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

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.

Evaluation of the Implementation Effect of the Ecological Compensation Policy in the Poyang Lake River Basin Based on Difference-in-Difference Method

“…Differences in the control group before and after the policy implementation can be seen as indicating the pure time effect, which when subtracted from the changes in the treatment group yields the "net effect" of the policy [46]. The quasi-natural experiment of the DID method can effectively avoid the problems of endogeneity and missing variables in the process of evaluating environmental policy effects [47].…”

Difference-in-Differences With Multiple Time Periods and an Application on the Minimum Wage and Employment

“…Most methodological extensions of DID methods focus on this standard two periods, two groups setup, see e.g. Heckman et al (1997Heckman et al ( , 1998, Abadie (2005), Athey and Imbens (2006), Qin and Zhang (2008), Bonhomme and Sauder (2011), Botosaru and Gutierrez (2017), de Chaisemartin and D'Haultfoeuille (2017), and Callaway et al (2018).…”

Treatment Effects Using Inverse Probability Weighting and Contaminated Treatment Data: An Application to the Evaluation of a Government Female Sterilization Campaign in Peru

“…A similar assumption is made by Botosaru and Gutierrez (2014) to estimate the probability of treatment for the period where treatment status is missing.…”

“…Our approach is also related to work by Botosaru and Gutierrez (2014), who develop a difference-in-difference estimator when treatment status is observed in only one period. Their methodology uses repeated cross-sections and relies on the ability to predict treatment status in one period based on knowledge of treatment status in the other period and auxiliary information available in both cross-sections.…”

“…Their methodology uses repeated cross-sections and relies on the ability to predict treatment status in one period based on knowledge of treatment status in the other period and auxiliary information available in both cross-sections. Similar to our approach, the Botosaru and Gutierrez (2014) method provides point estimates of the average treatment on the treated. Our empirical problem is different, however, in that we aim to estimate impacts for a subgroup of interest whose identity is not observable.…”