"Economics". 3. Financial relations

Rud’ O.V.

Cherkasy State Technological University, Ukraine

Multiple regression model of corporate income tax

The tax system fiscal efficiency is set on the ability of earning cash resources to the budget on time and in full, and is a prerequisite for economic growth, competitiveness for the national economy and population welfare. As an integral part of modern tax systems, corporate income tax is an important regulation of socioeconomic processes and is one of budgeting taxes. The proportion of tax fiscal and regulating functions is important for the tax fiscal efficiency. That is why it is so important to discover the factors influence earning corporate income tax to consolidated budget of Ukraine.

We use the methods of multiple regression analysis which allow to see the factors influence dependent parameter degree. Multiple linear regression model is a feature that describes the mutual connection between dependent parameter y and regressors , ,…, . It can be represented in such a way:

Μ(y, , ,…, )=α( , ,…, ), (1)

where a – the parameter of the model’s regressor.

The construction and analysis of the multiple linear regression model should be done in such steps [1, p.58-59]:

1. The multiple linear regression model’s parameters rating.

2. The constructed model and selected data adequacy rating.

3. The dispersion analysis of the model and the multiple determination coefficient calculation.

4. The multiple determination coefficient materiality statistics test of Fisher’s criterion.

Firstly, formalize the problem with finding out the endogenous characteristics and exogenous parameters. Y is the results parameter of the corporate income tax earnings to the consolidated budget of Ukraine. We use the following variables to analyze the research:

x₁ – the amount of tax benefits;

x₂ – the financial result before taxing(income);

x₃ – taxes losses;

x₄ – the nominal rate of corporate income tax;

x₅ – the effective tax rate for corporate income tax;

x₆ – the amount of tax debt;

x₇ – GDP.

We used the data of 2001-2012 years to construct the empire model of the factors influence the corporate income tax (table 1).

Table 1

The original data for the model’s construction in the period of 2001-2012 years.

	Tax benefits, billion UAH	The financial result before taxing (income), billion UAH	Taxes losses, billion UAH	The nominal rate of the tax	The effective tax rate	Tax debt, billion UAH	GDP, billion UAH	Income tax, billion UAH
	x1	x2	x3	x4	x5	x6	x7	y
2001	5,46	39,80	1,53	0,3	0,26	1,34	204,19	8,28
2002	5,33	37,41	1,49	0,3	0,26	4,41	225,81	9,40
2003	4,14	45,82	1,16	0,3	0,29	4,08	267,34	13,24
2004	3,71	73,69	1,08	0,25	0,22	2,41	345,11	16,16
2005	4,91	89,17	0,42	0,25	0,26	2,33	441,45	23,46
2006	6,68	110,65	0,74	0,25	0,24	2,33	544,15	26,17
2007	9,56	182,99	1,06	0,25	0,19	2,12	720,73	34,41
2008	15,76	193,67	1,67	0,25	0,25	2,00	948,06	47,86
2009	30,65	143,71	1,99	0,25	0,23	2,34	913,35	33,05
2010	26,99	212,01	2,10	0,25	0,19	3,86	1082,57	40,36
2011	47,56	272,73	15,41	0,235	0,20	1,61	1316,60	55,10
2012	25,87	277,94	15,11	0,21	0,20	1,91	1408,89	55,79

The source: based on [2;3;4]

Two matrix are formed based on the data table 1: the Y matrix corresponds to the values the dependent variable; the X matrix – the first column corresponds number 1, the second, third, fourth, fifth, sixth and seventh columns correspond the variables x₁, x₂, x₃, x₄, x₅, x₆, x₇.

Let us construct the multiple linear regression model. Herewith, the factors of the equation should be significant and linearly independent, meaning the absence of the multicollinearity what spoils the model quality. The partial information for the analysis is given by the correlation matrix (table 2).

Table 2

Pair correlation coefficients

	x1	x2	x3	x4	x5	x6	x7	y
x1	1
x2	0,81	1
x3	0,74	0,74	1
x4	-0,57	-0,83	-0,58	1
x5	-0,58	-0,77	-0,46	0,72	1
x6	-0,26	-0,37	-0,36	0,48	0,29	1
x7	0,87	0,98	0,75	-0,82	-0,71	-0,32	1
y	0,80	0,98	0,71	-0,84	-0,67	-0,39	0,97	1

According to the table 2 data the tax debt influence the resulting factor is absent. Thought the connection between GDP and corporate income tax earnings is present, there is a linearly dependence with other variables. Having analyzed the correlation matrix, we exclude single variables to better the model: x₆ (the amount of tax debt) and x₇ (GDP).

To confirm the absence of the multicollinearity the out-put factors have been teased for the Farrar-Hlober criterion.

Let us construct the mathematical model as a linear multiple regression [1, p.45]:

, (2)

Where – the unknown parameters of the model what we font with the help of the least squares method;

a₀ – free term of equation;

n – the number of the factors included to the model.

Having taken into consideration the used variables the model will look like:

, (3)

where ─ the unknown parameters of the model.

The model is as follows:

(4)

We test the model’s adequacy and accuracy. The regression equation and all the parameters of the equation are significant for the statistics criterions. The model has got the approximation properties what can be seen with the help of the schedule (figure 1). The determination coefficient 96%, average relative approximation error – 4,3%.

Figure 1. Schedule of the actual (real) and theoretical (listed) values corporate income tax

Here's economic interpretation of multiple linear regression coefficients: the tax benefits increase for 1 billion UAH influences the increase of the corporate income tax by 70 million UAH; the result of the income increase for 1 billion UAH is the increase of the resulting factor by 220 million UAH; the tax losses increase for 1 billion UAH influences the corporate income tax decrease by 380 million UAH; the nominal rate increase for 1% influences the corporate income tax decrease by 911 million UAH; the effective tax rate increase for 1% influences the corporate income tax increase for 1,466 billion UAH.

Based on the model constructed we can make such conclusions: among the considered factors the effective and nominal tax rates influence the corporate income tax earnings in the greatest way. The effective tax rate increase influences the tax earnings in a positive way while the nominal tax rate increase influences the tax earnings negatively and this fact is a problem for the future research.

Literature:

1. Berezhna L.V. Ekonomiko-matematychni metody ta modeli v finansakh / L.V. Berezhna, O.I. Snytiuk - K: Kondor, - 2009. - 301 s.

2. Ofitsiyniy sayt Derzhavnoyi fiskalnoyi sluzhbi Ukrayini [Elektronniy resurs]. – Rezhim dostupu: URL: http:// www.sfs.gov.ua/.

3. Ofitsiyniy sayt Derzhavnoi sluzhby statystyky Ukrainy [Elektronnyi resurs]. – Rezhym dostupu: URL: http://: www.ukrstat.gov.ua.

4. Ofitsiyniy sayt Ministerstva finansiv Ukrainy [Elektronnyi resurs]. – Rezhym dostupu: URL: http://www.minfin.gov.ua/.