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RE: st: Multiple endogenous regressors

From   Cameron McIntosh <>
Subject   RE: st: Multiple endogenous regressors
Date   Thu, 20 Oct 2011 19:00:52 -0400

Hi Elizabeth,
Your questions aren't too basic, but at the same time are not neatly separable into packets of references for each. :) There are several related discussions (multiple endogenous regressors) in the Stata archives, so I would search there. Also, see the following papers:
Abrevaya, J., Hausman, J.A., & Khan, S. (2010). Testing for Causal Effects in a Generalized Regression Model With Endogenous Regressors. Econometrica, 78(6), 2043–2061.
Chalak, K., & White, H. (2011). An Extended Class of Instrumental Variables for the Estimation of Causal Effects. Canadian Journal of Economics, 44(1), 1-51.
Baum, C.F., & Schaffer, M.E. (2003). Instrumental variables and GMM: Estimation and testing. The Stata Journal, 3(1), 1…-31.
Baum, C.F., Schaffer, M.E., & Stillman, S. (2007). Enhanced routines for instrumental variables/generalized method of moments estimation and testing. The Stata Journal, 7(4), 465-506.
Baum, C.F., Schaffer, M.E., & Stillman, S. (2002). IVENDOG: Stata module to calculate Durbin-Wu-Hausman endogeneity test after ivreg.Statistical Software Components S494401, Boston College Department of Economics (revised 29 May 2007).
Schaffer, M.E. (Nov. 1, 2005). IXTIVREG2: Stata module to perform extended IV/2SLS, GMM and AC/HAC, LIML and k-class regression for panel data models.
Baum, C.F., Schaffer, M.E., & Stillman, S. (Feb. 5, 2010). IVREG29: Stata module for extended instrumental variables/2SLS and GMM estimation (v9). ;
One other thing I would caution you on (and which I have mentioned recently on the list) is that no statistical test can certify whether a given variable (e.g., Z) is an instrument for a purported causal relation (X--->Y). Graphical methods are also required:
Brito, C., & Pearl, J. (2002). Generalized instrumental variables. In A. Darwiche and N Friedman (Eds.), Uncertainty in Artificial Intelligence: Proceedings of the Eighteenth Conference (pp. 85-93). San Francisco, CA:  Morgan Kaufmann.
Pearl, J. (August 3, 2011). The Causal Foundations of Structural Equation Modeling. Technical Report R-370, UCLA Computer Science Department. Chapter for R. H. Hoyle (Ed.), Handbook of Structural Equation Modeling. New York: Guilford Press.
Kyono, T.M. (2010). Commentator: A Front-End User-Interface Module for Graphical and Structural Equation Modeling. Technical Report R-364. Los Angeles, CA: Department of Computer Science, UCLA. Los Angeles, CA.
Chan, H., & Kuroki, M. (2010). Using Descendants as Instrumental Variables for the Identification of Direct Causal Effects in Linear SEMs. In Proceedings of the 13th International Conference on Artificial Intelligence and Statistics (AISTATS) 2010, Chia Laguna Resort, Sardinia, Italy. Journal of Machine Learning Research, Workshop &Conference Proceedings, 9, 73-80.
Stanghellini, E. (2004). Instrumental variables in Gaussian directed acyclic graph models with an unobserved confounder. Environmetrics, 15(5), 463–469.
> From:
> To:
> Subject: st: Multiple endogenous regressors
> Date: Thu, 20 Oct 2011 20:38:56 +0000
> Hello,
> I'm new to the STATA list, and I don't have much econometrics background, so please forgive me if my questions sounded too basic. I've also read the discussion threads in the archives but did not find the information adequate for my purpose/understanding.
> I am running the two-stage least squares (2SLS) test for 5 endogenous regressors. Here are my questions:-
> (1) Theoretically, the literature suggests that it is possible to generalize the 2SLS mechanism for a single endogenous regressor to multiple endogenous regressors. I've read articles in finance, accounting, economics, etc, that control for endogeneity. So far, the studies that I've come across only control for one endogenous variable. I suspect that it's complicated to run 2SLS for multiple endogenous regressors. From an implementation standpoint, what are the potential econometrics and statistical problems related to running multiple endogenous regressors with 2SLS?
> (2) If I can't find sufficient instruments to run all 5 endogenous regressors at the same time, what potential problems might arise if I run each of the 5 endogenous regressors independently in 5 different 2SLS models?
> (3) Assuming that I can find adequate instruments, I want to run the first stage F statistics to check the validity of my instruments for these 5 endogenous regressors. For a single endogenous regressor, the literature suggests that the first stage F statistics greater than 10 indicates a valid instrument. Can I use this same rule of thumb for multiple endogenous regressors?
> (4) Again assuming that I can find adequate instruments, I want to run the overidentification test akin to Basmann's F test and Hansen's J test. Can I still use these same overidentification tests for multiple endogenous variables?
> References related to any of these four questions would be greatly appreciated. Thanks in advance for your advice and suggestions.
> Regards,
> Elizabeth
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