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

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  • Karim Chalak

    () (Boston College)

  • Halbert White

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.

Suggested Citation

  • Karim Chalak & Halbert White, 2007. "An Extended Class of Instrumental Variables for the Estimation of Causal Effects," Boston College Working Papers in Economics 692, Boston College Department of Economics, revised 30 Nov 2009.
  • Handle: RePEc:boc:bocoec:692
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    References listed on IDEAS

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    1. White, Halbert, 2006. "Time-series estimation of the effects of natural experiments," Journal of Econometrics, Elsevier, vol. 135(1-2), pages 527-566.
    2. James J. Heckman & Sergio Urzua & Edward Vytlacil, 2006. "Understanding Instrumental Variables in Models with Essential Heterogeneity," The Review of Economics and Statistics, MIT Press, vol. 88(3), pages 389-432, August.
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    5. 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.
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    Citations

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    Cited by:

    1. Yingyao Hu & Susanne M. Schennach, 2008. "Instrumental Variable Treatment of Nonclassical Measurement Error Models," Econometrica, Econometric Society, vol. 76(1), pages 195-216, January.
    2. Graevenitz, Georg von & Weber, Richard, 2011. "How to Educate Entrepreneurs?," Discussion Papers in Business Administration 12280, University of Munich, Munich School of Management.
    3. 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.
    4. Dionissi Aliprantis, 2013. "Covariates and causal effects: the problem of context," Working Papers (Old Series) 1310, Federal Reserve Bank of Cleveland.
    5. Santos, Andres, 2011. "Instrumental variable methods for recovering continuous linear functionals," Journal of Econometrics, Elsevier, vol. 161(2), pages 129-146, April.
    6. Cameron McIntosh, 2014. "The presence of an error term does not preclude causal inference in regression: a comment on Krause (2012)," Quality & Quantity: International Journal of Methodology, Springer, vol. 48(1), pages 243-250, January.
    7. Montes-Rojas, Gabriel & Galvao, Antonio F., 2014. "Bayesian endogeneity bias modeling," Economics Letters, Elsevier, vol. 122(1), pages 36-39.
    8. Guasch, J. Luis & Escribano, Álvaro, 2012. "Robust investment climate effects on alternative firm-level productivity measures," UC3M Working papers. Economics we1201, Universidad Carlos III de Madrid. Departamento de Economía.
    9. Schennach, Susanne M., 2008. "Quantile Regression With Mismeasured Covariates," Econometric Theory, Cambridge University Press, vol. 24(04), pages 1010-1043, August.
    10. 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.
    11. 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.
    12. 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.
    13. 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.
    14. 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.
    15. Pearl Judea, 2010. "An Introduction to Causal Inference," The International Journal of Biostatistics, De Gruyter, vol. 6(2), pages 1-62, February.

    More about this item

    Keywords

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

    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C20 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - General
    • C30 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - General
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation

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