Horizontal Fiscal Imbalance In The United States

Abstract Regional inequalities are currently a challenge for the majority of countries, in particular large ones, certain of which are federations. The federal state system is more complex than the unitary system. This results in specific problems. One of them is the issue of differing level of economic development of individual territorial units, whereby the problem of income redistribution emerges. The difference between income and expenses results in the formation of fiscal gaps, both horizontal and vertical ones. The aim of the paper is to present the measures applied for measuring the horizontal fiscal imbalance. It is also the starting point for conducting measurements of those imbalances in the USA based on the presented measures. The paper presents the measures applied in the literature for the purposes of measuring horizontal fiscal imbalance. In addition, the measurement of those imbalances in the USA are presented.


Introduction
The decentralisation of public finances coupled with the state federal structure results also in the emergence of specific problems and subsequently their solution, apart from benefits.
The main problem is the decentralisation of tax authority and financial equalisation. Due to possible differentiation of the economic development level of territorial units of a federation, the problem of public income redistribution emerges -both horizontal and vertical. The most often considered one is the vertical distribution of income between individual levels of the public authority. At the same time units richer than others can occur at each lower government level. The differences arising from the resources possessed at the same level may be defined as horizontal fiscal imbalance, horizontal fiscal gap 1 . It occurs when it is impossible to achieve income which is equal to the needs of the authorities at the same level of authority. A certain level of mismatch between income and expenses at different levels is unavoidable in the case of all federations. Effective tax administration for certain types of income requires central administration, which contributes to the problems of vertical imbalance. After assigning tax obligations and expenses, the division of income and transfers may adjust the imbalance which results from the assignment of liability. Difficulties in planning or the opposing needs of different levels of public administration mean that the division of income and the transfer mechanism may not fully solve the problem of imbalance 2 . A fiscal deficit at the federation level does not indicate a correlation with the degree of federation's control over the regional authorities but with their financial dependence on the central authority.
The horizontal division of income is considered far less frequently and it seems to have a supplementary significance. Nevertheless, A. Shah argues, despite hardly any empirical evidence, that horizontal fiscal imbalance or regional tax inequalities seem to be graver than the vertical imbalance, particularly in developing countries 3 . It is important to remember that horizontal inequalities are a natural phenomenon. If they are not eliminated, they may lead to movement of persons and capital from less efficient regions to more efficient regions. If they are excessively equalised, they may impede effective allocation of funds within the entire country, thereby influencing economic growth. Horizontal inequalities are most often eliminated by equalisation transfers.
The issues of fiscal imbalance encourage comparative research of states, especially those with a federal form. According to M. Bitner and, K.S. Cichocki, comparative research on local government subsector finance is particularly rare in public finance literature 4 . There are no up-todate measurements and comparisons of horizontal fiscal imbalance between countries. Results obtained by the end of the 20th century can be found in English-language literature. R. Bird and A.V. Tarasov as well as R. Shankar and A. Shah performed measurement of horizontal fiscal imbalance. The calculations were conducted based on data before 2000 in the case of R. Bird and A.V. Tarasov 5 and before 1998 in the case of R. Shankar and A. Shah 6 . Apparently, the European Union is an exception as it calculates the regional GDP for its regions within the NUTS classification as % of the European Union average and dispersion, on the basis of which comparisons are made.
where: y max y min y ---region with maximum parameter 9 per capita (e.g. GDP), region with minimum parameter per capita, national average of given parameter, Source: own elaboration.
As can be seen, attempts to measure horizontal imbalance and the impact of equalisation transfers have been made with use of simple measures of dispersion or concentration. The literature does not describe more effective techniques of inequality measurement. Attempts are made to use two statistics concepts which are useful for considering the dynamics of regional inequalities 10 . They are dynamic measures of beta (β) convergence 11 and sigma (σ) convergence 12 based on the convergence hypothesis or the divergence hypothesis 13 . Catching up the distance in income of the relatively poorer regions by faster growth is called beta convergence, while decreasing the regional dispersion in income in time is referred to as sigma convergence 14 .
According to S.J. Rey and M.V. Janikas 15 , the introductory work on the convergence hypothesis was based on the neoclassical theory of economic growth. The convergence hypothesis holds that the growth rate is directly proportional to the distance between the present level of income distribution and the steady-state growth rate. The convergence rate index is based on the assumption that the distance between the present and the steady-state ratios can be closed. This approach to convergence does not necessarily indicate that all state economies converge to the same income-level distribution rate, since it accounts for growth-rate differences between countries of different steady-state ratios and/or other differences between the present and the steady-state ratios. The above reasoning has stimulated numerous empirical studies and has led to the formulation of a growth regression model referencing the growth rate of GDP per capita within a timeframe of t 0 to t 0 + T and the set of steady-state determinants (Z). The rate of convergence, in this approach, is a function of the β T parameter and represents β-convergence. (lny(T) -lny(0)) = α 0 -α 1 lny(0) (16) where: y(T)regional GDP per capita in the end year, y(0)regional GDP per capita in the initial year.
The left side of the above formula determines economic growth rate. The first variable on the right side of lny(0) represents the initial level of regional GDP, and hence the α 1 parameter informs about the occurrence of real β-convergence. Such a convergence occurs where α 1 is negative and statistically significant. β-value can be determined in the following manner 17 : As can be seen, it is very similar to the formula proposed by J. Villaverde and A. Maza 18 , who defined the rate of convergence as b = -log[1 -βT]/T.
The maximum-to-minimum ratio for the USA suggests that similar level of disproportion was only observed till the late 1970s. The maximum point was registered in 1981, with the ratio reaching over 5.5. It dropped to 3.943 in 1986, but never returned to the pre-increase levels. A steady growth rate of the ratio was observed since mid-90s, suggesting increased disproportion between the richest and the poorest state. Another maximum was registered in 2011. And again, over the last three years, the disproportion has decreased (Figure 3).
Weighted values are lower than unweighted values, thus proving that the regions with the highest regional GDP p.c. have a low population.

Conclusions
Convergence of regions is currently one of the most frequently addressed research problems, in particular in the context of equalising inequalities among the European Union member states. Despite the growing interest of research on convergence in the regional approach, the measurement of fiscal inequalities between and inside regions are rarely analysed.
The public finance system, in particular in federations, is often very complex. Public finance of federations and federated states are not often placed within the same assumptions.
This leads to differences between regions, both vertical and horizontal. The use of the presented measures helps identify those differences and permits developing mechanisms equalising those inequalities. It should be remembered that those measures may have certain drawbacks, and they mainly focus on certain specific values of income redistribution. Thereby several measures should be applied in measurements and the obtained results should be compared.
The most frequently applied measures of horizontal fiscal imbalance are the minimum and maximum indicators, range, maximum to minimum, weighted and unweighted variation coefficient and Gini and Theil indexes.
The United States of America is the oldest and largest federal state in the world. States have independent taxing powers and substantial expenditure responsibilities. Federal and state taxes are essentially independent, but there is no formal "revenue-sharing" system between federal and state or local governments. Indeed, there are no transfers specifically intended to deal with vertical and horizontal fiscal imbalance 22 . Therefore, as shown by the results, horizontal fiscal imbalance in the USA is relatively high. However in the recent years it has a decreasing tendency, what shows a beta convergence indicator. Nonetheless, there are very substantial intergovernmental fiscal transfers in the USA, especially to finance various social programs carried out at the state and local levels. 23 Notes 1 The two notions are used interchangeably.
5 Bird, Tarasov (2002). 6  . 7 They may be static -they show inequalities in the given moment, or dynamic -they reflect historical trends. Dynamic measures are based on the hypothesis of convergence or divergence.