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This paper introduces time-varying grouped patterns of heterogeneity in linear panel data models. A distinctive feature of our approach is that group membership is left unrestricted. We estimate the parameters of the model using a \"grouped fixed-effects\" estimator that minimizes a least squares criterion with respect to all possible groupings of the cross-sectional units. Recent advances in the clustering literature allow for fast and efficient computation. We provide conditions under which our estimator is consistent as both dimensions of the panel tend to infinity, and we develop inference methods. Finally, we allow for grouped patterns of unobserved heterogeneity in the study of the link between income and democracy across countries.

Meta-analysis is a common tool for synthesizing results of multiple studies. Among methods for performing meta-analysis, the approach known as 'fixed effects' or Inverse variance weighting' is popular and widely used. A common interpretation of this method is that it assumes that the underlying effects in contributing studies are identical, and for this reason it is sometimes dismissed by practitioners. However, other interpretations of fixed effects analyses do not make this assumption, yet appear to be little known in the literature. We review these alternative interpretations, describing both their strengths and their limitations. We also describe how heterogeneity of the underlying effects can be addressed, with the same minimal assumptions, through either testing or meta-regression. Recommendations for the practice of meta-analysis are given; it is hoped that these will foster more direct connection of the questions that meta-analysts wish to answer with the statistical methods they choose.

This paper considers a class of generalized methods of moments (GMM) estimators for general dynamic panel models, allowing for weakly exogenous covariates and cross-sectional dependence due to spatial lags, unspecified common shocks, and time-varying interactive effects. We significantly expand the scope of the existing literature by allowing for endogenous time-varying spatial weight matrices without imposing explicit structural assumptions on how the weights are formed. An important area of application is in social interaction and network models where our specification can accommodate data dependent network formation. We consider an exemplary social interaction model and show how identification of the interaction parameters is achieved through a combination of linear and quadratic moment conditions. For the general setup we develop an orthogonal forward differencing transformation to aid in the estimation of factor components while maintaining orthogonality of moment conditions. This is an important ingredient to a tractable asymptotic distribution of our estimators. In general, the asymptotic distribution of our estimators is found to be mixed normal due to random norming. However, the asymptotic distribution of our test statistics is still chi-square.

Multilevel models with persons nested in countries are increasingly popular in cross-country research. Recently, social scientists have started to analyze data with a three-level structure: persons at level 1, nested in year-specific country samples at level 2, nested in countries at level 3. By using a country fixed-effects estimator, or an alternative equivalent specification in a random-effects framework, this structure is increasingly used to estimate within-country effects in order to control for unobserved heterogeneity. For the main effects of country-level characteristics, such estimators have been shown to have desirable statistical properties. However, estimators of cross-level interactions in these models are not exhibiting these attractive properties: as algebraic transformations show, they are not independent of between-country variation and thus carry country-specific heterogeneity. Monte Carlo experiments consistently reveal the standard approaches to within estimation to provide biased estimates of cross-level interactions in the presence of an unobserved correlated moderator at the country level. To obtain an unbiased within-country estimator of a cross-level interaction, effect heterogeneity must be systematically controlled. By replicating a published analysis, we demonstrate the relevance of this extended country fixed-effects estimator in research practice. The intent of this article is to provide advice for multilevel practitioners, who will be increasingly confronted with the availability of pooled cross-sectional survey data.

We consider estimation and inference in panel data models with additive unobserved individual specific heterogeneity in a high-dimensional setting. The setting allows the number of time-varying regressors to be larger than the sample size. To make informative estimation and inference feasible, we require that the overall contribution of the time-varying variables after eliminating the individual specific heterogeneity can be captured by a relatively small number of the available variables whose identities are unknown. This restriction allows the problem of estimation to proceed as a variable selection problem. Importantly, we treat the individual specific heterogeneity as fixed effects which allows this heterogeneity to be related to the observed time-varying variables in an unspecified way and allows that this heterogeneity may differ for all individuals. Within this framework, we provide procedures that give uniformly valid inference over a fixed subset of parameters in the canonical linear fixed effects model and over coefficients on a fixed vector of endogenous variables in panel data instrumental variable models with fixed effects and many instruments. We present simulation results in support of the theoretical developments and illustrate the use of the methods in an application aimed at estimating the effect of gun prevalence on crime rates.

Subgroup analysis is the process of comparing a treatment effect for two or more variants of an intervention—to ask, for example, if an intervention’s impact is affected by the setting (school versus community), by the delivery agent (outside facilitator versus regular classroom teacher), by the quality of delivery, or if the long-term effect differs from the short-term effect. While large-scale studies often employ subgroup analyses, these analyses cannot generally be performed for small-scale studies, since these typically include a homogeneous population and only one variant of the intervention. This limitation can be bypassed by using meta-analysis. Meta-analysis allows the researcher to compare the treatment effect in different subgroups, even if these subgroups appear in separate studies. We discuss several statistical issues related to this procedure, including the selection of a statistical model and statistical power for the comparison. To illustrate these points, we use the example of a meta-analysis of obesity prevention.

We review developments in conducting inference for model parameters in the presence of intertemporal and cross-sectional dependence with an emphasis on panel data applications. We review the use of heteroskedasticity and autocorrelation consistent (HAC) standard error estimators, which include the standard clustered and multiway clustered estimators, and discuss alternative sample-splitting inference procedures, such as the Fama–Macbeth procedure, within this context. We outline pros and cons of the different procedures. We then illustrate the properties of the discussed procedures within a simulation experiment designed to mimic the type of firm-level panel data that might be encountered in accounting and finance applications. Our conclusion, based on theoretical properties and simulation performance, is that sample-splitting procedures with suitably chosen splits are the most likely to deliver robust inferential statements with approximately correct coverage properties in the types of large, heterogeneous panels many researchers are likely to face.

[Objective:] This study examines whether paternal part-time employment is related to greater involvement by fathers in child care and housework, both while fathers are working part-time and after they return to full-time employment. [Background:] The study draws on four strands of theory—time availability, bargaining, gender ideology, and gender construction. It studies couples' division of labor in Germany, where policies increasingly support a dual-earner, dual-carer model. [Method:] The study uses data from the German Socio-Economic Panel from 1991 to 2015 on employed adult fathers living together with at least one child younger than age 17 and the mother. The analytic sample comprises 51,230 observations on 8,915 fathers. Fixed effects regression techniques are used to estimate the effect of (previous) part-time employment on fathers' child-care hours, housework hours, and share of child care and housework. [Results:] Fathers did more child care and housework while they worked part time. Yet, most fathers reverted to previous levels of involvement after returning to full-time work. The only exception was fathers with partners in full-time employment, who spent more time doing child care and took on a greater share of housework after part-time employment than before. [Conclusion:] The findings are largely consistent with the time availability perspective, although the results for fathers with full-time employed partners indicate that the relative resources and gender ideology perspectives have some explanatory power as well.

Fixed-effects modeling has become the method of choice in several panel data settings, including models for stochastic frontier analysis. A notable instance of stochastic frontier panel data models is the true fixed-effects model, which allows disentangling unit heterogeneity from efficiency evaluations. While such a model is theoretically appealing, its estimation is hampered by incidental parameters. This note proposes a simple and rather general estimation approach where the unit-specific intercepts are integrated out of the likelihood function. We apply the theory of composite group families to the model of interest and demonstrate that the resulting integrated likelihood is a marginal likelihood with desirable inferential properties. The derivation of the result is provided in full, along with some connections with the existing literature and computational details. The method is illustrated for three notable models, given by the normal-half normal model, the heteroscedastic exponential model, and the normal-gamma model. The results of simulation experiments highlight the properties of the methodology.

Background The fixed effects model is a useful alternative to the mixed effects model for analyzing stepped-wedge cluster randomized trials (SW-CRTs). It controls for all time-invariant cluster-level confounders and has proper control of type I error when the number of clusters is small. While all clusters in a SW-CRT are typically designed to crossover from the control to receive the intervention, some trials can end with unexposed clusters (clusters that never receive the intervention), such as when a trial is terminated early due to safety concerns. It was previously unclear whether unexposed clusters would contribute to the estimation of the intervention effect in a fixed effects analysis. However, recent work has demonstrated that including an unexposed cluster can improve the precision of the intervention effect estimator in a fixed effects analysis of SW-CRTs with continuous outcomes. Still, SW-CRTs are commonly designed with binary outcomes and it is unknown if those previous results extend to SW-CRTs with non-continuous outcomes. Methods In this article, we mathematically prove that the inclusion of unexposed clusters improves the precision of the fixed effects intervention effect estimator for SW-CRTs with binary and count outcomes. We then explore the benefits of including an unexposed cluster in simulated datasets with binary or count outcomes and a real palliative care data example with binary outcomes. Results The simulations show that including unexposed clusters leads to tangible improvements in the precision, power, and root mean square error of the intervention effect estimator. The inclusion of the unexposed cluster in the SW-CRT of a novel palliative care intervention with binary outcomes yielded smaller standard errors and narrower 95% Wald Confidence Intervals. Conclusions In this article, we demonstrate that the inclusion of unexposed clusters in the fixed effects analysis can lead to the improvements in precision, power, and RMSE of the fixed effects intervention effect estimator for SW-CRTs with binary or count outcomes.