A Nonlinear Filtering Application to the Stochastic Volatility of Labor Income Across Schooling Groups

The recent literature on estimation of structural models relies heavily on the specification of dynamic factors to control for unobserved heterogeneity across agents. A general filtering technique is the Particle Filtering, as shown in Fernandez-Villaverde and Rubio-Ramirez (2007). The main obstacle in using the Particle Filtering in panel data is that it is computationally very expensive: it requires sampling and resampling for a large number of individuals over a long period of time. This paper builds on the unscented Kalman Filter by using a Mixture of Normals for the distribution of the states and error terms. The empirical application contains an analysis of stochastic volatility in labor income and employment shocks across schooling group using monthly labor income data from 1978 to 2004 for approximately 1,500 individuals. The analysis shows that the variance of shocks in income tends to increase during a recession for high-school graduates, but decrease for college graduates. This result suggests that a college education provides a form of insurance against the aggregate shocks.