This paper presents a hidden Markov model designed to investigate the complex nature of earnings persistence. The proposed model assumes that the residuals of log-earnings consist of a persistent component and a transitory component, both following general Markov processes. Nonparametric identification is achieved through spectral decomposition of linear operators, and a modified stochastic EM algorithm is introduced for model estimation. Applying the framework to the Panel Study of Income Dynamics (PSID) dataset, we find that the earnings process displays nonlinear persistence, conditional skewness, and conditional kurtosis. Additionally, the transitory component is found to possess non-Gaussian properties, resulting in a significantly asymmetric distributional impact when high-earning households face negative shocks or low-earning households encounter positive shocks. Our empirical findings also reveal the presence of ARCH effects in earnings at horizons ranging from 2 to 8 years, further highlighting the complex dynamics of earnings persistence.

翻译：本文提出一个隐马尔可夫模型，旨在探究收入持续性的复杂特征。该模型假设对数收入残差由持续性成分与暂时性成分构成，二者均遵循一般马尔可夫过程。通过线性算子的谱分解实现非参数识别，并引入改进的随机EM算法进行模型估计。基于收入动态追踪研究（PSID）数据集的应用表明，收入过程呈现非线性持续性、条件偏度与条件峰度特征。此外，暂时性成分具有非高斯性质，导致高收入家庭遭受负面冲击或低收入家庭遭遇正面冲击时，产生显著非对称的分布效应。实证结果还揭示收入在2至8年时间跨度内存在ARCH效应，进一步凸显收入持续性的复杂动态特征。