Panel Data Analysis: A Guide for Nonprofit Studies

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.

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Panel Data Analysis

Panel Data Analysis

Non-linear Panel Data Models

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Notes

Regarding different types of data, in general, time-series data refers to a collection of observations made chronologically on one subject, for instance, historical stock prices of one firm. In this case, in order to have enough variation, the length of a time series is an important determinant of the usefulness of such data, panel data, as we mentioned in the paper, entail observations made on the same sample of subjects over time. The difference here is in the data structure. Compared with time-series data, panel data have more than one cross-sectional subject. Accordingly, both its length (i.e., number of time periods) and its width (i.e., number of cross-sectional subjects) jointly decide the usefulness of a panel dataset. Additionally, some studies also use the term time-series cross-sectional (TSCS) data to refer to panel data (Lewis-Beck et al., 2004), while some others suggest that TSCS data have comparatively fewer cross-sectional subjects than panel data (see Bell & Jones, 2015). As for the term longitudinal data, researchers often use it interchangeably with the term panel data (Frees, 2004).

Here, a necessary yet challenging sampling strategy in panel data analysis is to keep track of the same sampled subjects until the completion of data collection, as attrition of subjects out of the sample could lead to incorrect inferences (Baltagi, 2008).

Here, we acknowledge that it is common for nonprofit scholars to choose other publication outlets such as Journal of Public Administration Research and Theory (e.g., Cheng, 2018; de Wit & Bekkers, 2017) and Public Performance & Management Review (e.g., Pandey & Johnson, 2019). Given the broad coverage of these journals, however, we decided to narrow our focus on VOLUNTAS, NML, and NVSQ, which focus solely on nonprofit studies.

In practice, the presence of different levels of multicollinearity is common given the implicit and/or explicit interconnectedness of many variables in social sciences. The disadvantage of having multicollinearity is that it could lead to relatively large estimated standard errors for the coefficient estimates of independent variables that are correlated with others, which would undermine their statistical significance (Allen, 1997).

Here, it is important to acknowledge that directly adding an LDV as an independent variable could violate the OLS assumption that independent variables do not correlate with the error term. This is because the error term is supposed to encapsulate all the variation that is left in the dependent variable but are not explained by the independent variable(s). An LDV is thus likely to correlate with such remaining variation as it represents the variation in the DV that is from the previous period. This issue would be further complicated if the model specification includes panel-specific error terms such as FE terms (Zhu, 2013). In this case, we do not recommend directly adding an LDV to account for the dynamics process. We introduce this approach because it is our intention to provide the basic assumptions and modeling approaches that are involved in panel data analysis. To deal with such potential correlations that an LDV might induce, however, researchers could rely on instrumentation techniques such as a second-order LDV (the DV that is two periods before the current one; Anderson & Hsiao, 1981) or the generalized method of movements (GMM) estimator proposed by Arellano & Bond (1991).

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Funding

This study was not funded by any funding/grants.