Short panel data quantile regression model with flexible correlated effects
提出一种新的短面板数据分位数回归模型，通过非参数相关效应处理个体异质性，避免冗余参数问题，并应用于估计吸烟对出生体重的分布效应。
I propose an alternative linear model for short panel data quantile regression. The model assumes a nonparametric correlated effect (CE) that is τ-quantile-specific and time-invariant. The resulting partially linear model provides inference robust to misspecification, and it is characterized as a best linear approximation to the truth under a generalized correlated random effect assumption. At the cost of modeling the individual heterogeneity, the model is free of incidental parameters, and it does not restrict within-group dependence of idiosyncratic errors at all. The modeled heterogeneity is still well-aligned with the fixed effect approach in the linear mean regression model. For estimation, sieve-approximated CE is regularized by nonconvex penalization which enjoys the oracle property against ultra-high dimensionality. Unpenalized sieve estimation is also available. As an empirical application, the proposed method is used to estimate the distributional effect of smoking on birth weights. Using a dataset where fixed effects quantile regression is computationally infeasible, the method yields more refined estimates compared to the one based on a linear CE.