Comparing Dynamic Pies: A Strategy for Modeling Compositional Variables in Time and Space

Abstract

Across a broad range of fields in political science, there are many theoretically interesting dependent variables that can be characterized as compositions. We build on recent work that has developed strategies for modeling variation in such variables over time by extending them to models of time series cross-sectional data. We discuss how researchers can incorporate the influence of contextual variables and spatial relationships into such models. To demonstrate the utility of our proposed strategies, we present a methodological illustration using an analysis of budgetary expenditures in the US states.

Dividing the Pie: Parties, Institutional Limits, and State Budget Trade-Offs

“…We build on his work by examining pairwise budget trade-offs among these four expenditure categories. As demonstrated by Philips, Rutherford, and Whitten (2016) and Lipsmeyer et al (2017), we use the log-ratio transformation of composition data (Aitchison 1982) to measure state budget trade-offs. Using improved measurements and focusing on theoretically meaningful expenditure categories, the empirical analysis shows consistent results in explaining budget trade-offs.…”

“…Budget trade-offs for each pair can be correlated with those for others because the budgeting decisions are likely to be made simultaneously. Consistent with Philips, Rutherford, and Whitten (2016) and Lipsmeyer et al (2017), we construct log ratios of state expenditure categories to measure budget trade-offs. As Philips, Rutherford, and Whitten (2016) show, this method is invariant with the choices of base categories.…”

“…For compositional data with log-ratio transformation, Tomz, Tucker, and Wittenberg (2002) demonstrate that seemingly unrelated regression (SUR) is "an easy and accurate regression model. " Philips, Rutherford, and Whitten (2016) and Lipsmeyer et al (2017) estimate the equations for budget trade-offs using SUR. Consistent with these studies, we use the SUR as the method of estimation.…”

“…Following Philips, Rutherford, and Whitten (2016) and Lipsmeyer et al (2017), we use the log-ratio method to measure budget trade-offs. We deviate from previous studies two ways.…”

“…Prior studies usually focus on four main categories of state expenditure as reported by the Census Bureau, including education, highways, welfare, and health (Hendrick and Garand 1991; Nicholson-Crotty, Theobald, and Wood 2006). As one exception, Lipsmeyer et al (2017) focus on all state expenditure categories by reclassifying them into five groups partly based on relative sizes. Moreover, efforts to explain state budget trade-offs have generated limited success.…”