# Nonparametric Identification and Estimation of Earnings Dynamics using a Hidden Markov Model: Evidence from the PSID

**Authors:** Tong Zhou  
**arXiv:** [2306.01760](https://arxiv.org/abs/2306.01760)  
**Date:** 2023-05-25  
**Summary page:** https://www.summarizepaper.com/en/arxiv-id/2306.01760v1/

## Key points

- The paper presents a hidden Markov model to investigate earnings persistence
- Residuals of log-earnings consist of a persistent and transitory component
- Nonparametric identification achieved through spectral decomposition of linear operators
- Modified stochastic EM algorithm used for model estimation
- Primary data source is the Panel Study of Income Dynamics (PSID)
- Empirical findings reveal nonlinear persistence, conditional skewness, and kurtosis in earnings process
- Transitory component possesses non-Gaussian properties resulting in significant distributional impact on household income levels during positive or negative shocks
- ARCH effects found in earnings at horizons ranging from 2 to 8 years
- Findings have implications for policymakers and researchers interested in understanding the complex dynamics of earnings persistence and its impact on households' economic well-being.

## Summary

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. To ensure high-quality data, the study draws on the Panel Study of Income Dynamics (PSID) as its primary data source. The sample selection procedure and data preprocessing mainly follow the works of [3], [4]. However, changes in survey methodology or sample composition can affect the accuracy and reliability of PSID data over time, requiring careful attention to data cleaning and quality control procedures. Applying the framework to the PSID dataset, empirical findings reveal that the earnings process displays nonlinear persistence, conditional skewness, and conditional kurtosis. Figure 2 illustrates the marginal distributions of the persistent and transitory earnings components at mean age. The persistent component Uit displays small deviations from Gaussianity; however, strong evidence rejects Gaussianity for Vit due to its high kurtosis and fat tails. Additionally, Figure 3 reports conditional skewness for τ = 11/12 for both U component and V component. Furthermore, our findings highlight that the transitory component possesses non-Gaussian properties resulting in significantly asymmetric distributional impact when high-earning households face negative shocks or low-earning households encounter positive shocks. Moreover, we find ARCH effects in earnings at horizons ranging from 2 to 8 years further highlighting complex dynamics of earnings persistence. In conclusion, this study contributes to understanding earnings dynamics by providing non-parametric identification and estimation using a hidden Markov model approach. Our empirical results provide insights into nonlinear persistence with conditional skewness and kurtosis while highlighting non-Gaussian properties in transitory components with significant distributional impacts on household income levels during positive or negative shocks. The study's findings have implications for policymakers and researchers interested in understanding the complex dynamics of earnings persistence and its impact on households' economic well-being.