The Long and Winding Road to Local Fiscal Equity in the United States: A Fifty-Year Retrospective

Jorge Martinez-Vazquez; Andrey Timofeev

doi:10.1515/jbnst-2021-0038

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The Long and Winding Road to Local Fiscal Equity in the United States: A Fifty-Year Retrospective

Jorge Martinez-Vazquez und Andrey Timofeev

Veröffentlicht/Copyright: 10. November 2022

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Aus der Zeitschrift Jahrbücher für Nationalökonomie und Statistik Band 242 Heft 5-6

Abstract

Unlike many other countries, the United States does not have a comprehensive federal transfer scheme for explicit fiscal equalization but rather employs an array of categorical and block grants, some of which are formula-based while others are project-driven. However, the allocation of many of these grants has equalization effects resulting in the narrowing of fiscal disparities among jurisdictions. Few studies have attempted to quantify the extent of equalization achieved with federal and state grants in a manner that would allow comparisons across states and over time. In this study, we set out to measure the extent of equalization across local governments in the United States that is implicit in the federal grants system and more explicit in the grants implemented by the individual states. Rather than focusing on specific types of local services, we look at the evolution of per capita resources available to all types of local governments combined.

Keywords: United States; fiscal disparities; intergovernmental grants; local government

JEL Classification: H73; H77

Corresponding author: Andrey Timofeev, Andrew Young School of Policy Studies, Georgia State University, Atlanta, GA, USA, E-mail: atimofeev@gsu.edu

Appendix A

A.1 Decomposing the aggregate inequality by factor components and subgroups

In mathematical terms, the total variation computed for the entire sample comprises the sum of the squared deviations of a locality level variable y _i from the grand mean y ‾ of this variable:

∑ i ∑ j n i j ( y i j − y ‾ ) 2 .

This total sum can be rearranged into two components:

∑ i n i ( y ‾ i − y ‾ ) 2 + ∑ i ∑ j n i j ( y i j − y ‾ i ) 2 .

Here, n _i and n _ij denote the population of region i and locality j in that region, respectively, y ‾ i stands for region i’s mean value of variable y _ij. Further, if we divide this expression by (Σn _i − 1), we get the total variance, which is again a sum of two components. The first component, called “between-group variance”, characterizes the average dispersion of regional means from the grand mean. The second, component, called “within-group variance”, characterizes the average dispersion of data points from the corresponding regional means. Note that the “between-group variance” weights regions in proportion to their population, unlike the variance computed over the sample of regional means equally weighing all regions. To make this measure mean independent, we can divide the variance by the square mean y ‾ 2 and thus obtain the square coefficient of variation I ₂ = I ₂ ^b + I ₂ ^w, which is a sum of its between-region and within-region components.

In a similar manner, we can decompose the mean log deviation I ₀ = I ₀ ^b + I ₀ ^w:

∑ i ∑ j n i j ( ln y ‾ − ln y i j ) = ∑ i n i ( ln y ‾ − ln y ‾ i ) + ∑ i ∑ j n i j ( ln y ‾ i − ln y i j ) .

In addition, all general entropy measures, including I ₀ and I ₂, are also amenable to decomposition by various components of our variable of interest y _ij. Thus, if y _ij = Σy ^k _ij, then we can express I c = ∑ k s k I c ,

w h e r e s k = C O V ( y k , y ) V A R ( y ) .

Note that

s k = C O V ( y k , y ) V A R ( y ) = C O R R ( y k , y ) V A R ( y k ) V A R ( y ) = C O R R ( y k , y ) I 2 ( y k ) I 2 ( y ) E ( y k ) E ( y ) .

Therefore, the contribution of a revenue component to the total inequality is above its share in the total revenue, that is s _k > E(y ^k)/E(y), if it is more unequally distributed than the total revenue, that is I ₂(y ^k) > I ₂(y). On the other hand, the contribution of a revenue component is below its respective share in the total revenue, s _k < E(y ^k)/E(y), when it is either weakly correlated with the total revenue or more evenly distributed than the total revenue, that is I ₂(y ^k) < I ₂(y).

Moreover, the relative contribution of each component of y can be further broken down into a between-region subcomponent and a within-region subcomponent (Tsui 1998):

s k = s k b + s k w , w h e r e

s k b = C O V ( y ‾ i k , y ) V A R ( y ) , s k w = E [ ( y k − y ‾ i k ) ( y − y ‾ ) ] V A R ( y ) , a n d

y ‾ i k stands for region i’s mean value of variable y ^k _ij.

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Article Note

This article is part of the special issue “Redistribution in a Globalized World“ published in the Journal of Economics and Statistics. Access to further articles of this special issue can be obtained at www.degruyter.com/jbnst.

Received: 2021-09-19

Revised: 2022-09-01

Accepted: 2022-09-16

Published Online: 2022-11-10

Published in Print: 2022-12-16

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United States; fiscal disparities; intergovernmental grants; local government