Sieve Estimation of Time-Varying Panel Data Models With Latent Structures
提出一种允许系数随个体和时间变化的时变面板数据模型，通过惩罚筛估计的分类-套索方法同时识别个体分组和估计组内系数，模拟和实际数据（91国人均GDP）验证了有效性。
We propose a heterogeneous time-varying panel data model with a latent group structure that allows the coefficients to vary over both individuals and time. We assume that the coefficients change smoothly over time and form different unobserved groups. When treated as smooth functions of time, the individual functional coefficients are heterogeneous across groups but homogeneous within a group. We propose a penalized-sieve-estimation-based classifier-Lasso (C-Lasso) procedure to identify the individuals’ membership and to estimate the group-specific functional coefficients in a single step. The classification exhibits the desirable property of uniform consistency. The C-Lasso estimators and their post-Lasso versions achieve the oracle property so that the group-specific functional coefficients can be estimated as well as if the individuals’ membership were known. Several extensions are discussed. Simulations demonstrate excellent finite sample performance of the approach in both classification and estimation. We apply our method to study the heterogeneous trending behavior of GDP per capita across 91 countries for the period 1960–2012 and find four latent groups.