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28.02.2017

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 non-linear 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 non-linear 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. Cobb-Douglas production function has been taken as a basis within our research, since it represents non-linear processes taking place on the micro-level:
                                                                      (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 non-linear, 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 first-order 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 1999-2009 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 macro-economic indicators of Ukraine for 1999-2012. (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

R-square

0.990

0.995

Normalized R-square

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 (R-square> 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 1999-2012 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 1999-2004 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 off-budget 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.

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