It is well known that income effect caused by federal general lump-sum to the region results in tax decrease and expenditure growth20. Accordingly, if the transfer is aimed at public goods supply increase, then private goods consumption incentives (i.e. incentives to regional tax burden relief resulted from the grant) could be considered as negative. Consequently, financial aid allocation strategy should be devised so as the incentives to tax cuts could be minimized but positive incentives to public goods provision increase (the increasing expenditures for public goods provision) could be maximized. The model analyzed in this section makes it possible to distinguish cases of diverse changes in regional budget revenues and expenditure value selected by the regional authorities, which are determined by changes in financial aid amount received within the range of transfer calculation methodology. Empirical analysis made below gives us a chance to define in practice incentive intensity as well as its dependence upon the factors of financial aid calculation structure.

At the same time it should be noted that definition of financial aid effect produced upon regional budget revenues and expenditure as positive or negative depends on the interbudgetary equalization goal pursued by federal authorities. It is obvious that reductions in tax collection resulted from financial aid can be regarded as negative effect if federal authorities’ policy is aimed at equalization of regional potentials concerning public goods provision. But if interbudgetary transfers are aimed at regional welfare growth, then resulted from federal financial aid corresponding value changes in the selected by regional authorities tax revenues and budget expenditures can’t be regarded as totally negative for the goal consisted in interregional welfare equalization will be achieved (by means of income effect). Alongside with that the amount of regional compensation for the gap between revenues and expenditure, i.e. transfer amount, can be defined only within the framework of a more general problem concerning all the regions and the center and determining the population welfare maximization in all the regions attained by allocation of limited resources established in order to support the regions.

The federal financial aid being viewed as a part of aggregate interbudgetary financial flows, taking account of the federal tax revenue sharing between the regional and the federal budgets, there should be a negative coefficient item thus added up to the formula representing tax revenues of the federal budget collected on the region's territory. In this case for some regions, which can be defined as «federal budget donors», the transfer amount will be negative. It should be noted that negative transfer amount could also be observed within the set of regions defined as federal financial aid recipients (if federal financial aid amount received is less than total tax revenues collected in the region and accrued to the federal budget)21.

But such model modification won’t be considered below. According to interbudgetary equalization procedure transfer value received by the region in model (21)–(23) can be either positive or negative. Up to 1994 value-added tax revenue received by the regional budget and specified for each federal subject in individual manner was regarded as negative transfer if value added tax amount in a region was less than country average. But at present negative transfers do not exist in Russia. Therefore, in order to avoid additional restrictions in further calculations (if transfer value calculated in the given formula is negative, the transfer equals zero) we will make a general analysis but pay close attention to the regions receiving positive transfer (in Fig. 1 corresponding points are placed above 45˚line).

In the model it is premised that budget constraint (22) be performed as equality. Indeed, any transfer is positively determined by actual regional budget expenditure as long as it is determined negatively by actual budget revenues. And consequently, the constraint being performed as inequality, it is possible that expenditure be increased (tax revenue be reduced) and utility value of regional authorities be raised. Therefore, budget constraint will be regarded as equality constraint in further calculations. Picture 1 provides graphic illustration of positive transfer received by the region.

Figure 1

In order to get a more detailed result than the one possible in the general model analysis it is advisable that regional authority utility function of Cobb-Douglas type be mentioned. The regional authorities define the value of private and public goods consumption. Public goods consumption is characterized by regional budget expenditure value and private goods consumption is determined by regional tax and income value. Alongside with that income value can be regarded as exogenously given factor of utility function specification.

Therefore, utility function variant suggested goes as follows:

U(Ε, Τ) = ln Ε + α ln (Ψ-Τ) (24)

Utility function maximization can be performed under two conditions:

Budget constraint

E = T + Tr (25)

Transfer allocation methodology

Τρ = γ.{[α.Ε + (1-α)] -- [β.Τ + (1-β).]} ( 26)

where most variables are analogous to the ones given in the previous section:

E – regional budget expenditures;

T – regional budget revenues;

Tr – federal center financial aid (transfer) to the region;

– expenditure standards (exogenously given and correspondent to objective needs of a region in budget expenditures)

-- regional fiscal capacity (exogenously given and correspondent to objective tax collections level, e.g. within average tax efforts);

Y – before tax revenue of regional economic agents;

α, β, γ – model parameters (α – characterizes the degree of actual expenditure influence exerted upon financial aid allocation strategy in comparison to theoretical value, β – the degree of financial aid allocation being determined by actual tax revenues, γ – covered part of the gap between regional budget revenues and expenditures regarded as standard (or 'normative) and actual revenues or expenditure value defined by α and β)

It should be noted that relations between taxation level and regional economic agents’ income, which could be performed as additional constraint like T=иY on the account of the assumption that taxes dependent upon regional authorities’ choice prove to be lump-sum, has not been considered here.

In order to simplify the model we can transform the constraints substituting one for another and grouping their items with E and T. As a result we’ll get the only constraint for utility maximization problem:

Ε∙(1-γ∙α) - Τ (1-γ∙β) = γ∙Α ( 27)

where

A = (1-α)- (1-β).. ( 28)

The equation (28) multiplied by parameter γ can be regarded as objective part of the financial aid to the region, i.e. the parts determined by exogenous regional features such as expenditure needs standards and tax capactiy but independent from their actual value. In a word, this part of transfer to region is defined by fiscal capacity and expenditure needs estimates adjusted according to coefficients (l–-β) and (l–α), the latter two characterizing the degree of transfer allocation methodology orientation to objective regional features. Then quantity Tr – γА = γ(αE - βT) proves to be the part of the transfer assigned according to actual regional revenue and expenditure values, corrected by weights α and β.

First order conditions (necessary and sufficient when it is required that authorities' preferences and respective indifference curves be convex), after being transformed and Lagrange multiplier being excluded, lead to the following optimum condition for this simplified model: relation between marginal rate of substitution of expenditure increase for tax burden relief:

MRSΕΤ = (29)

Thus marginal rate of substitution of change in expenditures for tax burden change depends upon the rules applied to transfers allocation. Some following particular cases of financial aid allocation parameters can serve as an example to the assumption.

Let γ=0. Actually it presupposes that there are no transfers within IGFR system. Then optimum choice of budget expenditure value and tax burden level made by the regional authorities will be characterized by MRSET=1, i.e. marginal utility of public expenditures in the optimal point must equal marginal loss inflicted by tax burden increase. This situation is characterized by lack of any incentives caused by transfers within regional authorities’ fiscal behavior. Interbudgetary financial aid system (i.e. its absence) offers no incentives to expenditure growth or tax rate reduction on account of their compensation at the federal budget expense. Analogously, revenues growth does not result in corresponding financial aid amount decrease (as it is not available) and therefore, revenues growth attained by tax rate increase or (and) tax base growth proves to be stimulated. The regions deprived of federal financial aid experience the same when γ≠0.

If γ is bigger than zero but less than unity, then the share of the gap between calculated regional expenditures and revenues equal to γ, is covered by the transfer. Now some particular cases can be considered: α=0 and β=0; α>0 and β=0; α=0 and β>0.

If both weights α and β equal zero, then while calculating the gap between revenues and expenditure the transfer allocation methodology will be focused on expenditure and revenues 'normative' or 'potential' values independent from regional authorities’ behavior like in γ=0 case (the transfer is defined by expenditure and revenues 'normative' value). Therefore, the system will lack incentives to expenditure growth and tax reduction on account of bigger transfer amount but will create incentives to own revenues growth and expenditures cutting in order to balance the budget. In this case marginal rate of substitution of taxes for expenditure MRSET equals unity, i.e. public expenditure increase essential to the compensation for tax burden growth equals the latter (tangent slope to objective function level line in the optimal point equals minus unity).

It should be noted that analogous situation might occur if any α, β values equal each other22. Thus, if 'normative' and actual values of tax revenues and budget expenditure are regarded according to the symmetrical rules applied in order to calculate the gap between the latter, regional authorities’ marginal utility of expenditure increase equals in the optimum point marginal loss inflicted by tax burden growth. The reason for it is that, α and β being equal, the slope of budget constraint is 45º as well as transfer amount with any E and T values lying on the boundary of the tolerance range is determined by γ.(1‑α)(‑)/1-γα independent from actual E and T values. The case when γ=1, α=1 and β=1 makes an exception to the rule. It consists in total covering the gap between actual public revenues and expenditures in the region, i.e. in absence of budget constraint.

Transfer value defined only by federal 'normative' revenues and expenditure for the region, which performs a particular case of symmetrical (in the sense mentioned above) transfers allocation model, draws our interest as long as regional authorities lack incentives to modify fiscal behavior in order to change financial aid amount for actual regional decisions exert no influence upon transfer value (in short-term period). Within symmetrical model transfer value modification causes fiscal incentives resulted from income effect, which lead to actual tax revenue decrease and actual expenditure growth in the region.

If financial aid model is not symmetrical, then transfer value modification results not only in parallel shift of budget constraint line but in its slope change as well, i.e. it causes both income effect and substitution effect. Regional authorities’ fiscal incentives caused by income effect prove to be similar to the previous case. Besides, within the model described, optimum tax and expenditure values selection exerts an influence upon the transfer amount, i.e. being determined by substitution effect the choice of revenue and expenditure levels is exercised considering their influence exerted upon transfer amount. The transfer made according to asymmetrical methodology based on 'normative' or actual revenues and expenditures produces an effect similar either to change in relative prices in a simplified model of consumer’s choice or to matching grant in the model of regional authority choice namely – to modifying price of public goods. Asymmetrical transfer calculation methodology results in influence exerted by transfers upon relative prices for private and public goods attained by matching of budget expenditures (public goods price) and participation in regional budget revenues formation (private goods price).

If parameter α is greater than zero and β=0, then revenue and expenditure policy pursued by the regional authorities loses its symmetry and proves to be independent (as in the previous case) from objective function features. If β=0, the transfer while being calculated is based upon fiscal capacity amount rather than actual revenues amount. Alongside with that parameter α value determines the degree of 'normative' or actual expenditure presence in the transfers allocation mechanism.

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