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Register a new userControlling for Unmeasured Confounding in Panel Data Using Minimal Bridge Functions: From Two-Way Fixed Effects to Factor Models
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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.
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Factor structures or interactive effects are convenient devices to incorporate latent variables in panel data models. We consider fixed effect estimation of nonlinear panel single-index models with factor structures in the unobservables, which include logit, probit, ordered probit and Poisson specifications. We establish that fixed effect estimators of model parameters and average partial effects have normal distributions when the two dimensions of the panel grow large, but might suffer of incidental parameter bias. We show how models with factor structures can also be applied to capture important features of network data such as reciprocity, degree heterogeneity, homophily in latent variables and clustering. We illustrate this applicability with an empirical example to the estimation of a gravity equation of international trade between countries using a Poisson model with multiple factors.
We present the Stata commands probitfe and logitfe, which estimate probit and logit panel data models with individual and/or time unobserved effects. Fixed effect panel data methods that estimate the unobserved effects can be severely biased because of the incidental parameter problem (Neyman and Scott, 1948). We tackle this problem by using the analytical and jackknife bias corrections derived in Fernandez-Val and Weidner (2016) for panels where the two dimensions ($N$ and $T$) are moderately large. We illustrate the commands with an empirical application to international trade and a Monte Carlo simulation calibrated to this application.
Bayesian causal inference offers a principled approach to policy evaluation of proposed interventions on mediators or time-varying exposures. We outline a general approach to the estimation of causal quantities for settings with time-varying confounding, such as exposure-induced mediator-outcome confounders. We further extend this approach to propose two Bayesian data fusion (BDF) methods for unmeasured confounding. Using informative priors on quantities relating to the confounding bias parameters, our methods incorporate data from an external source where the confounder is measured in order to make inferences about causal estimands in the main study population. We present results from a simulation study comparing our data fusion methods to two common frequentist correction methods for unmeasured confounding bias in the mediation setting. We also demonstrate our method with an investigation of the role of stage at cancer diagnosis in contributing to Black-White colorectal cancer survival disparities.
Nonseparable panel models are important in a variety of economic settings, including discrete choice. This paper gives identification and estimation results for nonseparable models under time homogeneity conditions that are like time is randomly assigned or time is an instrument. Partial identification results for average and quantile effects are given for discrete regressors, under static or dynamic conditions, in fully nonparametric and in semiparametric models, with time effects. It is shown that the usual, linear, fixed-effects estimator is not a consistent estimator of the identified average effect, and a consistent estimator is given. A simple estimator of identified quantile treatment effects is given, providing a solution to the important problem of estimating quantile treatment effects from panel data. Bounds for overall effects in static and dynamic models are given. The dynamic bounds provide a partial identification solution to the important problem of estimating the effect of state dependence in the presence of unobserved heterogeneity. The impact of $T$, the number of time periods, is shown by deriving shrinkage rates for the identified set as $T$ grows. We also consider semiparametric, discrete-choice models and find that semiparametric panel bounds can be much tighter than nonparametric bounds. Computationally-convenient methods for semiparametric models are presented. We propose a novel inference method that applies in panel data and other settings and show that it produces uniformly valid confidence regions in large samples. We give empirical illustrations.
In this study, we develop a novel estimation method of the quantile treatment effects (QTE) under the rank invariance and rank stationarity assumptions. Ishihara (2020) explores identification of the nonseparable panel data model under these assumptions and propose a parametric estimation based on the minimum distance method. However, the minimum distance estimation using this process is computationally demanding when the dimensionality of covariates is large. To overcome this problem, we propose a two-step estimation method based on the quantile regression and minimum distance method. We then show consistency and asymptotic normality of our estimator. Monte Carlo studies indicate that our estimator performs well in finite samples. Last, we present two empirical illustrations, to estimate the distributional effects of insurance provision on household production and of TV watching on child cognitive development.
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