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Difference‐in‐differences when the treatment status is observed in only one period

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  • Irene Botosaru
  • Federico H. Gutierrez

Abstract

This paper considers the difference‐in‐differences (DID) method when the data come from repeated cross‐sections and the treatment status is observed either before or after the implementation of a program. We propose a new method that point‐identifies the average treatment effect on the treated (ATT) via a DID method when there is at least one proxy variable for the latent treatment. Key assumptions are the stationarity of the propensity score conditional on the proxy and an exclusion restriction that the proxy must satisfy with respect to the change in average outcomes over time conditional on the true treatment status. We propose a generalized method of moments estimator for the ATT and we show that the associated overidentification test can be used to test our key assumptions. The method is used to evaluate JUNTOS, a Peruvian conditional cash transfer program. We find that the program significantly increased the demand for health inputs among children and women of reproductive age.

Suggested Citation

  • Irene Botosaru & Federico H. Gutierrez, 2018. "Difference‐in‐differences when the treatment status is observed in only one period," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 33(1), pages 73-90, January.
  • Handle: RePEc:wly:japmet:v:33:y:2018:i:1:p:73-90
    DOI: 10.1002/jae.2583
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    File URL: https://doi.org/10.1002/jae.2583
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    Cited by:

    1. Brantly Callaway & Pedro H. C. Sant'Anna, 2018. "Difference-in-Differences with Multiple Time Periods and an Application on the Minimum Wage and Employment," DETU Working Papers 1804, Department of Economics, Temple University.
    2. Brantly Callaway & Pedro H. C. Sant'Anna, 2018. "Difference-in-Differences with Multiple Time Periods," Papers 1803.09015, arXiv.org, revised Dec 2020.
    3. de Araujo, Douglas Kiarelly Godoy & Barroso, Joao Barata Ribeiro Blanco & Gonzalez, Rodrigo Barbone, 2020. "Loan-to-value policy and housing finance: Effects on constrained borrowers," Journal of Financial Intermediation, Elsevier, vol. 42(C).
    4. Tanya Byker & Italo A. Gutierrez, 2016. "Treatment Effects Using Inverse Probability Weighting and Contaminated Treatment Data An Application to the Evaluation of a Government Female Sterilization Campaign in Peru," Working Papers WR-1118-1, RAND Corporation.
    5. Douglas Kiarelly Godoy de Araujo & João Barata Ribeiro Blanco Barroso & Rodrigo Barbone Gonzalez, 2016. "Loan-To-Value Policy and Housing Loans: effects on constrained borrowers," Working Papers Series 445, Central Bank of Brazil, Research Department.
    6. Yanqin Fan & Carlos A. Manzanares, 2017. "Partial identification of average treatment effects on the treated through difference-in-differences," Econometric Reviews, Taylor & Francis Journals, vol. 36(6-9), pages 1057-1080, October.
    7. Hiroyuki Kasahara & Katsumi Shimotsu, 2019. "Identification of Regression Models with a Misclassified and Endogenous Binary Regressor," Papers 1904.11143, arXiv.org, revised Dec 2020.
    8. Gonçalves, S. & Rodrigues, T.P. & Chagas, A.L.S., 2020. "The impact of wind power on the Brazilian labor market," Renewable and Sustainable Energy Reviews, Elsevier, vol. 128(C).

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