Difference-in-Differences When Treatment Status Is Observed in Only One Period

Efficient GMM Estimation with Incomplete Data

“…Furthermore, the results in the present manuscript apply to generalizations of this seup: (1) D may not be available in either period 1, but identification can be obtained by obtaining (D, Z) in a third stratum (see note 12 in Botosaru and Gutierrez, 2018); (2) The moment functions in (C.1)…”

“…Example 5 (Botosaru and Gutierrez, 2018). Consider a difference-in-differences setting with two time periods.…”

“…The ATT can be recovered from the distributions (D,Y 0 ) and (D,Y 1 ), both of which are observable in the standard differencein-differences setup. Botosaru and Gutierrez (2018) consider the case where D is not observable for the individuals with T = 0. They propose an estimator that relies on the availability of a proxy Z t , some additional exclusion and stationarity conditions, and the following form for the conditional outcome equations:…”

Loan-to-value policy and housing finance: Effects on constrained borrowers

“…This section presents the identification strategy and data description. We use the differences-in-difference estimator described by Botosaru and Gutierrez (2017); the reader is referred to their paper for further details on the estimator.…”

“…This probability is used to instrument ATT parameters and estimate the effects after policy implementation. Botosaru and Gutierrez (2017) propose consistent and efficient estimators for the case of partially observed treatment status. We rely on their twostage estimator to recover the ATT of LTV limits imposed in Brazil.…”