ASSIGNMENT OF ECONOMETRICS TOPIC the relationship between economic growth and school enrollment

National Economics University ASSIGNMENT OF ECONOMETRICS TOPIC The Relationship between Economic Growth and School Enrollment BFI 63 – GROUP 4 Lecturer Nguyen Hai Duong Student Name & ID Pham Huu Manh[.]

National Economics University

ASSIGNMENT OF ECONOMETRICS

TOPIC: The Relationship between Economic Growth and School Enrollment

BFI 63 – GROUP 4 Lecturer:

Nguyen Hai Duong

Student Name & ID:

Pham Huu Manh - 11213747 Nguyen Thi Kim Ngan - 11214216

Do Bao Ngoc - 11214288 Nguyen Mai Vinh - 11216262 Dang Thi Ha Mi - 11219454 Nguyen Thanh Vinh - 11216267 Cao Thi Phuong Uyen - 11219463 Nguyen Phuong Linh – 11213313

INTRODUCTION: 4

A PART 1: 5

I Basic Theory 5

II Review: 6

1 Research 1: 6

2 Research 2: 7

3 Research gap: 8

B PART 2: 9

I Method and data: 9

II Evaluate the functions of data: 9

1 Linear function 9

2 Logarithm function: 10

3 Semi Logarithm function: 11

4 Quadratic function 12

III Test of economical assumptions 13

1 Linear function: 13

2 Logarithm function 13

3 Semi Logarithm function 14

4 Quadratic function 15

IV Testing for the most efficient model: 16

1 RAMSEY TEST 16

a Linear function: 16

b Logarithm function 16

c Semi Logarithm function 17

d Quadratic function 17

2 WHITE TEST 18

a Linear function: 18

c Semi Logarithm function: 19

d Quadratic function: 19

3 Most selection criteria: 20

4 Interpret estimation of the most efficient 20

C PART 3 21

APPENDIX 24

This study aims to evaluate the factors that the influence of education on economicgrowth in different countries around the world The model is estimated using themethod of Ordinary Least Squares (OLS), employing data for the year 2018available on WorldBank, and using the econometric tools of Eview12 The samplesize consisted of 142 countries The evaluation identified that economic growth beaffected significant by education, including school enrollments: primary level,secondary level, tertiary level In particular, the estimated elasticities arestatistically remarkable and have the expected signs, and their values are inaccordance with the empirical literature

INTRODUCTION:

The activities of getting or acquiring general knowledge, learning process of basicsskills such as mathematics, geography and also developing elementaryunderstanding of some other subjects e.g., history, natural sciences, social sciences,and art, developing reasoning and judgmental mental power, and preparing oneself

or others intellectually for mature life School enrollment, primary, secondary andtertiary (% gross) has been taken as a proxy for primary, secondary and tertiaryeducation, respectively (Loening, 2005) The relationship between education andthe GDP is positive that shows education is a significant primary input factor forthe growth of an economy Barro (1991) argued that there is significant andpositive association between economic growth and the education Bils and Klenow(2000) argued that high enrollment rate causes rapid improvement in productivity;therefore, faster growth in per capita income (PCI) resulted in countries wherethere is high rate of enrollment in schools Hanushek and Kimko (2000) argued

that there is remarkable increase in productivity and national growth rates due tothe quality of the education.

This thesis aims to analyze the relationship between education and economicgrowth includes 142 countries in different continents With the following studieswill make accurate assertions about the important influence of education on thedevelopment of countries

A PART 1:

I Basic Theory

1 Input – output model:

GDPP = f (PRM, SEC, TER)

+ Output: GDPP: Gross Domestic Product Per Capita

+ Input : PRM: Gross School Enrollment Ratio Primary Level (%)

SEC: Gross School Enrollment Ratio Secondary Level (%)

TER: Gross School Enrollment Ratio Tertiary Level (%)

(3)

e) Result and discussion:

- There is a closer relationship between educational attainment andeconomic growth at the primary school level as compared to thesecondary and higher levels of education

2 Research 2:

 Research name: The Influence of Education on Economic Growth

 Author: ŞTEFAN CRISTIAN CIUCU, RALUCA DRAGOESCU

 Date: May 2014

a) Purpose of research: to analyze the effect of education on economicgrowth in  Bulgaria and Czech Republic, during the transition periodand to compare it to the situation in a  developed country theNetherlands

b) Method: the multiple regression model

c) Sample size: in all three countries (Bulgaria, Czech Republic and theNetherlands)

d) Model:

e) Result and discussion:

- The most important thing to be taken into consideration is thateducation quantity has an effect  on economic growth after someyears The graduates have to start their career in order to affect the economy of a country For this reason a time lag will be introduced inthe model The time lag for  primary education will be set to 10 yearsand the time lag for secondary education to 5 years

- Education has an influence on economic growth in both transitionand developed countries The level of influence varies and depends onother factors from country to country

3 Research gap:

a) Observation

- Research 1: 1 country: Turkey quite small

- Research 2: focus on 3 countries Bulgaria, Czech Republic and the Netherlands Quite small also

- Our research: includes 142 countries in different continents

b) Research purpose: 3 researchs have the same purpose, that is prove the impact

of eduction on economic growth We find some limitations of 2 researchs before:

 Research 1: The study has some limitations In Turkey, there have been some significant policy changes in both the economic and educational

sectors These policy changes, as well as international economic trends, mayhave impacted both economic growth and school enrollment patterns The data does not make it possible to take factors

 Reasearch 2: The study has limitation too The few data are used so the results not too much convincing

Therefore, our research aims to a diverse view considering influence of education on economic growth in several developed and developing

countries around the world which is identified by the following factors: gross school enrollment ratio in 3 levels: primary, secondary, tertiary

c) Methodology

 Research 1: used Toda-Yamamoto’s (1995) causality test It is the modified Wald (MWALD) test developed by Toda and Yamamoto

 Research 2: regression model

 Our research: OLS method

B PART 2:

I Method and data:

1 Method: OLS method

2 Data: The data is available online on World Development Indicators (WDI) website – the World Bank's premier compilation of cross-country comparable data

20.0977613077*TER + 𝑢

(107.5432)

n = 142, R2 = 0.312214, SSR = 5.84E+10

 Interpret estimation results:

- 𝛽0 = -1914.25600286 has shown that when other independentvariables equal 0, GDPP will equal to -1914.25600286 USD onaverage

- 𝛽1 = -247.677037229 has shown that when gross school enrollmentprimary level changes by 1%, GDPP will decrease by 247.677037229USD on average (other remain constant)

- 𝛽2 = 502.349750612 has shown that when gross school enrollmentsecondary level changes by 1%, GDPP will increase by502.349750612 USD on average (other remain constant).

- 𝛽3 = 20.0977613077 has shown that when gross school enrollmenttertiary level changes by 1%, GDPP will increase by 20.0977613077USD on average (other remain constant)

3 Semi Logarithm function:

LOG (GDPP) = 𝛽0 + 𝛽1PRM + 𝛽2SEC + 𝛽3TER+ 𝑢From the EViews result in table 2.3 (APPENDIX), we have a new linear function:

LOG(GDPP) = 8.2224560203 - 0.0257129079552*PRM + (0.815861) (0.007843)

0.0327100528963*SEC + 0.0113444825181*TER + 𝑢

(0.003968) (0.003771)

n = 142, R2 = 0.329034, SSR = 5.70E+10

 Interpret estimation results:

- 𝛽0 = 8.222 has shown that when other independent variables equal 0,GDPP will equal to 8.222 USD on average

- 𝛽1 = -0.0257 has shown that when gross school enrollment primarylevel changes by 1%, GDPP will decrease by 2.57% on average (otherremain constant)

- 𝛽2 = 0.0327 has shown that when gross school enrollment secondarylevel changes by 1%, GDPP will increase by 3.27% on average (otherremain constant)

- 𝛽3 = 0.0113 has shown that when gross school enrollment tertiarylevel changes by 1%, GDPP will increase by 1.13% on average (otherremain constant)

4 Quadratic function

From the EViews result in table 2.4 (APPENDIX), we have a new linear function:

GDPP = 16942.0173004 - 209.649882769*PRM - 82.505590253*SEC + (25211.23) (222.6880) (334.9384)

3.26898451751*(SEC)^2 + 43.4247617404*TER (1.763946) (107.3475)

n = 142, R2 = 0.329034, SSR = 5.70E+10

 Interpret estimation results:

- 𝛽0 = 16942.0173004 has shown that when other independentvariables equal 0, GDPP will equal to 16942.0173004 USD onaverage.

- 𝛽1 = -209.649882769 has shown that when gross school enrollmentprimary level changes by 1%, GDPP will decrease by 209.649882769USD on average (other remain constant)

- 𝛽2 = -82.505590253 has shown that when gross school enrollmentsecondary level changes by 1%, GDPP will decrease first by82.505590253 USD on average

- 𝛽3 = 3.26898451751 has shown that when gross school enrollmentsecondary level changes by 1%^2units, GDPP will increase by3.26898451751 USD on average (other remain constant)

- 𝛽4 = 43.4247617404 has shown that when gross school enrollmenttertiary level changes by 1%, GDPP will increase by 43.4247617404USD on average (other remain constant)

III Test of economical assumptions

1 Linear function:

GDPP = 𝛽0 + 𝛽1PRM + 𝛽2SEC + 𝛽3TER+ 𝑢From the EViews result in table 2.1 (APPENDIX), we have:

3 Semi Logarithm function

LOG (GDPP) = 𝛽0 + 𝛽1PRM + 𝛽2SEC + 𝛽3TER+ 𝑢From the EViews result in table 2.3 (APPENDIX), we have:

From the EViews result in table 2.4 (APPENDIX), we have:

- GDPP not influenced by TER

IV Testing for the most efficient model:

=>P-value < α => We reject Ho, that means (2) has incorrect form or it is biased.

c Semi Logarithm function

P-value = 0.0509

α = 0.05

=>P-value > α => We accept Ho, that means (4) has correct form or it is unbiased

2 WHITE TEST

Following results, we want to know whether the variance of the errors in a

regression model is constant or not, therefore, we use WHITE test

a Linear function:

Hypothesis pair: {H0:homoskedasticity

H1:heteroskedasticity

Heteroskedasticity Test: White

Null hypothesis: Homoskedasticity

F-statistic 2.606309     Prob F(9,132) 0.0084

Obs*R-squared 21.42629    Prob Chi-Square(9) 0.0109

Scaled explained SS 187.0351    Prob Chi-Square(9) 0.0000

Test Equation:

Dependent Variable: RESID^2

Method: Least Squares

P-value = 0.0084

α = 0.05

=> P-value < α => We reject H0, that means (1) is heteroskedasticity

o The model is Homoskedasticity.

c Semi Logarithm function:

Hypothesis pair: {H0: Homoskedasticity

d Quadratic function:

Hypothesis pair: {H0:homoskedasticity

H1:heteroskedasticity 

Heteroskedasticity Test: White

Null hypothesis: Homosckedasticity

F-statistic 3.187045     Prob F(13,128) 0.0004

Obs*R-squared 34.72367     Prob Chi-Square(13) 0.0009

Scaled explained SS 319.8923     Prob Chi-Square(13) 0.0000

P-value = 0.0004

α = 0.05

=> P-value < α => We reject H0, that means (3) is heteroskedasticity

3 Most selection criteria:

Because all three models are unbiased and heteroskedasticity, we use five criteria

to select the most efficient model

4 Interpret estimation of the most efficient

LOG(GDPP) = 8.222 - 0.026*PRM + 0.033*SEC + 0.011*TER

(0.816) (0.008) (0.004) (0.004)

From model (2) - Semi Logarithm function:

equal to 8.222 USD

variables constant, on average, GDPP will decrease by 2.6%

variables constant, on average, SEC will increase by 3.3%

variables constant, on average, TER will increase by 1.1%

independent variables in this regression model

C PART 3

COMMUNICATION

In this study, we tested and compared 4 models:

(1) Linear function: GDPP = 𝛽0 + 𝛽1PRM + 𝛽2SEC + 𝛽3TER+ 𝑢

(2) Logarithm function: LOG(GDPP) = 𝛽0 + 𝛽1LOG(PRM) +

We employed the Ramsey RESET test to see whether our models were unbiased

The result suggested that 3 models (1), (3), (4) had its correct form and model (4)

is biased Next, the WHITE test was used to gauge whether the variance of the

errors in a regression model is constant Since 3 models were found to be unbiased

and heteroskedasticity, we used 5 criteria that are R2, Adjusted R2, AIC, HQ, SC

to find out the most efficient model

According to the result was showed at table 3.1, the most efficient model was model (2) – semi logarithm function

In the econometric model used, education in primary, secondary and tertiary have impact on economic growth This means that these countries should be adjust teaching methods in every schools to suitable for the student’s learning style The general conclusion is that policy-makers have to draw and apply a education policy employing diligence, timely planning, responsibility, and realism.

Table Data Collection

TABLE 2.1

TABLE 2.2

TABLE 2.3

TABLE 2.4