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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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    1. 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).
    2. 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.
    3. Callaway, Brantly & Sant’Anna, Pedro H.C., 2021. "Difference-in-Differences with multiple time periods," Journal of Econometrics, Elsevier, vol. 225(2), pages 200-230.
    4. Card, David & Colella, Fabrizio & Lalive, Rafael, 2021. "Gender Preferences in Job Vacancies and Workplace Gender Diversity," IZA Discussion Papers 14758, Institute of Labor Economics (IZA).
    5. Yu Lu & Fanbin Kong & Luchen Huang & Kai Xiong & Caiyao Xu & Ben Wang, 2021. "Evaluation of the Implementation Effect of the Ecological Compensation Policy in the Poyang Lake River Basin Based on Difference-in-Difference Method," Sustainability, MDPI, vol. 13(15), pages 1-14, August.
    6. Kasahara, Hiroyuki & Shimotsu, Katsumi, 2022. "Identification Of Regression Models With A Misclassified And Endogenous Binary Regressor," Econometric Theory, Cambridge University Press, vol. 38(6), pages 1117-1139, December.
    7. Cl'ement de Chaisemartin & Xavier D'Haultfoeuille & F'elix Pasquier & Doulo Sow & Gonzalo Vazquez-Bare, 2022. "Difference-in-Differences Estimators for Treatments Continuously Distributed at Every Period," Papers 2201.06898, arXiv.org, revised Jul 2024.
    8. 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.
    9. Jiping Sheng & Xiaoge Gao & Yongqi Sun, 2024. "Sustainability of the Food Industry: Ecological Efficiency and Influencing Mechanism of Carbon Emissions Trading Policy in China," Sustainability, MDPI, vol. 16(5), pages 1-25, March.
    10. 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.
    11. 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.
    12. Augustine Denteh & D'esir'e K'edagni, 2022. "Misclassification in Difference-in-differences Models," Papers 2207.11890, arXiv.org, revised Jul 2022.
    13. Wang, Xuhui & Xi, Haonan, 2023. "Carbon mitigation policy and international tourism. Does the European Union Emissions Trading System hit international tourism from member states?," Annals of Tourism Research, Elsevier, vol. 103(C).
    14. Matteo CM Casiraghi & Eugenio Cusumano & Angelos Chryssogelos, 2024. "European integration and political party logos: A ‘visual Europeanization’?," European Union Politics, , vol. 25(1), pages 86-105, March.
    15. Sun, Liyang & Abraham, Sarah, 2021. "Estimating dynamic treatment effects in event studies with heterogeneous treatment effects," Journal of Econometrics, Elsevier, vol. 225(2), pages 175-199.
    16. 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).
    17. Jiang, Zhangsheng & Xu, Chenghao, 2023. "Policy incentives, government subsidies, and technological innovation in new energy vehicle enterprises: Evidence from China," Energy Policy, Elsevier, vol. 177(C).
    18. Jin, Yu & Xi, Haonan & Wang, Xuhui & Ren, Xin & Yuan, Libin, 2022. "Evaluation of the Integration Policy in China: Does the Integration of Culture and Tourism Promote Tourism Development?," Annals of Tourism Research, Elsevier, vol. 97(C).
    19. Brantly Callaway, 2022. "Difference-in-Differences for Policy Evaluation," Papers 2203.15646, arXiv.org.
    20. Adam M. Lavecchia, 2024. "Family‐level responses to the introduction of Tax‐Free Savings Accounts," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 57(1), pages 108-139, February.

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