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. 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.
|Date of creation:||30 Dec 2014|
|Date of revision:|
|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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- Hatice Balli & Bent Sørensen, 2013.
"Interaction effects in econometrics,"
Springer, vol. 45(1), pages 583-603, August.
- 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.
- Richard Paap & Frank Kleibergen, 2004.
"Generalized Reduced Rank Tests using the Singular Value Decomposition,"
Econometric Society 2004 Australasian Meetings
195, Econometric Society.
- 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.
- 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.
- Frank Kleibergen & Richard Paap, 2003. "Generalized Reduced Rank Tests using the Singular Value Decomposition," Tinbergen Institute Discussion Papers 03-003/4, Tinbergen Institute.
- 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.
- 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.
- Nizalova Olena Y. & Murtazashvili Irina, 2016.
"Exogenous Treatment and Endogenous Factors: Vanishing of Omitted Variable Bias on the Interaction Term,"
Journal of Econometric Methods,
De Gruyter, vol. 5(1), pages 71-77, January.
- 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.
- 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.
- 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.
- 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.
- 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, 2005. "The Effect of Financial Development on Convergence: Theory and Evidence," The Quarterly Journal of Economics, Oxford University Press, vol. 120(1), pages 173-222.
- 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.
- 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.
- Rajan, Raghuram G & Zingales, Luigi, 1998.
"Financial Dependence and Growth,"
American Economic Review,
American Economic Association, vol. 88(3), pages 559-86, June.
- 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.
- Raghuram G. Rajan & Luigi Zingales, 1996. "Financial Dependence and Growth," NBER Working Papers 5758, National Bureau of Economic Research, Inc.
- Braumoeller, Bear F., 2004. "Hypothesis Testing and Multiplicative Interaction Terms," International Organization, Cambridge University Press, vol. 58(04), pages 807-820, October.
- 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.
- 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.
- Jan F. Kiviet, 2012. "Identification and Inference in a Simultaneous Equation under Alternative Information Sets and Sampling Schemes," Tinbergen Institute Discussion Papers 12-128/III, Tinbergen Institute.
- Davidson, Russell & MacKinnon, James G., 1993. "Estimation and Inference in Econometrics," OUP Catalogue, Oxford University Press, number 9780195060119, December.
- Cameron,A. Colin & Trivedi,Pravin K., 2005. "Microeconometrics," Cambridge Books, Cambridge University Press, number 9780521848053, December.
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