterdam, Valckenierstraat 65, NL - 1018 XE Amsterdam, The Netherlands
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Web page: http://www.ase.uva.nl/uva-econometrics
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  1. Howitt, Peter & Mayer-Foulkes, David & Aghion, Philippe, 2005. "The Effect of Financial Development on Convergence: Theory and Evidence," Scholarly Articles 4481509, Harvard University Department of Economics.
  2. Richard Paap & Frank Kleibergen, 2004. "Generalized Reduced Rank Tests using the Singular Value Decomposition," Econometric Society 2004 Australasian Meetings 195, Econometric Society.
  3. Braumoeller, Bear F., 2004. "Hypothesis Testing and Multiplicative Interaction Terms," International Organization, Cambridge University Press, vol. 58(04), pages 807-820, October.
  4. Hatice Balli & Bent Sørensen, 2013. "Interaction effects in econometrics," Empirical Economics, Springer, vol. 45(1), pages 583-603, August.
  5. Raghuram G. Rajan & Luigi Zingales, 1996. "Financial Dependence and Growth," NBER Working Papers 5758, National Bureau of Economic Research, Inc.
  6. Amemiya, Takeshi, 1974. "Multivariate Regression and Simultaneous Equation Models when the Dependent Variables Are Truncated Normal," Econometrica, Econometric Society, vol. 42(6), pages 999-1012, November.
  7. Jan F. Kiviet, 2013. "Identification and inference in a simultaneous equation under alternative information sets and sampling schemes," Econometrics Journal, Royal Economic Society, vol. 16(1), pages S24-S59, 02.
  8. White, Halbert, 1980. "A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity," Econometrica, Econometric Society, vol. 48(4), pages 817-38, May.
  9. Douglas Staiger & James H. Stock, 1994. "Instrumental Variables Regression with Weak Instruments," NBER Technical Working Papers 0151, National Bureau of Economic Research, Inc.
  10. Christopher Dougherty, 2005. "Why Are the Returns to Schooling Higher for Women than for Men?," Journal of Human Resources, University of Wisconsin Press, vol. 40(4), pages 969-988.
  11. Andreas Steinhauer & Tobias Wuergler, 2010. "Leverage and covariance matrix estimation in finite-sample IV regressions," IEW - Working Papers 521, Institute for Empirical Research in Economics - University of Zurich.
  12. Davidson, Russell & MacKinnon, James G., 1993. "Estimation and Inference in Econometrics," OUP Catalogue, Oxford University Press, number 9780195060119.
  13. Nizalova, Olena Y. & Murtazashvili, Irina, 2012. "Exogenous Treatment and Endogenous Factors: Vanishing of Omitted Variable Bias on the Interaction Term," IZA Discussion Papers 6282, Institute for the Study of Labor (IZA).
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