Economic growth and GDP estimation:

Introduction:

Economic growth is determined by the level of GDP, economic growth is therefore determined by the changes in the level of GDP, Keynes model of measuring economic growth states that the level of income in a country is determined by adding up consumption, investment, government expenditure and net exports. There are however various approaches in the measurement of the level og GDP and this includes the income approach, expenditure approach and the product approach. In this paper we determine the level of GDP as a function of inflation, net exports, foreign direct investment and domestic investment. The estimation of this model was made using data for the UK economy for the period 1970 to 2002, however for any estimated model there is ned to determine the statistical significance oif the model and also whether all the assumptions of the OLS estimation model are met such as the absence of autocorrelation and Heteroscedasticity.

In this case we will use time series data and this type of data there is a risk of autocorrelation, autocorrelation can be defined as the case where one of the assumptions OLS is violated which states that the error terms in two different periods of observations have zero covariance. Therefore the existence of autocorrelation means that our estimates are not BLU. This paper therefore involves the effort to remove the problem of autocorrelation and therefore involves the estimation of three different models.

Results:

The first estimated model states that LGDPt = b1 + b2LXt + b3LFDIt + b4LDIt+b5INF, meaning that the GDP level is a function of exports, foregn direct investment, domestic investment and the level of inflation, the results of our estimated model are as follows:

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

This means that if we increase the level of exports LX by one unit then the level of LGDP will increase by 0.366704 assuming all factors are held constant, if we increase the level of foreign direct investment LFDI by one unit then the level of LGDP will decline by 0.006544  assuming all factors are held constant, if we increase the level of LDI by one unit then the level of LGDP will increase by 0.265253 assuming all factors are held constant and finally if we increase the level of inflation INF by one unit then the level of LGDP will decrease by 0.001313.

Statistical significance:

We perform a two tail test on the estimated coefficient at 98% level, the following table summarizes the results of the test:

98% level of test(two tail test)

variable

coefficient

T statistic

T critical

null hypothesis

alternative hypothesis

null hypothesis

C

b1

14.3179

1.281552

b1 = 0

b1 ≠ 0

reject

LX

b2

13.04894

1.281552

b2 = 0

b2 ≠ 0

reject

LFDI

b3

-1.01064

1.281552

b3 = 0

b3 ≠ 0

accept

LDI

b4

5.183639

1.281552

b4 = 0

b4 ≠ 0

reject

INF

b5

-1.45926

1.281552

b5 = 0

b5 ≠ 0

reject

All the estimated coefficients are statistically significant at 98% two tail test apart from the LFDI coefficients which is not statistically significant.

Coefficient of determination R square for this model is 99.2292% meaning that there is a very strong relationship between the explanatory variables and the dependent variable, this value means that 99.229% of variations in LGDP are explained by the explanatory variable.

Other tests:

98% level of test(two tail test)

null hypothesis

alternative hypothesis

t statistics:

T critical

null hypothesis

b2

b2 = 0

b2 > 0

13.04894

1.281552

reject

b3

b3 = 0

b3 > 0

-1.010641

1.281552

accept

b4

b4 = 1

b4 > 1

-14.35866018

1.281552

reject

b5

b5 = 0

b5< 0

-1.459259

1.281552

reject

From the above test it is clear that b2 is greater than 1, b3 is equal to zero, b4 is greater than 1 and b5 is less than zero, further a test for autocorrelation with reference to the Durbin Watson test whose coefficient is 0.646833  shows that there is autocorrelation.

Estimation two involved the estimation of the model LGDPt = b1 + b20LXt + b21LXt–1 + b30LFDIt + b31LFDIt–1 + b40LDIt + b41LDIt–1 + b50INFt + b51INFt–1 + b5LGDPt–1 + ut, this model involves time lagging the variable in the model, it involves increasing other variables that describe the previous values, after estimation the results are as follows:

LGDPt = 3.251747+ 0.068721 LXt + 0.011649 LXt–1 + 0.001123 LFDIt – 0.003232 LFDIt–1 + 0.250335 LDIt – 0.156964 LDIt–1 – 0.001963 INFt + 0.000493 INFt–1 + 0.719464 LGDPt–1

Test statistics for statistical significance are summarised in the following table:

98% level of test(two tail test)

variable

coefficient

T statistic

T critical

null hypothesis

alternative hypothesis

null hypothesis

C

b1

2.447224

1.281552

b1 = 0

b1 ≠ 0

reject

LXT

b20

0.959683

1.281552

b20 = 0

b20 ≠ 0

accept

LXT_1

b21

0.154077

1.281552

b21 = 0

b21 ≠ 0

accept

LFDIT

b30

0.293811

1.281552

b30 = 0

b30 ≠ 0

accept

LFDIT_1

b31

-0.79871

1.281552

b31 = 0

b31 ≠ 0

accept

LDIT

b40

4.820457

1.281552

b40 = 0

b40 ≠ 0

reject

LDIT_1

b41

-2.78611

1.281552

b41 = 0

b41 ≠ 0

reject

INFT

b50

-2.94661

1.281552

b50 = 0

b50 ≠ 0

reject

INFT_1

b51

0.738533

1.281552

b51 = 0

b51 ≠ 0

accept

LGDPT_1

b5

6.532978

1.281552

b5 = 0

b5 ≠ 0

reject

The coefficients of LXt , LXt–1 , LFDIt , LFDIt–1 and  INFt–1 are not statistically significant at 98% test level, however all the other coefficients are statistically significant.

The correlation of determination value for this model R squared is equal to 0.997893 which means that there is still a very strong relationship between the explanatory variables and the dependent variable, the value means that 99.7893% of variations in LGDP are explained by the independent variables.

Regarding autocorrelation the Durbin Watson test value is equal to 2.026241, the value two mean that there is zero autocorrelation and therefore we can conclude that the addition of lagged variables into our first model has eliminated autocorrelation although there is a certain level of autocorrelation in the model and therefore the estimates are not BLU.

Our third estimation involves the estimation of the model LGDPt = b1 + b20LXt + b21LXt–1 + b30LFDIt + b31LFDIt–1 +b40LDIt + b41LDIt–1 + b5LGDPt–1 + ut, this model involves the removal of the inflation variable in the model, after estimation the model the following were the results:

LGDPt = 2.322694+ 0.137682 LXt – 0.054333 LXt–1 – 0.002289LFDIt – 0.004492 LFDIt–1 + 0.278083 LDIt – 0.185637 LDIt–1 +  0.750794LGDPt–1

Statistical significance of the estimated coefficients is summarized in the table below:

98% level of test(two tail test)

variable

coefficient

T statistic

T critical

null hypothesis

alternative hypothesis

null hypothesis

C

b1

1.734605

1.281552

b1 = 0

b1 ≠ 0

reject

LXT

b20

1.799921

1.281552

b20 = 0

b20 ≠ 0

reject

LXT_1

b21

-0.66139

1.281552

b21 = 0

b21 ≠ 0

accept

LFDIT

b30

-0.55771

1.281552

b30 = 0

b30 ≠ 0

accept

LFDIT_1

b31

-1.03266

1.281552

b31 = 0

b31 ≠ 0

accept

LDIT

b40

5.274759

1.281552

b40 = 0

b40 ≠ 0

reject

LDIT_1

b41

-2.99087

1.281552

b41 = 0

b41 ≠ 0

reject

LGDPT_1

b5

6.101389

1.281552

b5 = 0

b5 ≠ 0

reject

From the above summary of statistical tests it is clear that The coefficients of LXt–1 , LFDIt ,and LFDIt–1 are not statistically significant, however all the other coefficients are statistically significant at 98% test level.

Correlation of determination in this model R squared is equal to 0.997034 meaning that 99.7034% of variation in the dependent vatrriable is explained by the explanatory variables, therefore there is s strong relationship between the independent and dependent variable.

Tests for autocorrelation show that the Durbin Watson test value is 1.959273, this shows that autocorrelation has been reduced from the previous estimates, however the value is not equal to 2 and therefore the estimates are not BLU

Conclusion:

From the above analysis it is evident that the level of GDP which signify economic growth can be estimated using the value of exports, foreign direct investment, domestic investment and inflation, the first estimated model violates the assumptions of OLS regarding autocorrelation and therefore there is a need to state the model again, the second model estimated includes time lagged variables for all the independent variables involved and also the time lagged GDP level. This helps reduce the level of autocorrelation in the first model although it is still exhibits autocorrelation, our third model involves the stating the model again but this time in the absence of inflation and the time lagged inflation variable, this also reduces autocorrelation but the model  still exhibits autocorrelation.

From the above study therefore the second and third model can be used to estimate the level of GDP because they exhibit low autocorrelation, the level of R squared from the model show that there are very strong relationship between the variables, this discussion above shows how we can reduce autocorrelation and remove the problem so that we come up with a best linear unbiased model, therefore the models can be used to estimate GDP and also for forecasting.

References:

David Cox (2001) Applied Statistics: Principles and Examples, McGraw Hill press, New York

Leonard Henry (1991) Statistics, Oxford University Press, Oxford

Appendixes:

Dependent Variable: LGDP

Method: Least Squares

Date: 04/17/08   Time: 14:20

Sample: 1970 2002

Included observations: 33

Variable

Coefficient

Std. Error

t-Statistic

Prob.

C

11.15785

0.779293

14.31790

0.0000

LX

0.366704

0.028102

13.04894

0.0000

LFDI

-0.006544

0.006475

-1.010641

0.3208

LDI

0.265253

0.051171

5.183639

0.0000

INF

-0.001313

0.000899

-1.459259

0.1556

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

-4.812252

Sum squared resid

0.011601

Schwarz criterion

-4.585509

Log likelihood

84.40216

F-statistic

901.1990

Durbin-Watson stat

0.646833

Prob(F-statistic)

0.000000

Dependent Variable: LGDPT

Method: Least Squares

Date: 04/17/08   Time: 14:33

Sample: 1971 2002

Included observations: 32

Variable

Coefficient

Std. Error

t-Statistic

Prob.

C

3.251747

1.328749

2.447224

0.0228

LXT

0.068721

0.071608

0.959683

0.3476

LXT_1

0.011649

0.075604

0.154077

0.8790

LFDIT

0.001123

0.003823

0.293811

0.7717

LFDIT_1

-0.003232

0.004046

-0.798710

0.4330

LDIT

0.250335

0.051932

4.820457

0.0001

LDIT_1

-0.156964

0.056338

-2.786108

0.0108

INFT

-0.001963

0.000666

-2.946612

0.0075

INFT_1

0.000493

0.000667

0.738533

0.4680

LGDPT_1

0.719464

0.110128

6.532978

0.0000

R-squared

0.997893

Mean dependent var

27.57356

Adjusted R-squared

0.997031

S.D. dependent var

0.211029

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

1157.767

Durbin-Watson stat

2.026241

Prob(F-statistic)

0.000000

Dependent Variable: LGDPT

Method: Least Squares

Date: 04/17/08   Time: 14:40

Sample: 1971 2002

Included observations: 32

Variable

Coefficient

Std. Error

t-Statistic

Prob.

C

2.322694

1.339033

1.734605

0.0956

LXT

0.137682

0.076493

1.799921

0.0845

LXT_1

-0.054333

0.082150

-0.661392

0.5147

LFDIT

-0.002289

0.004104

-0.557712

0.5822

LFDIT_1

-0.004492

0.004350

-1.032660

0.3121

LDIT

0.278083

0.052720

5.274759

0.0000

LDIT_1

-0.185637

0.062068

-2.990870

0.0063

LGDPT_1

0.750794

0.123053

6.101389

0.0000

R-squared

0.997034

Mean dependent var

27.57356

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

-5.259463

Log likelihood

98.01435

F-statistic

1152.491

Durbin-Watson stat

1.959273

Prob(F-statistic)

0.000000

Oxford College