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An Extended Class of Instrumental Variables for the Estimation of Causal Effects

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Author Info

  • Karim Chalak

    ()
    (Boston College)

  • Halbert White

    (University of California-San Diego)

Abstract

This paper examines the ways in which structural systems can yield observed variables, other than the cause or treatment of interest, that can play an instrumental role in identifying and estimating causal effects. We focus speciÖcally on the ways in which structures determine exclusion restrictions and conditional exogeneity relations that act to ensure identification. We show that by carefully specifying the structural equations and by extending the standard notion of instrumental variables, one can identify and estimate causal effects in the endogenous regressor case for a broad range of economically relevant structures. Some of these have not previously been recognized. Our results there create new opportunities for identifying and estimating causal effects in non-experimental situations. Our results for more familiar structures provide new insights. For example, we extend results of Angrist, Imbens, and Rubin (1996) by taking into account an important distinction between cases where Z is an observed exogenous instrument and those where it is a proxy for an unobserved exogenous instrument. A main message emerging from our analysis is the central importance of sufficiently specifying the causal relations governing the unobservables, as these play a crucial role in creating obstacles or opportunities for identification. Because our results exhaust the possibilities for identification, we ensure that there are no other opportunities for identification based on exclusion restrictions and conditional independence relations still to be discovered. To accomplish this characterization, we introduce notions of conditioning and conditional extended instrumental variables (EIVs). These are not proper instruments, as they are endogenous. They nevertheless permit identification and estimation of causal effects. We analyze methods using these EIVs either singly or jointly.

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Bibliographic Info

Paper provided by Boston College Department of Economics in its series Boston College Working Papers in Economics with number 692.

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Date of creation: 23 Nov 2007
Date of revision: 30 Nov 2009
Handle: RePEc:boc:bocoec:692

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Related research

Keywords: causality; conditional exogeneity; endogeneity; exogeneity; identification; instrumental variables; and simultaneous equations.;

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References

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  1. Joshua Angrist & Alan B. Krueger, 2001. "Instrumental Variables and the Search for Identification: From Supply and Demand to Natural Experiments," NBER Working Papers 8456, National Bureau of Economic Research, Inc.
  2. Stefan Hoderlein & Enno Mammen, 2007. "Identification of Marginal Effects in Nonseparable Models Without Monotonicity," Econometrica, Econometric Society, vol. 75(5), pages 1513-1518, 09.
  3. Guido W. Imbens, 2003. "Nonparametric Estimation of Average Treatment Effects under Exogeneity: A Review," NBER Technical Working Papers 0294, National Bureau of Economic Research, Inc.
  4. Hausman, Jerry A & Taylor, William E, 1983. "Identification in Linear Simultaneous Equations Models with Covariance Restrictions: An Instrumental Variables Interpretation," Econometrica, Econometric Society, vol. 51(5), pages 1527-49, September.
  5. White, Halbert, 2006. "Time-series estimation of the effects of natural experiments," Journal of Econometrics, Elsevier, vol. 135(1-2), pages 527-566.
  6. Susanne Schennach & Halbert White & Karim Chalak, 2007. "Estimating average marginal effects in nonseparable structural systems," CeMMAP working papers CWP31/07, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  7. Karim Chalak & Halbert White, 2008. "Causality, Conditional Independence, and Graphical Separation in Settable Systems," Boston College Working Papers in Economics 689, Boston College Department of Economics, revised 04 Jul 2010.
  8. James J. Heckman & Edward Vytlacil, 2005. "Structural Equations, Treatment Effects and Econometric Policy Evaluation," NBER Technical Working Papers 0306, National Bureau of Economic Research, Inc.
  9. James J. Heckman & Edward J. Vytlacil, 2000. "Local Instrumental Variables," NBER Technical Working Papers 0252, National Bureau of Economic Research, Inc.
  10. Rosa L. Matzkin, 1999. "Nonparametric Estimation of Nonadditive Random Functions," Working Papers 38, Universidad de San Andres, Departamento de Economia, revised Sep 2001.
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  17. Heckman, James J & Ichimura, Hidehiko & Todd, Petra, 1998. "Matching as an Econometric Evaluation Estimator," Review of Economic Studies, Wiley Blackwell, vol. 65(2), pages 261-94, April.
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  19. Schennach, Susanne & White, Halbert & Chalak, Karim, 2012. "Local indirect least squares and average marginal effects in nonseparable structural systems," Journal of Econometrics, Elsevier, vol. 166(2), pages 282-302.
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Citations

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Cited by:
  1. Graevenitz, Georg von & Weber, Richard, 2011. "How to Educate Entrepreneurs?," Discussion Papers in Business Administration 12280, University of Munich, Munich School of Management.
  2. Halbert White & Karim Chalak, 2008. "Identifying Structural Effects in Nonseparable Systems Using Covariates," Boston College Working Papers in Economics 734, Boston College Department of Economics.
  3. Alvaro Escribano & J. Luis Guasch, 2012. "Robust investment climate effects on alternative firm-level productivity measures," Economics Working Papers we1201, Universidad Carlos III, Departamento de Economía.
  4. Montes-Rojas, G. & Galvao, A. F., 2013. "Bayesian Endogeneity Bias Modeling," Working Papers 13/09, Department of Economics, City University London.
  5. Dionissi Aliprantis, 2013. "Covariates and causal effects: the problem of context," Working Paper 1310, Federal Reserve Bank of Cleveland.
  6. Karim Chalak & Halbert White, 2008. "Causality, Conditional Independence, and Graphical Separation in Settable Systems," Boston College Working Papers in Economics 689, Boston College Department of Economics, revised 04 Jul 2010.
  7. Susanne Schennach & Halbert White & Karim Chalak, 2007. "Local Indirect Least Squares and Average Marginal Effects in Nonseparable Structural Systems," Boston College Working Papers in Economics 680, Boston College Department of Economics, revised 26 Dec 2009.
  8. Paulo Parente & Richard Smith, 2012. "Exogeneity in semiparametric moment condition models," CeMMAP working papers CWP30/12, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  9. Schennach, Susanne M., 2008. "Quantile Regression With Mismeasured Covariates," Econometric Theory, Cambridge University Press, vol. 24(04), pages 1010-1043, August.
  10. Richard H. Spady, 2007. "Semiparametric Methods for the Measurement of Latent Attitudes and the Estimation of Their Behavioural Consequences," Economics Working Papers ECO2007/29, European University Institute.
  11. Yingyao Hu & Susanne M. Schennach, 2008. "Instrumental Variable Treatment of Nonclassical Measurement Error Models," Econometrica, Econometric Society, vol. 76(1), pages 195-216, 01.

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