Abstract
This study builds on the history of economic well-being (EWB) index construction to develop such an index for urban U.S. counties (population > 62,437). Unlike previous studies, we rely on external validation of economic well-being to construct a best-fit index, where our external validation approach follows the Tiebout Hypothesis. We estimate a best-fit, linear regression-based index, in which lagged features of economic well-being are weighted based on ability to explain subsequent county population change. Compared to an arbitrarily equally-weighted model using a composite index a model using lagged weighted EWB individual variables provide greater transparency while also explaining substantially more variation in population change across urban counties (19.9% vs. 15.7%).
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All authors contributed to the study conception and design. Medcalfe and Sanders wrote the introduction and data and methods sections. Ehrlich organized, analyzed and provided visualizations of the data. Sanders wrote the theoretical and empirical implications of social choice violations under EWB. Ehrlich, Medcalfe and Sanders wrote the results section. Medcalfe and Sanders wrote the discussion and conclusion sections. All authors reviewed drafts and made changes.
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Appendix 1 Variable selection using VIF and forward stepwise regression.
Appendix 1 Variable selection using VIF and forward stepwise regression.
We used a two-stage approach to trim our parameters. The first stage involved fitting a model with all fifteen parameters from our dataset, which is summarized in Table
7. This model was then input into the stepVIF R function (Samuel-Rosa, 2020), which removes any parameters with high collinearity. All fifteen parameters survived this pairing step and the VIF and importance of each parameter is reported in Table
8. The second stage trimmed this model from fifteen parameters to nine perimeters by using a forward step regression model (Lumley, 2020). The forward step regression algorithm seeks to minimize the RMSE of out of sample test data. We chose to use tenfold cross validation, repeated three times. By minimizing the average RMSE, the forward step regression algorithm found that a model with 9 parameters was the best at predicting out of sample population change (Fig.
Forward step model selection by minimizing RMSE
5). Table 7 also includes whether the input parameters were included in this final model. The parameter categories trimmed from the original 15-parameters included county Gini coefficient obtained from the U.S. Census Bureau, 1-year estimates, and percentage of population that attended some college obtained from the American Community Survey, 5-year estimates.
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Ehrlich, J., Medcalfe, S. & Sanders, S. Constructing and validating a best-fit economic well-being index for urban U.S. counties: a Tiebout model approach. Public Choice 199, 45–63 (2024). https://doi.org/10.1007/s11127-023-01055-y
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DOI: https://doi.org/10.1007/s11127-023-01055-y