Graduate School of Business
Stanford, CA 94305
Institutional Affiliation: Stanford University
NBER Working Papers and Publications
|October 2018||Matrix Completion Methods for Causal Panel Data Models|
with Susan Athey, Mohsen Bayati, Guido Imbens, Khashayar Khosravi: w25132
In this paper we study methods for estimating causal effects in settings with panel data, where a subset of units are exposed to a treatment during a subset of periods, and the goal is estimating counterfactual (untreated) outcomes for the treated unit/period combinations. We develop a class of matrix completion estimators that uses the observed elements of the matrix of control outcomes corresponding to untreated unit/periods to predict the “missing” elements of the matrix, corresponding to treated units/periods. The approach estimates a matrix that well-approximates the original (incomplete) matrix, but has lower complexity according to the nuclear norm for matrices. From a technical perspective, we generalize results from the matrix completion literature by allowing the patterns of m...
|October 2016||Balancing, Regression, Difference-In-Differences and Synthetic Control Methods: A Synthesis|
with Guido W. Imbens: w22791
In a seminal paper Abadie et al (2010) develop the synthetic control procedure for estimating the effect of a treatment, in the presence of a single treated unit and a number of control units, with pre-treatment outcomes observed for all units. The method constructs a set of weights such that covariates and pre-treatment outcomes of the treated unit are approximately matched by a weighted average of control units. The weights are restricted to be nonnegative and sum to one, which allows the procedure to obtain the weights even when the number of lagged outcomes is modest relative to the number of control units, a setting that is not uncommon in applications. In the current paper we propose a more general class of synthetic control estimators that allows researchers to relax some of the ...