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 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 ABSTRACT: INTRODUCTION: A PART 1: .5 I Basic Theory II Review: Research 1: Research 2: Research gap: B PART 2: .9 I Method and data: II Evaluate the functions of data: Linear function Logarithm function: 10 Semi Logarithm function: 11 Quadratic function .12 III Test of economical assumptions .13 Linear function: 13 Logarithm function 13 Semi Logarithm function 14 Quadratic function .15 IV Testing for the most efficient model: 16 RAMSEY TEST 16 a Linear function: 16 b Logarithm function 16 c Semi Logarithm function 17 d Quadratic function 17 WHITE TEST 18 a Linear function: 18 b Logarithm function: 18 c Semi Logarithm function: 19 d Quadratic function: 19 Most selection criteria: .20 Interpret estimation of the most efficient 20 C PART 21 APPENDIX 24 ABSTRACT: This study aims to evaluate the factors that the influence of education on economic growth in different countries around the world The model is estimated using the method of Ordinary Least Squares (OLS), employing data for the year 2018 available on WorldBank, and using the econometric tools of Eview12 The sample size consisted of 142 countries The evaluation identified that economic growth be affected significant by education, including school enrollments: primary level, secondary level, tertiary level In particular, the estimated elasticities are statistically remarkable and have the expected signs, and their values are in accordance with the empirical literature INTRODUCTION: The activities of getting or acquiring general knowledge, learning process of basics skills such as mathematics, geography and also developing elementary understanding 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 and tertiary (% gross) has been taken as a proxy for primary, secondary and tertiary education, respectively (Loening, 2005) The relationship between education and the GDP is positive that shows education is a significant primary input factor for the growth of an economy Barro (1991) argued that there is significant and positive 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 where there is high rate of enrollment in schools Hanushek and Kimko (2000) argued that there is remarkable increase in productivity and national growth rates due to the quality of the education This thesis aims to analyze the relationship between education and economic growth includes 142 countries in different continents With the following studies will make accurate assertions about the important influence of education on the development of countries A PART 1: I Basic Theory 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 (%) II Review: Research 1:  Research name: The Relationship between Economic Growth and School Enrollment Rates: Time Series Evidence from Turkey  Author: Sedat Gumus, Selim Kayhan  Date: 2012 a) Purpose of research: to explore the relationship between economic growth and educational attainment in Turkey b) Method: The variables of GDP per capita and gross school enrollment ratios at the primary, secondary, and tertiary levels c) Sample size: in Turkey d) Model: (1) (2) (3) e) Result and discussion: - There is a closer relationship between educational attainment and economic growth at the primary school level as compared to the secondary and higher levels of education 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 economic growth in Bulgaria and Czech Republic, during the transition period and to compare it to the situation in a developed country the Netherlands b) Method: the multiple regression model c) Sample size: in all three countries (Bulgaria, Czech Republic and the Netherlands) d) Model: e) Result and discussion: - The most important thing to be taken into consideration is that education quantity has an effect on economic growth after some years 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 in the model The time lag for primary education will be set to 10 years and the time lag for secondary education to years - Education has an influence on economic growth in both transition and developed countries The level of influence varies and depends on other factors from country to country Research gap: a) Observation - Research 1: country: Turkey quite small - Research 2: focus on countries Bulgaria, Czech Republic and the Netherlands Quite small also - Our research: includes 142 countries in different continents b) Research purpose: researchs have the same purpose, that is prove the impact of eduction on economic growth We find some limitations of 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, may have 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 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: Method: OLS method Data: The data is available online on World Development Indicators (WDI) website – the World Bank's premier compilation of cross-country comparable data on development II Evaluate the functions of data: Linear function GDPP = 𝛽0 + 𝛽1PRM + 𝛽2SEC + 𝛽3TER+ 𝑢 From the EViews result in table 2.1 (APPENDIX), we have a new linear function: GDPP = -1914.25600286 - 247.677037229*PRM + 502.349750612*SEC + (23269.39) (223.6879) (113.1806) 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 independent variables equal 0, GDPP will equal to -1914.25600286 USD on average - 𝛽1 = -247.677037229 has shown that when gross school enrollment primary level changes by 1%, GDPP will decrease by 247.677037229 USD on average (other remain constant) 10 - 𝛽0 = 16942.0173004 has shown that when other independent variables equal 0, GDPP will equal to 16942.0173004 USD on average - 𝛽1 = -209.649882769 has shown that when gross school enrollment primary level changes by 1%, GDPP will decrease by 209.649882769 USD on average (other remain constant) - 𝛽2 = -82.505590253 has shown that when gross school enrollment secondary level changes by 1%, GDPP will decrease first by 82.505590253 USD on average - 𝛽3 = 3.26898451751 has shown that when gross school enrollment secondary level changes by 1%^2units, GDPP will increase by 3.26898451751 USD on average (other remain constant) - 𝛽4 = 43.4247617404 has shown that when gross school enrollment tertiary level changes by 1%, GDPP will increase by 43.4247617404 USD on average (other remain constant) III Test of economical assumptions Linear function: GDPP = 𝛽0 + 𝛽1PRM + 𝛽2SEC + 𝛽3TER+ 𝑢 From the EViews result in table 2.1 (APPENDIX), we have: { H : β =0 a Hypothesis pair: H : β1 ≠ 1  P – value = 0.2701  α = 0.05  Conclusion: - P – value > α - Accept Ho 13 - GDPP not influenced by PRM { H : β =0 b Hpothesis pair: H : β3 ≠  P-value = 0.8520  α = 0.05  Conclusion: - P-value > α - Accept H0 - GDPP not influenced by TER Logarithm function LOG(GDPP) = 𝛽0 + 𝛽1LOG(PRM) + 𝛽2LOG(SEC) + 𝛽3LOG(TER)+ 𝑢 From the EViews result in table 2.2 (APPENDIX), we have: { H : β =0 a Hypothesis pair: H : β1 ≠ 1  P-value = 0.0004  α = 0.05  Conclusion: - P-value < α - Reject H0, accept H1 - GDPP be influenced by PRM { H : β =0 b Hypothesis pair: H : β3 ≠  P-value = 0.0073  α = 0.05  Conclusion: - P-value < α - Reject H0, accept H1 - GDPP be influenced by TER 14 Semi Logarithm function LOG (GDPP) = 𝛽0 + 𝛽1PRM + 𝛽2SEC + 𝛽3TER+ 𝑢 From the EViews result in table 2.3 (APPENDIX), we have: { H : β =0 a Hypothesis pair: H : β1 ≠ 1  P-value = 0.0013  α = 0.05  Conclusion: - P-value < α - Reject H0, accept H1 - GDPP be influenced by PRM { H : β =0 b Hypothesis pair: H : β3 ≠  P-value = 0.0031  α = 0.05  Conclusion: - P-value < α - Reject H0, accept H1 - GDPP be influenced by TER Quadratic function GDPP = 𝛽0 + 𝛽1PRM + 𝛽2SEC + 𝛽3SEC2 + 𝛽4TER+ 𝑢 From the EViews result in table 2.4 (APPENDIX), we have: { H : β =0 a Hypothesis pair: H : β1 ≠ 1  P-value = 0.3481  α = 0.05  Conclusion: - P-value > α 15 - Accept H0 - GDPP not influenced by PRM { H : β =0 b Hypothesis pair: H : β3 ≠  P-value = 0.6865  α = 0.05  Conclusion: - P-value > α - Accept H0 - GDPP not influenced by TER IV Testing for the most efficient model: RAMSEY TEST Following results, we want to know whether our models are unbiased or not, therefore, we use Ramsey RESET test with fitted values a Linear function: Hypothesis pair: { H : β =0 H : β 24 ≠ P-value = 0.0519 α = 0.05 =>P-value > α => We accept Ho, that means (1) has correct form or it is unbiased 16 b Logarithm function Hypothesis pair: { H : β =0 H : β 24 ≠ P-value = 0.0162 α = 0.05 =>P-value < α => We reject Ho, that means (2) has incorrect form or it is biased c Semi Logarithm function Hypothesis pair: { H : β =0 H : β 24 ≠ P-value = 0.0604 α = 0.05 =>P-value > α => We accept Ho, that means (3) has correct form or it is unbiased d Quadratic function Hypothesis pair: { H : β =0 H : β 24 ≠ 17 P-value = 0.0509 α = 0.05 =>P-value > α => We accept Ho, that means (4) has correct form or it is unbiased 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: { H :homoskedasticity Hypothesis pair: H 0:heteroskedasticity Heteroskedasticity Test: White Null hypothesis: Homoskedasticity F-statistic Obs*R-squared Scaled explained SS 2.606309 Prob F(9,132) Prob Chi21.42629 Square(9) Prob Chi187.0351 Square(9) 0.0084 0.0109 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 18 b Logarithm function: { H : Homoskedasticity Hypothesis pair: H 0: Heteroskedasticity  P – value = 0.1543  α = 0.05  Conclusion: o P-value > α o Accept Ho o The model is Homoskedasticity c Semi Logarithm function: { H : Homoskedasticity Hypothesis pair: H 0: Heteroskedasticity  P – value = 0.0097  α = 0.05  Conclusion: o P-value < α o Reject Ho o The model (2) is Heteroskedasticity 19 d Quadratic function: { H :homoskedasticity Hypothesis pair: H 0:heteroskedasticity Heteroskedasticity Test: White Null hypothesis: Homosckedasticity F-statistic Obs*R-squared Scaled explained SS 3.187045 34.72367 319.8923 Prob F(13,128) 0.0004 Prob Chi-Square(13) 0.0009 Prob Chi-Square(13) 0.0000 P-value = 0.0004 α = 0.05 => P-value < α => We reject H0, that means (3) is heteroskedasticity Most selection criteria: Because all three models are unbiased and heteroskedasticity, we use five criteria to select the most efficient model Model R2 0.312214 (1) (2) 0.720987 (3) 0.329034 (table 3.1) Adjusted R2 0.297262 0.714922 0.309444 AIC 22.72921 2.212395 22.71853 HQ 22.76304 2.246230 22.76082 SC 22.81247 2.295658 22.82261 According to the table above, the most efficient model is model (2), semi logarithm function 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) n = 142, R2 = 0.720987, in SSR = 71.80880 20 (0.004) ... national growth rates due to the quality of the education This thesis aims to analyze the relationship between education and economic growth includes 142 countries in different continents With the. .. explore the relationship between economic growth and educational attainment in Turkey b) Method: The variables of GDP per capita and gross school enrollment ratios at the primary, secondary, and tertiary... e) Result and discussion: - There is a closer relationship between educational attainment and economic growth at the primary school level as compared to the secondary and higher levels of education