Functional Data Inference in a Parametric Quantile Model applied to Lifetime Income Curves

A parametric quantile function estimation procedure is developed for functional data. The approach involves minimizing the sum of integrated functional distances that measure the functional gap between each functional observation and the quantile curve in terms of the check function. The procedure is validated under both correctly specified and misspecified models by allowing for the presence of nuisance parameter estimation effects. Testing methodology is developed using Wald, Lagrange multiplier, and quasi-likelihood ratio procedures in this functional data setting. Finite sample performance is assessed using simulations and the methodology is applied to study how lifetime income paths differ between genders and among different education levels using continuous work history samples. The methodology enables the analysis of full career income paths with temporal and possibly persistent dependence structures embodied in the observations.The results capture both gender and education effects but these empirical differences are shown to be mitigated upon rescaling to take account of lifetime experience and job mobility.