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The fixed-effects estimator is biased in the presence of dynamic misspecification and omitted within variation correlated with one of the regressors. We argue and demonstrate that fixed-effects estimates can amplify the bias from dynamic misspecification and that with omitted time-invariant variables and dynamic misspecifications, the fixed-effects estimator can be more biased than the 'naïve' OLS model. We also demonstrate that the Hausman test does not reliably identify the least biased estimator when time-invariant and time-varying omitted variables or dynamic misspecifications exist. Accordingly, empirical researchers are ill-advised to rely on the Hausman test for model selection or use the fixed-effects model as default unless they can convincingly justify the assumption of correctly specified dynamics. Our findings caution applied researchers to not overlook the potential drawbacks of relying on the fixed-effects estimator as a default. The results presented here also call upon methodologists to study the properties of estimators in the presence of multiple model misspecifications. Our results suggest that scholars ought to devote much more attention to modeling dynamics appropriately instead of relying on a default solution before they control for potentially omitted variables with constant effects using a fixed-effects specification.

Difference-in-differences (DID) is commonly used for causal inference in time-series cross-sectional data. It requires the assumption that the average outcomes of treated and control units would have followed parallel paths in the absence of treatment. In this paper, we propose a method that not only relaxes this often-violated assumption, but also unifies the synthetic control method (Abadie, Diamond, and Hainmueller 2010) with linear fixed effects models under a simple framework, of which DID is a special case. It imputes counterfactuals for each treated unit using control group information based on a linear interactive fixed effects model that incorporates unit-specific intercepts interacted with time-varying coefficients. This method has several advantages. First, it allows the treatment to be correlated with unobserved unit and time heterogeneities under reasonable modeling assumptions. Second, it generalizes the synthetic control method to the case of multiple treated units and variable treatment periods, and improves efficiency and interpretability. Third, with a built-in cross-validation procedure, it avoids specification searches and thus is easy to implement. An empirical example of Election Day Registration and voter turnout in the United States is provided.

Plümper and Troeger (2007) propose a three-step procedure for the estimation of a fixed effects (FE) model that, it is claimed, "provides the most reliable estimates under a wide variety of specifications common to real world data." Their fixed effects vector decomposition (FEVD) estimator is startlingly simple, involving three simple steps, each requiring nothing more than ordinary least squares (OLS). Large gains in efficiency are claimed for cases of time-invariant and slowly time-varying regressors. A subsequent literature has compared the estimator to other estimators of FE models, including the estimator of Hausman and Taylor (1981) also (apparently) with impressive gains in efficiency. The article also claims to provide an efficient estimator for parameters on time-invariant variables (TIVs) in the FE model. None of the claims are correct. The FEVD estimator simply reproduces (identically) the linear FE (dummy variable) estimator then substitutes an inappropriate covariance matrix for the correct one. The consistency result follows from the fact that OLS in the FE model is consistent. The "efficiency" gains are illusory. The claim that the estimator provides an estimator for the coefficients on TIVs in an FE model is also incorrect. That part of the parameter vector remains unidentified. The "estimator" relies upon a strong assumption that turns the FE model into a type of random effects model.

The present study analyzed the relationship between various parenting practices and an array of adolescent psychosocial outcomes in South Korea, while controlling for demographic, family, school, and neighborhood factors. Analyses were based on five waves of the nationally representative Korea Youth Panel Survey using 3,263 youth ( Person Years = 13,121). All parenting (warmth, monitoring, and hostility) and youth's psychosocial (confidence, depressive symptoms, and aggressive behaviors) measures were reported by the youth. Within-person fixed-effects regression results indicated that parental warmth not only facilitated youth's confidence, but also protected them against feelings of depression and aggression. Parental monitoring was a predictor of positive self-perception. As a parental measure with a preventive-orientation, monitoring exhibited a trend toward reducing aggressive behavior. On the other hand, hostile parenting was significantly associated with depressive symptoms and aggressive behaviors. Factors external to the family, such as school and neighborhoods were also associated with mental health outcomes among Korean youth.