3. Regional budget actual expenditures (per capita).Within the assumption that budget expenditure efficiency of different regions can be hold up under comparison it is possible to arrive at the conclusion that regarding objective factors, which come to determine regional budget expenditure needs, the Federal Center aims at establishing similar expenditure value for each region attained by equalization. Alongside with that it is assumed that the difference in actual budget expenditures results from the influence exerted by the factors, which characterize objectively different regional needs connected, for example, with population structure, climate etc. Although the premise that actual and standard expenditure be close to each other might fail to come true and interbudgetary equalization might be aimed at equalization of regional capacity for minimum (standard) public goods provision level, financial aid allocation could not be influenced by regional expenditures, which is determined by objective differences in volume and price, but by regional budget actual expenditures. The usage of actual regional budget expenditures within transfer calculations is caused by several reasons inclusive of budget reform inertness in the region (in case of sufficient gap between actual and 'normative' expenditure, the one determined by the existing network of public organizations and agencies) as well as different subjective factors (regional authorities’ lobbying for the Center's support for certain expenditure items, etc.)

4. The 'norms' of regional budget expenditure needs. As it was mentioned above, interbudgetary equalization should be aimed at achievement of equal regional capacity to finance some standard level of public goods provision. But it can be stated that actual expenditures fail to characterize well enough regional objective needs in public services provision. Besides objective factors, interregional differentiation of the actual public goods provision level in different regions can be caused by the regional level of fiscal capacity provided as well as with different regional efficiency in budget expenditure execution. That’s why, proceeding from federal authorities’ rational behavior, it can be assumed that within budget equalization formula the Federal Center is orientated to both actual expenditure and 'normative' expenditure needs value the latter being different for different regions and dependent upon a number of objective factors29.

In general intergovernmental equalization mechanism can be formulated as follows (all indexes are given in per capita terms):

(42)

where

Tri - financial aid value (The sum of all kinds of financial support for i-region: the transfers from regional financial aid fun, mutual settlements, budget loans, funds in support for north import)

– actual tax revenues of i-region budget;

– fiscal capacity of i-region budget;

– actual expenditures of i-region budget;

– 'normative' expenditure needs;

– actual financial aid deviation from calculated value, which might be caused by additional factors dependent, for example, upon the political power of regional administration.

It can be assumed that within the framework of budget execution financial aid to the region in current year is determined both by figures of current year (actual revenues and expenditure) and also by actual revenues and expenditure during the previous year as well as by revenues and expenditures, fiscal capacity and expenditure needs standards with two-year lag. The latter can be explained by some peculiarities of budget planning timing process, which demand that the data of the year before the previous be the only data available for transfer allocation calculation from FFAR and some other kinds of financial aid for the next year calculated within the current year. (e.g. the transfers from FFAF for 2000 were distributed on the basis of 1997 data as well as planning of financial aid for 2001 was based upon 1999 data). Alongside with that the allocation of some other kinds of financial aid to the regions is determined by the indexes of either the previous or the current year.

Practically all the 89 russian regions prove to be financial aid recipients of this or that kind. That’s why all the Federation subjects except for Chechenskaya Republic will be considered within the estimation of equalization parameters offered. Besides, some equations will be calculated for one third of the transferees receiving the highest amount of federal financial aid (per capita). Let’s estimate the hypotheses assuming that different financial aid allocation formulas, which are orientated to various combinations of the mentioned above parameters characteristic of the regional need in federal support, be applied by the Federal authorities. Then it will be possible to estimate if the budget constraint of the regional administration assumed within fiscal behavior model conforms with the real life on the basis of comparison between the estimation results for different models.

Equalization of actual tax revenues is one of the simplest variants of interbudgetary equalization. Alongside with that transfer value is calculated by the formula:

( 43)

where – tax revenues after equalization (per capita, the same for all the regions)

Corresponding regression is as follows:

(44)

If a1 significantly different from zero (at 5% critical level), then equation (43) parameters can be calculated as follows:

( 45)

The results of OLS estimations of this equation for 1994-1999 are given in the tables below (statistically significant coefficients are written in the bold type, gray color means lag combinations, which were not calculated, significance for adjusted R-square is given according to F-statistics significance at 5% critical level). In the table the years of financial aid actual allocation are given vertically, and the years for which corresponding lagged explanatory variables are used are given horizontally30.

Another possible variant of equalization is the equalization of regional fiscal capacity. The equalization formula is similar to (43):

( 46)

where – fiscal capacity of i-th regional budget;

γ – share of the gap between regional revenue and expenditure values that is covered by equalization transfers (equal for all regions participating in the equalization and determined by the amount assigned for equalization transfers in the federal budget).

Corresponding regression is as follows (the model (46) parameters are calculated by (45) formula):

(47)

The results of OLS estimations of this regression for 1994-1999 are given in the tables below (statistically significant coefficients are written in the bold type).

A great number of similar results given for different years in the tables are explained by the fact that fiscal capacity estimates for 1997 –1998 were the only available. For earlier time periods fiscal capacity was estimated by deflating the base value. Thus, some regression equations estimated prove to be the same equations but in different prices.

It is in the same manner with intergovernmental equalization according to revenues criteria that regional equalization according to actual or necessary expenditures criteria. But we won’t shape equalization models based only on expenditure criteria but will include both expenditures (expenditure needs) and tax revenues (fiscal capacity).into the equalization models. In this case it can be assumed that the Center allocating financial aid to the regions be orientated to actual regional budget deficit and (or) the gap range between 'normative' expenditures and fiscal capacity.

Equalization based upon partial compensation for actual deficit results in financial aid calculation by formula:

( 48)

Corresponding regression is as follows:

( 49)

Unlike theoretical part of the work this section contains no assumptions that each region should follow budget constraint T+Tr=E for it is possible that the deficit be financed for by regional borrowings. Therefore, the estimation of this equation can’t be considered just as the estimation of budget constraint parameters in the region.

OLS estimation results of the equation for 1994-1999 are given below (statistically significant coefficients are in the bold type).

Besides, equalization mechanisms similar to (43) and (46), which are not based upon actual revenues and expenditures but upon their 'normative' or potential values, i.e. fiscal capacity and expenditure needs, prove to be possible. Corresponding formula for calculating financial aid amount allocated by the Federal Center goes as follows:

( 50)

Corresponding regression is as follows:

( 51)

OLS estimation results of this equation for 1994-1999 are given in the tables below (statistically significant coefficients are in the bold type).

In theory, it is possible that equations (49) and (51) be estimated so as they won’t include deficit variable but separate budget revenues and expenditures variables (fiscal capacity and expenditure needs). In practice it means that revenue and expenditure weights are different in the transfer allocation formula. But there is a multicollinearity between these variables and for that reason estimations for these two simple equations were not made.

The most general linear formula of financial aid allocation can be written as follows:

( 52)

If this formula is transformed to the (26) type considering that transfers for all regions are calculated according to one and the same equalization formula, then equation (52) corresponds to the following equalization mechanism:

( 53)

Such formula includes fixed amount of aid (per capita) Tr0 and aid to cover a share of the gap between regional revenues and expenditures. Revenue and expenditure sides within this formula are weighted sums of actual and 'normative' or potential values, besides, the sum of weights in this case is less than unity (only cases when γα<1 и γβ<1 are considered). Unlike previous interbudgetary equalization formulae, the equation (53) can’t be transformed so as multicollinearity of the variables could be reduced, that’s why no estimations were made directly for this equation at present stage of research31. (30)

Less general model for federal financial aid allocation also containing both regional budget actual revenues and expenditures and fiscal capacity with expenditure needs could be presented by a linear formula like:

( 54)

As it was mentioned above this equation corresponds to equalization formula, which partially covers the gap between budget revenues and expenditures calculated as weighted sum of actual and 'normative' of potential values. In order to avoid multicollinearity of the variables as well as to insert necessary constraints on coefficients into the equation (54),the latter can be rewritten into:

( 55)

The equation transformed in this way gives the following additional meaning of this equalization formula: the transfer can be decomposed into three parts such as partial compensation for theoretical (predicted) deficit (the gap between expenditure needs and fiscal capacity), compensation for deviation of actual expenditure form its 'normative' value (if α>0) and compensation for actual revenues deviation from fiscal capacity (if fiscal capacity is bigger than actual revenues, otherwise the item is less than zero).

Corresponding regression is:

( 56)

Alongside with that it is assumed that the following hypotheses be not rejected:

a0=0, a1>0, a2<0, a3>0, a3>a1, a3>|a2|. (57)

Thus, α, β and γ can be calculated as;

α = a1/a3, β = -a2/a3, γ = a3. (58)

The OLS estimation results of the equation for 1994-1999 are given in the tables below (statistically significant coefficients are in the bold type).

Comparing the estimations done for the models (43), (46), (48), (50) and (54) we can arrive at the conclusion that the latter model is the best, which corresponds with the hypothesis that within these years Russian Federal Center allocated financial aid among the regions on the basis of the factors used in formula (54) and was aimed at partial compensation for revenues and expenditure gap calculated as weighted actual and 'normative' or potential values. Besides, as it was mentioned above (see the theoretical section as well), coefficients α and β characterize the impact of actual expenditures and tax revenues on financial aid amount: the bigger the coefficients are, the less financial aid amount depends upon 'normative' value, which means that the regions have more options to manipulate modifying own expenditures and revenues in order to exert an influence upon financial aid amount. Analyzing the dynamics of estimated coefficients α, β and γ, almost all of which prove to be significant, we can conclude the follows:

1. According to successive comparison of the calculations done for each year it can be stated that coefficient γ was decreasing. It shows that within the last years regional authorities have been accounting less on federal financial aid allocated in order to cover the gap between budget revenues and expenditures. If the transfer amount (see formula (55)) is calculated as the sum of equal gap shares between actual revenues and expenditure as well as between 'normative' values, γ value decrease creates incentives for regional authorities to adjust their actual revenues and expenditures with 'normative' or potential values (revenue capacity is usually higher than actual revenues and 'normative' expenditures is usually lower than actual ones).

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