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Semiparametric Estimation of Instrumental Variable Models for Causal Effects

  • Alberto Abadie

This article introduces a new class of instrumental variable (IV) estimators of causal treatment effects for linear and nonlinear models with covariates. The rationale for focusing on nonlinear models is to improve the approximation to the causal response function of interest. For example, if the dependent variable is binary or limited, or if the effect of the treatment varies with covariates, a nonlinear model is likely to be appropriate. However, identification is not attained through functional form restrictions. This paper shows how to estimate a well-defined approximation to a nonlinear causal response function of unknown functional form using simple parametric models. As an important special case, I introduce a linear model that provides the best linear approximation to an underlying causal relation. It is shown that Two Stage Least Squares (2SLS) does not always have this property and some possible interpretations of 2SLS coefficients are brie y studied. The ideas and estimators in this paper are illustrated using instrumental variables to estimate the effects of 401(k) retirement programs on savings.

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Paper provided by National Bureau of Economic Research, Inc in its series NBER Technical Working Papers with number 0260.

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Date of creation: Sep 2000
Date of revision:
Publication status: published as Abadie, Alberto. "Bootstrap Tests For Distributional Treatment Effects In Instrumental Variable Models," Journal of the American Statistical Association, 2002, v97(457,Mar), 284-292.
Handle: RePEc:nbr:nberte:0260
Note: TWP PE
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  1. James M. Poterba & Steven F. Venti, 1994. "401(k) Plans and Tax-Deferred Saving," NBER Chapters, in: Studies in the Economics of Aging, pages 105-142 National Bureau of Economic Research, Inc.
  2. Angrist, J.D. & Imbens, G.W., 1992. "Average Causal Response with Variable Treatment Intensity," Papers 9234, Tilburg - Center for Economic Research.
  3. Newey, Whitney K, 1994. "The Asymptotic Variance of Semiparametric Estimators," Econometrica, Econometric Society, vol. 62(6), pages 1349-82, November.
  4. Alberto Abadie & Joshua D. Angrist & Guido W. Imbens, 1998. "Instrumental Variables Estimation of Quantile Treatment Effects," NBER Technical Working Papers 0229, National Bureau of Economic Research, Inc.
  5. Newey, Whitney K., 1994. "Series Estimation of Regression Functionals," Econometric Theory, Cambridge University Press, vol. 10(01), pages 1-28, March.
  6. Heckman, James J, 1990. "Varieties of Selection Bias," American Economic Review, American Economic Association, vol. 80(2), pages 313-18, May.
  7. Heckman, James J & Ichimura, Hidehiko & Todd, Petra E, 1997. "Matching as an Econometric Evaluation Estimator: Evidence from Evaluating a Job Training Programme," Review of Economic Studies, Wiley Blackwell, vol. 64(4), pages 605-54, October.
  8. Imbens, Guido W & Rubin, Donald B, 1997. "Estimating Outcome Distributions for Compliers in Instrumental Variables Models," Review of Economic Studies, Wiley Blackwell, vol. 64(4), pages 555-74, October.
  9. Andrews, Donald W K, 1991. "Asymptotic Normality of Series Estimators for Nonparametric and Semiparametric Regression Models," Econometrica, Econometric Society, vol. 59(2), pages 307-45, March.
  10. James M. Poterba & Steven F. Venti, 1998. "Personal Retirement Saving Programs and Asset Accumulation: Reconciling the Evidence," NBER Chapters, in: Frontiers in the Economics of Aging, pages 23-124 National Bureau of Economic Research, Inc.
  11. James M. Poterba & Steven F. Venti & David A. Wise, 1993. "Do 401(k) Contributions Crowd Out Other Persoanl Saving?," NBER Working Papers 4391, National Bureau of Economic Research, Inc.
  12. Eric M. Engen & William G. Gale & John Karl Scholz, 1996. "The Illusory Effects of Saving Incentives on Saving," Journal of Economic Perspectives, American Economic Association, vol. 10(4), pages 113-138, Fall.
  13. Hausman, J.A. & Newey, W.K., 1992. "Nonparametric Estimation of Exact Consumers Surplus and Deadweight Loss," Working papers 93-2, Massachusetts Institute of Technology (MIT), Department of Economics.
  14. Eric M. Engen & William G. Gale & John Karl Scholz, 1994. "Do Saving Incentives Work?," Brookings Papers on Economic Activity, Economic Studies Program, The Brookings Institution, vol. 25(1), pages 85-180.
  15. Alberto Abadie, 2000. "Bootstrap Tests for the Effect of a Treatment on the Distribution of an Outcome Variable," NBER Technical Working Papers 0261, National Bureau of Economic Research, Inc.
  16. Imbens, Guido W & Angrist, Joshua D, 1994. "Identification and Estimation of Local Average Treatment Effects," Econometrica, Econometric Society, vol. 62(2), pages 467-75, March.
  17. Newey, Whitney K. & Powell, James L., 1993. "Efficiency bounds for some semiparametric selection models," Journal of Econometrics, Elsevier, vol. 58(1-2), pages 169-184, July.
  18. David Card, 1993. "Using Geographic Variation in College Proximity to Estimate the Return to Schooling," Working Papers 696, Princeton University, Department of Economics, Industrial Relations Section..
  19. Newey, Whitney K, 1990. "Semiparametric Efficiency Bounds," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 5(2), pages 99-135, April-Jun.
  20. Heckman, James J. & Robb, Richard Jr., 1985. "Alternative methods for evaluating the impact of interventions : An overview," Journal of Econometrics, Elsevier, vol. 30(1-2), pages 239-267.
  21. repec:att:wimass:9604 is not listed on IDEAS
  22. repec:cup:etheor:v:10:y:1994:i:1:p:1-28 is not listed on IDEAS
  23. Newey, Whitney K., 1997. "Convergence rates and asymptotic normality for series estimators," Journal of Econometrics, Elsevier, vol. 79(1), pages 147-168, July.
  24. Newey, Whitney K. & McFadden, Daniel, 1986. "Large sample estimation and hypothesis testing," Handbook of Econometrics, in: R. F. Engle & D. McFadden (ed.), Handbook of Econometrics, edition 1, volume 4, chapter 36, pages 2111-2245 Elsevier.
  25. Charles F. Manski, 1997. "Monotone Treatment Response," Econometrica, Econometric Society, vol. 65(6), pages 1311-1334, November.
  26. J.D. Angrist & Guido W. Imbens & D.B. Rubin, 1993. "Identification of Causal Effects Using Instrumental Variables," NBER Technical Working Papers 0136, National Bureau of Economic Research, Inc.
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