Klein model of macroeconomic model: BRICS

The purpose of this work is to analyze the Klein’s Investment function. The initial equation of the Klein’s Investment function looks like this:

Ii=a0+a1Yt+a2rt+Ƹi

In this research work I have constructed econometric models of this function for the analysis of the Gross capital formation formerly gross domestic investments and the influence of GDP and Interest rate on its value.

Yi=a0+a1X1t+a2x2t+Ƹi; E(w)=0; Ϭ=const

(Yi) is the Gross Capital Formation or just Gross domestic investment.

(X1t) - is Gross Domestic Product that is defined by OECD as an aggregate measure of production.

(X2t) – is interest rate is the rate at which interest is paid by a borrower from a creditor.

A0, a1 and a2 are the coefficients of our linear equation

Ƹi is an unobserved random variable, or disturbance term.

In this work I estimated 5 countries that are BRICS

Tests:

Correlation matrix ;

R² – helps to calculate rate of explanatory ability between independent and dependent variables.

F – test is any statistical test in which the test statistic has an F -distribution under the null hypothesis.

T – test is any statistical hypothesis test in which the test statistic follows a Student’s t distribution if the null hypothesis is supported.

Goldfield-Quandt test is a test for heteroscedasticity.

F test
	Brazil	Russia	India	China	South Africa
F	28,161	8646,2	71,141	109,527	11,467
Ftest	3,8055	3,682	3,315	3,3403	3,315
F>Ftest	True	True	True	True	True

T-test

Brazil and Russia have the same =СТЬЮДРАСПОБР(0,05;18) = 2,1009

India and South Africa have the same =СТЬЮДРАСПОБР(0,05;33) = 2,034

China has =СТЬЮДРАСПОБР(0,05;31) = 2,039

Brazil:

StatY= -0,63655< t-crit – coefficient is not significant

StatX1= 6,29969> t-crit coefficient is significant

StatX2= 0,85583< t-crit coefficient is not significant

Russia:

StatY= -1,55070> t-crit coefficient is not significant

StatX1= 10,1174> t-crit coefficient is significant

StatX2= -1,07447< t-crit coefficient is not significant

India:

StatY= -1,60219< t-crit – coefficient is not significant

StatX1= 9,41773> t-crit coefficient is significant

StatX2= 0,3488< t-crit coefficient is not significant

China:

StatY= -8,7702> t-crit coefficient is not significant

StatX1= 14,7326> t-crit coefficient is significant

StatX2= -0,8807> t-crit coefficient is not significant

South Africa:

StatY= -1,86310> t-crit coefficient is not significant

StatX1= 4,61979> t-crit coefficient is significant

StatX2= 0,8576> t-crit coefficient is not significant

In all countries we have not got significant coefficients it means that it is possible that after checking adequacy of this model we will have to reestimate them without this variables or change the time limits.

GQ-test

GQ
	Brazil	Russia	India	China	South Africa
GQ	+	+	+	+	+
1/GQ	-	-	-	-	-

For all countries the residuals are heteroscedastic

DW-test

0        dl            du       2      4-du        4-dl      4

0	1,114	1,358		2,642	2,886	4

Country	Stat
Brazil	1,31766
Russia	0,79695
India	1,19083
China	0,89328
South Africa	1,73473

• •     The DWstat for Brazil, South Africa and India lies between DU and

4-DU – it means that the residuals aren’t autocorrelated and 3rd Gauss-Markov condition is not broken

• •     DWstat for Russia, China lies between 0 and DL, which means that

residuals are positively autocorrelated

Adequacy:

For South Africa model is not adequate, as Yreal is not lay between two boundaries. It means that we cant use this model to predict changes in Investment in Netherlands. In other cases Y real lay in the interval between two boundaries. For other countries this model is adequate and can be used for predictions.

Conclusion:

For South Africa model is not adequate, as Yreal is not lay between two boundaries. It means that we cant use this model to predict changes in Investment in Netherlands. In other cases Y real lay in the interval between two boundaries. For other countries this model is adequate and can be used for predictions.