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Adaptive Experimental Design Using the Propensity Score

Author

Listed:
  • Jinyong Hahn

    () (Department of Economics, UCLA)

  • Keisuke Hirano

    () (University of Arizona)

  • Dean Karlan

    () (Economic Growth Center, Yale University)

Abstract

Many social experiments are run in multiple waves, or are replications of earlier social experiments. In principle, the sampling design can be modified in later stages or replications to allow for more efficient estimation of causal effects. We consider the design of a two-stage experiment for estimating an average treatment effect, when covariate information is available for experimental subjects. We use data from the first stage to choose a conditional treatment assignment rule for units in the second stage of the experiment. This amounts to choosing the propensity score, the conditional probability of treatment given covariates. We propose to select the propensity score to minimize the asymptotic variance bound for estimating the average treatment effect. Our procedure can be implemented simply using standard statistical software and has attractive large-sample properties.

Suggested Citation

  • Jinyong Hahn & Keisuke Hirano & Dean Karlan, 2009. "Adaptive Experimental Design Using the Propensity Score," Working Papers 969, Economic Growth Center, Yale University.
  • Handle: RePEc:egc:wpaper:969
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    File URL: http://www.econ.yale.edu/growth_pdf/cdp969.pdf
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    References listed on IDEAS

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    1. Alfonso Flores-Lagunes & Arturo Gonzalez & Todd Neumann, 2010. "Learning But Not Earning? The Impact Of Job Corps Training On Hispanic Youth," Economic Inquiry, Western Economic Association International, vol. 48(3), pages 651-667, July.
    2. Duncan I. Simester & Peng Sun & John N. Tsitsiklis, 2006. "Dynamic Catalog Mailing Policies," Management Science, INFORMS, pages 683-696.
    3. Chamberlain, Gary, 1986. "Asymptotic efficiency in semi-parametric models with censoring," Journal of Econometrics, Elsevier, pages 189-218.
    4. Dean Karlan & John A. List, 2007. "Does Price Matter in Charitable Giving? Evidence from a Large-Scale Natural Field Experiment," American Economic Review, American Economic Association, pages 1774-1793.
    5. Keisuke Hirano & Guido W. Imbens & Geert Ridder, 2003. "Efficient Estimation of Average Treatment Effects Using the Estimated Propensity Score," Econometrica, Econometric Society, pages 1161-1189.
    6. Dean S. Karlan & Jonathan Zinman, 2008. "Credit Elasticities in Less-Developed Economies: Implications for Microfinance," American Economic Review, American Economic Association, pages 1040-1068.
    7. Paul J. Gertler & Sebastian W. Martinez & Marta Rubio-Codina, 2012. "Investing Cash Transfers to Raise Long-Term Living Standards," American Economic Journal: Applied Economics, American Economic Association, pages 164-192.
    8. Imbens, Guido W & Angrist, Joshua D, 1994. "Identification and Estimation of Local Average Treatment Effects," Econometrica, Econometric Society, vol. 62(2), pages 467-475, March.
    9. Jinyong Hahn, 1998. "On the Role of the Propensity Score in Efficient Semiparametric Estimation of Average Treatment Effects," Econometrica, Econometric Society, vol. 66(2), pages 315-332, March.
    10. Dean S. Karlan & Jonathan Zinman, 2008. "Credit Elasticities in Less-Developed Economies: Implications for Microfinance," American Economic Review, American Economic Association, pages 1040-1068.
    11. Flores-Lagunes, Alfonso & Gonzalez, Arturo & Neumann, Todd C., 2005. "Learning but Not Earning? The Value of Job Corps Training for Hispanic Youths," IZA Discussion Papers 1638, Institute for the Study of Labor (IZA).
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    Citations

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    Cited by:

    1. Denis Chetverikov & Daniel Wilhelm, 2015. "Nonparametric instrumental variable estimation under monotonicity," Papers 1507.05270, arXiv.org.
    2. Timothy B. Armstrong & Shu Shen, 2013. "Inference on Optimal Treatment Assignments," Cowles Foundation Discussion Papers 1927RR, Cowles Foundation for Research in Economics, Yale University, revised Apr 2015.
    3. Pedro Carneiro & Sokbae Lee & Daniel Wilhelm, 2016. "Optimal data collection for randomized control trials," CeMMAP working papers CWP15/16, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    4. John List & Sally Sadoff & Mathis Wagner, 2011. "So you want to run an experiment, now what? Some simple rules of thumb for optimal experimental design," Experimental Economics, Springer;Economic Science Association, pages 439-457.
    5. Bhattacharya, Debopam & Dupas, Pascaline, 2012. "Inferring welfare maximizing treatment assignment under budget constraints," Journal of Econometrics, Elsevier, pages 168-196.
    6. Aufenanger, Tobias, 2017. "Machine learning to improve experimental design," FAU Discussion Papers in Economics 16/2017, Friedrich-Alexander University Erlangen-Nuremberg, Institute for Economics.
    7. Timothy B. Armstrong & Shu Shen, 2013. "Inference on Optimal Treatment Assignments," Cowles Foundation Discussion Papers 1927R, Cowles Foundation for Research in Economics, Yale University, revised Apr 2014.
    8. Karlan, Dean & Wood, Daniel H., 2017. "The effect of effectiveness: Donor response to aid effectiveness in a direct mail fundraising experiment," Journal of Behavioral and Experimental Economics (formerly The Journal of Socio-Economics), Elsevier, vol. 66(C), pages 1-8.
    9. Pedro Carneiro & Sokbae Lee & Daniel Wilhelm, 2017. "Optimal data collection for randomized control trials," CeMMAP working papers CWP45/17, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    10. Günther Fink & Margaret McConnell & Sebastian Vollmer, 2014. "Testing for heterogeneous treatment effects in experimental data: false discovery risks and correction procedures," Journal of Development Effectiveness, Taylor & Francis Journals, pages 44-57.
    11. Günther Fink & Margaret McConnell & Sebastian Vollmer, 2014. "Testing for heterogeneous treatment effects in experimental data: false discovery risks and correction procedures," Journal of Development Effectiveness, Taylor & Francis Journals, pages 44-57.
    12. Timothy B. Armstrong & Shu Shen, 2013. "Inference on Optimal Treatment Assignments," Cowles Foundation Discussion Papers 1927, Cowles Foundation for Research in Economics, Yale University.
    13. Guido Menzio & Shouyong Shi, 2008. "Efficient Search on the Job and the Business Cycle," PIER Working Paper Archive 08-029, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
    14. Víctor Casero-Alonso & Jesús López-Fidalgo, 2015. "Experimental designs in triangular simultaneous equations models," Statistical Papers, Springer, pages 273-290.
    15. Aufenanger, Tobias, 2017. "Treatment allocation for linear models," FAU Discussion Papers in Economics 14/2017, Friedrich-Alexander University Erlangen-Nuremberg, Institute for Economics.

    More about this item

    Keywords

    experimental design; propensity score; efficiency bound;

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C9 - Mathematical and Quantitative Methods - - Design of Experiments
    • C93 - Mathematical and Quantitative Methods - - Design of Experiments - - - Field Experiments
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General

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