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TESTING LIMITED OVERLAP

Published online by Cambridge University Press:  13 May 2024

Xinwei Ma Open the ORCID record for Xinwei Ma [Opens in a new window] ,
Yuya Sasaki Open the ORCID record for Yuya Sasaki [Opens in a new window]  and
Yulong Wang Open the ORCID record for Yulong Wang [Opens in a new window]
Xinwei Ma
Affiliation:
University of California, San Diego
Yuya Sasaki*
Affiliation:
Vanderbilt University
Yulong Wang
Affiliation:
Syracuse University
*
Address correspondence to Yuya Sasaki, Department of Economics, Vanderbilt University, 415 Calhoun Hall, Nashville, TN 37240, USA; e-mail: yuya.sasaki@vanderbilt.edu.
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Abstract

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Extreme propensity scores arise in observational studies when treated and control units have very different characteristics. This is commonly referred to as limited overlap. In this paper, we propose a formal statistical test that helps assess the degree of limited overlap. Rejecting the null hypothesis in our test indicates either no or very mild degree of limited overlap and hence reassures that standard treatment effect estimators will be well behaved. One distinguishing feature of our test is that it only requires the use of a few extreme propensity scores, which is in stark contrast to other methods that require consistent estimates of some tail index. Without the need to extrapolate using observations far away from the tail, our procedure is expected to exhibit excellent size properties, a result that is also borne out in our simulation study.

Type
ARTICLES
Information
Econometric Theory , First View , pp. 1 - 34
Copyright
© The Author(s), 2024. Published by Cambridge University Press

Footnotes

We would like to express our sincere gratitude to Peter C. B. Phillips and three anonymous reviewers for their invaluable comments and insights, which greatly enhanced the quality of this paper. Sasaki thanks Brian and Charlotte Grove, Chair for research support.

References

REFERENCES

Andrews, D. W. K., & Ploberger, W. (1994). Optimal tests when a nuisance parameter is present only under the alternative. Econometrica , 62(2), 1383–1414.CrossRefGoogle Scholar
Andrews, D. W. K., & Ploberger, W. (1995). Admissibility of the likelihood ratio test when a nuisance parameter is present only under the alternative. Annals of Statistics , 23(5), 1609–1629.CrossRefGoogle Scholar
Arnold, B. C., Balakrishnan, N., & Nagaraja, H. N. (2008). A first course in order statistics . Society for Industrial and Applied Mathematics.CrossRefGoogle Scholar
Belloni, A., Chernozhukov, V., Chetverikov, D., Hansen, C., & Kato, K. (2018). High-dimensional econometrics and regularized GMM. arXiv:1806.01888.Google Scholar
Bierens, H. J. (2014). Consistency and asymptotic normality of sieve ML estimators under low-level conditions. Econometric Theory , 30(5), 1021–1077.CrossRefGoogle Scholar
Cattaneo, M. D. (2010). Efficient semiparametric estimation of multi-valued treatment effects under ignorability. Journal of Econometrics , 155(2), 138–154.CrossRefGoogle Scholar
Cattaneo, M. D., Jansson, M., & Ma, X. (2020). Simple local polynomial density estimators. Journal of the American Statistical Association , 115(531), 1449–1455.CrossRefGoogle Scholar
Cattaneo, M. D., Jansson, M., & Ma, X. (2024). Local regression distribution estimators. Journal of Econometrics , 240(2), 105074.CrossRefGoogle Scholar
Chaudhuri, S., & Hill, J. B. (2014). Heavy tail robust estimation and inference for average treatment effects. Technical report.Google Scholar
Connors, A. F., Speroff, T., Dawson, N. V., Thomas, C., Harrell, F. E., Wagner, D., et al. (1996). The effectiveness of right heart catheterization in the initial care of critically ill patients. JAMA , 276(11), 889–897.CrossRefGoogle ScholarPubMed
Crump, R. K., Hotz, V. J., Imbens, G. W., & Mitnik, O. A. (2009). Dealing with limited overlap in estimation of average treatment effects. Biometrika , 96(1), 187–199.CrossRefGoogle Scholar
Danielsson, J., de Haan, L., Peng, L., & de Vries, C. G. (2001). Using a bootstrap method to choose the sample fraction in tail index estimation. Journal of Multivariate Analysis , 76(2), 226–248.CrossRefGoogle Scholar
de Haan, L., & Ferreira, A. (2007). Extreme value theory: An introduction . New York: Springer.Google Scholar
Dehejia, R. H., & Wahba, S. (1999). Causal effects in nonexperimental studies: Reevaluating the evaluations of training programs. Journal of the American Statistical Association , 94(448), 1053–1062.CrossRefGoogle Scholar
Dehejia, R. H., & Wahba, S. (2002). Propensity score-matching methods for nonexperimental causal studies. Review of Economics and Statistics , 84(1), 151–161.CrossRefGoogle Scholar
Drees, H., & Kaufmann, E. (1998). Selecting the optimal sample fraction in univariate extreme value estimation. Stochastic Processes and Their Applications , 75 (2), 149–172.CrossRefGoogle Scholar
Elliott, G., Müller, U. K., & Watson, M. W. (2015). Nearly optimal tests when a nuisance parameter is present under the null hypothesis. Econometrica , 83(2), 771–811.CrossRefGoogle Scholar
Farrell, M. H. (2015). Robust inference on average treatment effects with possibly more covariates than observations. Journal of Econometrics , 189(1), 1–23.CrossRefGoogle Scholar
Farrell, M. H., Liang, T., & Misra, S. (2021). Deep neural networks for estimation and inference. Econometrica , 89(1), 181–213.CrossRefGoogle Scholar
Feller, W. (1991). An introduction to probability theory and its applications (Vol. II, 2nd ed.). New York: John Wiley.Google Scholar
Girard, S., Stupfler, G., & Usseglio-Carleve, A. (2021). Extreme conditional expectile estimation in heavy-tailed heteroscedastic regression models. Annals of Statistics , 49(6), 3358–3382.CrossRefGoogle Scholar
Gomes, M. I., & Oliveira, O. (2001). The bootstrap methodology in statistics of extremes—choice of the optimal sample fraction. Extremes , 4(4), 331–358.CrossRefGoogle Scholar
Guillou, A., & Hall, P. (2001). A diagnostic for selecting the threshold in extreme value analysis. Journal of the Royal Statistical Society: Series B (Statistical Methodology) , 63(2), 293–305.CrossRefGoogle Scholar
Hill, B. M. (1975). A simple general approach to inference about the tail of a distribution. Annals of Statistics , 3(5), 1163–1174.CrossRefGoogle Scholar
Hirano, K., & Imbens, G. W. (2001). Estimation of causal effects using propensity score weighting: An application to data on right heart catheterization. Health Services and Outcomes Research Methodology , 2(3–4), 259–278.CrossRefGoogle Scholar
Hirano, K., Imbens, G. W., & Ridder, G. (2003). Efficient estimation of average treatment effects using the estimated propensity score. Econometrica , 71(4), 1161–1189.CrossRefGoogle Scholar
Hong, H., Leung, M. P., & Li, J. (2020). Inference on finite-population treatment effects under limited overlap. Econometrics Journal , 23(1), 32–47.CrossRefGoogle Scholar
Khan, S., & Tamer, E. (2010). Irregular identification, support conditions, and inverse weight estimation. Econometrica , 78(6), 2021–2042.Google Scholar
LaLonde, R. J. (1986). Evaluating the econometric evaluations of training programs with experimental data. American Economic Review , 76(4), 604–620.Google Scholar
Lehmann, E. L., & Romano, J. P. (2005). Testing statistical hypothesis . New York: Springer.Google Scholar
Ma, X., & Wang, J. (2020). Robust inference using inverse probability weighting. Journal of the American Statistical Association , 115(532), 1851–1860.CrossRefGoogle Scholar
Müller, U. K., & Wang, Y. (2017). Fixed-k asymptotic inference about tail properties. Journal of the American Statistical Association , 112(519), 1134–1143.CrossRefGoogle Scholar
Newey, W. K., & McFadden, D. L. (1994). Large sample estimation and hypothesis testing. In Engle, R. F., & McFadden, D. L. (Eds.), Handbook of econometrics (Vol. IV, pp. 2111–2245). Elsevier.Google Scholar
Rosenbaum, P. R. (1989). Optimal matching for observational studies. Journal of the American Statistical Association , 84(408), 1024–1032.CrossRefGoogle Scholar
Rosenbaum, P. R., & Rubin, D. B. (1983). The central role of the propensity score in observational studies for causal effects. Biometrika , 70(1), 41–55.CrossRefGoogle Scholar
Rubin, D. B. (1974). Estimating causal effects of treatments in randomized and nonrandomized studies. Journal of Educational Psychology , 66(5), 688–701.CrossRefGoogle Scholar
Rubin, D. B. (1997). Estimating causal effects from large data sets using propensity scores. Annals of Internal Medicine , 127(8 Part 2), 757–763.CrossRefGoogle ScholarPubMed
Sasaki, Y., & Ura, T. (2022). Estimation and inference for moments of ratios with robustness against large trimming bias. Econometric Theory , 38(1), 66–112.CrossRefGoogle Scholar
Sasaki, Y., & Wang, Y. (2022). Fixed-k inference for conditional extremal quantiles. Journal of Business & Economic Statistics , 40(2), 829–837.CrossRefGoogle Scholar
Sasaki, Y., & Wang, Y. (2023). Diagnostic testing of finite moment conditions for the consistency and root-n asymptotic normality of the GMM and M estimators. Journal of Business & Economic Statistics , 41(2), 339–348.CrossRefGoogle Scholar
Scarrott, C., & MacDonald, A. (2012). A review of extreme value threshold estimation and uncertainty quantification. REVSTAT-Statistical Journal , 10(1), 33–60.Google Scholar
Smith, J. A., & Todd, P. E. (2005). Does matching overcome LaLonde’s critique of nonexperimental estimators. Journal of Econometrics , 125(1–2), 305–353.CrossRefGoogle Scholar
Vershynin, R. (2018). High-dimensional probability . Cambridge University Press.CrossRefGoogle Scholar