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Beyond LATE: Estimation of the Average Treatment Effect with an Instrumental Variable

Published online by Cambridge University Press:  04 January 2017

Peter M. Aronow  and
Allison Carnegie
Peter M. Aronow*
Affiliation:
Department of Political Science, Yale University, New Haven, CT 06520
Allison Carnegie
Affiliation:
Department of Political Science, Princeton University, Princeton, NJ 08540, and Department of Political Science, University of Chicago, Chicago, IL 60637 e-mail: acarnegie@uchicago.edu
*
e-mail: peter.aronow@yale.edu (corresponding author)
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Abstract

Political scientists frequently use instrumental variables (IV) estimation to estimate the causal effect of an endogenous treatment variable. However, when the treatment effect is heterogeneous, this estimation strategy only recovers the local average treatment effect (LATE). The LATE is an average treatment effect (ATE) for a subset of the population: units that receive treatment if and only if they are induced by an exogenous IV. However, researchers may instead be interested in the ATE for the entire population of interest. In this article, we develop a simple reweighting method for estimating the ATE, shedding light on the identification challenge posed in moving from the LATE to the ATE. We apply our method to two published experiments in political science in which we demonstrate that the LATE has the potential to substantively differ from the ATE.

Type
Research Article
Information
Political Analysis , Volume 21 , Issue 4 , Autumn 2013 , pp. 492 - 506
Copyright
Copyright © The Author 2013. Published by Oxford University Press on behalf of the Society for Political Methodology 

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Footnotes

Authors' note: The replication archive for this article is available online at Aronow and Carnegie (2013). The authors acknowledge support from the Yale University Faculty of Arts and Sciences High-Performance Computing facility and staff. Helpful comments from Jake Bowers, John Bullock, Dan Butler, Lara Chausow, Adam Dynes, Ivan Fernandez-Val, Adam Glynn, Holger Kern, Malte Lierl, Mary McGrath, Joel Middleton, Cyrus Samii, two anonymous reviewers, and the participants of the Yale American Politics and Public Policy Workshop, the New Faces in Political Methodology Conference, and the Midwest Political Science Association Conference are greatly appreciated. We also thank Jonathan Katz for helpful editorial guidance. Special thanks to Bethany Albertson, Adria Lawrence, and David Nickerson for generous data sharing and to Dean Eckles, Alan Gerber, Don Green, Greg Huber, and Ken Scheve for particularly helpful conversations. All remaining errors are our own. Supplementary materials for this article are available on the Political Analysis Web site.

References

Abadie, Alberto. 2002. Bootstrap tests for distributional treatment effects in instrumental variable models. Journal of the American Statistical Association 97(457): 284–92.Google Scholar
Albertson, Bethany, and Lawrence, Adria. 2009. After the credits roll: The long-term effects of educational television on public knowledge and attitudes. American Politics Research 37(2): 275–300.CrossRefGoogle Scholar
Altonji, J. G., and Dunn, T. A. 1996. The effects of family characteristics on the return to education. Review of Economics and Statistics 78: 692–704.Google Scholar
Angrist, Joshua D., and Imbens, Guido W. 1995. Two-stage least squares estimation of average causal effects in models with variable treatment intensity. Journal of the American Statistical Association 90(430): 431–42.Google Scholar
Angrist, Joshua D., Imbens, Guido W., and Rubin, Donald B. 1996. Identification of causal effects using instrumental variables. Journal of the American Statistical Association 91: 444–55.Google Scholar
Angrist, Joshua D., and Fernandez-Val, Ivan. 2013. ExtrapoLATE-ing: External validity and overidentification in the LATE framework. In Advances in economics and econometrics: Tenth world congress, Vol. 3, eds. Arellano Daron Acemoglu, Manuel, and Deke, Eddie, 401–36. Cambridge: Cambridge University Press.Google Scholar
Angrist, Joshua D., and Pischke, Jörn-Steffen. 2009. Mostly harmless econometrics: An empiricist's companion. Princeton, NJ: Princeton University Press.Google Scholar
Arceneaux, K., and Nickerson, D. W. 2009. Who is mobilized to vote? A re-analysis of 11 field experiments. American Journal of Political Science 53(1): 1–16.Google Scholar
Arceneaux, Kevin, and Nickerson, David W. 2010. Comparing negative and positive campaign messages. American Politics Research 38(1): 54–83.Google Scholar
Aronow, Peter M., and Carnegie, Allison. 2013. Replication data for: Beyond LATE: Estimation of the average treatment effect with an instrumental variable. Dataverse Network. http://hdl.handle.net/1902.1/21729 (accessed August 1, 2013).Google Scholar
Deaton, Angus. 2009. Instruments of development: Randomization in the tropics, and the search for the elusive keys to economic development. Proceedings of the British Academy, 2008 Lectures 162: 123–60.Google Scholar
Elliott, Michael R. 2009. Model averaging methods for weight trimming in generalized linear regression models. Journal of Official Statistics 25(1): 1–20.Google Scholar
Esterling, Kevin M., Neblo, Michael A., and Lazer, David M. J. 2011. Estimating treatment effects in the presence of noncompliance and nonresponse: The generalized endogenous treatment model. Political Analysis 19(2): 205–26.Google Scholar
Fodor, Imola. K. 2002. A survey of dimension reduction techniques. Center for Applied Scientific Computing, Lawrence Livermore National Laboratory, Vol. 9: 1–18.Google Scholar
Follmann, Dean A. 2000. On the effect of treatment among would-be treatment compliers: An analysis of the multiple risk factor intervention trial. Journal of the American Statistical Association 95(452): 1101–9.Google Scholar
Frangakis, Constantine E., and Rubin, Donald B. 1999. Addressing complications of intention-to-treat analysis in the combined presence of all-or-none treatment-noncompliance and subsequent missing outcomes. Biometrika 86(2): 365–79.Google Scholar
Funk, Michele Jonsson, Westreich, Daniel, Wiesen, Chris, Strmer, Til, Alan Brookhart, M., and Davidian, Marie. 2011. Doubly robust estimation of causal effects. American Journal of Epidemiology 173(7): 761–7.CrossRefGoogle ScholarPubMed
Geman, Stuart, and Hwang, Chii-Ruey. 1982. Nonparametric maximum likelihood estimation by the method of sieves. Annals of Statistics 10(2): 401–14.Google Scholar
Green, Donald P., Gerber, Alan S., and Nickerson, David W. 2003. Getting out the vote in local elections: Results from six door-to-door canvassing experiments. Journal of Politics 65(4): 1083–96.CrossRefGoogle Scholar
Heckman, James J., and Urzua, Sergio. 2010. Comparing IV with structural models: What simple IV can and cannot identify. Journal of Econometrics 156(1): 27–37.CrossRefGoogle ScholarPubMed
Hidalgo, F. D., Naidu, S., Nichter, S., and Richardson, N. 2010. Economic determinants of land invasions. Review of Economics and Statistics 92(3): 505–23.Google Scholar
Hirano, Keisuke, Imbens, Guido W., Rubin, Donald B., and Zhou, Xiao-Hua. 2000. Assessing the effect of an influenza vaccine in an encouragement design. Biostatistics 1(1): 69–88.Google Scholar
Horvitz, D. G., and Thompson, D. J. 1952. A generalization of sampling without replacement from a finite universe. Journal of the American Statistical Association 47(260): 663–85.Google Scholar
Humphreys, Macartan. 2009. Bounds on least squares estimates of causal effects in the presence of heterogeneous assignment probabilities. Working paper.Google Scholar
Imbens, Guido W. 2009. Better LATE than nothing: Some comments on Deaton (2009) and Heckman and Urzua (2009). NBER Working paper.Google Scholar
Imbens, Guido W., and Rubin, Donald B. 1997. Bayesian inference for causal effects in randomized experiments with noncompliance. Annals of Statistics 25(1): 305–27.Google Scholar
Joffe, Marshall M., and Brensinger, Colleen. 2003. Weighting in instrumental variables and G-estimation. Statistics in Medicine 22(1): 1285–303.Google Scholar
Joffe, Marshall M., Ten Have, Thomas R., and Brensinger, Colleen. 2003. The compliance score as a regressor in randomized trials. Biostatistics 4(3): 327–40.CrossRefGoogle ScholarPubMed
Putnam, Robert C. 2000. Bowling alone: The collapse and renewal of American Community. New York: Simon and Schuster.Google Scholar
Rosenstone, Steven J., and Hansen, John Mark. 1993. Mobilization, participation, and democracy in America. New York: Macmillan Publishing Company.Google Scholar
Roy, Jason, Hogan, Joseph W., and Marcus, Bess H. 2008. Principal stratification with predictors of compliance for randomized trials with 2 active treatments. Biostatistics 9(2): 277–89.Google Scholar
Rubin, Donald B. 1978. Bayesian inference for causal effects: The role of randomization. Annals of Statistics 6(1): 34–58.Google Scholar
Rubin, Donald B. 2009. Author's reply: Should observational studies be designed to allow lack of balance in covariate distributions across treatment groups? Statistics in Medicine 28(9): 1420–23.Google Scholar
Verba, Sidney, Schlozman, Kay Lehman, and Brady, Henry E. 1995. Voluntarism in American Politics. Cambridge, MA: Harvard University Press.Google Scholar
Wald, A. 1940. The fitting of straight lines if both variables are subject to error. Annals of Mathematical Statistics 11: 284–300.Google Scholar
Yau, Linda H.Y., and Little, Roderick J. 2001. Inference for the complier-average causal effect from longitudinal data subject to noncompliance and missing data, with application to a job training assessment for the unemployed. Journal of the American Statistical Association 96: 1232–44.Google Scholar
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