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Controlling for Unmeasured Confounding in Panel Data Using Minimal Bridge Functions: From Two-Way Fixed Effects to Factor Models
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TLDR
It is shown that analogous, albeit more complex, transformations exist in the more general linear factor model, providing a new means to identify the effect in that model, and is proved that the resulting average causal effect estimator is root-N consistent and asymptotically normal.Abstract:
We develop a new approach for identifying and estimating average causal effects in panel data under a linear factor model with unmeasured confounders. Compared to other methods tackling factor models such as synthetic controls and matrix completion, our method does not require the number of time periods to grow infinitely. Instead, we draw inspiration from the two-way fixed effect model as a special case of the linear factor model, where a simple difference-in-differences transformation identifies the effect. We show that analogous, albeit more complex, transformations exist in the more general linear factor model, providing a new means to identify the effect in that model. In fact many such transformations exist, called bridge functions, all identifying the same causal effect estimand. This poses a unique challenge for estimation and inference, which we solve by targeting the minimal bridge function using a regularized estimation approach. We prove that our resulting average causal effect estimator is root-N consistent and asymptotically normal, and we provide asymptotically valid confidence intervals. Finally, we provide extensions for the case of a linear factor model with time-varying unmeasured confounders.read more
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References
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Chapter 36 Large sample estimation and hypothesis testing
Whitney K. Newey,Daniel McFadden +1 more
TL;DR: In this paper, conditions for obtaining cosistency and asymptotic normality of a very general class of estimators (extremum estimators) are given to enable approximation of the SDF.
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Determining the Number of Factors in Approximate Factor Models
Jushan Bai,Serena Ng +1 more
TL;DR: In this article, the convergence rate for the factor estimates that will allow for consistent estimation of the number of factors is established, and some panel criteria are proposed to obtain the convergence rates.
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