Determinant Of Gross Domestic Production

Determinant of  Gross Domestic Production.

Introduction:

This paper focuses on the estimation of a model that states what determines the gross domestic production. The variables considered in this analysis include the GDP level, exports, foreign direct investment, domestic investment and inflation. The data used is for the period 1970 to 2002 regarding the UK economy; series include gross domestic production, exports, foreign direct investment, domestic investment and inflation which is all in log. Estimation of the models uses the Eviews statistical program.

The estimated model must meet all the assumptions of OLS (ordinary least square method) method, due to the nature of the data which in this case is time series data there is a high possibility of the occurrence of autocorrelation, the existence of autocorrelation will violate the assumptions of the OLS estimation method and therefore our model will not be BLUE. The existence of autocorrelation in our estimation is determined using the Durbin Watson test and the Breusch Godfrey test to check for first order correlation. Autocorrelation however has its own remedies and one of the remedies involves time lagging variables also known as general least square method, this method involves replacement of the model with the serially correlated error term with a model with a serially independent error term.

This paper focuses on the estimation of three models which are stated as follows:

Model 1

LGDPt = b1 + b2LXt + b3LFDIt + b4LDIt+b5INF

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Determinant of Gross Domestic Production.

Model 2

LGDPt = b1 + b20LXt + b21LXt–1 + b30LFDIt + b31LFDIt–1 + b40LDIt + b41LDIt–1 + b50INFt + b51INFt–1 + b

5

LGDP

t–1

+ u

t

Model 3

LGDPt = b1 + b20LXt + b21LXt–1 + b30LFDIt + b31LFDIt–1 +b40LDIt + b41LDIt–1 + b5LGDPt–1 + ut

Results:

Model 1

Estimation of the model one LGDPt = b1 + b2LXt + b3LFDIt + b4LDIt+b5INF involves the use of the data for the period 1970 to 2002 regarding the UK economy, estimation of the above model using Eviews had the following results:

LGDPt = 11.15785+ 0.366704LXt – 0.006544LFDIt + 0.265253LDIt – 0.001313INF

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From the results of the correlation of determination R squared which is equal to 0.99229 we can conclude that 99.22% of variations in LGDP are explained by the independent variables, this shows a very strong relationship between the dependent and the independent variables.

From the results if we hold all other factors constant and the level of LX, LFDI, LDI and INF are equal to zero then the level of LGDP will be equal to 11.158 which is also our autonomous value, we can explain the coefficient of the log of exports by stating that if we hold all other factors constant and increase the level of LX by one unit then the level of LGDP will increase by 0.366704 units, also if we hold all other factors constant and increase the level of LFDI by one unit then the level of LGDP will decrease by 0.006544 units.

If we also hold all the other factors constant and increase the level of LDI by one unit then the level of LGDP will increase by 0.265253 units, finally if we hold all factors constant and increase the level of INF by one unit then the level of LGDP will decline by 0.00131. Having explained the coefficients of the estimated model we can conclude that if we increase the level of exports and domestic investment then the level of gross domestic product will increase, on the other hand an increase in the level of inflation and foreign direct investment will reduce the level of gross domestic production.

Statistical significance:

Our estimated coefficients may be statistically significant of statistically insignificant, for this reason there is a need to undertake hypothesis test to determine their significance in the model, a two tail T test at 95% level of test showed the following results:

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Determinant of Gross Domestic Production.

95% TEST LEVEL

VARIABLE

coefficient

null hypothesis

alternative hypothesis

T calculated T critical

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reject or accept null

C

B1

B1=0

B1≠0

14.3179

2.04841

REJECT

INF

B2

B2=0

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B2≠0

-1.459259

2.04841

ACCEPT

LDI

B3

B3=0

B3≠0

5.183639

2.04841

REJECT

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LFDI

B4

B4=0

B4≠0

-1.010641

2.04841

ACCEPT

LX

B5

B5=0

B5≠0

13.04894

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2.04841

REJECT

From the above test of hypothesis it is clear that at 95% test level the autonomous value, LDI coefficient and LX coefficient are statistically significant following the rejection of the null hypothesis that they are equal to zero, the rest of the coefficient which include the INF coefficient and the LFDI coefficient are not statistically significant at the 95% level of test, this follows the acceptance of the null hypothesis that they are equal to zero.

Despite the two coefficients that are not statistically significant in the model we can still use the model to forecast, this is due to the strength of the model portrayed by the correlation of determination r squared which shows that 99% of variations in the dependent variables is explained by the independent variables.

Hypothesis test:

LGDPt = b1 + b2LXt + b3LFDIt + b4LDIt+b5INF

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LGDPt = 11.15785+ 0.366704LXt – 0.006544LFDIt + 0.265253LDIt – 0.001313INF

The export (LX) coefficient:

Null hypothesis

b2 = 0

Alternative hypothesis

b2 > 0

The test

T calculated = B2 / SB2

T calculated = 0.366704/0.028102

T calculated = 13.049036

A two tail test At 95% test level

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T critical from the T table taking into consideration degrees of freedom due to the 5 coefficients in the model therefore degrees of freedom for the test will be 33 – 5 = 28, therefore:

T critical = 2.04841

Because our T calculated is greater than our T critical we reject the null hypothesis and accept the alternative hypothesis, therefore the coefficient of LX is statistically significant.

The foreign direct investment (LFDI) coefficient:

Null hypothesis

b3 = 0

Alternative hypothesis

b3 > 0

The test

T calculated = B3 / SB3

T calculated = -0.006544/0.006475

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T calculated = -1.010641

A two tail test At 95% test level

T critical from the T table taking into consideration degrees of freedom due to the 5 coefficients in the model therefore degrees of freedom for the test will be 33 – 5 = 28, therefore:

T critical = 2.04841

Because our T calculated is less than our T critical we accept the null hypothesis and reject the alternative hypothesis, therefore the coefficient of LFDI is not statistically significant.

The domestic investment (LDI) coefficient:

Null hypothesis

b4 = 1

Alternative hypothesis

b4 > 1

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The test

T calculated = B4 – 1 / SB4

T calculated = (0.265253 – 1)/ 0.051171

T calculated = -0.734747/ 0.051171

T calculated = -14.35866018

A two tail test At 95% test level

T critical from the T table taking into consideration degrees of freedom due to the 5 coefficients in the model therefore degrees of freedom for the test will be 33 – 5 = 28, therefore:

T critical = 2.04841

Because our T calculated is greater than our T critical we reject the null hypothesis and accept the alternative hypothesis, therefore we reject the hypothesis that b4 = 1 and accept that b4 > 1.

The Inflation (INF) coefficient:

Null hypothesis

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b5 = 0

Alternative hypothesis

b5 < 0

The test

T calculated = B5/ SB5

T calculated = -0.001313/ 0.000899

T calculated = -1.459259

A two tail test At 95% test level

T critical from the T table taking into consideration degrees of freedom due to the 5 coefficients in the model therefore degrees of freedom for the test will be 33 – 5 = 28, therefore:

T critical = 2.04841

Because our T calculated is less than our T critical we accept the null hypothesis and reject the alternative hypothesis, therefore we accept the hypothesis that b5 = 0 and accept that b5 < 0.

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Autocorrelation:

The Durbin Watson test is a test used to determine the presence of autocorrelation, it is a problem which occurs in time series data, and the test involves the calculation of a value d which is estimated as follows:

∑ (et – et-1)2

D =             _____________

∑et2

The value of D derived from the above function usually lies between the number 0 and 4, a d value of 2 indicates that there exist no autocorrelation, if the d value is less than two then there is positive correlation, however if the value is greater than two this shows negative correlation, in our case the value of d from the Eviews estimate is 0.646833 showing that our error terms in the model are correlated.

The presence of autocorrelation violates the OLS estimation assumptions, for this reason therefore the existence of autocorrelation leads to our conclusion that the estimates are not BLUE, meaning best linear unbiased estimates.

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Model two:

This involves the estimation of the model that involves variables that are time lagged as follows:

LGDPt = b1 + b20LXt + b21LXt–1 + b30LFDIt + b31LFDIt–1 + b40LDIt + b41LDIt–1 + b50INFt + b51INFt–1 + b

5

LGDP

t–1

+ u

t

This model includes the addition of other variables which include time lagged exports(LXt-1), foreign direct investment(LFDIt_1), time lagged domestic investment(LDIt–1) time lagged inflation (INF

t–1

) and time lagged gross

domestic production

(

5

LGDP

t–1

).

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When we time lag these variables we will have 32 variables and not 33 variables this is because when we lag the first year which is 1970 then the first year lagged variable is unknown so we need to start at 1971 in order to have complete data.

Results of the estimated model using eveiws are as follows:

LGDPt = 3.251747 + 0.068721 LXt + 0.011649 LXt–1 + 0.001123 LFDIt – 0.003232 LFDIt–1 + 0.250335 LDI

t

-0.156964 LDI

t–1

– 0.001963 INF

t

+ 0.000493 INF

t–1

+ 0.719464 LGDP

t–1

From the above estimated model it is clear that if we hold all other factors constant and all independent variables are equal to zero then the level of LGDP will be 3.251747, if we hold all other factors constant and increase level of exports (LX) by one unit then the level of LGDP will increase by 0.068721, also if we hold all other factors constant and the previous level of LX increase by one unit then the level of LGDP will increase by 0.011649. the level of foreign direct investment and the previous level will also affect the level of LGDP, is we hold all factors constant and increase level of LFDI by one unit then the LGDP will increase by 0.001123 however if the previous level of LFDI increase by one unit then the level of LGDP will reduce by 0.003232, the previous level of LGDP has a positive sign in the model meaning that if we increase the previous LGDP level by one unit then the level of LGDP will increase by 0.719464 units.

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Autocorrelation:

From our estimated value using the Durbin Watson test it is clear that the value of d = 2.026241 showing that there is still autocorrelation, this is because the value of d =2 shows no autocorrelation in our model, however our estimate exceeds this value. For this reason therefore because the estimated model violates the assumptions of OLS then the estimates are not BLUE.

Model 3:

This model is similar to model two but this model does not inflaude inflation or lagged inflation independent variable, the model estimated is as follows:

LGDPt = b1 + b20LXt + b21LXt–1 + b30LFDIt + b31LFDIt–1 +b40LDIt + b41LDIt–1 + b5LGDPt–1 + ut.

After estimation the results of this model is as follows:

LGDPt = 2.322694+ 0.137682LXt -0.054333LXt–1 -0.002289LFDIt -0.004492LFDIt–1 +

0.278083LDI t -0.185637LDI

t–1

+ 0.750794LGDP

t–1

Having estimated outr model we can test for autocorrelation using the Durbin Watson test, the test give us a value of d = 1.959, if we round off this value to the nearest whole number then the

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value is 2 and we can conclude that this model does not show the existence of autocorrelation, for this reason therefore we can conclude that this model is BLUE because it does not violate the assumptions of OLS estimation.

Conclusion:

From our estimated models it is clear that the best model to use in the estimation of gross domestic production is the final model that involves time lagged variables in the absence of inflation, this is because the probability of the existence of autocorrelation in this model from the Durbin Watson test shows that this model has no correlation, for this reason therefore the final model is the best because it is BLUE.

References:

Bluman A. (2000) Elementary Statistics: A Step by Step Approach, McGraw Hill press, New York

Patton M. (1990) Qualitative evaluation and research method, Sage publishers, Newbury

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Appendixes:

Estimation 1:

Dependent Variable: LGDP

Method: Least Squares

Date: 04/12/08  Time: 01:28

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Sample: 1970 2002

Included observations: 33

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Variable

Coefficient

Std. Error

t-Statistic

Prob.

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C

11.15785

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0.779293

14.31790

0.0000

INF

-0.001313

0.000899

-1.459259

0.1556

LDI

0.265253

0.051171

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5.183639

0.0000

LFDI

-0.006544

0.006475

-1.010641

0.3208

LX

0.366704

0.028102

13.04894

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0.0000

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R-squared

0.992292

Mean dependent  var

27.56269

Adjusted R-squared

0.991191

S.D. dependent  var

0.216879

S.E. of regression

0.020355

Akaike info  criterion

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-4.812252

Sum squared resid

0.011601

Schwarz  criterion

-4.585509

Log likelihood

84.40216

F-statistic

901.1990

Durbin-Watson stat

0.646833

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Prob(F-statistic)

0.000000

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Estimation 2:

Dependent Variable: LGDP

Method: Least Squares

Date: 04/12/08  Time: 01:32

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Sample (adjusted): 1 32

Included observations: 32 after  adjustments

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Variable

Coefficient

Std. Error

t-Statistic

Prob.

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C

3.251747

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1.328749

2.447224

0.0228

INF

-0.001963

0.000666

-2.946612

0.0075

INFT_1

0.000493

0.000667

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0.738533

0.4680

LDI

0.250335

0.051932

4.820457

0.0001

LDIT_1

-0.156964

0.056338

-2.786108

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0.0108

LFDI

0.001123

0.003823

0.293811

0.7717

LFDIT_1

-0.003232

0.004046

-0.798710

0.4330

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LGDPT_1

0.719464

0.110128

6.532978

0.0000

LX

0.068721

0.071608

0.959683

0.3476

LXT_1

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0.011649

0.075604

0.154077

0.8790

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R-squared

0.997893

Mean dependent  var

27.57356

Adjusted R-squared

0.997031

S.D. dependent  var

0.211029

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S.E. of regression

0.011498

Akaike info  criterion

-5.842928

Sum squared resid

0.002909

Schwarz  criterion

-5.384885

Log likelihood

103.4868

F-statistic

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1157.767

Durbin-Watson stat

2.026241

Prob(F-statistic)

0.000000

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Estimation 3:

Dependent Variable: LGDP

Method: Least Squares

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Date: 04/12/08  Time: 01:35

Sample (adjusted): 1 32

Included observations: 32 after  adjustments

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Variable

Coefficient

Std. Error

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t-Statistic

Prob.

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C

2.322694

1.339033

1.734605

0.0956

LDI

0.278083

0.052720

5.274759

0.0000

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LDIT_1

-0.185637

0.062068

-2.990870

0.0063

LFDI

-0.002289

0.004104

-0.557712

0.5822

LFDIT_1

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-0.004492

0.004350

-1.032660

0.3121

LGDPT_1

0.750794

0.123053

6.101389

0.0000

LX

0.137682

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0.076493

1.799921

0.0845

LXT_1

-0.054333

0.082150

-0.661392

0.5147

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R-squared

0.997034

Mean dependent  var

27.57356

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Adjusted R-squared

0.996169

S.D. dependent  var

0.211029

S.E. of regression

0.013062

Akaike info  criterion

-5.625897

Sum squared resid

0.004095

Schwarz  criterion

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-5.259463

Log likelihood

98.01435

F-statistic

1152.491

Durbin-Watson stat

1.959273

Prob(F-statistic)

0.000000

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