Andrea Junqueira (Texas A&M University), Ali Kagalwala (Texas A&M University), Andrew Philips (University of Colorado Boulder) and Guy Whitten (Texas A&M University)
Abstract: In this paper, we use new data on economic inequality to introduce and demonstrate the utility of several extensions to the dynamic pie modeling approach for time series compositional dependent variables. Specifically, we introduce solutions to three different issues that arise when modeling such data: the endogenous pie problem, the continuous pie problem, and the heterogeneous pie variance problem. Our solution to the endogenous pie problem entails the estimation of a system of equations using a vector autoregressive (VAR) approach instead of the usual seemingly unrelated regressions approach. Our solution to the continuous pie problem is to explore the robustness of model results to different cut points in the dependent variables. And our solution to the heterogeneous pie variance problem is the adaptation of a general autoregressive heteroscedasticity (GARCH) approach to modeling of dynamic compositions. With each solution, we will present new software developed to implement our recommended approach and software and advice for graphical approaches to the interpretation of the model results.