OLS and IV estimation of regression models including endogenous interaction terms
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.
|Date of creation:||28 Jan 2014|
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|Contact details of provider:|| Web page: http://www.lebow.drexel.edu/|
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- Jan F. Kiviet, 2013.
"Identification and inference in a simultaneous equation under alternative information sets and sampling schemes,"
Royal Economic Society, vol. 16(1), pages S24-S59, 02.
- Jan F. KIVIET, 2012. "Identification and Inference in a Simultaneous Equation Under Alternative Information Sets and Sampling Schemes," Economic Growth Centre Working Paper Series 1207, Nanyang Technological University, School of Humanities and Social Sciences, Economic Growth Centre.
- 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.
- Kleibergen, Frank & Paap, Richard, 2006. "Generalized reduced rank tests using the singular value decomposition," Journal of Econometrics, Elsevier, vol. 133(1), pages 97-126, July.
- Richard Paap & Frank Kleibergen, 2004. "Generalized Reduced Rank Tests using the Singular Value Decomposition," Econometric Society 2004 Australasian Meetings 195, Econometric Society.
- 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.
- 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.
- Philippe Aghion & Peter Howitt & David Mayer-Foulkes, 2004. "The Effects of Financial Development on Convergence: Theory and Evidence," DEGIT Conference Papers c009_021, DEGIT, Dynamics, Economic Growth, and International Trade.
- Philippe Aghion & Peter Howitt & David Mayer-Foulkes, 2004. "The Effect of Financial Development on Convergence: Theory and Evidence," NBER Working Papers 10358, National Bureau of Economic Research, Inc.
- Ozer-Balli, Hatice & Sørensen, Bent E, 2010.
"Interaction Effects in Econometrics,"
CEPR Discussion Papers
7929, C.E.P.R. Discussion Papers.
- Davidson, Russell & MacKinnon, James G., 1993. "Estimation and Inference in Econometrics," OUP Catalogue, Oxford University Press, number 9780195060119, March.
- Raghuram G. Rajan & Luigi Zingales, 1996.
"Financial Dependence and Growth,"
NBER Working Papers
5758, National Bureau of Economic Research, Inc.
- 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.
- 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).
- 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.
- 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.
- Braumoeller, Bear F., 2004. "Hypothesis Testing and Multiplicative Interaction Terms," International Organization, Cambridge University Press, vol. 58(04), pages 807-820, October.
- 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.
- Douglas Staiger & James H. Stock, 1994.
"Instrumental Variables Regression with Weak Instruments,"
NBER Technical Working Papers
0151, National Bureau of Economic Research, Inc.
- Douglas Staiger & James H. Stock, 1997. "Instrumental Variables Regression with Weak Instruments," Econometrica, Econometric Society, vol. 65(3), pages 557-586, May.
- 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.
- 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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