The methodology to determine the optimal fiscal burden on country’s economy (using the example of Ukraine)
PhD. BARDAS’ V.,
Investment and forecasting expert
The methodology to determine the optimal fiscal burden on country’s economy (using the example of Ukraine)
Under the conditions of world economic conjuncture changeability and high energy consumption of developing countries’ economy, the problem of effective resources management and withdrawal of raw rent into public sector is of utmost importance. In such cases it comes to the processes having complex structure and inherent multifunctional connections, therefore it is expedient to apply linear or nonlinear multiple regression analysis and differential calculus methods.
It is expedient to use Laffer curve in order to determine the optimal level of tax burden on an economy. The general aspect of the curve is presented on the Figure 1.
Figure 1. Laffer curve
where T is a fiscal withdrawal from GDP, Y is a nominal GDP, T/Y is a level of fiscal burden, N is an optimal level of fiscal burden, and ТА is maximum possible fiscal income under given amount of nominal GDP. Given linear connection follows the parabolic equation in accordance with the formula: у=ах2+bх+с, where а, b and с are numbers, it being known that а<0, so long as branches are downward directed, that is why it is important that final version of nonlinear multiple regression is parabolic equation under the condition а<0.
It is common knowledge that fiscal burden influences the amount of nominal GDP and, in its turn, the fiscal income depends on GDP. That is why when calculating levies, it is important to consider the factors forming nominal GDP. GDP is generally formed by means of economic entities, and the fiscal burden directly influences the results of their activity, reasoning from this fact, the production level is determined by the production function. CobbDouglas production function has been taken as a basis within our research, since it represents nonlinear processes taking place on the microlevel:
(1)
where Y is production level, L is remuneration expenses, K is investment in stock capital, α0, α1 and α2 are empirical coefficients. Given functional dependence does not take into account the level of fiscal burden, that is why, using Ye. Balatskiy’s approach, we will hold the replacement of the parameters: α1 = n*q + m*q2 та а2 = a*q + b*q2 [1]. Having applied this approach, we got production function described by the following equation:
(2)
where q is a level of fiscal burden, a, b, n and m are empirical coefficients.
Taking into consideration the amount of square fiscal burden (q2) will allow getting parabolic equation, clearly outlining the Laffer curve and determining the optimal level of fiscal burden in the result. The sum of empirical coefficients b and m is to be less than zero that will be an additional index of the possibility to apply multiple regression model for further research.
function (2) is nonlinear, therefore it is necessary to make it linear. Having taken logarithmation of the right and left parts of equation, the identical equation (2) can be written down in the form:
(3)
Having expanded the brackets and applied the algebraic transformations, the formula (3) can be presented in parabolic form the following way:
(4)
where , and accordingly are parabolic numbers.
Empiric coefficients a, b, n and m can be calculated by the least square method based on the equation of multiple linear regression presented below:
(5)
where is the resulting index, , , and are regressors influencing resulting index. Consequently, having all data to write down the parabolic equation (4), it is possible to determine the optimum of given function by means of the methods of differential calculus, namely, having calculated the firstorder derivative by q. Parabolic form subsequent to the results of differentiation:
(6)
To be determined from the equation (6) that equals to:
(7)
Thus the formula (7) shows the highest point, i.e. parabola vertex that illustrates the optimal level of fiscal burden on an economy.
Within the framework of the research, let us calculate the optimal amount not only of fiscal burden on GDP (below are the calculations by the example of Ukraine, where apart from fiscal charges, the income to the Pension fund and target funds are taken into consideration), but also the fiscal burden (only fiscal income to the Consolidated budget of Ukraine is taken in consideration). The dynamics of indicators used to calculate the Laffer optimum for the Ukrainian economy during 19992009 is presented in Table 1. Investment in stock capital represents capital mobilisation (K) to obtain nominal GDP. Income to target funds and the Pension fund also represents levies that in general influence investment decisions and, as a result, the amount of actual GDP.
Table 1
Main macroeconomic indicators of Ukraine for 19992012. (million UAH)
Years 
Nominal GDP 
Investment in stock capital 
Fiscal income to the Consolidated budget 
Remuneration expenses 
Pension fund’s own income 
Income to other target funds 

Y 
К 
T 
L 
— 
— 
1999 
130442 
17552.1 
25175.3 
42139 
11745 
3908.0 
2000 
170070 
23629.5 
31292.9 
55853 
11553 
5079.0 
2001 
204190 
32573.1 
36754.2 
67389 
13283 
1098.7 
2002 
225810 
37177.9 
45392.5 
78950 
19439 
472.0 
2003 
264165 
51011.2 
54321.0 
94608 
23154 
736.7 
2004 
344822 
75714.4 
63161.7 
117227 
30000 
844.0 
2005 
441452 
93096.1 
98065.2 
160621 
42200 
1353.6 
2006 
544153 
125253.7 
125743.1 
205120 
54300 
2148.3 
2007 
720731 
188486.1 
161264.2 
278968 
76000 
3641.2 
2008 
948056 
233081.0 
227164.8 
366387 
102000 
3347.0 
2009 
913345 
151776.8 
208073.2 
365300 
103100 
2159.5 
2010 
1094607 
171091.9 
234447.7 
459153 
119300 
2487.2 
2011 
1302079 
238174.6 
261604.0 
529133 
139055 
3153.0 
2012 
1408889 
263727.7 
274715.0 
593213 
157980 
3524.6 
Having held mathematical processing by the least square method, let us write down the regression model (5), interpreted to the correlation of capital and labour resources attraction in Ukrainian economy.
For tax burden:
(8)
and for fiscal burden:
(9)
Moreover, the sum of empirical coefficients under q2 is negative (e.g., for (8):46,476+27,635=18,841; for (9): 8,109+1,957=6,152), i.e. appropriate models are parabolas with downward directed branches, analogously to Laffer curve.
Table 2
Regression statistics indicators
Regression statistics 
Multiple linear model (8) 
Multiple linear model (9) 
Multiple R 
0.995 
0.998 
Rsquare 
0.990 
0.995 
Normalized Rsquare 
0.986 
0.993 
Standard error 
0.094 
0.068 
Number of observations 
14 
14 
Subsequent to the presented results (Table 2), it follows that the dependence between resulting indicator and regressors is strong (Rsquare> 0,75) that points to the correct selection of the regression model type and adequate selection of factors.
An important characteristic of regression analysis is excess, namely, checking the conditions of correct practical application of regression analysis against conformity excess distribution law to the normal distribution law.
Figure 1. Distribution of regression model excess for tax and fiscal burden on the normal distribution law
From the Figure 1 one can see the conformity of excess distribution corresponds to the normal distribution law. Thus, the multiple linear models are adequate for further analysis of tax and fiscal burden in order to determine their optimal level.
The results of optimal tax and fiscal burden obtained by means of empirical coefficients substitution from the formulae (8) and (9) to the formulae (7) are presented in the Table 3.
Table 3
The actual and calculated level of yax and fiscal burden on the Ukrainian economy for 19992012 period
Periods 
Actual tax burden 
Optimal level of tax burden 
Actual fiscal burden 
Optimal level of fiscal burden 
1999 
0.193 
0.204 
0.372 
0.382 
2000 
0.184 
0.204 
0.387 
0.382 
2001 
0.180 
0.206 
0.339 
0.383 
2002 
0.201 
0.206 
0.363 
0.383 
2003 
0.206 
0.208 
0.375 
0.384 
2004 
0.183 
0.211 
0.355 
0.386 
2005 
0.222 
0.210 
0.403 
0.385 
2006 
0.231 
0.210 
0.419 
0.385 
2007 
0.224 
0.212 
0.416 
0.386 
2008 
0.240 
0.211 
0.425 
0.386 
2009 
0.228 
0.206 
0.414 
0.383 
2010 
0.214 
0.205 
0.398 
0.382 
2011 
0.201 
0.207 
0.415 
0.384 
2012 
0.195 
0.207 
0.431 
0.384 
As follows from the Table 3, the optimum of quadratic parabola with downward directed branches averages to 0.207 for tax burden and 0.384 for fiscal burden. Besides, the actual level of tax and fiscal burden for 19992004 was on the optimal level or below it. Starting from 2005, the actual burden surpassed the optimal one. It applies both to tax (2.7 pp in average) and fiscal (5 pp) ones. Although, in 2012 the tax burden on the national economy was optimal whereas fiscal one significantly surpassed the margin line. Exceeding function’s optimum means that further growth of tax rate will result in decreasing the income to the Consolidated budget of Ukraine and other offbudget funds (Figure 3).
Figure 3. Graphical interpretation of Laffer curve for Ukraine
Based on the calculations, 67 billion UAH were excessively withdrawn from the Ukrainian economy in 2012, so long as under 1409 billion UAH GDP, fiscal withdrawals should have amounted to 540 billion UAH. Moreover, the previous calculations allowed determining that excessive fiscal burden is due to the high pressure on salary fund because of the Pension fund deficiency, since the optimal tax burden remains on the level close to optimal.
Using the given methodology, it is possible to determine the level of optimal tax burden on developing countries’ economies. That will allow harmonizing the tax system and intensifying the economic growth.