Usage of the ordinary least squares method for parameter estimation of economic growth by effects of macroeconomic variables in BRICS countries on the basis of capital market model

< E(st) = 0; o-(st) = const;

E(i9t) = 0; ^(^t) = const;

 0; b0,b1,b2 > 0.

• Figure 1.    Capital market model

However, with the purpose of simplification we have conducted our research using only the second part of capital market model which includes only second part of the model (Figure 2).

( Yt = bo + b!*Rt + b2^It + ^t;

\   Etyt) = 0; cr(i9t) = co'nst;

[         bo,b1,b2>0

• Figure 2.    Initial form of the model.

As for BRICS countries, so BRICS is the acronym for an association of five major emerging national economies: Brazil, Russia, India, China, and South Africa. The grouping was originally known as "BRIC" before the inclusion of South Africa in 2011. The BRICS members are alldeveloping or newly industrialised countries, but they are distinguished by their large, fast-growing economies and significant influence on regional and global affairs; all five are G-20 members.

The foreign ministers of the initial four BRIC states (Brazil, Russia, India, and China) met in New York City in September 2006, beginning a series of high-level meetings. A full-scale diplomatic meeting was held in Yekaterinburg, Russia, on 16.6.2009.

It is predicted that the large size of the economies of these countries will allow them in the future to transform the economic growth into political influence. It will lead to the loss of the leading position of modern Western economic elites and the transition to another model of economic governance.

As of 2014, the five BRICS countries represent almost 3 billion people which is 40% of the world population, with a combined nominal GDP of US$16.039 trillion (20% world GDP) and an estimated US$4 trillion in combined foreign reserves [1]. As of 2014, the BRICS nations represented 18 percent of the world economy [2].

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 BRICS in more detail by the example of Brazil. As a data source we used the Word Bank website databank from 1995 to 2013 [3].

Based on the results of research we have found out following (Figure 2):

• Figure 3.    Results of the research

According to the results, all BRICS countries have very high value of R². An R² close to 1 indicates that the regression line perfectly fits the data and almost all independent variables (in our case R t and I t ) describe variants of dependent variable (in our case Y t ).

Regression analysis showed that R t has the biggest influence on the resultant variable Y t in case of China (If R t will increase on 10 % Y t will decrease on $131 209 000 000) and I t has the biggest influence on Y t in case of Brazil (if I t will increase on $1 billion Y t will also increase on $4 840 000 000).

In all cases |t b1 |< t crit . It means that b 1 is not statistically valuable and we can exclude b 1 (R t ) from the model.

For all countries mathematical expectation is close to zero what means that 1st Gauss-Markov condition is confirmed and we can use OLS in order to estimate coefficients of the model [4].

Goldfeld–Quandt test has been failed in most cases. It means that almost all that residuals are heteroscedastic, 2nd Gauss-Markov condition is not confirmed and it is impossible use OLS in order to estimate coefficients.

The same thing is with Durbin–Watson test. For vast majority of BRICS countries there is autocorrelation (a relationship between values separated from each other by a given time lag) in the residuals (prediction errors), 3rd Gauss-Markov condition is not confirmed and it’s impossible to use OLS in order to estimate coefficients [5].

However, in most cases model is adequate (except India). So we can assume that we can analyze these countries using capital market model but the results can be inaccurate. Thus, it is better to use another models in order to conduct analysis for BRICS countries.

To sum up, we can assume that such results could be because capital market model is a variance of Keynesian model which was aimed to developed capitalistic countries. However, in the current research we have investigated BRICS countries that are newly industrialised and developing. Therefore, it can also be a cause to choose another model for current analysis.