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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.

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.

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.

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.

Afghanistan frequently faces drought and other climate change-related challenges due to rising temperatures and decreased precipitation in many areas of the country. Therefore, acquiring a thorough comprehension of the implications of climate change on the cultivation of key cereal crops is of the utmost importance. This is particularly significant in the context of Afghanistan, where the agricultural sector plays a pivotal role, contributing close to a quarter of the country’s national gross domestic product and serving as the primary source of employment for 70% of the rural workforce. In this paper, we employ a panel regression model to evaluate the relationship between climate change and cereal productivity in Afghanistan’s agro-climatic zones. Temperature had a significant negative impact, implying that a mean temperature increase of 1 °C decreased wheat and barley yields by 271 and 221 kg/ha, respectively. Future medium- and high-emission scenarios (RCP4.5 and RCP8.5, respectively) for the period 2021–2050 were considered for future yield predictions. To project future climate change impacts, the estimated panel data regression coefficients were used to compute the projected changes in cereal yields. During the period 2021–2050, the mean yield of wheat is projected to decrease by 21 or 28%, the rice yield will decrease by 4.92 or 6.10%, and the barley yield will decrease by 387 or 535 kg/ha in the RCP4.5 and RCP8.5 emission scenarios, respectively, further emphasizing the need for targeted actions to tackle the effects of climate change on agriculture in Afghanistan in alignment with SDG 2 (Zero Hunger) and SDG 13 (Climate Action).

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.

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.

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.

Objectives Shift work is a risk factor for chronic diseases, and physical inactivity can have an influence on this association. We examined whether intra-individual changes in working time characteristics were associated with changes in physical inactivity and examined the risk factors for physical inactivity among shift workers in a 17-year longitudinal study cohort. Methods Study participants were 95 177 employees from the Finnish public sector. Work schedule information was based on questionnaire responses and additional register-based working time characteristics for 26 042 employees. The associations between working time characteristics and physical inactivity were examined using a fixed-effects logistic model. To investigate the risk factors for physical inactivity among shift workers, the odds ratios (OR) of worktime control and having small children were calculated. Results Compared with day work, shift work without night shifts was associated with physical inactivity among men [OR 1.38, 95% confidence interval (CI) 1.09-1.74], whereas shift work with night shifts was negatively associated with physical inactivity among women (OR 0.85, 95% CI 0.76-0.96). Register-based working time data confirmed that workers with a higher percentage of night shifts had a lower risk of physical inactivity. Having small children was associated with physical inactivity among shift workers (OR 1.47, 95% CI 1.32-1.65). Conclusions Both survey and objective working hour data revealed that workers having work schedules with night shifts were more likely to be physically active. Having small children was a risk factor for physical inactivity among shift workers.

This paper estimates the impact of U.S. school food programs on the distribution of child dietary quality during 2005-10. The distributional approach allows one to better understand how school food impacts children prone to low-quality diets separately from those prone to higher-quality diets. Using a fixed-effects quantile estimator, I find notable heterogeneity in the general population — school food has positive impacts below the median of the dietary-quality distribution, and negative but insignificant impacts at upper quantiles. Children demonstrating substantial nutritional needs (i.e., food insecure or receiving free/reduced price meals) exhibit positive impacts at all levels of diet quality with especially high benefits at low quantiles. Although school food programs may not benefit the \"above-average\" child, they do improve the diets of the most nutritionally disadvantaged.