Regional Policy Evaluation: Interactive Fixed Effects and Synthetic Controls

Abstract

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Dynamic Linear Panel Regression Models With Interactive Fixed Effects

“…A more general low-rank regressor can be obtained by interacting Z i and W t multiplicatively, i.e. X l,it = Z i W t , an empirical example of which is given in Gobillon and Magnac (2013). In these examples, and probably for the vast majority of applications, the low-rank regressors all satisfy rank(X l ) = 1, but our results can easily be extended to more general low-rank regressors.…”

“…time-invariant and common regressors, or interactions of those two) and "high-rank-regressor" (almost all other regressors that vary across individuals and over time) are present simultaneously, while Bai (2009) only considers the "low-rank regressor" separately and in a restrictive setting (in particular not allowing for regressors that are obtained by interacting time-invariant and common variables). A general treatment of "low-rank regressors" is desirable since they often occur in applied work, e.g., Gobillon and Magnac (2013). The analysis of those regressors is challenging, however, since the unobserved interactive fixed effects also represent a low-rank N × T matrix, thus posing a non-trivial identification problem for low-rank regressors, which needs to be addressed.…”

Synthetic Control Estimation Beyond Case Studies: Does the Minimum Wage Reduce Employment?

“…λ t is a 1 × F vector of common unobserved factors and μ i is a F × 1 vector of factor loadings. Gobillon and Magnac (2016) compares the synthetic control approach to panel data models with interactive fixed effects (e.g., Bai (2009)). Both approaches are useful for relaxing the restriction that the fixed effects are additive.…”

ARCO: An Artificial Counterfactual Approach For High-Dimensional Panel Time-Series Data

“…A thorough Monte Carlo experiment is conducted in order to evaluate the small sample performance of the ArCo methodology and to compare it to well-established alternatives, namely: the before-and-after (BA) estimator, the differences-in-differences (DiD) estimator assuming each peer to be an individual in the control group, the PF approach of Gobillon and Magnac (2016), hereafter PF-GM, and the SC method. We show that the bias of the ArCo method is, in general, negligible and much smaller than competing alternatives.…”

“…Contrary to Hsiao, Ching, and Wan (2012), Gobillon and Magnac (2016) consider directly the estimation of a correctly specified linear panel model with interactive fixed effects, strictly exogenous regressors and known number of common factors. The model is an extension of the usual DiD specification augmented by a known number of common factors and the estimation is carried out in the whole sample.…”