The growing push in nonprofit studies toward panel data necessitates a methodological guide tailored for nonprofit scholars and practitioners. Panel data analysis can be a robust tool in advancing the understanding of causal and/or more nuanced inferences that many nonprofit scholars seek. This study provides a walk-through of the assumptions and common modeling approaches in panel data analysis, as well as an empirical illustration of the models using data from the nonprofit housing sector. In addition, the paper compiles applications of panel data analysis by scholars in leading nonprofit journals for further reference.

This paper empirically compares the use of straightforward verses more complex methods to estimate public goods game data. Five different estimation methods were compared holding the dependent and explanatory variables constant. The models were evaluated using a large out-of-sample cross-country public goods game data set. The ordered probit and tobit random-effects models yielded lower p values compared to more straightforward models: ordinary least squares, fixed and random effects. However, the more complex models also had a greater predictive bias. The straightforward models performed better than expected. Despite their limitations, they produced unbiased predictions for both the in-sample and out-of-sample data.

Recently, there has been a surge in interest in exploring how common macroeconomic factors impact different economic results. We propose a semiparametric dynamic panel model to analyze the impact of common regressors on the conditional distribution of the dependent variable (global output growth distribution in our case). Our model allows conditional mean, variance, and skewness to be influenced by common regressors, whose effects can be nonlinear and time-varying driven by contextual variables. By incorporating dynamic structures and individual unobserved heterogeneity, we propose a consistent two-step estimator and showcase its attractive theoretical and numerical properties. We apply our model to investigate the impact of US financial uncertainty on the global output growth distribution. We find that an increase in US financial uncertainty significantly shifts the output growth distribution leftward during periods of market pessimism. In contrast, during periods of market optimism, the increased uncertainty in the US financial markets expands the spread of the output growth distribution without a significant location change, indicating increased future uncertainty.

In this paper, we study the identification of a particular case of the 3PL model, namely when the discrimination parameters are all constant and equal to 1. We term this model, 1PL-G model. The identification analysis is performed under three different specifications. The first specification considers the abilities as unknown parameters. It is proved that the item parameters and the abilities are identified if a difficulty parameter and a guessing parameter are fixed at zero. The second specification assumes that the abilities are mutually independent and identically distributed according to a distribution known up to the scale parameter. It is shown that the item parameters and the scale parameter are identified if a guessing parameter is fixed at zero. The third specification corresponds to a semi-parametric 1PL-G model, where the distribution G generating the abilities is a parameter of interest. It is not only shown that, after fixing a difficulty parameter and a guessing parameter at zero, the item parameters are identified, but also that under those restrictions the distribution G is not identified. It is finally shown that, after introducing two identification restrictions, either on the distribution G or on the item parameters, the distribution G and the item parameters are identified provided an infinite quantity of items is available.

In psychometrics, the canonical use of conditional likelihoods is for the Rasch model in measurement. Whilst not disputing the utility of conditional likelihoods in measurement, we examine a broader class of problems in psychometrics that can be addressed via conditional likelihoods. Specifically, we consider cluster-level endogeneity where the standard assumption that observed explanatory variables are independent from latent variables is violated. Here, “cluster” refers to the entity characterized by latent variables or random effects, such as individuals in measurement models or schools in multilevel models and “unit” refers to the elementary entity such as an item in measurement. Cluster-level endogeneity problems can arise in a number of settings, including unobserved confounding of causal effects, measurement error, retrospective sampling, informative cluster sizes, missing data, and heteroskedasticity. Severely inconsistent estimation can result if these challenges are ignored.

A close reading of the literature on radical right parties (RRPs) suggests that these parties erode trust and solidarity in European democracies when they pit ‘the pure people’ against political and legal institutions, elites, and immigrants. I propose the conjecture that RRPs with seats in the national parliament have better conditions for spreading nativist and populist messages that may erode trust and solidarity between a society’s residents, between ethnic groups, and towards its political and legal institutions. To test this research question, I combine nine waves of European Social Survey data from 17 countries and data on national elections spanning the years 1999 to 2020. Two-way fixed effects models estimate that RRPs representation in the national parliament is associated with a reduction in public support for redistribution of ca. 18% of a standard deviation. Additionally, I demonstrate that this inverse relationship runs parallel to growing welfare chauvinistic beliefs and that it is stronger in countries with weak integration policies. Contra theoretical expectations, the radical rights’ political representation has not produced any change in societal levels of anti-immigration attitudes, institutional trust, or social trust. While the findings persist across a wide range of robustness checks and other model specifications, threats to identification in the form of non-parallel pre-trends and unobserved sources of confounding, means that one should be cautious in interpreting the findings in a causal manner.

Increased credit availability facilitates land acquisition, but higher land values also hinder it. We investigate the impact of credit availability on land values, after regulatory changes in the lending system. We build an index of increased credit availability using Federal Reserve and Federal Deposit Insurance Corporation data. County-level panel fixed effects estimations are performed controlling for land value determinants, credit availability, and county-level macroeconomic factors. We find that estimating the effects of credit availability separately masks its total effect. Results show a 0.1 change in the index for increased credit availability is associated with 1.64–1.96% increase in land values.

When working with grouped data, investigators may choose between “fixed effects” models (FE) with specialized (e.g., cluster-robust) standard errors, or “multilevel models” (MLMs) employing “random effects.” We review the claims given in published works regarding this choice, then clarify how these approaches work and compare by showing that: (i) random effects employed in MLMs are simply “regularized” fixed effects; (ii) unmodified MLMs are consequently susceptible to bias—but there is a longstanding remedy; and (iii) the “default” MLM standard errors rely on narrow assumptions that can lead to undercoverage in many settings. Our review of over 100 papers using MLM in political science, education, and sociology show that these “known” concerns have been widely ignored in practice. We describe how to debias MLM’s coefficient estimates, and provide an option to more flexibly estimate their standard errors. Most illuminating, once MLMs are adjusted in these two ways the point estimate and standard error for the target coefficient are exactly equal to those of the analogous FE model with cluster-robust standard errors. For investigators working with observational data and who are interested only in inference on the target coefficient, either approach is equally appropriate and preferable to uncorrected MLM.

This letter deals with a very simple question: if we have grouped data with a binary-dependent variable and want to include fixed effects in the specification, can we meaningfully compare results using a linear model to those estimated with a logit? The reason to doubt such a comparison is that the linear specification appears to keep all observations, whereas the logit drops the groups where the dependent variable is either all zeros or all ones. This letter demonstrates that a linear specification averages the estimates for all the homogeneous outcome groups (which, by definition, all have slope coefficients of zero) with the slope coefficients for the groups with a mix of zeros and ones. The correct comparison of the linear to logit form is to only look at groups with some variation in the dependent variable. Researchers using the linear specification are urged to report results for all groups and for the subset of groups where the dependent variable varies. The interpretation of the difference between these two results depends upon assumptions which cannot be empirically assessed.

In recent years, the employment rates of people of pension age have increased considerably. However, longitudinal evidence on the effects of this employment on wellbeing which might contribute to an evaluation of this late-life work is scarce. Based on empirical findings so far and on theoretical approaches to wellbeing, work and retirement, both negative and positive effects of post-retirement work on life satisfaction are plausible. In this paper, we investigate the effects of taking up work again between the ages of 65 and 75 on life satisfaction in different occupational classes in Germany and the United Kingdom. We expect that not only the heterogeneous conditions and experiences of working are crucial for the consequences that post-retirement work has for life satisfaction, but also the institutional arrangements surrounding this form of work. We use data from the German Socio-Economic Panel and the British Household Panel Survey, covering the 1990s and 2000s. Based on fixed-effects regression modelling, we find positive effects of working in both countries, although not all effects are significant. Differentiating by the class of the job in which the older person works, we find mainly positive effects and no significant differences between those who work in a lower-class job and all others. In addition, we find that the positive effect of working on life satisfaction is partly explained by increased satisfaction with household income for those working in a lower-class job in the United Kingdom. We conclude that many of the pessimistic assumptions about people working after pension age cannot be confirmed for our time of observation. However, there are several reasons for believing that the results will be different in the future or for differently defined populations of people working past pension age.

Zoning decisions related to residential lot size and density affect residential land value. Effects of size on residential parcel value in Roanoke County, VA, are estimated with fixed effects hedonic models. Parcel size; elevation; soil permeability; proximity to urban areas, malls, and roads; and location influence parcel value, but the effects vary by value of construction and development status. Parcel value per square meter declines with increasing parcel size. The estimated relationships could be used to evaluate zoning decisions in terms of land values and tax revenues if model estimation uncertainties and responses by developers to zoning strategies are considered.

In order to contribute to the genetic breeding programs of buffaloes, this study aimed to determine the influence of environmental effects on the stayability (ST) of dairy female Murrah buffalo in the herd. Data from 1016 buffaloes were used. ST was defined as the ability of the female to remain in the herd for 1, 2, 3, 4, 5 or 6 years after the first calving. Environmental effects were studied by survival analysis, adjusted to the fixed effects of farm, year and season of birth, class of first-lactation milk yield and age at first calving. The data were analyzed using the LIFEREG procedure of the SAS program that fits parametric models to failure time data (culling or ST = 0), and estimates parameters by maximum likelihood estimation. Breeding farm, year of birth and first-lactation milk yield significantly influenced (P < 0.0001) the ST to the specific ages (1 to 6 years after the first calving). Buffaloes that were older at first calving presented higher probabilities of being culled 1 year after the first calving, without any effect on culling at older ages. Buffaloes with a higher milk yield at first calving presented a lower culling probability and remained for a longer period of time in the herd. The effects of breeding farm, year of birth and first-lactation milk yield should be included in models used for the analysis of ST in buffaloes.

This paper examines the validity of some stylized statements that can be found in the actuarial literature about random effects models. Specifically, the actual meaning of the estimated parameters and the nature of the residual heterogeneity are discussed. A numerical illustration performed on a Belgian motor third party liability portfolio supports this discussion.