The consequence of educational outgo on economic growing is one of the cardinal issues in economic literature. Educational outgo is portion of public outgo and since after World War II populace outgos have increased in developed and developing states. Over clip, many economic growing theories and theoretical accounts ( such as Romer, 1990 and Lucas, 1988 ) have developed associating instruction and economic growing. The belief, that instruction promotes growing has led authoritiess of many developing states to put in the instruction sector. Even the theoretical literature besides provides a backup for such a policy ( Pissarides, 2000 ) . However, the empirical literature has failed to set up a robust relationship between instruction outgos and growing. India has been no exclusion. Harmonizing to the economic theory, we will anticipate a positive causal relationship to be between the two.

Economic growing is the addition in value of the goods and services produced by an economic system. It is conventionally measured as the per centum rate of addition in existent gross domestic merchandise, or GDP. Growth is normally calculated in existent footings, i.e. inflation-adjusted footings, in order to sack out the consequence of rising prices on the monetary value of the goods and services produced. In economic sciences, “ economic growing ” or “ economic growing theory ” typically refers to growing of possible end product, i.e. , production at “ full employment, ” which is caused by growing in aggregative demand or observed end product. As economic growing is measured as the one-year per centum alteration of National Income it has all the advantages and drawbacks of that degree variable. But people tend to attach a peculiar value to the one-year per centum alteration, possibly since it tells them what happens to their wage cheque.

The purpose of this paper is to set up a relation between instruction and economic growing in Pakistan. The survey explores that betterment in instruction bring economic growing in Pakistan. There has been difference among researches about the positive or negative relationship between educational outgo and economic growing while some surveies indicates no impart of instruction on economic growing. Time series informations from the period of 1981-2010 is used for the analysis and co-integration and mistake rectification theoretical accounts are used to find the long and short tally relationship of instruction and economic growing. In this survey, an effort is made to find the significance of instruction in economic development in Pakistan. The information has been taken from Misinstry of Education ‘s web site, Pakistan Economic Survey assorted issues and web site of World Bank.

## Education Sector in Pakistan

Pakistan is an international outlier in footings of gender spreads in instruction. The instruction system in Pakistan is mostly distributed into five degrees: primary ( grades one through five ) ; middle ( classs six through eight ) ; high ( classs nine and 10s ; intermediate ( classs eleven and twelve, taking to a Higher Secondary ( School ) Certificate ( HSC ) ; and university plans taking to undergraduate and graduate grades.

To augment the human capital different authoritiess in Pakistan have taken legion stairss to better the instruction and educational criterions. Harmonizing to the Education Statistics of 2008-9 Shows that literacy rate was high in urban countries ( 74 % ) so the rural countries ( 48 % ) . Literacy rate in work forces are more the adult females ‘s, as for work forces ( 69 % ) compared to adult females ( 45 % ) . Province wise literacy rate indicates, “ Literacy rate in Punjab is ( 59 % ) , Sindh, ( 59 % ) , Khyber Pakhtunkhwa ( 50 % ) and Balochistan at ( 45 % ) ” . Entire big literacy rate show the figure of 57 % . Preaˆ?Primary Education is a critical component of Early Childhood Education. An addition of 2.2 % enrolment rate is estimated for the twelvemonth 2009-2010. 156, 653 Primary Schools with 465,334 Teaching staff are working in Pakistan. An addition of 0.6 % in Primary registration ( 18.468 million ) in 2009 comparison to ( 18.360 million ) in 2008. Statistics indicates that, 24,322 Secondary Schools with 439,316 Teaching staff are working in Pakistan. Furthermore, the enrolment rate of 2.9 % ( 2.556 million ) is observed in 2009-2010.

Pakistan has one of the lowest ratios in the universe, of people holding entree to higher instruction in the state. National Commission for Human Development ( NCHD ) has planned to literate 82,500 grownup literacy centres in three old ages ( 2009-12 ) to increase the literacy rate, nevertheless so far 26,000 literacy centres have been opened. Merely 5.1 per cent of people aged 17-23 old ages are presently enrolled in higher instruction in Pakistan.

Pakistan is blessed with natural resources and gifted persons. Due to low employment chances, and deficient research activities, a figure of professionals have left Pakistan for the interest of healthier career and life. To undertake this job of encephalon drain, during last few old ages authoritiess have taken legion stairss to advance research activities and better the quality of installations in instruction institutes. Many scholarships plans have been offered throughout the twelvemonth for higher instruction, including clever scholarship, particular scholarship plan for the pupils of Fata and Balochistan. At present 3,237 pupils are analyzing in HEC recognized universities. HEC has sent about 2,600 pupils for surveies abroad under different foreign scholarship plans. In order to better and advance research activities, 20 Research Laboratories have been established in major universities.

## Literature Review

Education is considered as a tool for economic promotion of any state. It is nem con accepted that states holding developed human accomplishments and capablenesss tend to come on briskly. Education plays an indispensable portion in developing human capital and speed uping productiveness. The interrelatedness between instruction and economic growing has been discussed since antediluvian Greece. Adam Smith and the classical economic experts emphasized the importance of investing in human accomplishments. In modern-day times when the focal point is on the ‘knowledge economic system ‘ the function of instruction becomes all the more of import in the development of human capital. Several surveies have investigated the relationship between economic growing and instruction such as Psaharoupolous, 1988 ; De Meulmester et. al. , 1995 ; Jorgenson and Fraumeni, 1998. Their starting point was ever the root of the economic growing itself. Over a period of clip research workers have found a that correlativities exist across states between economic growing rates and schooling registration rates including registration in higher instruction, another group of research workers such as De Meulmester et. Al. ( 1995 ) , utilizing more sophisticated econometric techniques, found that this relationship is non ever a direct one.

Few empirical surveies have tried to analyze the relation between investing in human capital and economic growing. The relationship has been tested for states 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 consequences from the above mentioned documents indicate that instruction outgos do impact growing positively.

Harmonizing to Bils and Klenow, ( 2000 ) , “ Countries holding high rate of registration in schools made faster growing in per capita income because high registration rate causes rapid betterment in productiveness ” . Hanushek and Kimko ( 2000 ) show that quality of instruction have a singular impact on productiveness and national growing rates.

Chandra ( 2010 ) has tested for a causal relationship between instruction investings and economic growing for India for the clip period 1951-2009 utilizing additive and non-linear Granger causality methods. He found that there is bi-directional causality between instruction disbursement and GDP for India. Therefore, it can be seen that overall, the empirical grounds sing this relationship for India excessively is rather assorted.

Krueger and Lindahl ( 2000 ) say that a state which is bettering its instruction policy is likely to alter or better other economic policies as good which will heighten its growing. That ‘s why it can be really hard to divide the consequence of instruction policy from that of the other policies. If we look at the South East Asiatic states with respect to the benefits of higher instruction for a state ‘s economic system, many perceivers attribute India ‘s spring onto the universe economic phase as stemming from its decades-long successful attempts to supply high-quality, technically oriented third instruction to a important figure of its citizens ( World Bank, 2004 ) .

## Summary of related articles

## Year

## Survey

## Time Period

## Dependent variable

## Independent Variable

## Data beginning

## Methodology/ Technique

2011

Do Public Education Expenditures Really Lead to Economic

Growth? Evidence from Turkey

1973 – 2009

GDP

Educational Outgo

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 indexs in different governments of Pakistan

1978-2008

Literacy rate

Outgo on instruction, Entire registration, entire establishments.

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

Bank of Pakistan Annual Reports and 50 Old ages of Pakistan in Statistics.

Multiple arrested development, Post hoc and Ginni coefficient.

2008

Impact of Higher Education on Economic

Growth of Pakistan

1972-2009

GDP

Registration in Higher Education, Higher

Education Outgo, Employment Rate, Labor Force, Labor Force Engagement

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

map, in its stochastic signifier, Time Series Analysis

2011

Relationship between Education and Economic Growth in

Pakistan: A clip series analysis.

1980-2009

Real GDP

Government outgo on instruction on instruction as % of GDP, Labour force engagement rate, Gross fixed capital formation, Error Correction Term

Education Statisticss of 2008-9

Economic Survey of Pakistan

Multiple Regression utilizing production Function, co-integration and vector mistake

rectification techniques for period 1980-2009

2011

Does Government Expenditure on

Education Promote Economic Growth?

An Econometric Analysis

1950 – 2009

GDP

Educational Outgo

hypertext transfer protocol: //www.mospi.gov.in,

hypertext transfer protocol: //www.education.nic.in/secondary.html

The Linear Granger Causality Test.

Vector Autoregression ( VAR )

## Hypothesis

After making literature reexamine a below hypothesis is developed to look into in Pakistani scenario:

H0: There is a positive relationship between educational outgo and economic growing of Pakistan.

As per literature reappraisal and old work above hypothesis has non been rejected. This research will look into the hypothesis for the clip period between 1981-2010.

## Methodology

The theoretical account used in this paper is based on sum end product map:

LnY = I± + I?1Ln ( EDUEXP ) + I?2Ln ( LFPR ) + I?3Ln ( GFCF ) + Aµi

List of variables with abbreviations:

Ln = Natural Logarithm

Y = Real GDP

EDUEXP = authorities outgo on instruction on instruction as % of GDP

LFPR = Labor force engagement rate

GFCF = gross fixed capital formation

Aµi = Error Correction Term

Real GDP is state ‘s entire end product of goods and services, adjusted for monetary value alterations.

Educational Outgo is authorities outgo in stead of instruction in state. It is portion of Human Capital which refers to educational and wellness outgo, the range of this research is to happen the impact of instruction on economic growing.

Labor Force is a cardinal index of economic system specially states holding big population or labour intensive states. It refers to the figure of skilled workers available to work.

Gross fixed capital formation or “ GFCF ” is a macroeconomic construct used as step of the net investing in an economic system in “ fixed capital assets ” during one fiscal twelvemonth.

## Analysis of the Model

To look into the hypothesis arrested development utilizing OLS technique was run, below are the consequences of running arrested development on theoretical account:

LnY = I± + I?1Ln ( EDUEXP ) + I?2Ln ( LFPR ) + I?3Ln ( GFCF ) + Aµi

Sample: 1981 2010

Included observations: 30

Variable

Coefficient

Std. Mistake

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

Average dependant volt-ampere

Adjusted R-squared

-0.028757

S.D. dependant volt-ampere

S.E. of arrested development

0.425489

Akaike info standard

Sum squared resid

4.707053

Schwarz standard

Log likeliness

-14.78612

F-statistic

Durbin-Watson stat

1.657983

Prob ( F-statistic )

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

## Interpretation of Consequences

As per theoretical account Y-intercept is 2.36 which mean that Real GDP will hold 2.36 growing when all of the variables of our theoretical account are ‘0 ‘ This is because GDP does non depend merely on instruction even if there is no outgo on instruction.

Coefficient of EDUEXP is positive which means that 1 % alteration in EDUEXP will convey on mean 0.41 % alteration in Real GDP.

Coefficients of GFCG and LFPR are negative but as per priori they are supposed to be positive. This job will be catered in ulterior portion of this study.

## Significance of Coefficients

Individual coefficients of all three independent variables are statistically undistinguished.

## Coefficient of Determination ( RA? )

Value of RA? is really low which states that about 7.76 % fluctuation in Real GDP is explained by Government outgo on instruction as % of GDP, Labor force engagement rate, Gross fixed capital formation.

The above graph tells us that remainders are right skewed and from the JB value of 4.49 with chance of 0.10 suggest that hypothesis that mistake footings are usually distributed is non true. This can go on because of our little sample size of 30 observations.

The above graph shows that existent values are non good fitted with the estimated which is the ground of low R2.

## Decision

The above arrested development analysis and its reading do non formalize that instruction and economic growing has a long term relationship. Few consequences are against priori as good. In most of old researches and literature available instruction has brought an economic growing in a given state.

We can besides state that in short tally instruction does non hold relationship with economic growing because our sample size was merely 30. Other dedection that can be made is since in Pakistan authorities has failed to make employment chances hence after finishing instruction people do non happen occupations to lend to the national economic system and at times people go abroad doing encephalon drain in Pakistan.

Therefore authorities must pull international companies and local investors every bit good to make such ventures that could take to the employment chances and finally increase in economic growing of Pakistan. Spending merely on instruction will non lend as such towards economic growing, there must be a system to suit and use those educated people for the best involvement of state ‘s economic system.

## Hetrosedasticity Testing

## Informal Method – Graphic

The above graph shows that seemingly there is some systematic form followed by u2 values with the fluctuation in Y. This gives an indicant that there is hetrosedastcitiy.

## Formal Method

## Park Test

Sample: 1981 2010

Included observations: 30

Variable

Coefficient

Std. Mistake

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

Average dependant volt-ampere

Adjusted R-squared

0.438859

S.D. dependant volt-ampere

S.E. of arrested development

1.519611

Akaike info standard

Sum squared resid

60.03968

Schwarz standard

Log likeliness

-52.97528

F-statistic

Durbin-Watson stat

2.020812

Prob ( F-statistic )

We can see that there is non statistically important relationship therefore there is no opportunity 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. Mistake

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

Average dependant volt-ampere

Adjusted R-squared

-0.001908

S.D. dependant volt-ampere

S.E. of arrested development

1.018895

Akaike info standard

Sum squared resid

26.99182

Schwarz standard

Log likeliness

-40.98320

F-statistic

Durbin-Watson stat

2.071385

Prob ( F-statistic )

This trial is really much related to Park ‘s Test. Since there is no relationship between u term and regressors therefore we will formalize the consequences of park ‘s Test.

## Spearman ‘s rank Correlation Test

Spearman ‘s Rank correlativity

Residual

Ranking

RGDP

Ranking

vitamin 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 [ a?‘dA?/ N ( nA?

src =0.16

T = R a?sn-2 / a?s1-rA?

T = 0.847

df=28

T value is non important at 10 % degree of significance. Therefore there is no hetrosedasticity.

## Goldfeld-Quant Trial

First 13 observations

Dependent Variable: LOGGDP

Method: Least Squares

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

Sample ( adjusted ) : 1981 1993

Included observations: 13 after seting end points

Variable

Coefficient

Std. Mistake

t-Statistic

C

2.651573

0.681057

3.893319

LOGEDUEXP

-1.257336

0.922248

-1.363338

R-squared

0.144548

Average dependant volt-ampere

Adjusted R-squared

0.066779

S.D. dependant volt-ampere

S.E. of arrested development

0.335531

Akaike info standard

Sum squared resid

1.238391

Schwarz standard

Log likeliness

-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 seting end points

Variable

Coefficient

Std. Mistake

t-Statistic

C

0.049376

2.287818

0.021582

LOGEDUEXP

1.555899

2.381743

0.653260

R-squared

0.037346

Average dependant volt-ampere

Adjusted R-squared

-0.050167

S.D. dependant volt-ampere

S.E. of arrested development

0.430289

Akaike info standard

Sum squared resid

2.036634

Schwarz standard

Log likeliness

-6.397470

F-statistic

Durbin-Watson stat

0.919369

Prob ( F-statistic )

I» = RSSa‚‚ / df

RSSaµ? / df

=1.64

Since it does non transcend the crticial value therefoe we can state there is no hetrosedasticity in mistake footings.

## White Trial

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. Mistake

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

Average dependant volt-ampere

Adjusted R-squared

-0.115200

S.D. dependant volt-ampere

S.E. of arrested development

0.276470

Akaike info standard

Sum squared resid

1.758020

Schwarz standard

Log likeliness

-0.013017

F-statistic

Durbin-Watson stat

2.310125

Prob ( F-statistic )

n. RA? = 3.4659, which has asymptotically a qi 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 intents we can reason on the footing of white trial that there is no heteroscedasticity.

## Remedial Measures

## White ‘s Heterosedasticity- Consistent Discrepancies and Standard Mistakes

Dependent Variable: LOGRGDP

Method: Least Squares

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

Sample: 1981 2010

Included observations: 30

White Heteroskedasticity-Consistent Standard Errors & A ; Covariance

Variable

Coefficient

Std. Mistake

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

Average dependant volt-ampere

Adjusted R-squared

-0.028757

S.D. dependant volt-ampere

S.E. of arrested development

0.425489

Akaike info standard

Sum squared resid

4.707053

Schwarz standard

Log likeliness

-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

Burdening series: 5

Variable

Coefficient

Std. Mistake

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

Leaden Statisticss

R-squared

0.077666

Average dependant volt-ampere

Adjusted R-squared

-0.028757

S.D. dependant volt-ampere

S.E. of arrested development

0.425489

Akaike info standard

Sum squared resid

4.707053

Schwarz standard

Log likeliness

-14.78612

F-statistic

Durbin-Watson stat

1.657983

Prob ( F-statistic )

Unweighted Statisticss

R-squared

0.077666

Average dependant volt-ampere

Adjusted R-squared

-0.028757

S.D. dependant volt-ampere

S.E. of arrested development

0.425489

Sum squared resid

Durbin-Watson stat

1.657983

## Detection of Multicollinearity

## High RA? but important t ratios

RA? is really low in Log theoretical account i.e. 0.077666 while all of the T statistics are statistically insignifcant while F statistics is besides in important. It means there is non 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 consequences reveal that there is non multicollinearity because all of the cross sectional values are significantly low.

## Auxilary Arrested development

Below are the consequences of subsidiary arrested developments ( i.e. regressing each independent variable on staying regressors one by one )

Model ‘s RA? = 0.07766

## Dependent Variable

## RA?

## Logeduexp

0.144137

## Loggfccg

0.070811

## Loglfpr

0.104947

We can see after running subsidiary arrested developments that two RA? are greater than theoretical accounts RA? ( using regulation of pollex ) which states that there is some multicollinearity.

## Redresss of Multicollinearity

## Droping a variable and specification prejudice

Below are the consequences of dropping loggfcg from the theoretical account but still we can see that there is no important addition in t-stat of logeduexp. Therefore we can state that dropping a variable will non 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. Mistake

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

Average dependant volt-ampere

Adjusted R-squared

-0.006762

S.D. dependant volt-ampere

S.E. of arrested development

0.420915

Akaike info standard

Sum squared resid

4.783585

Schwarz standard

Log likeliness

-15.02805

F-statistic

Durbin-Watson stat

1.637438

Prob ( F-statistic )

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

## Detection of Autocorrelation

## Graphic Method

From the above graph we can see a systematic relationship among the residuary footings. Therefore there are opportunities of autocorrelation.

## The tallies trial

## ( +++ ) ( – ) ( ++++ ) ( — ) ( ++ ) ( — – ) ( + ) ( — — — ) ( ++++++ ) ( – ) ( + )

N1= 17

N2 = 13

Runs = 11

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

## Discrepancy: ( I? ) 2R = { 2N1N2 ( 2N1N2 – Nitrogen ) } / { N2 ( N-1 ) } = 6.97

## Standard Deviation: I? = 2.64

Prob [ E ( R ) – 1.96I?R & lt ; R & lt ; E ( R ) +1.96I?R ]

Prob [ 10.525 & lt ; 11 & lt ; 20.874 ]

Therefore do non reject the hypothesis that the remainders in the theoretical account are random. Since figure tallies are many hence there is a negative car correlativity.

## Durbin – Watson d Test

n = 30

K = 3

Durbin – Watson d stat: 1.657983

deciliter = 1.006 and du = 1.421

Below is the determination tabular array:

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

## Redresss 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 & A ; Covariance ( lag truncation=3 )

Variable

Coefficient

Std. Mistake

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

Average dependant volt-ampere

Adjusted R-squared

-0.028757

S.D. dependant volt-ampere

S.E. of arrested development

0.425489

Akaike info standard

Sum squared resid

4.707053

Schwarz standard

Log likeliness

-14.78612

F-statistic

Durbin-Watson stat

1.657983

Prob ( F-statistic )

Comparing original theoretical account with Newey-West theoretical account we find that estimated coefficients and R2 are same, but HAC standard mistakes are much greater than consequences of original theoretical account ‘s standard mistakes and hence HAC T ratios are much smaller that original t ratios. This shows that original theoretical account has underestimated the true standard mistakes.

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

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

Sample: 1981 2010

Included observations: 30

Variable

Coefficient

Std. Mistake

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

Average dependant volt-ampere

Adjusted R-squared

-0.008678

S.D. dependant volt-ampere

S.E. of arrested development

0.421316

Akaike info standard

Sum squared resid

4.792686

Schwarz standard

Log likeliness

-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. Mistake

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

Average dependant volt-ampere

Adjusted R-squared

-0.006762

S.D. dependant volt-ampere

S.E. of arrested development

0.420915

Akaike info standard

Sum squared resid

4.783585

Schwarz standard

Log likeliness

-15.02805

F-statistic

Durbin-Watson stat

1.637438

Prob ( F-statistic )

We can see that dropping variables one by one is non as such making any difference on over all consequences.

## Chow Test

Dependent Variable: LOGY

Method: Least Squares

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

Sample: 1981 2001

Included observations: 21

Variable

Coefficient

Std. Mistake

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

Average dependant volt-ampere

Adjusted R-squared

0.326618

S.D. dependant volt-ampere

S.E. of arrested development

0.363422

Akaike info standard

Sum squared resid

2.245285

Schwarz standard

Log likeliness

-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. Mistake

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

Average dependant volt-ampere

Adjusted R-squared

0.599030

S.D. dependant volt-ampere

S.E. of arrested development

0.228506

Akaike info standard

Sum squared resid

0.261074

Schwarz standard

Log likeliness

3.160337

F-statistic

Durbin-Watson stat

2.105995

Prob ( F-statistic )

Sample: 1981 2010

Included observations: 30

Variable

Coefficient

Std. Mistake

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

Average dependant volt-ampere

Adjusted R-squared

-0.028757

S.D. dependant volt-ampere

S.E. of arrested development

0.425489

Akaike info standard

Sum squared resid

4.707053

Schwarz standard

Log likeliness

-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 a?’ RSSUR ) /k

( RSSUR ) / ( n1 + n2 a?’ 2k )

After computation we get:

F = 0.55/0.113

F = 4.86

F check = 2.82 with Confidence Interval of 0.95

Since Fcal & gt ; Ftab

Therefore we do non reject the void hypothesis of parametric quantity stableness ( i.e. no structural alteration ) .

## 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. Mistake

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

Average dependant volt-ampere

Adjusted R-squared

-0.050985

S.D. dependant volt-ampere

S.E. of arrested development

0.430061

Akaike info standard

Sum squared resid

4.808755

Schwarz standard

Log likeliness

-15.10677

F-statistic

Durbin-Watson stat

1.655873

Prob ( F-statistic )

We can see that consequences related tp significane obtained from Log theoretical account are relatively better than consequences of Log Linear theoretical account.