Dmitry Arkhangelsky

We develop an estimator for applications where the variable of interest is endogenous and researchers have access to aggregate instruments. Our method addresses the critical identification challenge -- unobserved confounding, which renders conventional estimators invalid. Our proposal relies on a new data-driven aggregation scheme that eliminates the unobserved confounders. We illustrate the advantages of our algorithm using data from Nakamura and Steinsson (2014) study of local fiscal multipliers. We introduce a finite population model with aggregate uncertainty to analyze our estimator. We establish conditions for consistency and asymptotic normality and show how to use our estimator to conduct valid inference.

We propose a new estimator for average causal effects of a binary treatment with panel data in settings with general treatment patterns. Our approach augments the popular two-way-fixed-effects specification with unit-specific weights that arise from a model for the assignment mechanism. We show how to construct these weights in various settings, including the staggered adoption setting, where units opt into the treatment sequentially but permanently. The resulting estimator converges to an average (over units and time) treatment effect under the correct specification of the assignment model, even if the fixed effect model is misspecified. We show that our estimator is more robust than the conventional two-way estimator: it remains consistent if either the assignment mechanism or the two-way regression model is correctly specified. In addition, the proposed estimator performs better than the two-way-fixed-effect estimator if the outcome model and assignment mechanism are locally misspecified. This strong double robustness property underlines and quantifies the benefits of modeling the assignment process and motivates using our estimator in practice. We also discuss an extension of our estimator to handle dynamic treatment effects.

We analyze the synthetic control (SC) method in panel data settings with many units. We assume the treatment assignment is based on unobserved heterogeneity and pre-treatment information, allowing for both strictly and sequentially exogenous assignment processes. We show that the critical property that determines the behavior of the SC method is the ability of input features to approximate the unobserved heterogeneity. Our results imply that the SC method delivers asymptotically normal estimators for a large class of linear panel data models as long as the number of pre-treatment periods is sufficiently large, making it a natural alternative to the Difference-in-Differences.

We develop a new approach for estimating average treatment effects in observational studies with unobserved group-level heterogeneity. We consider a general model with group-level unconfoundedness and provide conditions under which aggregate balancing statistics—group-level averages of functions of treatments and covariates—are sufficient to eliminate differences between groups. Building on these results, we re-interpret commonly used linear fixed-effect regression estimators by writing them in the Mundlak form as linear regression estimators without fixed effects but including group averages. We use this representation to develop Generalized Mundlak Estimators that capture group differences through group averages of (functions of) the unit-level variables and adjust for these group differences in flexible and robust ways in the spirit of the modern causal literature.

Summary: We study identification and estimation of causal effects in settings with panel data. Traditionally, researchers follow model-based identification strategies relying on assumptions governing the relation between the potential outcomes and the observed and unobserved confounders. We focus on a different, complementary approach to identification, where assumptions are made about the connection between the treatment assignment and the unobserved confounders. Such strategies are common in cross-section settings, but rarely used with panel data. We introduce different sets of assumptions that follow the two paths to identification and develop a double robust approach. We propose estimation methods that build on these identification strategies.

We study identification and estimation of causal effects in settings with panel data. Traditionally researchers follow model-based identification strategies relying on assumptions governing the relation between the potential outcomes and the observed and unobserved confounders. We focus on a different, complementary approach to identification where assumptions are made about the connection between the treatment assignment and the unobserved confounders. Such strategies are common in cross-section settings but rarely used with panel data. We introduce different sets of assumptions that follow the two paths to identification and develop a doubly robust approach. We propose estimation methods that build on these identification strategies.

We present a new estimator for causal effects with panel data that builds on insights behind the widely used difference in differences and synthetic control methods. Relative to these methods we find, both theoretically and empirically, that this "synthetic difference in differences" estimator has desirable robustness properties, and that it performs well in settings where the conventional estimators are commonly used in practice. We study the asymptotic behavior of the estimator when the systematic part of the outcome model includes latent unit factors interacted with latent time factors, and we present conditions for consistency and asymptotic normality.