A Guide to Estimating Income Processes in Quasidifferences

We provide a guide to estimating the canonical income process that includes autoregressive, transitory, and fixed effect components using quasidifferences. Estimation in quasidifferences has its advantages over estimations in levels and differences, yet it is rarely used in practice, and nothing is known about its effectiveness. Using Monte Carlo simulations, we are the first to provide a catalog of biases in the estimated parameters for various N , T , initial conditions, and weighting schemes. Using Danish administrative data on male earnings, estimation in quasidifferences yields divergent estimates of the autoregressive parameter for different weighting schemes, which conforms to our simulated results when the variance of transitory shocks is higher than that of permanent shocks, true persistence is high, and the variance of the permanent component in the first sample year is nonzero. We further apply quasidifferences to the data from a calibrated standard incomplete markets model to jointly estimate the income process parameters and consumption insurance against permanent and transitory shocks. We find that estimation in quasidifferences yields significant biases in the autoregressive parameter and the estimated insurance of shocks. Our results warn against the routine use of estimation in quasidifferences. The income process parameters can be reliably estimated using quasidifferences only when the variance of permanent shocks is higher than that of transitory shocks, and one uses equal weighting of the moments