Practical usage of the ordinary least squares method for economic growth valuation using macroeconomic variables of developed countries on the basis of capital market model

Econometrics is a field of economics that concerns itself with the application of mathematical statistics and is a tool of statistical inference to empirical measurement of relations postulated by economic theory. Thus, it helps analysing various economic phenomena, forecast their development and predict future fluctuations.

Creation of econometrical models provides an empirical evidence to support the evaluation of economic relationships, which occur in a modern society. These models are usually designed to examine the dynamics of aggregate quantities such as the total amount of goods and services produced, total income earned, the level of employment of productive resources, and the level of prices.

The purpose of this research is to identify and quantify the adequacy of the econometric model in practice and to analyze the relationship between endogenous and exogenous variables within the developed countries, which consist of Norway, Australia, Switzerland, Netherlands and USA.

Here we can see the model of personal consumption expenditure.

(C_t = a ₀ + a i * Y t + a 2 * C t-1 + а з * P t + £ t

{                   E(£t) = 0,

(                 c(£t) = co'n.S't where Y - gross domestic product (GDP) ;

C - private consumption expenditure;

P – consumer price index (CPI);

This model includes one endogenous variable ( C_t ) and three predefined variables (two exogenous - Y _t , P _t and one lag endogenous variable - C_t-1 ). We are going to analyze how exogenous variables influence endogenous variable so it will be wise to understand what economic concept is included in each of these variables.

Y – gross domestic product (GDP). GDP is macroeconomic indicator of the market value of all final goods and services (that is intended for direct consumption), produced for the year in all sectors of the economy in the state for consumption, export and storage, regardless of the nationality of the factors of production used.

C – private consumption expenditure. Household final consumption expenditure is the market value of all goods and services, including durable products (such as cars, washing machines, and home computers), purchased by households. It excludes purchases of dwellings but includes imputed rent for owner-occupied dwellings. It also includes payments and fees to governments to obtain permits and licenses.

P – consumer price index (CPI). CPI measures the average change in prices of a fixed basket of goods and services, in other words it is inflation in prices of consumer goods in a specific "basket", and is the main indicator of inflation in the country.

In order to examine these countries in detail we used ordinary least squares method (OLS) (linear least squares method) and have done following tests: F-test, Student’s t-test, R2-test, GQ-test and DW-test. Moreover, we have proved model adequacy and calculated mathematical expectation. Let’s consider these tests applicable to developed countries in more detail by the example of Norway. As a data source we used the Word Bank website databank from 1999 to 2013 [3].

Based on the results of research we have found out following (Figure 1):

	Norway	Australia	Switzerland	Netherlands	USA
R2	0,996	0,99	0,997	0,998	0,998
F-test	|F|> Fcrit	|F|> Fcrit	|F|> Fcrit	|F|> Fcrit	|F|> Fcrit
t-test	|t b1 |< t crit	|t b1 |< t crit	|t b1 |< t crit	|t b1 |< t crit	|t b1 |< t crit
GQ-test	-	+	-	-	-
DW-test	-	-	-	-	+
Adequacy	-	-	-	-	-

Figure 1. Results of the research

One of the central problems of econometric modeling is the prediction (forecasting) the values of the dependent variable for certain values of the explanatory variables. It is possible two-pronged approach: either to predict the conditional expectation of the dependent variable for certain values of the explanatory variables (the prediction of the mean), or to predict a specific value of the dependent variable (the prediction of a specific value).

Model by which the goal is achieved, is called an adequate goal. In this definition, which does not fully coincide with the requirements of completeness, accuracy and correctness of the (true) value means that these requirements are not met at all (so to say, immensely), but only to the extent that is sufficient to achieve the goal. Quality of the regression model is called the initial value of the constructed model (observed) data.

To check adequacy of the model, it is necessary to build confidence interval and to compare real value with the predicted by linear model.

However, tests show that this linear model is not the best way to analyze data. Adequacy wasn’t confirmed in all counties. Even though real parameter is included in confidence interval and coefficients a0 are significant, Gauss Markov theory cannot be used to estimate coefficients, since second and third conditions are not confirmed.

Since the model is reliable, it may imply that the dependence between variables is not linear. May be that linear model is not the best way to estimate the data and logarifm model is more preferable.

Resources:

• 1.    Tregub Ilona V. Investment Project Risk Analysis in the Environment of Russian Economy / Foreign Investment, Ljubljana Empirical Trade Conference 2012

• 2.    Tregub Ilona V. The method of constructing a model to predict the dynamics of arima time series/Bulletin of the Moscow State Forest University - the Forest Bulletin. 2011. № 5. pages 179-183 .

• 3.    The World Bank URL: http://data.worldbank.org/country

• 4.    Statistical data all over the world URL: http://www.tradingeconomics.com/

Peleckis Kęstutis

Associate Professor, Doctor of social sciences Vilnius University, Vilnius, Lithuania Peleckienė Valentina Associate Professor, Doctor of social sciences Vilnius Gediminas Technical University, Vilnius, Lithuania COMPARATIVE ANALYSIS ON INJURY LUMP SUMS DIFFERENCES AMONG EU MEMBER STATES