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OLS and IV estimation of regression models including endogenous interaction terms

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  • Bun, Maurice J.G.

    ()
    (University of Amsterdam)

  • Harrison, Teresa D.

    ()
    (School of Economics LeBow College of Business Drexel University)

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 con.rm recent empirical findings on the nonlinear causal relation between financial development and economic growth.

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Bibliographic Info

Paper provided by LeBow College of Business, Drexel University in its series School of Economics Working Paper Series with number 2014-3.

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Length: 37 pages
Date of creation: 28 Jan 2014
Date of revision:
Handle: RePEc:ris:drxlwp:2014_003

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Web page: http://www.lebow.drexel.edu/
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Keywords: endogeneity; instrumental variables; interaction term; ordinary least squares;

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  1. Douglas Staiger & James H. Stock, 1994. "Instrumental Variables Regression with Weak Instruments," NBER Technical Working Papers 0151, National Bureau of Economic Research, Inc.
  2. 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.
  3. Raghuram G. Rajan & Luigi Zingales, 1996. "Financial Dependence and Growth," NBER Working Papers 5758, National Bureau of Economic Research, Inc.
  4. Kleibergen, F.R. & Paap, R., 2003. "Generalized Reduced Rank Tests using the Singular Value Decomposition," Econometric Institute Research Papers EI 2003-01, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
  5. Ozer-Balli, Hatice & Sorensen, Bent E, 2010. "Interaction Effects in Econometrics," CEPR Discussion Papers 7929, C.E.P.R. Discussion Papers.
  6. 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.
  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. 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.
  9. 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.
  10. Braumoeller, Bear F., 2004. "Hypothesis Testing and Multiplicative Interaction Terms," International Organization, Cambridge University Press, vol. 58(04), pages 807-820, October.
  11. 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.
  12. Davidson, Russell & MacKinnon, James G., 1993. "Estimation and Inference in Econometrics," OUP Catalogue, Oxford University Press, number 9780195060119.
  13. 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.
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