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OLS and IV estimation of regression models including endogenous interaction terms

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

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. 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 show that an implementation assuming exogeneity of the interaction term is valid under fairly weak conditions. In the more general case, we derive that instruments need to be interacted with the exogenous part of the interaction to achieve identification. Finally, we propose several specification tests to empirically assess the validity of OLS and IV inference for the interaction model. Using our theoretical results we confirm recent empirical findings on the nonlinear causal relation between financial development and economic growth.

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File URL: http://aseri.uva.nl/binaries/content/assets/subsites/amsterdam-school-of-economics-research-institute/uva-econometrics/dp-2014/1402.pdf
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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: 30 Dec 2014
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Handle: RePEc:ame:wpaper:1402
Contact details of provider: 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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  1. Raghuram G. Rajan & Luigi Zingales, . "Financial Dependence and Growth," CRSP working papers 344, Center for Research in Security Prices, Graduate School of Business, University of Chicago.
  2. 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.
  3. Philippe Aghion & Peter Howitt & David Mayer-Foulkes, 2005. "The Effect of Financial Development on Convergence: Theory and Evidence," The Quarterly Journal of Economics, MIT Press, vol. 120(1), pages 173-222, January.
  4. Olena Nizalova & Irina Murtazashvili, 2011. "Exogenous Treatment and Endogenous Factors: Vanishing of Omitted Variable Bias on the Interaction Term," Discussion Papers 37, Kyiv School of Economics.
  5. 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.
  6. Frank Kleibergen & Richard Paap, 2003. "Generalized Reduced Rank Tests using the Singular Value Decomposition," Tinbergen Institute Discussion Papers 03-003/4, Tinbergen Institute.
  7. 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.
  8. Braumoeller, Bear F., 2004. "Hypothesis Testing and Multiplicative Interaction Terms," International Organization, Cambridge University Press, vol. 58(04), pages 807-820, October.
  9. Hatice Balli & Bent Sørensen, 2013. "Interaction effects in econometrics," Empirical Economics, Springer, vol. 45(1), pages 583-603, August.
  10. Davidson, Russell & MacKinnon, James G., 1993. "Estimation and Inference in Econometrics," OUP Catalogue, Oxford University Press, number 9780195060119, March.
  11. 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.
  12. Cragg, John G. & Donald, Stephen G., 1993. "Testing Identifiability and Specification in Instrumental Variable Models," Econometric Theory, Cambridge University Press, vol. 9(02), pages 222-240, April.
  13. 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.
  14. Douglas Staiger & James H. Stock, 1994. "Instrumental Variables Regression with Weak Instruments," NBER Technical Working Papers 0151, National Bureau of Economic Research, Inc.
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