(LUẬN văn THẠC sĩ) returns to education in vietnam, a clustered data approach

UNIVERSITY OF ECONOMICS HO CHI MINH CITY VIETNAM INSTITUTE OF SOCIAL STUDIES THE HAGUE THE NETHERLANDS VIETNAM - NETHERLANDS PROGRAMME FOR M.A IN DEVELOPMENT ECONOMICS RETURNS TO EDUCATION IN VIETNAM: A CLUSTERED DATA APPROACH BY: NGUYEN THI NGOC THANH MASTER OF ARTS IN DEVELOPMENT ECONOMICS HOCHIMINH CITY, DECEMBER 2012 TIEU LUAN MOI download : skknchat@gmail.com UNIVERSITY OF ECONOMICS HO CHI MINH CITY VIETNAM INSTITUTE OF SOCIAL STUDIES THE HAGUE THE NETHERLANDS VIETNAM - NETHERLANDS PROGRAMME FOR M.A IN DEVELOPMENT ECONOMICS RETURNS TO EDUCATION IN VIETNAM: A CLUSTERED DATA APPROACH A thesis submitted in partial fulfilment of the requirements for the degree of MASTER OF ARTS IN DEVELOPMENT ECONOMICS By: NGUYEN THI NGOC THANH Academic Supervisor(s): Assoc Prof Dr NGUYEN TRONG HOAI Dr PHAM KHANH NAM HOCHIMINH CITY, DECEMBER 2012 TIEU LUAN MOI download : skknchat@gmail.com ACKNOWLEDGEMENT First of all, I would like to express my sincere thank to the Vietnam – Netherlands Programme (VNP) for such a challenging but interesting programme, whereby I enjoyed unforgettable time beside my classmates and broadened my networking via class I am much grateful to famous whole-hearted professors at home and abroad for advanced knowledge and updated information they gave us in class and beyond the class-time Specially, I would like to deeply thank two supervisors: Assoc Prof Dr Nguyen Trong Hoai and Dr Pham Khanh Nam for their helpful and valuable advices on the last but utmost duty, this thesis, that helps me fulfill my study career From the bottom of my heart, I always feel thankful to my Family for their daily care, daily worries, daily happiness with every failure or achievement I get in life I keep looking for chances to bring them happiness To my C16 Classmates, I can say that two-year was a great memory when I am with you all Thank you for your kindness, sharing and support Especially, I cannot forget the enthusiastic disinterested help from Mr Le Anh Khang – our class “Hero” before every final exam He has inspired and motivated me a lot I would like to take this opportunity to say thanks to him formally .Life is still ahead of us, let’s just stop a moment to celebrate our achievement today and keep going forward afterward I wish you all good health, happiness and success for the coming New Year 2013 Cheers ! TIEU LUAN MOI download : skknchat@gmail.com ABSTRACT Moock et al (2003) did an attempt to analyze the returns to education in Vietnam by using Mincer earnings function based on the 1992–93 Vietnam Living Standards Survey (VLSS) data In this paper, I replicate the job of Moock et al (2003) to reestimate the returns to education by using the 2008 Vietnam Household Living Standard Survey (VHLSS) and Mincerian earnings functions, but with a different regression method, called clustered data at household level using panel commands The study reveals that (1) an additional year of schooling associates with 8.95% increasing in the average rate of return to education, comparing with only 5% in 1992/1993 In terms of gender gap, females experience higher returns to school than males (11.47% vs 8.33%) This pattern is unchanged when referring to result in 1992/1993 (6.8% vs 3.4%); (2) workers in public sector get higher rates of return to education than those in private sector (9.95% vs 5.59%) However, foreign sector is the one has the highest rates of return among the three, 11.9%; (3) university is the best option for schooling investment with the rate of return of 19% higher than upper secondary level while this number was 11% in 1992/1993 Primary level brings back 16% rate of return vs no level (13% in 1992) The rates are 10% for vocational vs primary (4% in 1992); 8% for upper secondary vs lower secondary; while only 2% for lower secondary vs primary Key Words: return to schooling, education, Vietnam, Human Capital, Mincer earnings function, clustered data, random effect model TIEU LUAN MOI download : skknchat@gmail.com TABLE OF CONTENTS CHAPTER INTRODUCTION 1.1 Problem Statement 1.2 Research Objectives 1.3 Research Questions 1.4 Research Methodology 1.5 Structure of the Thesis CHAPTER LITERATURE REVIEW 2.1 Definition 2.2 A Standard Model of Human-Capital Investment 10 2.3 Empirical Studies on Estimating Returns to Education 12 2.3.1 Selective Empirical Studies in the World 12 2.3.2 Empirical Studies in Vietnam 15 2.4 Analytical Framework 19 2.5 Chapter Remarks 19 CHAPTER RESEARCH METHODOLOGY 21 3.1 Data 21 3.2 Research Methodology 23 3.3 New Approach - CLUSTERED DATA APPROACH in Estimating the Returns to Education 24 3.4 Empirical Models of the Returns to Education 27 3.5 Variable Coding 29 CHAPTER RESEARCH FINDINGS AND DISCUSSION 32 4.1 Descriptive Statistics 32 4.1.1 Distribution of the Dependent and Explanatory Variables 32 4.1.2 Descriptive Statistics of the Dataset 37 TIEU LUAN MOI download : skknchat@gmail.com 4.2 Regression Results 38 4.3 Chapter Remarks 43 CHAPTER CONCLUSION AND POLICY RECOMMENDATION 45 5.1 Conclusion of the Study 45 5.2 Policy Recommendation 46 5.3 Limitations of the Study 47 5.4 Suggestion for further Studies 48 REFERENCE TIEU LUAN MOI download : skknchat@gmail.com LIST OF TABLES Table 2.1: Empirical studies in Vietnam utilizing Mincer earnings function over the period 1992-2008 17 Table 3.1: Sample of cross-sectional data 26 Table 3.2: Sample of clustered data 27 Table 3.3: Description of the Variables and Variable Coding 30 Table 4.1: Descriptive statistics 38 Table 4.2: Earnings function by years of schooling 39 Table 4.3: Earnings function by sector of employment 40 Table 4.4: Earnings function with schooling levels (for all, males, and females) 41 Table 4.5: Private rates of return to schooling by level of education (%) 42 LIST OF FIGURES Figure 4.1: Histograms of log of earnings (by gender) 32 Figure 4.2: Histograms of log of earnings (by sector) 33 Figure 4.3: Histograms of years of schooling and log of hours worked/week 34 Figure 4.4: Scatterplots of monthly earnings and years of schooling 35 Figure 4.5: Scatterplots of monthly earnings and education levels 36 Figure 4.6: Scatterplots of monthly earnings and years of experience 36 TIEU LUAN MOI download : skknchat@gmail.com LIST OF ABBREVIATIONS ADB : Asian Development Bank GSO : General Statistics Office IV : Instrument Variable RE : Random Effect OLS : Ordinary Least Squares VHLSS : Vietnam Household Living Standard Survey VLSS : Vietnam Living Standard Survey TIEU LUAN MOI download : skknchat@gmail.com CHAPTER INTRODUCTION This chapter explains the context of the thesis, its objectives and research questions In addition, a brief of methodology is also mentioned in this part Finally, the structure of the thesis is presented 1.1 PROBLEM STATEMENT Education plays an important role in modern labor markets Hundreds of studies in many different countries and time periods have confirmed that better educated individuals earn higher wage than the less-educated ones A variety of studies have been started with the seminal work by Mincer (1974) who was the first to derive an empirical formulation of earning over the lifecycle In his basic formulation, the logarithm of earnings can be interpreted as years of schooling, years of experience and squared years of experience In Vietnam, since the Vietnam Living Standards Survey (VLSS) firstly conducted in 1992–93 till present, many studies have employed the VLSS data and the Mincerian earnings function to examine rates of return to education in Vietnam, such as: Glewwe & Patrinos, 1998; Gallup, 2002; Moock et al., 2003; Liu, 2006; Nguyen Xuan Thanh, 2006; Vu Trong Anh, 2008; Vu Thanh Liem, 2009; Doan & Gibson, 2010; etc The results are also diverse The most cite study is from Moock et al (2003), in which the authors attempt to analyze the returns to education in Vietnam by using Mincerian earnings function based on the data of VLSS 1992–93 The authors find that the estimated rates of return are quite low (4.8%) In particular, on average, the rates of return to primary and Psacharopoulos and Patrinos (2002) contains rate of return estimates for 98 countries spanning more than 30 years; Trostel, Walker and Woodley (2002) contains estimates for 28 countries; Polachek (2007) contains estimates for 42 countries; etc TIEU LUAN MOI download : skknchat@gmail.com university education are 13% and 11% But these rates are just 4% and 5% at secondary and vocational levels For higher education (colleges, universities or above), the returns are higher for females (12%) than for males (10%) Now, 20 years have passed, I return to the issue and question for now, what are the returns to education in Vietnam? How have the returns changed? Especially, in term of gender gap, between males and females who receive higher returns to education? In term of sectoral gap, among public, private, and foreign sectors, any discrepancies among these three? The findings are important implications for policy makers in directing the wage and educational policies I would like to replicate the job of Moock et al (2003) to answer these questions by using the Vietnam Household Living Standard Survey (VHLSS), conducted by General Statistic Office (GSO), in 2008 and Mincerian earnings function, but with a different regression method which is first time applied in this kind of estimation, called Clustered data at household level using panel commands 2, instead of using a simple standard cross-sectional OLS estimator From the results, I would like to suggest some policy implications 1.2 RESEARCH OBJECTIVES There are 03 main objectives in this study: (1) To estimate private returns to education by years of schooling and by levels of schooling for both sexes, for males and females; and in private, public and foreign sectors recently; (2) To assess the variation in returns to education by comparing with the findings from Moock et al (2003); Please refer to the chapter on methodology (Chapter 3) for more details TIEU LUAN MOI download : skknchat@gmail.com Mean monthly earnings are around VND 1,428,000 (USD 68.84) , while this number was VND 152,000 (USD 14)10 in Moock et al (2003)) Males’ earnings are about 17% higher than females (VND 1,513,460 vs VND 1,293,880) This number was 40% higher in Moock et al (2003)), revealing that the gender earning gap has been narrowing after 15 years, a good point in Vietnamese economic growth The average hours worked per week is 47, comparing with 46 in Moock et al (2003) Table 4.1: Descriptive statistics Variable Age (years) Years of schooling Years of experience Education levels No education Primary Lower secondary Upper secondary Vocational University Earnings/month (1,000 VND) Public sector Private sector Foreign sector Hours worked/week N All 34.01 9.51 24.51 Males 34.60 9.34 25.25 Females 33.10 9.77 23.33 0.13 0.21 0.25 0.14 0.13 0.14 1,428.07 0.33 0.61 0.06 47.37 6,956 0.12 0.23 0.27 0.13 0.12 0.12 1,513.46 0.31 0.66 0.04 47.65 4,251 0.13 0.19 0.22 0.14 0.14 0.18 1,293.88 0.38 0.52 0.10 46.94 2,705 Source: Author’s calculation using data from VHLSS 2008 4.2 REGRESSION RESULTS The outcomes of estimating simple Mincerian earnings functions by years of schooling are revealed in Table 4.2 In general, the average private rate of return to additional year of schooling is nearly 9%, comparing to only 5% in Moock et al Exchange rate year 2008: 1USD = 16,977 VND (source: ADB) Exchange rate year 1993: 1USD = 10,857 VND (source: ADB) 10 38 TIEU LUAN MOI download : skknchat@gmail.com (2003), nearly double during the last 15 years Females enjoy higher returns to school than males (11.47% vs 8.33%) This pattern unchanged when comparing with Moock et al (2003), whereas 6.8% vs 3.4% Table 4.2: Earnings function by years of schooling Variable Constant Years of schooling Years of experience Squared years of experience Log of hours worked/week Number of observations Number of groups sigma_u sigma_e rho All 2.6296 0.0895 0.0731 -0.0011 0.6480 6,956 4,335 0.41 0.55 0.36 **** **** **** **** Males 2.6773 0.0833 0.0725 -0.0011 0.6784 4,251 3,510 0.39 0.53 0.35 **** **** **** **** Females 2.4317 0.1147 0.0701 -0.0010 0.6043 2,705 2,337 0.37 0.57 0.29 **** **** **** **** Note: * significant at 10% level , **significant at 5% level, *** significant at 1% level, **** significant at 0.1% level Source: Author’s calculation using data from VHLSS 2008 Post-schooling investment in general brings back 7.31% rate of return to additional year of experience This rate was 6.4% in Moock et al (2003) Men and women have nearly the same returns to Post-schooling investment (7.25% vs 7.01%) The intraclass correlation, rho = 0.36, lets us know about the correlation of individuals within a household 11 If the intraclass correlation reaches to zero, the clustering by households is no meaning, and we may run a simple regression, no need random effects In other word, there is no difference between OLS and RE estimators If the intraclass correlation approaches 1, there is no variation between individuals, everyone is the same Here, rho = 0.36, indicating that individuals within a household are correlated Hence, RE estimator is a better fit 11 http://statistics.ats.ucla.edu/stat/stata/library/cpsu.htm 39 TIEU LUAN MOI download : skknchat@gmail.com sigma_u = 0.41 (Table 4.2) is the standard deviation of the unobserved household characteristics, and actually, it is the standard deviation of the intercept at household level sigma_e = 0.55 (Table 4.2) is the standard deviation of the residual at individual level We can calculate the intraclass correlation, rho, from sigma_u and sigma_e by using the following formula: ( sigma _ u ) 0.412 Intraclass _ correlation    0.36 ( sigma _ u )  ( sigma _ e) 0.412  0.55 The standard deviation, sigma_u = 0.41, reveals that beside a common intercept, Constant = 2.6296 (Table 4.2), individuals are added a household-level component which follows normal distribution with SD = 0.41 This result shows that individuals from different households have different intercepts and these intercepts are distributed normal with SD = 0.41, mean = 2.6296 Table 4.3: Earnings function by sector of employment Variable Constant Years of schooling Years of experience Squared years of experience Log of hours worked/week Number of observations Number of groups sigma_u sigma_e rho Public 2.7412 0.0995 0.0800 -0.0012 0.5891 2,322 1,700 0.47 0.47 0.50 Sector of employment Private 2.6802 0.0594 **** **** 0.0638 **** **** -0.0010 **** **** 0.7117 **** **** 4,209 2,816 0.42 0.55 0.37 Foreign 2.6522 0.1190 0.0815 -0.0012 0.5898 425 337 0.43 0.43 0.50 **** **** **** **** Note: * significant at 10% level , **significant at 5% level, *** significant at 1% level, **** significant at 0.1% level Source: Author’s calculation using data from VHLSS 2008 Employees in public sector record higher rates of return to schooling than those in private sector, 9.95% vs 5.59% (Table 4.3) However, foreign sector discloses the 40 TIEU LUAN MOI download : skknchat@gmail.com highest rates of return among the three, 11.9% In Moock et al (2003), the rates were 6.2% for workers in public sector and 3.9% in private sector Foreign sector was not accounted in Moock et al (2003) as it was just a small fraction, compared to others Similar to schooling investment, post-schooling investment displays the highest rates of return to additional year of market experience in foreign sector (8.15%), following by public sector (8%), and ending at private sector with the lowest rate (6.38%) Comparing with 15 years ago (Moock et al., 2003), these rates were 4.6% for public, 7.2% for private, the returns have significantly changed Foreign sector emerged to be the highest return to post-schooling investment Public and private sectors have exchanged their positions Table 4.4: Earnings function with schooling levels (for all, males, and females) Variable Constant Primary Lower secondary Upper secondary Vocational University Years of experience Squared years of experience Log of hours worked/week Number of observations Number of groups sigma_u sigma_e rho All 2.9261 0.1621 0.2591 0.5067 0.7690 1.2670 0.0723 -0.0011 0.6856 6,956 4,335 0.39 0.55 0.33 **** **** **** **** **** **** **** **** Males 2.9593 0.1454 0.1880 0.4338 0.6820 1.2264 0.0715 -0.0011 0.7178 4,251 3,510 0.36 0.53 0.31 **** **** **** **** **** **** **** **** Females 2.7749 0.1610 0.3913 0.7045 0.9736 1.5118 0.0727 -0.0011 0.6540 2,705 2,337 0.35 0.57 0.28 **** **** **** **** **** **** **** **** Note: * significant at 10% level , **significant at 5% level, *** significant at 1% level, **** significant at 0.1% level Source: Author’s calculation using data from VHLSS 2008 Dummy variables are converted from years of schooling to estimate the earnings premium affiliated with each level of education (Table 4.4) Overall, university level 41 TIEU LUAN MOI download : skknchat@gmail.com enjoys the highest rate of return to schooling investment Comparing to workers with no educational level, university-level employees get 126% higher in earnings premium (43.7% in Moock et al (2003)), vocational-level workers obtain 77% higher (20.7% in Moock et al (2003)), 50% and 26% higher for upper and lower secondary level workers respectively (32.5% for secondary level in Moock et al (2003)), and 16.21% for primary-level labors (13.4% in Moock et al (2003)) The outcomes of earnings function with schooling levels in Table 4.4 provide the earnings premiums at different educational levels comparing with no educational level as reference The results in Table 4.5 reveal the private rates of return to schooling by levels of education, comparing with flexible level that we want to compare Large earnings premiums result in relatively high private returns to schooling (Moock et al., 2003, p.507) The outcomes in Table 4.5 obtains from equation (3.3) and the earning function results disclosed in Table 4.4 Table 4.5: Private rates of return to schooling by level of education (%) Educational level Primary (vs less than primary) Lower secondary (vs primary) Upper secondary (vs lower secondary) Vocational (vs lower secondary) University (vs upper secondary) All 16 8 19 Males 15 8 20 Females 16 10 10 20 Source: Author’s calculation using data from VHLSS 2008 From the Table 4.5 results, university shows to be the best option for schooling investment With years invested in obtaining university level, the rate of return to this deal is 19% higher than upper secondary level Both males and females get the same rate of return to schooling at university level (20% vs 20%) This outcome is relatively similar to Moock et al (2003) where university was the best investment at that time Due to different reference system and different partition education levels, I just compare with Moock et al (2003) where appropriate 42 TIEU LUAN MOI download : skknchat@gmail.com Primary level seems to be the second profitable investment with 16% rate of return (13% in Moock et al (2003)) Vocational and upper secondary share the same rates of returns, 8% compared with lower secondary However, ones need years to finish vocational education, while others only spend years to finish upper secondary school level, but both enjoy the same rates of returns, therefore, investment in upper secondary seems to be the better alternative choice than investment in vocational level Lower secondary education is relatively poor deal, only 2% overall If a person with primary level spending years more in obtaining lower secondary education level, he/she just gets 2% rate of return to this investment If he/she spends at least years more to obtain upper secondary level, he/she may get additional 8% of returns In most of cases, investment in females’ educational levels brings back higher rates of return than males, i.e., at upper secondary level and vocational level, females enjoy 10% vs 8% for males; lower secondary with 6% for females vs 1% for males 4.3 CHAPTER REMARKS In general, the sample profile contains variables which follow normal distribution The bivariate analysis reveals an upward-sloping relationship between log of monthly earnings and its determinants years of schooling as well as education levels, while log of monthly earning and years of experience conform to a quadratic relation The mean age of the sample is 34 years The average year of schooling is 9.5 years Nearly 13% labor forces with no educational level or illiterates, 21% obtained primary, 25% completed lower secondary, 14% for upper secondary, and 14% accomplished colleges and above Public sector absorbs 33% labor forces, while this number is 61% for private sector and only 6% for foreign sector Average monthly earnings are around VND 1,428,000 (USD 84) 43 TIEU LUAN MOI download : skknchat@gmail.com The multivariate analysis explores that an additional year of schooling associates with 8.95% increasing in the average rate of return to education, in which females experience higher returns to school than males (11.47% vs 8.33%) Workers in foreign sector enjoys the highest rates of return among the three with 11.9%, while this number is 9.95% for public and 5.59% for private sector University and primary education are good investment, while lower secondary education is relatively poor deal Investment in upper secondary and vocational educations are medium good choice 44 TIEU LUAN MOI download : skknchat@gmail.com CHAPTER CONCLUSION AND POLICY RECOMMENDATION As the final chapter, this section comes up with some main conclusion of the study, some policy recommendation, limitation of the study and suggestion for further studies 5.1 CONCLUSION OF THE STUDY By using clustered data at household level which are transferred from crosssectional data VHLSS 2008, and a Random-effects model which allow the effects at household level to be randomly assigned among households, and a Mincerian earnings function to estimate the rates of return to education in Vietnam, I have found that: (1) An additional year of schooling associates with 8.95% increasing in the average rate of return to education Comparing with 15 years ago when the average rate of return to schooling in Moock et al (2003) was only 5%, this rate has increased nearly double In terms of gender gap, females experience higher returns to school than males (11.47% vs 8.33%) Referring to 15 years ago, this pattern is unchanged (6.8% vs 3.4%); (2) Workers in public sector get higher rates of return to education than those in private sector (9.95% vs 5.59%) But foreign sector has the highest rates of return among the three, 11.9% Comparing with 15 years ago when the rates were 6.2% in public sector and 3.9% in private sector, these rates have really expanded although the pattern is unchanged (3) By levels of schooling, the higher the levels of schooling the greater the rates of return to education Specifically, if we take no education level as reference, university-level workers enjoys the highest rate of return to schooling investment with 126% higher, vocational-level workers with 77% 45 TIEU LUAN MOI download : skknchat@gmail.com higher, 50% and 26% higher for upper and lower secondary level workers respectively, and 16.21% for primary-level labors Comparing with 15 years ago, these numbers were 43.7% for university level, 20.7% for vocational level, 32.5% for secondary level, and 13.4% for primary level; (4) The best option for schooling investment is university level With 04 years spending in acquiring university level, the rate of return to this investment is 19% higher than upper secondary level Investment in primary level brings back 16% rate of return vs no level (13% in 1992) The rates are the same 8% for upper secondary and vocational vs lower secondary, while only 2% for lower secondary vs primary 5.2 POLICY RECOMMENDATION (1) The disparity in rates of return between public sector and foreign sector suggests that it is hard for public sector to keep and attract skilled workers once the wage gap does exist The government should consider on increasing the wage rate in public sector to at least equal to the wage rate in foreign sector By doing so, public sector not only retains and attracts skilled employees but also increases working efficiency because workers have no other sector with higher returns to compare and so they can focus all their power on current jobs (2) The higher levels of education provide higher rates of return to education suggests that there exists rooms for private financing at higher levels, specifically university and upper secondary levels It is implying that if the government shifts a part of its cost burden in education to individuals and their family, it is not likely to reduce incentive of investment in upper secondary and university levels, since these levels bring back high rates of return The government should encourage private financing institutions to 46 TIEU LUAN MOI download : skknchat@gmail.com engage in education loans and create favorable conditions for individuals to access to preferential loans (3) The rates of returns on vocational and upper secondary are the same (8%) compared with lower secondary reveals alternative choice for those who are making up their mind after graduating from lower secondary school This result also give out the fact for policy makers who aim at harmonizing the society employment at different level requirement, and for career advisers who give direction for lower-secondary graduates based on their demand, skills and ability 5.3 LIMITATIONS OF THE STUDY One of limitations in this paper is the empirical model (3.5), (3.6) may face the problem of endogeneity The error term may embody factors other than years of schooling that influence earnings, i.e., innate ability People with high/low innate ability may be associated with high/low years of schooling So, we are quite unsure how much of increase in earnings is due to years of schooling and how much is due to ability of that individual Therefore, the regressor years of schooling is considered to be endogenous The solution for endogeneity problem is to add in regressor controls for ability, such as IQ test However, this variable is not valid in available dataset Other solution to correct the endogeneity is Instrument Variable (IV) approach In this research, I not follow IV approach because it is not easy to obtain an instrument variable from VHLSS What I am trying in the study is to allow for such effect (ability) not at individual level but at household level These household-level effects will be randomly assigned to individuals between households through random-effect estimator Additionally, I am in doubt that the coefficient of years of experience is overestimated, especially for women who often temporarily quit jobs due to pregnancy or 47 TIEU LUAN MOI download : skknchat@gmail.com nursing their children over the lifecycle The time being out of labor force is not exhibited properly in the VHLSS survey Another concern is that the sample covers only wage earners Over 80% of the Vietnamese labor force is farm self-employment and non-farm self-employment If the paper expands to include this 80% portion, the outcomes might have significantly different values 5.4 SUGGESTION FOR FURTHER STUDIES From the limitation of the study, I would suggest the IV approach for further studies To alleviate the unobserved heterogeneity, one should find instrument variables that are correlated with years of schooling but uncorrelated with the error term and hence have no direct effect on earnings Alternative way for further research should include multi-level mixed-effect models which are suitable for VHLSS data which is grouped/nested by more than one category, i.e., households, villages, communes, provinces, etc Multi-level models allow for exploring effects that vary by groups The effects are randomly assigned to the intercepts 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Explanatory Variables This is a necessary step to understand the sample data A good way to visually explore data is by histograms, especially to check for a normal distribution The following... LUAN MOI download : skknchat@gmail.com The multivariate analysis explores that an additional year of schooling associates with 8.95% increasing in the average rate of return to education, in