The derivative of optimum expenditure value with respect to γ proves to be negative only if A>0 and Y<. The situation under consideration might be caused by close values of б and в, i.e. by symmetry between the rules of regional 'normative' and actual revenue and expenditure variables calculation sustained while allocating transfers. Then the region being a donor (transfer value proves to be negative), γ value growth results in shifting budget constraints downwards and reducing budget expenditures. Otherwise, if the region can be either a donor or a transferee (when A>0 and б>в, the region is only a transferee and when A<0 and Y>, it can be both)24, the derivative proves to be positive, i.e. transfer growth causes expenditure increase. In case of region-transferee it means that income effect dominates over substitution effect, and in case of donor region positive substitution effect exceeds negative income effect. In general such situation proves to be more probable when б exceeds в to a larger degree, which results in a bigger substitution effect. In the case under consideration objective function characteristics secure expenditure growth caused by γ value increase, when A<0 and Y>.
3. Let’s dwell upon the model, in which б<в. It means that the methodology for transfer value calculation is determined by actual tax revenues value rather than by actual expenditures. If A>0 and б<в, the region proves to be a transferee T>T0.Then if γ value is growing (see Fig. 9), regional authorities reduce taxes and increase expenditure by reason of revenues growth (the shift from point 1 to point 2).But the peculiarity of transfer calculation method mentioned above might cause a larger tax reduction on account of partial compensation for lost revenues attained by the transfer. Budgetary balance demands that expenditure be decreased for the transfer fails to provide an adequate compensation for tax reduction. Corresponding budget constraint turn, the slope of which is determined by the degree of в value excess over б, results in the solution that is achieved in point 3.
Thus, in the case under consideration tax revenue reduction is always determined by transfer growth and budget expenditures can either increase (if income effect exceeds substitution effect) or decrease (if it’s the other way round). Expenditure reduction within transfer value growth can be caused by sufficient excess of в value over б.
From equation (35) it can be concluded that the derivative of optimum expenditure value with respect to parameter γ proves to be positive, if A>0 and Y<. The latter are caused by value в sufficient excess over б (the transfer is focused upon actual tax revenues rather than actual public expenditures). Then optimum expenditure growth is dependent on increase in transfer value, which (the transfer) is always positive. Consequently, if Y value grows, income effect always exceeds substitution effect.
If Y>, then two variants are possible: 1) the region proves to be a financial aid recipient (0<Т*<). Then transfer growth results in expenditure increase analogously to the previous case. 2) The region proves to be a donor (<Т*<Y). Then transfer growth tapping off regional resources, causes expenditure increase for negative income effect is less than positive substitution effect by its absolute value (module).
If A>0, then when б<в the region never proves to be a financial aid recipient but a donor. The expenditure derivative with respect to transfer amount is negative. Therefore, γ growth can be interpreted as a decrease in the resources left at the regional authorities’ disposal, which results in expenditure reduction.
The sign of the derivative from optimum tax value with respect to γ value is defined by A sign. If A>0 the region proves to be a transferee (б<в, T*<T0) and as long as γ grows taxes are on the decrease on account of income effect domination. If the region proves to be a federal budget donor (it becomes possible when T*>T0), then along with γ growth the transfer, being in this case negative (budget constraint is shifted upwards as long as its slope diminishes), is also increased, which leads to tax revenue decrease for income effect (negative) is less than positive substitution effect.
If A<0 And б<в the region always proves to be a federal budget donor. Therefore, γ growth shifts budget constraint downwards, which results in regional tax revenue increase caused by income effect.
It should be mentioned that when б>в with A<0, the change in γ can lead to the transformation of a transferee region into a donor (in former case on account of budget constraint shift downwards, if A>0) and a donor region into a financial aid recipient (in the latter case on account of budget constraint shift upwards, when A>0). It should be considered that following the rules of transfer allocation asymmetrical to values actual taxes and expenditures calculation the turn of the budget constraint fails to provide any change in revenue and expenditure values, which in the former case proves to be the starting point and in the latter the last point for the region being a transferee (T*). Therefore, the shift of the region from one group into the other (the change in position of point T* relative to point T0) is determined by the substitution effect:
Now, let us analyze the impact of changes in б and в values on regional fiscal behavior. Change in б corresponds to the modification in the methodology of federal financial aid allocation. Alongside with that the degree of taking into account the regional budget expenditures while calculating financial aid value is changed. Corresponding private derivatives of optimal tax revenue and expenditure values with respect to б go as follows:
The derivative of optimal expenditure value with respect to б proves to be positive, if Y>((1-γ)+γ(1-β))/(1-γβ), i.e. regional public revenues are large in comparison with the equation dependent upon 'normative' expenditures, fiscal capacity and γβ parameter value. The derivative proves to be positive, if the product term is small. Under such conditions if the formula of transfers allocation is modified so as actual expenditures could be dominant, regional expenditures prove to be growing. When γ times β is large enough (i.e. the transfer covers the substantial part of expenditures and revenues gap and revenues calculation is largely determined by actual revenues), expenditure might decrease along with б growth (the derivative is negative).
Partial derivative of tax revenues with respect to б parameter characterizing the degree of actual expenditures influence exerted upon transfer calculation always proves to be positive. Tax revenue increase performed along with б growth means that while calculating the amount of financial aid to the region tax revenues increase as long as the influence exerted by actual expenditure grows. It can be explained by the fact that along with б growth regional administration profits by actual expenditure increase for the latter exerts a larger influence upon transfer amount (the federal government matches the expenditure with the grant). Intensifying the expenditure growth to a large extent regional authorities strengthen their influence upon transfer value and increase their utility function value even despite tax growth necessary for adhering to budget constraint.
The influence produced by the change in actual tax revenues participation in transfers allocation formula on regional administration optimal choice can be analyzed on the basis of optimal expenditure and tax value derivatives with respect to β parameter:
From equation (40) it can be concluded that the derivative of the optimal tax value with respect to β always proves to be negative, therefore, the more the Federal Center is orientated to actual regional tax revenues while calculating a transfer (i.e. participate in regional revenues formation), the less tax burden will be imposed by regional authorities. In other words, while transfer amount is being defined by the Federal center, β value, which characterizes the weights assigned to fiscal capacity and actual tax revenues while implementing transfers allocation formula, comes to determine the intensity of regional authorities’ fiscal incentives.
The negative sign of partial derivative E* with respect to β is defined by the fact that regional fiscal capacity always proves to be less than its gross income, i.e. even if actual tax revenues equals regional fiscal, net disposable income of regional economic agents still proves to be positive. The interpretation of regional budget expenditure decrease performed under higher weight assigned to actual tax revenues within transfer allocation mechanism is similar to tax revenue derivative with respect to б. The more financial aid calculation depends upon actual tax revenues, the more profitable it is for the regional administration to lower taxes though it might cause expenditure decrease (tax reduction is essential for adhering to the budget constraint as long as the transfer fails to provide complete compensation for tax revenues decrease).
The comparative statics analysis of the results produced by the model can be combined in the following table:
Derivative of E*
Derivative of T*
# – depends upon the correlation between all the parameters
## – «+”, if α>β, A>0; and «–”, when α<β, A<0; depends upon the correlation between Y (α-β) and A in other cases;
### – «+”, if A<0; «–», when A>0.
The following section consists in the statistic verification of some hypotheses advanced above within shaping and analyzing the model of regional authorities’ fiscal behavior.
First of all, we’ll consider the correspondence of budget constraint performed in the model to real state of things on the basis of regional budget statistics available. Budget constraint described is based upon the assumption that federal authority distribute financial aid to the regions partially compensating for regional budget revenues and expenditure gap and revenues as well as the assumption that estimates of regional expenditures and revenues proves to be the weighted average of actual and 'normative' or potential revenues and expenditure. In order to check up the correspondence of such hypothesis to empirical data we’ll analyze the parameters of the given budget constraint structure, which performs the model of financial aid allocation among the Federation subjects. Besides, we’ll try to analyze the parameters of other possible transfer allocation mechanisms and verifying adequacy of the latter to empirical data we’ll arrive at the conclusion whether chosen budget constraint within region fiscal behavior model proves to be correct.
Then we’ll try to analyze estimated values of α, β, γ and interpret the changes in these values within different time periods. Alongside with that it is possible to assume that α and β modification was determined by the change in both transfer allocation mechanism and transfer amount received from regional financial support fund, the latter being based on rather formalized rules if compared to other kinds of financial aid. It can be also assumed that γ value was changed along with the modification in financial aid amount regarding the gap between aggregate revenues and expenditure of the regions. Federal financial aid structure and its value are performed in table 2.
Table 2. Federal financial aid received by Federation subjects in 1992-2001 (% GDP)
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