Partial identification of average treatment effects on the treated through difference-in-differences |
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Authors: | Yanqin Fan Carlos A Manzanares |
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Institution: | 1. Department of Economics, University of Washington, Seattle, Washington, USAfany88@u.washington.edu;3. Department of Economics, Vanderbilt University, Nashville, Tennessee, USA |
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Abstract: | ABSTRACTThe difference-in-differences (DID) method is widely used as a tool for identifying causal effects of treatments in program evaluation. When panel data sets are available, it is well-known that the average treatment effect on the treated (ATT) is point-identified under the DID setup. If a panel data set is not available, repeated cross sections (pretreatment and posttreatment) may be used, but may not point-identify the ATT. This paper systematically studies the identification of the ATT under the DID setup when posttreatment treatment status is unknown for the pretreatment sample. This is done through a novel application of an extension of a continuous version of the classical monotone rearrangement inequality which allows for general copula bounds. The identifying power of an instrumental variable and of a ‘matched subsample’ is also explored. Finally, we illustrate our approach by estimating the effect of the Americans with Disabilities Act of 1991 on employment outcomes of the disabled. |
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Keywords: | Copula cross-sectional data identified interval instrumental variable matched subsample monotone rearrangement inequality |
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