By Bernd Fitzenberger, Roger Koenker, Jose A.F. Machado
Quantile regression has emerged as a necessary statistical device of up to date empirical economics and biostatistics. Complementing classical least squares regression equipment that are designed to estimate conditional suggest versions, quantile regression presents an ensemble of strategies for estimating households of conditional quantile types, therefore delivering a extra whole view of the stochastic dating between variables. This quantity collects 12 amazing empirical contributions in economics and provides an necessary creation to interpretation, implementation, and inference points of quantile regression.
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Extra info for Economic Applications of Quantile Regression
The IV estimates these differences are likely insignificant. Figure 4E still suggests some mild heterogeneity in the returns to education, the estimated returns are higher in the middle quantiles and similar at the tails. The estimates are also less precise at the tails. Indeed, when we test for differences across quantiles (Table 3, panel B), only in comparisons between the 25 th quantile and the middle quantiles do we find some evidence of heterogeneity in the returns (p-values between 5~1O%).
For a fixed year t, the function/(t, rx) yields the conventional cross-section wage profiles. Movements of 1 as a function of t describe how cross-section wage profiles shift over time. Recognizing relation (2-1), the cross-sectional relation 1 as a function of age does not describe life-cycle wage growth for any cohort or, put differently, the cross-section relation may very well be the result of cohort effects. In fact, cohort-earnings-profiles are statistically indistinguishable from age-earnings-profiles.
5 + . 9 ....... + .. 6,..... 9 + ~ + Figure 69. le: Family Effect. No IV All: Age, Race, Gender, Married, Union, Tenure Fig. 6. 8 u.. " ~" a ~ ~ 8 ~ 9:"! + Figure SA. 5 OilAntiiA + + QUantile Figure 6F. 1 j L, ~ E + ~. + Figure 6C. 9 +1 •• + + > ~ ~ en I" ::I. 9 ~ w Individual heterogeneity in the returns to schooling 35 without IV models based on the sparsity method. Inference conclusions are essentially unchanged if we use bootstrap confidence intervals. Note the anomalous negative effect of race of white on earnings which is also reported by Ashenfelter and Krueger (1994) and Ashenfelter and Rouse (1998), but that this cannot be estimated with precision at any quantile.
Economic Applications of Quantile Regression by Bernd Fitzenberger, Roger Koenker, Jose A.F. Machado