# Impact Of Education Economic Growth Of Pakistan Economics Essay

The effect of educational expenditure on economic growth is one of the key issues in economic literature. Educational expenditure is part of public expenditure and since after World War II public expenditures have increased in developed and developing countries. Over time, many economic growth theories and models (such as Romer, 1990 and Lucas, 1988) have developed relating education and economic growth. The belief, that education promotes growth has led governments of many developing countries to invest in the education sector. Even the theoretical literature also provides a backing for such a policy (Pissarides, 2000). However, the empirical literature has failed to establish a robust relationship between education expenditures and growth. India has been no exception. According to the economic theory, we will expect a positive causal relationship to exist between the two.

Economic growth is the increase in value of the goods and services produced by an economy. It is conventionally measured as the percent rate of increase in real gross domestic product, or GDP. Growth is usually calculated in real terms, i.e. inflation-adjusted terms, in order to net out the effect of inflation on the price of the goods and services produced. In economics, "economic growth" or "economic growth theory" typically refers to growth of potential output, i.e., production at "full employment," which is caused by growth in aggregate demand or observed output. As economic growth is measured as the annual percent change of National Income it has all the advantages and drawbacks of that level variable. But people tend to attach a particular value to the annual percentage change, perhaps since it tells them what happens to their pay check.

The aim of this paper is to establish a relation between education and economic growth in Pakistan. The study explores that improvement in education bring economic growth in Pakistan. There has been difference among researches about the positive or negative relationship between educational expenditure and economic growth while some studies indicates no impart of education on economic growth. Time series data from the period of 1981-2010 is used for the analysis and co-integration and error correction models are used to determine the long and short run relationship of education and economic growth. In this study, an attempt is made to determine the significance of education in economic development in Pakistan. The data has been taken from Misinstry of Education’s website, Pakistan Economic Survey various issues and website of World Bank.

## Education Sector in Pakistan

Pakistan is an international outlier in terms of gender gaps in education. The education system in Pakistan is largely distributed into five levels: primary (grades one through five); middle (grades six through eight); high (grades nine and ten; intermediate (grades eleven and twelve, leading to a Higher Secondary (School) Certificate (HSC); and university programs leading to undergraduate and graduate degrees.

To augment the human capital different governments in Pakistan have taken numerous steps to improve the education and educational standards. According to the Education Statistics of 2008-9 Shows that literacy rate was high in urban areas (74%) then the rural areas (48%). Literacy rate in men are more the women's, as for men (69%) compared to women (45%). Province wise literacy rate indicates, "Literacy rate in Punjab is (59 %), Sindh, (59%), Khyber Pakhtunkhwa (50%) and Balochistan at (45%)". Total adult literacy rate show the figure of 57%. Pre‐Primary Education is a vital element of Early Childhood Education. An increase of 2.2% enrolment rate is estimated for the year 2009-2010. 156, 653 Primary Schools with 465,334 Teaching staff are functioning in Pakistan. An increase of 0.6 % in Primary enrolment (18.468 million) in 2009 compare to (18.360 million) in 2008. Statistics indicates that, 24,322 Secondary Schools with 439,316 Teaching staff are functioning in Pakistan. Moreover, the enrolment rate of 2.9 % (2.556 million) is observed in 2009-2010.

Pakistan has one of the lowest ratios in the world, of people having access to higher education in the country. National Commission for Human Development (NCHD) has planned to literate 82,500 adult literacy centers in three years (2009-12) to increase the literacy rate, however so far 26,000 literacy centers have been opened. Only 5.1 per cent of people aged 17-23 years are currently enrolled in higher education in Pakistan.

Pakistan is blessed with natural resources and talented individuals. Due to low employment opportunities, and insufficient research activities, a number of professionals have left Pakistan for the sake of healthier vocation and life. To tackle this problem of brain drain, during last few years governments have taken numerous steps to promote research activities and improve the quality of facilities in education institutes. Many scholarships programs have been offered throughout the year for higher education, including ingenious scholarship, special scholarship program for the students of Fata and Balochistan. At present 3,237 students are studying in HEC recognized universities. HEC has sent about 2,600 students for studies abroad under different foreign scholarship programs. In order to improve and promote research activities, 20 Research Laboratories have been established in major universities.

## Literature Review

Education is considered as a tool for economic advancement of any country. It is unanimously accepted that countries having developed human skills and capabilities tend to progress briskly. Education plays an essential part in developing human capital and accelerating productivity. The interrelation between education and economic growth has been discussed since ancient Greece. Adam Smith and the classical economists emphasized the importance of investment in human skills. In contemporary times when the focus is on the 'knowledge economy' the role of education becomes all the more important in the development of human capital. Several studies have investigated the relationship between economic growth and education such as Psaharoupolous, 1988; De Meulmester et. al., 1995; Jorgenson and Fraumeni, 1998. Their starting point was always the root of the economic growth itself. Over a period of time researchers have found a that correlations exist across countries between economic growth rates and schooling enrollment rates including enrollment in higher education, another group of researchers such as De Meulmester et. al. (1995), using more sophisticated econometric techniques, found that this relationship is not always a direct one.

Few empirical studies have tried to examine the relation between investment in human capital and economic growth. The relationship has been tested for countries such as USA (Jorgenson and Fraumeni, 1992), Pakistan (Aziz, Khan and Aziz, 2008 Tanzania and Zambia (Jung and Thorbecke, 2001), Nigeria (Ogujiuba and Adeniyi, 2005 and India (Chandra, 2010). The results from the above mentioned papers indicate that education expenditures do affect growth positively.

According to Bils and Klenow, (2000), "Countries having high rate of enrollment in schools made faster growth in per capita income because high enrollment rate causes rapid improvement in productivity". Hanushek and Kimko (2000) show that quality of education have a remarkable impact on productivity and national growth rates.

Chandra (2010) has tested for a causal relationship between education investments and economic growth for India for the time period 1951-2009 using linear and non-linear Granger causality methods. He found that there is bi-directional causality between education spending and GDP for India. Thus, it can be seen that overall, the empirical evidence regarding this relationship for India too is quite mixed.

Krueger and Lindahl (2000) say that a country which is improving its education policy is likely to change or improve other economic policies as well which will enhance its growth. That’s why it can be very difficult to separate the effect of education policy from that of the other policies. If we look at the South East Asian countries with regard to the benefits of higher education for a country's economy, many observers attribute India's leap onto the world economic stage as stemming from its decades-long successful efforts to provide high-quality, technically oriented tertiary education to a significant number of its citizens (World Bank, 2004).

## Summary of related articles

## Year

## Study

## Time Period

## Dependent variable

## Independent Variable

## Data source

## Methodology/ Technique

2011

Do Public Education Expenditures Really Lead to Economic

Growth? Evidence from Turkey

1973 - 2009

GDP

Educational Expenditure

Republic of

Turkey Ministry of Finance and the General Directorate of Budget and Fiscal Control

Causality analysis by Toda and Yamamoto

2011

Analysis of Educational indicators in different regimes of Pakistan

1978-2008

Literacy rate

Expenditure on education, Total enrolment,total institutions.

Poverty Reduction Strategy Paper (PRSP), Pakistan Economic Survey, State

Bank of Pakistan Annual Reports and 50 Years of Pakistan in Statistics.

Multiple regression, Post hoc and Ginni coefficient.

2008

Impact of Higher Education on Economic

Growth of Pakistan

1972-2009

GDP

Enrollment in Higher Education, Higher

Education Expenditure, Employment Rate, Labor Force, Labor Force Participation

Rate and Per Capita Income

Economic Survey of

Pakistan. Pakistan’s Statistical Year Book.

www.finance.gov.pk, www.statpak.gov.pk

Cobb-Douglas production

function, in its stochastic form, Time Series Analysis

2011

Relationship between Education and Economic Growth in

Pakistan: A time series analysis.

1980-2009

Real GDP

Government expenditure on education on education as % of GDP, Labour force participation rate, Gross fixed capital formation, Error Correction Term

Education Statistics of 2008-9

Economic Survey of Pakistan

Multiple Regression using production Function, co-integration and vector error

correction techniques for period 1980-2009

2011

Does Government Expenditure on

Education Promote Economic Growth?

An Econometric Analysis

1950 - 2009

GDP

Educational Expenditure

http://www.mospi.gov.in,

http://www.education.nic.in/secondary.html

The Linear Granger Causality Test.

Vector Autoregression (VAR)

## Hypothesis

After doing literature review a below hypothesis is developed to check in Pakistani scenario:

H0: There is a positive relationship between educational expenditure and economic growth of Pakistan.

As per literature review and previous work above hypothesis has not been rejected. This research will check the hypothesis for the time period between 1981-2010.

## Methodology

The model used in this paper is based on aggregate output function:

LnY = α + β1Ln(EDUEXP) + β2Ln(LFPR) + β3Ln(GFCF) + µi

List of variables with abbreviations:

Ln = Natural Logarithm

Y = Real GDP

EDUEXP = government expenditure on education on education as % of GDP

LFPR = Labor force participation rate

GFCF = gross fixed capital formation

µi = Error Correction Term

Real GDP is nation's total output of goods and services, adjusted for price changes.

Educational Expenditure is government expenditure in lieu of education in country. It is part of Human Capital which refers to educational and health expenditure, the scope of this research is to find the impact of education on economic growth.

Labor Force is a key indicator of economy specially countries having large population or labor intensive countries. It refers to the number of skilled workers available to work.

Gross fixed capital formation or "GFCF" is a macroeconomic concept used as measure of the net investment in an economy in "fixed capital assets" during one financial year.

## Analysis of the Model

To check the hypothesis regression using OLS technique was run, below are the results of running regression on model:

LnY = α + β1Ln(EDUEXP) + β2Ln(LFPR) + β3Ln(GFCF) + µi

Sample: 1981 2010

Included observations: 30

Variable

Coefficient

Std. Error

t-Statistic

C

2.357915

1.439910

1.637543

LEDUEXP

0.419361

0.645301

0.649868

LGFCG

-0.044904

0.069065

-0.650178

LLFPR

-0.136647

0.198686

-0.687754

R-squared

0.077666

Mean dependent var

Adjusted R-squared

-0.028757

S.D. dependent var

S.E. of regression

0.425489

Akaike info criterion

Sum squared resid

4.707053

Schwarz criterion

Log likelihood

-14.78612

F-statistic

Durbin-Watson stat

1.657983

Prob(F-statistic)

*Since Log of all variables has been taken therefore before every variable L is written.

## Interpretation of Results

As per model Y-intercept is 2.36 which mean that Real GDP will have 2.36 growth when all of the variables of our model are ‘0’ This is because GDP does not depend only on education even if there is no expenditure on education.

Coefficient of EDUEXP is positive which means that 1% change in EDUEXP will bring on average 0.41% change in Real GDP.

Coefficients of GFCG and LFPR are negative but as per priori they are supposed to be positive. This problem will be catered in later part of this report.

## Significance of Coefficients

Individual coefficients of all three independent variables are statistically insignificant.

## Coefficient of Determination (R²)

Value of R² is very low which states that approximately 7.76% variation in Real GDP is explained by Government expenditure on education as % of GDP, Labor force participation rate, Gross fixed capital formation.

The above graph tells us that residuals are right skewed and from the JB value of 4.49 with probability of 0.10 suggest that hypothesis that error terms are normally distributed is not true. This can happen because of our small sample size of 30 observations.

The above graph shows that actual values are not well fitted with the estimated which is the reason of low R2.

## Conclusion

The above regression analysis and its interpretation do not validate that education and economic growth has a long term relationship. Few results are against priori as well. In most of previous researches and literature available education has brought an economic growth in a given country.

We can also say that in short run education does not have relationship with economic growth because our sample size was just 30. Other dedection that can be made is since in Pakistan government has failed to create employment opportunities therefore after completing education people do not find jobs to contribute to the national economy and at times people go abroad causing brain drain in Pakistan.

Therefore government must attract international companies and local investors as well to create such ventures that could lead to the employment opportunities and ultimately increase in economic growth of Pakistan. Spending only on education will not contribute as such towards economic growth, there must be a system to accommodate and utilize those educated people for the best interest of country’s economy.

## Hetrosedasticity Testing

## Informal Method – Graphical

The above graph shows that apparently there is some systematic pattern followed by u2 values with the variation in Y. This gives an indication that there is hetrosedastcitiy.

## Formal Method

## Park Test

Sample: 1981 2010

Included observations: 30

Variable

Coefficient

Std. Error

t-Statistic

C

15.22099

5.142569

2.959804

LOGEDUEXP

-1.913353

2.304660

-0.830211

LOGGFCG

0.074760

0.246661

0.303087

LOGLFPR

-3.561273

0.709597

-5.018725

R-squared

0.496908

Mean dependent var

Adjusted R-squared

0.438859

S.D. dependent var

S.E. of regression

1.519611

Akaike info criterion

Sum squared resid

60.03968

Schwarz criterion

Log likelihood

-52.97528

F-statistic

Durbin-Watson stat

2.020812

Prob(F-statistic)

We can see that there is not statistically significant relationship therefore there is no chance of hetrosedascticity.

## Glejser Test

Dependent Variable: ARESID

Method: Least Squares

Date: 01/16/12 Time: 02:06

Sample: 1981 2010

Included observations: 30

Variable

Coefficient

Std. Error

t-Statistic

C

5.363741

3.448077

1.555574

LOGLFPR

-0.809647

0.475783

-1.701716

LOGGFCG

0.026805

0.165385

0.162077

LOGEEXP

-1.063382

1.545268

-0.688154

R-squared

0.101738

Mean dependent var

Adjusted R-squared

-0.001908

S.D. dependent var

S.E. of regression

1.018895

Akaike info criterion

Sum squared resid

26.99182

Schwarz criterion

Log likelihood

-40.98320

F-statistic

Durbin-Watson stat

2.071385

Prob(F-statistic)

This test is very much related to Park’s Test. Since there is no relationship between u term and regressors therefore we will validate the results of park’s Test.

## Spearman’s rank Correlation Test

Spearman’s Rank correlation

Residual

Ranking

RGDP

Ranking

d

0.20

13

6.4

24

-11

0.38

22.5

7.6

26

-3.5

0.28

16.5

6.8

23.5

-7

0.31

19

4

8

11

0.48

26

8.7

28

-2

0.17

10

6.4

19.5

-9.5

0.08

5

5.8

17.5

-12.5

0.11

6

6.4

19.5

-13.5

0.12

7.5

4.8

15

-7.5

0.16

9

4.6

13

-4

0.05

4

5.6

16

-12

0.38

22.5

7.7

27

-4.5

0.83

29

2.3

3

26

0.19

11.5

4.5

12

-0.5

0.28

16.5

4.1

9

7.5

0.29

18

6.6

22

-4

1.11

30

1.7

1

29

0.35

20

3.5

5

15

0.21

14

4.2

10

4

0.12

7.5

3.9

7

0.5

0.72

28

2

2

26

0.04

3

3.1

4

-1

0.01

1

4.7

14

-13

0.44

25

7.5

26

-1

0.67

27

9

30

-3

0.24

15

5.8

17.5

-2.5

0.37

21

6.8

23.5

-2.5

0.43

24

7.2

23

1

0.19

11.5

3.6

6

5.5

0.02

2

4.4

11

-9

src = 1 - 6[∑d²/ n(n²

src =0.16

t = r √n-2 / √1-r²

t = 0.847

df=28

t value is not significant at 10% level of significance. Therefore there is no hetrosedasticity.

## Goldfeld-Quant Test

First 13 observations

Dependent Variable: LOGGDP

Method: Least Squares

Date: 01/15/12 Time: 12:31

Sample(adjusted): 1981 1993

Included observations: 13 after adjusting endpoints

Variable

Coefficient

Std. Error

t-Statistic

C

2.651573

0.681057

3.893319

LOGEDUEXP

-1.257336

0.922248

-1.363338

R-squared

0.144548

Mean dependent var

Adjusted R-squared

0.066779

S.D. dependent var

S.E. of regression

0.335531

Akaike info criterion

Sum squared resid

1.238391

Schwarz criterion

Log likelihood

-3.163812

F-statistic

Durbin-Watson stat

2.202716

Prob(F-statistic)

Last 13 observations

Dependent Variable: LOGRGDP

Method: Least Squares

Date: 01/15/12 Time: 12:35

Sample(adjusted): 1998 2010

Included observations: 13 after adjusting endpoints

Variable

Coefficient

Std. Error

t-Statistic

C

0.049376

2.287818

0.021582

LOGEDUEXP

1.555899

2.381743

0.653260

R-squared

0.037346

Mean dependent var

Adjusted R-squared

-0.050167

S.D. dependent var

S.E. of regression

0.430289

Akaike info criterion

Sum squared resid

2.036634

Schwarz criterion

Log likelihood

-6.397470

F-statistic

Durbin-Watson stat

0.919369

Prob(F-statistic)

λ = RSS₂ / df

RSSᵢ / df

=1.64

Since it does not exceed the crticial value therefoe we can say there is no hetrosedasticity in error terms.

## White Test

White Heteroskedasticity Test:

F-statistic

0.500718

Probability

Obs*R-squared

3.465937

Probability

Test Equation:

Dependent Variable: RESID^2

Method: Least Squares

Date: 01/16/12 Time: 01:45

Sample: 1981 2010

Included observations: 30

Variable

Coefficient

Std. Error

t-Statistic

C

63.04697

103.7328

0.607782

LOGLFPR

-23.88602

35.43197

-0.674137

LOGLFPR^2

2.338438

3.484467

0.671104

LOGGFCG

-0.756409

3.113424

-0.242951

LOGGFCG^2

0.033143

0.125704

0.263660

LOGEEXP

-2.178690

3.897969

-0.558930

LOGEEXP^2

1.328884

2.486743

0.534387

R-squared

0.115531

Mean dependent var

Adjusted R-squared

-0.115200

S.D. dependent var

S.E. of regression

0.276470

Akaike info criterion

Sum squared resid

1.758020

Schwarz criterion

Log likelihood

-0.013017

F-statistic

Durbin-Watson stat

2.310125

Prob(F-statistic)

n. R² = 3.4659, which has asymptotically a chi square distribution with 6 df. The 5% critical chi-square value for 14 df is 12.5916. 10% critical value is 10.6446 and 25% critical value is 7.84. For all practical purposes we can conclude on the basis of white test that there is no heteroscedasticity.

## Remedial Measures

## White’s Heterosedasticity- Consistent Variances and Standard Errors

Dependent Variable: LOGRGDP

Method: Least Squares

Date: 01/16/12 Time: 12:45

Sample: 1981 2010

Included observations: 30

White Heteroskedasticity-Consistent Standard Errors & Covariance

Variable

Coefficient

Std. Error

t-Statistic

C

2.357915

1.331251

1.771202

LOGLFPR

-0.136647

0.086096

-1.587140

LOGGFCG

-0.044904

0.057882

-0.775797

LOGEEXP

0.419361

0.801610

0.523148

R-squared

0.077666

Mean dependent var

Adjusted R-squared

-0.028757

S.D. dependent var

S.E. of regression

0.425489

Akaike info criterion

Sum squared resid

4.707053

Schwarz criterion

Log likelihood

-14.78612

F-statistic

Durbin-Watson stat

1.657983

Prob(F-statistic)

## Weighted Least Square Method

Dependent Variable: LOGRGDP

Method: Least Squares

Date: 01/16/12 Time: 12:47

Sample: 1981 2010

Included observations: 30

Weighting series: 5

Variable

Coefficient

Std. Error

t-Statistic

C

2.357915

1.439910

1.637543

LOGLFPR

-0.136647

0.198686

-0.687754

LOGGFCG

-0.044904

0.069065

-0.650178

LOGEEXP

0.419361

0.645301

0.649868

Weighted Statistics

R-squared

0.077666

Mean dependent var

Adjusted R-squared

-0.028757

S.D. dependent var

S.E. of regression

0.425489

Akaike info criterion

Sum squared resid

4.707053

Schwarz criterion

Log likelihood

-14.78612

F-statistic

Durbin-Watson stat

1.657983

Prob(F-statistic)

Unweighted Statistics

R-squared

0.077666

Mean dependent var

Adjusted R-squared

-0.028757

S.D. dependent var

S.E. of regression

0.425489

Sum squared resid

Durbin-Watson stat

1.657983

## Detection of Multicollinearity

## High R² but significant t ratios

R² is very low in Log model i.e. 0.077666 while all of the t statistics are statistically insignifcant while F statistics is also in significant. It means there is not multicollinearity.

## Correlation matrix

## Coefficient Covariance Matrix

C

LOGEDUEX

LOGGFCG

C

2.073342

-0.629216

-0.064762

LOGEDUEX

-0.629216

0.416413

0.009895

LOGGFCG

-0.064762

0.009895

0.004770

LOGLFPR

-0.176913

0.037209

-0.001042

The above matrix results reveal that there is not multicollinearity because all of the cross sectional values are significantly low.

## Auxilary Regression

Below are the results of auxiliary regressions (i.e. regressing each independent variable on remaining regressors one by one)

Model’s R² = 0.07766

## Dependent Variable

## R²

## Logeduexp

0.144137

## Loggfccg

0.070811

## Loglfpr

0.104947

We can see after running auxiliary regressions that two R² are greater than models R² (applying rule of thumb) which states that there is some multicollinearity.

## Remedies of Multicollinearity

## Dropping a variable and specification bias

Below are the results of dropping loggfcg from the model but still we can see that there is no significant increase in t-stat of logeduexp. Therefore we can say that dropping a variable will not be a good solution.

Dependent Variable: LOGY

Method: Least Squares

Date: 01/18/12 Time: 20:56

Sample: 1981 2010

Included observations: 30

Variable

Coefficient

Std. Error

t-Statistic

C

1.748246

1.080990

1.617263

LOGEDUEXP

0.512516

0.622431

0.823409

LOGLFPR

-0.146456

0.195983

-0.747287

R-squared

0.062670

Mean dependent var

Adjusted R-squared

-0.006762

S.D. dependent var

S.E. of regression

0.420915

Akaike info criterion

Sum squared resid

4.783585

Schwarz criterion

Log likelihood

-15.02805

F-statistic

Durbin-Watson stat

1.637438

Prob(F-statistic)

By increasing the number of variable or increasing the sample size, multicollinearity can be decreased.

## Detection of Autocorrelation

## Graphical Method

From the above graph we can see a systematic relationship among the residual terms. Therefore there are chances of autocorrelation.

## The runs test

## (+++)(-)(++++)(--)(++)(---)(+)(------)(++++++)(-)(+)

N1= 17

N2 = 13

Runs = 11

## Mean: E(R) = {(2N1 N2)/N} +1 = 15.7

## Variance: (σ)2R = {2N1N2(2N1N2 – N)}/{N2 (N-1)} = 6.97

## Standard Deviation: σ = 2.64

Prob[E(R) – 1.96σR < R < E(R) +1.96σR ]

Prob[10.525 < 11< 20.874]

Hence do not reject the hypothesis that the residuals in the model are random. Since number runs are many therefore there is a negative auto correlation.

## Durbin – Watson d Test

n = 30

k = 3

Durbin – Watson d stat: 1.657983

dL = 1.006 and du = 1.421

Below is the decision table:

Since d – stat is greater than du and less than 4 – du. Therefore there is no auto correlation positive or negative.

## Remedies of Autocorrelation

## Newey West Method

Dependent Variable: LOGY

Method: Least Squares

Date: 01/16/12 Time: 02:45

Sample: 1981 2010

Included observations: 30

Newey-West HAC Standard Errors & Covariance (lag truncation=3)

Variable

Coefficient

Std. Error

t-Statistic

C

2.357915

1.627020

1.449223

LOGEDUEXP

0.419361

0.908281

0.461708

LOGGFCG

-0.044904

0.081449

-0.551319

LOGLFPR

-0.136647

0.085849

-1.591711

R-squared

0.077666

Mean dependent var

Adjusted R-squared

-0.028757

S.D. dependent var

S.E. of regression

0.425489

Akaike info criterion

Sum squared resid

4.707053

Schwarz criterion

Log likelihood

-14.78612

F-statistic

Durbin-Watson stat

1.657983

Prob(F-statistic)

Comparing original model with Newey-West model we find that estimated coefficients and R2 are same, but HAC standard errors are much greater than results of original model’s standard errors and therefore HAC t ratios are much smaller that original t ratios. This shows that original model has underestimated the true standard errors.

## Incremental” or “Marginal” Contribution of an Explanatory Variable

Date: 01/16/12 Time: 02:17

Sample: 1981 2010

Included observations: 30

Variable

Coefficient

Std. Error

t-Statistic

C

1.745527

1.120494

1.557819

LOGEDUEXP

0.548159

0.611472

0.896458

LOGGFCG

-0.048511

0.068190

-0.711409

R-squared

0.060886

Mean dependent var

Adjusted R-squared

-0.008678

S.D. dependent var

S.E. of regression

0.421316

Akaike info criterion

Sum squared resid

4.792686

Schwarz criterion

Log likelihood

-15.05656

F-statistic

Durbin-Watson stat

1.593307

Prob(F-statistic)

Date: 01/16/12 Time: 02:23

Sample: 1981 2010

Included observations: 30

Variable

Coefficient

Std. Error

t-Statistic

C

1.748246

1.080990

1.617263

LOGEDUEXP

0.512516

0.622431

0.823409

LOGLFPR

-0.146456

0.195983

-0.747287

R-squared

0.062670

Mean dependent var

Adjusted R-squared

-0.006762

S.D. dependent var

S.E. of regression

0.420915

Akaike info criterion

Sum squared resid

4.783585

Schwarz criterion

Log likelihood

-15.02805

F-statistic

Durbin-Watson stat

1.637438

Prob(F-statistic)

We can see that dropping variables one by one is not as such creating any difference on over all results.

## Chow Test

Dependent Variable: LOGY

Method: Least Squares

Date: 01/18/12 Time: 23:32

Sample: 1981 2001

Included observations: 21

Variable

Coefficient

Std. Error

t-Statistic

C

40.00346

47.66441

0.839273

LOGEDUEXP

-0.169205

0.785097

-0.215521

LOGGFCG

-0.404357

0.135660

-2.980671

LOGLFPR

-8.510342

11.73128

-0.725440

R-squared

0.427625

Mean dependent var

Adjusted R-squared

0.326618

S.D. dependent var

S.E. of regression

0.363422

Akaike info criterion

Sum squared resid

2.245285

Schwarz criterion

Log likelihood

-6.322962

F-statistic

Durbin-Watson stat

2.679053

Prob(F-statistic)

Dependent Variable: LOGY

Method: Least Squares

Date: 01/18/12 Time: 23:37

Sample: 2002 2010

Included observations: 9

Variable

Coefficient

Std. Error

t-Statistic

C

2.633200

3.325530

0.791814

LOGEDUEXP

3.022314

1.159511

2.606542

LOGGFCG

-0.202077

0.196586

-1.027932

LOGLFPR

-0.116766

0.151969

-0.768355

R-squared

0.749394

Mean dependent var

Adjusted R-squared

0.599030

S.D. dependent var

S.E. of regression

0.228506

Akaike info criterion

Sum squared resid

0.261074

Schwarz criterion

Log likelihood

3.160337

F-statistic

Durbin-Watson stat

2.105995

Prob(F-statistic)

Sample: 1981 2010

Included observations: 30

Variable

Coefficient

Std. Error

t-Statistic

C

2.357915

1.439910

1.637543

LEDUEXP

0.419361

0.645301

0.649868

LGFCG

-0.044904

0.069065

-0.650178

LLFPR

-0.136647

0.198686

-0.687754

R-squared

0.077666

Mean dependent var

Adjusted R-squared

-0.028757

S.D. dependent var

S.E. of regression

0.425489

Akaike info criterion

Sum squared resid

4.707053

Schwarz criterion

Log likelihood

-14.78612

F-statistic

Durbin-Watson stat

1.657983

Prob(F-statistic)

RSS1 = 2.245285

RSS2 = 0.261074

RSSR = 4.707053

RSSUR = RSS1 + RSS2 = 2.5

F = (RSSR − RSSUR)/k

(RSSUR)/(n1 + n2 − 2k)

After calculation we get:

F = 0.55/0.113

F = 4.86

F tab = 2.82 with Confidence Interval of 0.95

Since Fcal > Ftab

Therefore we do not reject the null hypothesis of parameter stability (i.e. no structural change).

## Log – Linear Model

Dependent Variable: LOGY

Method: Least Squares

Date: 01/19/12 Time: 00:01

Sample: 1981 2010

Included observations: 30

Variable

Coefficient

Std. Error

t-Statistic

C

1.188664

0.746652

1.591992

EDUEXP

0.187304

0.294390

0.636245

GFCG

3.60E-08

1.24E-07

0.289489

LFPR

-0.000844

0.000998

-0.845446

R-squared

0.057738

Mean dependent var

Adjusted R-squared

-0.050985

S.D. dependent var

S.E. of regression

0.430061

Akaike info criterion

Sum squared resid

4.808755

Schwarz criterion

Log likelihood

-15.10677

F-statistic

Durbin-Watson stat

1.655873

Prob(F-statistic)

We can see that results related tp significane obtained from Log model are comparatively better than results of Log Linear model.

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