Communications for Statistical Applications and Methods

The Korean Statistical Society (한국통계학회)
권호 표지
DOI QR코드

DOI QR Code

Wage Determinants Analysis by Quantile Regression Tree

  • Received : 2012.01.24
  • Accepted : 2012.03.06
  • Published : 2012.03.31
Download PDF
⟨ Previous Next ⟩

Abstract

Quantile regression proposed by Koenker and Bassett (1978) is a statistical technique that estimates conditional quantiles. The advantage of using quantile regression is the robustness in response to large outliers compared to ordinary least squares(OLS) regression. A regression tree approach has been applied to OLS problems to fit flexible models. Loh (2002) proposed the GUIDE algorithm that has a negligible selection bias and relatively low computational cost. Quantile regression can be regarded as an analogue of OLS, therefore it can also be applied to GUIDE regression tree method. Chaudhuri and Loh (2002) proposed a nonparametric quantile regression method that blends key features of piecewise polynomial quantile regression and tree-structured regression based on adaptive recursive partitioning. Lee and Lee (2006) investigated wage determinants in the Korean labor market using the Korean Labor and Income Panel Study(KLIPS). Following Lee and Lee, we fit three kinds of quantile regression tree models to KLIPS data with respect to the quantiles, 0.05, 0.2, 0.5, 0.8, and 0.95. Among the three models, multiple linear piecewise quantile regression model forms the shortest tree structure, while the piecewise constant quantile regression model has a deeper tree structure with more terminal nodes in general. Age, gender, marriage status, and education seem to be the determinants of the wage level throughout the quantiles; in addition, education experience appears as the important determinant of the wage level in the highly paid group.

Keywords

References

  1. Barrodale, I. and Roberts, F. D. K. (1980). Solution of the constrained $l_1$ linear approximation problem, ACM Transactions on Mathematical Software, 6, 231-235. https://doi.org/10.1145/355887.355896
  2. Bartels, R. and Conn, A. (1980). Linearly constrained discrete 1 problems, ACM Transactions on Mathematical Software, 6, 594-608. https://doi.org/10.1145/355921.355930
  3. Chang, Y. (2010). The analysis of factors which affect business survey index using regression trees, The Korean Journal of Applied Statistics, 23, 63-71. https://doi.org/10.5351/KJAS.2010.23.1.063
  4. Charnes, A., Cooper, W. W. and Ferguson, R. O. (1955). Optimal estimation of executive compensation by linear programming, Management Science, Jan, 138-151.
  5. Chaudhuri, P. and Loh, W.-Y. (2002). Nonparametric estimation of conditional quantiles using quantile regression trees, Bernoulli, 8, 561-576.
  6. Koenker, R. (2005). Quantile Regression, Econometric Society Monograph Series, Cambridge University Press.
  7. Koenker, R. and Bassett, G. W. (1978). Regression quantiles, Econometrica, 46, 33-50. https://doi.org/10.2307/1913643
  8. Koenker, R. and D'Orey, V. (1987). Algorithm AS229: Computing regression quantiles, Applied Statistics, 36, 383-393. https://doi.org/10.2307/2347802
  9. Koenker, R. and Park, B. J. (1994). An interior point algorithm for nonlinear quantile regression, Journal of Econometrics, 71, 265-283.
  10. Lee, B.-J. and Lee, M. J. (2006). Quantile regression analysis of wage determinants in the Korean labor market, The Journal of the Korean Economy, 7, 1-31.
  11. Loh, W.-Y. (2002). Regression trees with unbiased variable selection and interaction detection, Statistica Sinica, 12, 361-386.
  12. Wagner, H. M. (1959). An integer linear-programming model for machine scheduling, Naval Research Logistics Quarterly, 6, 131-140. https://doi.org/10.1002/nav.3800060205