Short panel data quantile regression model with flexible correlated effects

I propose an alternative linear model for short panel data quantile regression. The model assumes a nonparametric correlated effect (CE) that is <i>τ</i>-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.

本文提出一种面向短面板数据分位数回归（short panel data quantile regression）的替代线性模型。该模型假定存在非参数相关效应（correlated effect, CE），该效应具有τ分位数特异性且为时不变。由此构建的部分线性模型具备对模型误设稳健的推断性能，且在广义相关随机效应假设下，可被视作对真实数据生成机制的最优线性近似。该模型以刻画个体异质性为代价，规避了附带参数问题，且未对个体内特异误差的组内依赖关系施加任何约束。其刻画的异质性仍与线性均值回归模型中的固定效应方法高度适配。在估计环节，通过非凸惩罚对筛近似得到的相关效应进行正则化，该惩罚在超高维场景下具备神谕性质（oracle property）；无惩罚筛估计同样可行。作为实证应用，本文所提方法被用于估计吸烟对新生儿出生体重的分布效应。在固定效应分位数回归计算上难以实现的数据集上，相较于基于线性相关效应的估计方法，该方法可获得更为精细的估计结果。