Unobserved Heterogeneity in Income Dynamics: An Empirical Bayes Perspective
使用经验贝叶斯方法处理纵向数据中的复合决策问题，通过非参数最大似然估计构建贝叶斯规则，并应用于收入动态模型，发现允许方差异质性时收入冲击的持续性较低，且个体截距与方差存在负相关。
Empirical Bayes methods for Gaussian compound decision problems involving longitudinal data are considered. The new convex optimization formulation of the nonparametric (Kiefer–Wolfowitz) maximum likelihood estimator for mixture models is employed to construct nonparametric Bayes rules for compound decisions. The methods are first illustrated with some simulation examples and then with an application to models of income dynamics. Using panel data, we estimate a simple dynamic model of earnings that incorporates bivariate heterogeneity in intercept and variance of the innovation process. Profile likelihood is employed to estimate an AR(1) parameter controlling the persistence of the innovations. We find that persistence is relatively modest, ρ^≈0.48$\hat{\rho }\approx 0.48$, when we permit heterogeneity in variances. Evidence of negative dependence between individual intercepts and variances is revealed by the nonparametric estimation of the mixing distribution, and has important consequences for forecasting future income trajectories.