GDP Growth Study- BRIC and South Africa

GITAM School Of International Business

GDP Growth Study- BRIC and South Africa

Multiple regression model

Students: Sumeet Shekhar Neeraj & R. P. Eashwar Singh Guide: Dr. R. Venkateswarlu

13 Sep 2010

GITAM School Of International BusinessGDP Growth Study- BRIC and South Africa

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ABSTRACTThe paper examines whether economic growth of countries is impacted by the independent

variables viz., investment in energy with private participation, Foreign Direct investment &

population, labour force, GNI per capita, agriculture etc.,

Utilizing multiple regression model study, the study suggests that foreign direct investment has

maximum influence on economic growth (GDP) of countries. The independent variables are

correlated and also individually they are significant predictors of Economic growth of countries

I – INTRODUCTION

Economic growth refers to the increase in prosperity and wealth of a nation or country.

Generally, economic growth is used as a synonym of GDP (gross domestic product). Economic

growth is a top priority for policy makers around the world. It is generally agreed that a number

of factors influence an economy to grow, including productivity increases, population growth,

better educated and healthier work force, and the ease of doing business, investments in energy

by private participation, FDI, government expenses, human capital accumulation, physical

capital accumulation, labour force ,technology improvement, foreign trade, foreign trade

investment and attitudes of people. Some factors have positive effect and some have negative

effect on economic growth of a nation.

COLLECTION OF SAMPLE

Every year the World Bank publishes data on economic variables. We have taken the data on

GDP, Foreign Direct Investment, population and labour force. We have compared economic

variables of BRIC countries (Brazil, Russia, India, and China) and South Africa.

BRIC (typically rendered as "the BRICs" or "the BRIC countries" or known as the "Big Four") is

a grouping acronym that refers to the countries of Brazil, Russia, India, and China that are

deemed to all be at a similar stage of newly advanced economic development.

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http://en.wikipedia.org/wiki/People's_Republic_of_China

http://en.wikipedia.org/wiki/India

http://en.wikipedia.org/wiki/Russia

http://en.wikipedia.org/wiki/Brazil

http://en.wikipedia.org/wiki/Countries

http://en.wikipedia.org/wiki/Acronym


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NATURE OF STUDY

We use these data and feed them into the Microsoft Excel’s ‘Data Analysis’ package. Any

computer loaded with Microsoft Excel Software is useful for this purpose. So this is a doctrinaire

study. It does not involve field survey. It includes an empirical element in the sense that it studies

real life data on GDP.

A) Definitions and Explanation of Chosen Economic Variables

GDP (Y)

“Without measures of economic aggregates like GDP, policy makers would be adrift in a sea of

unorganized data. The GDP and related data are like beacons that help policy makers steer the

economy towards the key economic objectives.”

Country GDP (Gross Domestic Product) is one of the primary economic indicators for a nation.

It is used to gauge the economic soundness of the country. Country GDP data is a measure of all

the services and goods produced within a particular country over a period of time, generally one

year. Economists evaluate the market value of goods and services to arrive at a number which is

called as country GDP. Thus, country GDP reports reflect the per capita economic well being in

a numeric form. Higher the per capita GDP, higher will be the economic soundness of the entire

nation and higher will be the standard of living.

GDP at purchaser's prices is the sum of gross value added by all resident producers in the

economy plus any product taxes and minus any subsidies not included in the value of the

products. It is calculated without making deductions for depreciation of fabricated assets or for

depletion and degradation of natural resources. Data are in current U.S. dollars. Dollar figures for

GDP are converted from domestic currencies using single year official exchange rates. For a few

countries where the official exchange rate does not reflect the rate effectively applied to actual

foreign exchange transactions, an alternative conversion factor is used.

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For our study we have chosen GDP as output, which is influenced by various independent

economic variables like population, investment in energy sector, productivity etc. We have

selected economic variables for over 1996-2008, in hopes that these variables would cover as

many facets as possible and thus build an accurate model of economic growth (GDP).

We study historic data of GDP i.e. dependent variable with the following independent variables:

FDI (X1)

Foreign direct investment are the net inflows of investment to acquire a lasting management

interest (10 percent or more of voting stock) in an enterprise operating in an economy other than

that of the investor. It is the sum of equity capital, reinvestment of earnings, other long-term

capital, and short-term capital as shown in the balance of payments. This series shows net

inflows (new investment inflows less disinvestment) in the reporting economy from foreign

investors. Data are in current U.S. dollars.

Population (X2)

Total population is based on the de facto definition of population, which counts all residents

regardless of legal status or citizenship--except for refugees not permanently settled in the

country of asylum, which are generally considered part of the population of their country of

origin.

Labour force (X3)

The labor force of a country (or other geographic entity) consists of everyone of working age

(typically above a certain age (around 14 to 16) and below retirement (around 65) who are

participating workers, that is people actively employed or seeking employment. People not

counted include students, retired people, stay-at-home parents, people in prisons or similar

institutions, people employed in jobs or professions with unreported income, as well as

discouraged workers who cannot find work

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B. Assumptions on the Regression Model

It is assumed that the chosen economic variables exert an observable and significant influence

on the GDP of a country. The relationship between GDP and these variables is assumed to be

linear and subject to random error.

C. Summary of Findings

We began our experiment with three major variables reflecting the GDP of countries. Our

preliminary regression with the three variables had an adjusted R2=0.9758. From our hypothesis

tests, we can conclude at the 97% level that three variables i.e., FDI, population and labour force

plays a significant role in determining GDP of countries.

II - ANALYSIS:

A. Single Regression Models

GDP of countries against various independent variables, to begin our analysis, single regression

models of GDP of a country were run against each of our chosen economic indicator to obtain a

graphical representation of how well each variable could explain variances in GDP.

Each of the three variables, FDI , population and labour force has significant linear relationship

with R2=0.95 , R2=0.53 , R2=0.74 respectively. Although significant in single regressions, it will

be interesting to observe whether these three variables will hold considerable weight in a

multiple regression.

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Single regression Graphs :

- 5.00 10.00 15.00 -

0.50

1.00

1.50

2.00

2.50

3.00

3.50

4.00

f(x) = 0.213581818713152 x + 0.390925446018146R² = 0.977738891179468

f(x) = NaN x + NaNR² = 0 X1 Line Fit Plot

Y

Linear (Y)

Predicted Y

Linear (Predicted Y)

X1

Y

SUMMARY OUTPUT Regression Statistics

Multiple R 0.416073773R Square 0.173117384Adjusted R Square -0.102510154Standard Error 1.196759623

Observations 5

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- 2.00 4.00 6.00 8.00 10.00 12.00 14.00 -

0.50

1.00

1.50

2.00

2.50

3.00

f(x) = 0.0314660446328489 x + 1.45330908296R² = 0.0525099587345049


Y

Linear (Y)

Predicted Y


X2

Y


Multiple R 0.729614703R Square 0.532337614Adjusted R Square 0.376450153Standard Error 0.900018047

Observations 5

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- 20.00 40.00 60.00 80.00 100.00 -

0.50

1.00

1.50

2.00

2.50

3.00

3.50

f(x) = 0.019606275740174 x + 1.01716546613713R² = 0.405795762505296


Y

Linear (Y)

Predicted Y


Axis Title

Y



Observations 5

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B) Initial Multiple Regression

Where single regressions take into account the effect of one variable at a time, multiple

regressions simultaneously consider the effects of many variables. A standard least square

multiple regressions was performed, plotting GDP of a country against our chosen economic

variables.

The results of our initial multiple regressions are as follows:

Whole Model TestActual by Predicted plot

- 1.00 2.00 3.00 4.00 0

0.51

1.52

2.53

3.54

f(x) = 0.975856108250236 x + 0.0360762617864432R² = 0.975856108250234

Y Line Fit Plot

Predicted YLinear (Predicted Y)Predicted Predicted YLinear (Predicted Predicted Y)

Y(actual)

Pred

icted

Y

SUMMARY OUTPUTRegression Statistics


Observations 5

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Coefficient

sStandard

Error t Stat P-valueLower 95%

Upper 95%

Lower 95.0%

Upper 95.0%

Intercept 0.03607626 0.16030194 0.225050.8363973

3-

0.474076060.54622859 -0.47407606 0.546229

Y 0.97585610 0.0886208411.0115

80.0016038

90.69382501 1.25788719 0.69382501 1.257887

This model shows a strong linear fit with an R2 value of 0.9758 this means that 97.58 % of the

variance has been accounted for in our model. Therefore, we can assume that our data set is

sufficient for creating a regression model for GDP of a country.

C. Test for Multicollinearity

The assumption of the absence of multicollinearity is essential to the multiple regression models.

In a regression, the X-variables are assumed to be independent, but with multicollinearity, these

variables are actually correlated with one another. For example, if X1 and X2 are highly

correlated, then when we add X1 to our model, we also add a bit of X2. Thus, the significance of

both X1 and X2 are diluted. This phenomenon leads to high standard error. Therefore, in order

to refine the model, a correlation plot between GDP of a country and our indicators was

performed. This plot identifies which variables are highly correlated.

Our initial multicorrelation test is shown below:

Y X1 X2 X3Y 1 X1 0.977510685 1 X2 0.729614703 0.633614037 1 X3 0.865044389 0.798643401 0.96627273 1

As can be seen from in the above tabular representation (studying the correlation between the

independent variable only):

i) There is a great deal of correlation between certain categorical variables viz.

population(X2) and labour force (X3) are highly correlated i.e. 99.6%.

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ii) Also labour force is moderately correlated to FDI.

iii) FDI (X1) & Population (X2) too are not that strongly correlated i.e. by 63%.

As can be seen from in the above tabular representation (studying the correlation between the

independent variable only):

Intuitively, these correlations make sense and improve our understanding. Since labour is higly

correlated to both population and FDI it increases standard error.So to avoid standard error we

neglect the independent variable labour force. We will consider only two variables X1 and X2.

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Testing the model used:

Y= βo+ β1X1+ β2X2

Test for the significance of the model:

We developed the null & alternate hypothesis as follows:-

Ho : β1=β2=0

Ha : atleast one of the βi ≠ 0

Now,

F- test = MSR/ MSE

Where MSR = Mean Square due to Regression

&

MSE= Mean Square due to Error

Now, F- test= 121 (as per the excel output)

At α= 0.05; Fcritical= 10.13 (checked from the F- distribution table)

Eventually we get Fcritical < Fcalculated, hence we reject the null hypothesis

We can infer that the deployed model is significant i.e, independent variables X1 and X2 are

significant predictors of Y.

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Test for finding significance of individual variables X1 and X2 :

Testing significance of X1 as a predictor of Y :

We developed Null and Alternate Hypothesis as follows:-

Ho : β1=0

Ha : β1 ≠ 0

Now,

T- test = b1/Sb1

i.e., t- test = Coefficient/ Standard Error

Now, T- test= 8.02 (as per the excel output)

At α=0.05, tcritical = 1.96

Tcalculated > tcritical , hence we reject Null hypothesis

We infer that variable X1 is significant predictor of Y

Testing significance of X2 as a predictor of Y :

We developed Null and Alternate Hypothesis as follows:-

Ho: β2=0

Ha: β2≠ 0

Now,

t- test = b2/Sb2

i.e.

T- test = Coefficient/ Standard Error

Now, T- test=1.84 (as per the excel output)

At α=0.05, tcritical = 1.96

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tstat > tcritical , hence we reject Null hypothesis

We infer that variable X2 is significant predictor of Y

III. CONCLUSION Multiple Regression Discussion

In the final multiple regression model, the four economic indicators were:

Foreign Direct investment & population. All of these indicators were highly significant, with p < 0.05, and accounted for

approximately 97.58 % of the variance.

The model is shown again below:

SUMMARY OUTPUT

Regression StatisticsMultiple R 0.9775817R Square 0.95566598Adjusted R Square 0.951635614Standard Error 0.602967917Observations 13

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Coefficien

tsStandard

Error t Stat P-value Lower 95% Upper 95%Lower 95.0%

Intercept-21.589664

5.047517496-4.277283767

0.002058155

-33.00794248

-10.17138681

-33.00794248

Investment in energy with private participation (current US$) bn (X1)

0.287878 0.137507662.093547704

0.065803579

-0.023185092

0.598942783

-0.023185092

Foreign direct investment, net inflows (BoP, current US$) in bn (X2)

0.020160 0.0524471810.384393576

0.709611691

-0.098483406

0.138804125

-0.098483406

Based on the model, GDP of a country is positively correlated to a its independent variables viz., FDI and population. The soundness of these results was discussed in detail following the stepwise regression.

Finally, we tested the significance of three variables (X1, X2 &X3) in predicting the output the GDP of a country(Y).From our hypothesis tests, we can conclude at the 95% level that all the three variables X1 and X2plays a significant role in determining GDP of a country. Also from individual hypothesis test at 95% level ,individually variables X1 and X2 were a significant predictor of the output i.e., GDP of a country. This underscores that GDP of a country is meaningfully determined by FDI and population of a country—and that to improve the GDP of a country one must concentrate in these critical issues.

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EXHIBITS

Raw Data for the Survey Study** (Source: World Bank Website)

Country Name[GDP (current

US$)]/1000000000000

[Foreign direct investment, net inflows (BoP, current

US$)]/10000000000(Population,

total)/100000000(Labour force, total)/10000000

Y X1 X2 X3 South Africa 0.28 0.57 0.48 1.79 India 1.18 2.51 11.25 44.09 Russian Federation 1.29 5.51 1.42 7.61 Brazil 1.33 3.46 1.90 9.79 China 3.38 13.84 13.18 77.11

MULTIPLE REGRESSIONS:

ANOVA Df SS MS F Significance F

Regression 3 5.0708064551.69026881

813.4727811

4 0.19704083

Residual 1 0.1254580480.12545804

8

Total 4 5.196264503

Coefficient

sStandard

Error t Stat P-value Lower 95%Upper 95%

Lower 95.0%

Upper 95.0%

Intercept 0.304714363 0.387503067 0.78635340.575779

3-

4.618978945 5.22840767 -4.618978945 5.228408

X1 0.193662308 0.125696846 1.54070930.366507

2-

1.4034675581.79079217

4 -1.403467558 1.790792

X2 0.041927826 0.250186455 0.16758630.894293

5-

3.136992497 3.22084815 -3.136992497 3.220848

X3-

0.001785055 0.060803375-

0.02935780.981315

5-

0.7743651890.77079507

9 -0.774365189 0.770795

SINGE REGRESSION Y & X1:

df SS MS F Significance FRegression 1 4.965171754 4.965171754 64.45686991 0.004034853Residual 3 0.231092749 0.077030916

Total 4 5.196264503

Coefficient

sStandard


Lower 95.0%

Upper 95.0%

Intercept

0.375621348 0.186597307

2.013005196

0.137582997

-0.218214561

0.969457256 -0.218214561 0.969457256

X10.21599954

4 0.0269040858.02850359

10.00403485

3 0.1303787380.30162035

1 0.130378738 0.301620351

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SINGLE REGRESSION Y & X2 :

ANOVA df SS MS F Significance F

Regression 1 2.766167049 2.766167049 3.414884098 0.161755393Residual 3 2.430097453 0.810032484

Total 4 5.196264503

Coefficient

sStandard


Lower 95.0%

Upper 95.0%

Intercept 0.71900322 0.581368126

1.23674345

0.30417343

-1.131169622 2.56917606 -1.131169622 2.569176066

X2 0.13731605 0.0743076171.8479405

00.1617553

9-

0.099163946 0.37379605 -0.099163946 0.373796054

SINGLE REGRESSION “Y & X3”:

ANOVA df SS MS F Significance F

Regression 1 3.888374053 3.888374053 8.919036118 0.058294479Residual 3 1.30789045 0.435963483

Total 4 5.196264503

Coefficien

tsStandard

Error t StatP-

valueLower 95%

Upper 95%

Lower 95.0%

Upper 95.0%

Intercept 0.63008 0.4134205

1.524065762

0.2248860

-0.68560858

71.94576878

2 -0.6856085 1.945768782

X3 0.03077 0.01030582.9864755

340.05829

44

-0.00201963

90.06357577

4 -0.0020196 0.063575774

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GDP Growth Study- BRIC and South Africa