Journal of the Korean Data and Information Science Society

The Korean Data and Information Science Society (한국데이터정보과학회)
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Bayesian quantile regression analysis of private education expenses for high scool students in Korea

일반계 고등학생 사교육비 지출에 대한 베이지안 분위회귀모형 분석

  • Oh, Hyun Sook (Department of Applied Statistics, Gachon University)
  • 오현숙 (가천대학교 응용통계학과)
  • Received : 2017.09.11
  • Accepted : 2017.10.23
  • Published : 2017.11.30
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Abstract

Private education expenses is one of the key issues in Korea and there have been many discussions about it. Academically, most of previous researches for private education expenses have used multiple regression linear model based on ordinary least squares (OLS) method. However, if the data do not satisfy the basic assumptions of the OLS method such as the normality and homoscedasticity, there is a problem with the reliability of estimations of parameters. In this case, quantile regression model is preferred to OLS model since it does not depend on the assumptions of nonnormality and heteroscedasticity for the data. In the present study, the data from a survey on private education expenses, conducted by Statistics Korea in 2015 has been analyzed for investigation of the impacting factors for private education expenses. Since the data do not satisfy the OLS assumptions, quantile regression model has been employed in Bayesian approach by using gibbs sampling method. The analysis results show that the gender of the student, parent's age, and the time and cost of participating after school are not significant. Household income is positively significant in proportion to the same size for all levels (quantiles) of private education expenses. Spending on private education in Seoul is higher than other regions and the regional difference grows as private education expenditure increases. Total time for private education and student's achievement have positive effect on the lower quantiles than the higher quantiles. Education level of father is positively significant for midium-high quantiles only, but education level of mother is for all but low quantiles. Participating after school is positively significant for the lower quantiles but EBS textbook cost is positively significant for the higher quantiles.

일반계 고등학생의 사교육비 지출은 대학입시와 맞물려 최근 더욱 증가하고 있는 동시에 가구소득 수준, 지역 등에 따라 양극화되고 있다. 기존의 사교육비 연구는 주로 다중회귀모형을 토대로 최소자승법을 이용하였으나 자료가 최소자승법의 기본가정인 정규성과 등분산성을 만족하지 않으면 분석결과의 신뢰성에 대한 문제가 발생된다. 본 연구는 2015년도 사교육실태조사자료에 대하여 정규성과 등분산성이 성립되지 않음을 확인하고 이를 통제할 수 있는 베이지안 분위회귀모형을 적합한 후 깁스 샘플링 방법을 이용하여 사교육비 지출규모 수준 (분위수)에 따라 영향요인들을 분석하였다. 분석결과 학생의 성별, 부모의 나이, 방과후 학교 참여시간과 비용은 사교육비 지출규모에 의미있는 영향을 주지 못하였다. 가구소득은 사교육비 지출규모의 모든 수준에서 동일하게 영향을 주는 요인으로 파악되었다. 그 외, 거주지역, 총사교육시간, 학생의 성적, 부모의 교육정도, 가구의 경제활동주체, 방과후 학교 참여여부, EBS 교재비용은 사교육비 지출 규모의 수준에 따라 다르게 영향을 주었다.

Keywords

References

  1. Choi, J. S. (2014). Type I projection sum of squares by weighted least squares. Journal of the Korean Data & Information Science Society, 25, 423-429. https://doi.org/10.7465/jkdi.2014.25.2.423
  2. Cook, R. D. and Weisberg, S. (1983). Diagnostics for heteroscedasticity in regression. Biometrika, 70, 1-10. https://doi.org/10.1093/biomet/70.1.1
  3. Jung, S. Y. (2014). Analysis of the impact of agglomeration on firm performance using quantile regression. Journal of Market Economy, 43, 95-121.
  4. Kang, S. H. and Lim, B. I. (2012). An analysis on determinants of the private education expenses from a viewpoint of housewives. Journal of the Korean Data & Information Science Society, 23, 543-558. https://doi.org/10.7465/jkdi.2012.23.3.543
  5. Kim, D., Eom, J. H. and Jeong, H. C. (2006). A comparison on the empirical power of some normality tests. Journal of the Korean Data & Information Science Society, 17, 31-39.
  6. Kim, H. J. (2008). Analyzing the impact of high school equalization policy on the private tutoring expenditure of academic high school second grade students in Korea. The Journal of Educational Administration, 26, 1-22.
  7. Koenker, R. and Park, B. J. (1996). An interior point algorithm for nonlinear quantile regression. Journal of Econometrics, 71, 265-283. https://doi.org/10.1016/0304-4076(96)84507-6
  8. Kozumi, H. and Kobayashi, G. (2011). Gibbs sampling methods for Bayesian quantile regression. Journal of Statistical Computation and Simulation, 81, 1565-1578. https://doi.org/10.1080/00949655.2010.496117
  9. Lee, D. H, Kim, D. H. and Kang, S. G. (2016). Noninformative priors for linear combinations of exponential means. Journal of the Korean Data & Information Science Society, 27, 565-575. https://doi.org/10.7465/jkdi.2016.27.2.565
  10. Lee, H. J. and Song, J. W. (2014). The analysis of private education cost for the elementary, middle, and high scholl students in Korea. The Korean Journal of Applied Statistics, 27, 1125-1137. https://doi.org/10.5351/KJAS.2014.27.7.1125
  11. Lee, S. J. (2007). An socio-psychological approach to the cause of shadow education in South Korea. The Journal of Educational Administration, 25, 455-484.
  12. Oh, M. S., Choi, J. and Park, E. S. (2016). Bayesian variable selection in quantile regression using the Savage-Dickey density ratio. Journal of the Korean Statistical Society, 45, 466-476. https://doi.org/10.1016/j.jkss.2016.01.006
  13. Oh, M. S. and Kim, J. H. (2011). Statistical analysis of private education expenses in Korea. The Korean Journal of Applied Statistics, 24, 193-206. https://doi.org/10.5351/KJAS.2011.24.1.193
  14. Reed, C. and Yu, K. (2009). An efficient gibbs sampler for Bayesian quantile regression, Department of Mathematical Sciences, Brunel University(Technical Report).
  15. Sung, N. I. and Hong, S. W. (2008). An empirical study on the Korean Household expenditure for private tutoring. Korea Review of Applied Economics, 10, 183-212.
  16. Statistics Korea. (2017). Private education expenditures survey in 2016.
  17. Statistics Korea. (2016). Private education expenditures survey in 2015.
  18. Yi, J. (2009). The permanent poverty of female headed household: the tendency and determinants. The Women’s Studies, 77, 49-79.
  19. Yu, K., Lu, Z. and Stander, J. (2003). Quantile regression: applications and current research areas. Jounal of the Royal Statistical Society: Series D (the Statistician), 52, 331-350. https://doi.org/10.1111/1467-9884.00363
  20. Yu, K. and Moyeed, R. A. (2001). Bayesian quantile regression. Statistics & Probability Letters, 54, 437-447. https://doi.org/10.1016/S0167-7152(01)00124-9