We develop a state-space model with a transition equation that takes the form of a functional vector autoregression (VAR) and stacks macroeconomic aggregates and a cross-sectional density. The measurement equation captures the error in estimating log densities from repeated cross-sectional samples. The log densities and their transition kernels are approximated by sieves, which leads to a finite-dimensional VAR for macroeconomic aggregates and sieve coefficients. With this model, we study the dynamics of technology shocks, GDP (gross domestic product), employment, and the earnings distribution. We find that spillovers between aggregate and distributional dynamics are generally small, that a positive technology shock tends to decrease inequality, and that a shock that raises earnings inequality leads to a small and insignificant GDP response.
We develop a state-space model with a state-transition equation that takes the form of a functional vector autoregression and stacks macroeconomic aggregates and a cross-sectional density. The measurement equation captures the error in estimating log densities from repeated cross-sectional samples. The log densities and the transition kernels in the law of motion of the states are approximated by sieves, which leads to a nite-dimensional representation in terms of macroeconomic aggregates and sieve coefficients. We use this model to study the joint dynamics of technology shocks, per capita GDP, employment rates, and the earnings distribution. We nd that the estimated spillovers between aggregate and distributional dynamics are generally small, a positive technology shock tends to decrease inequality, and a shock that raises the inequality of earnings leads to a small but not signifi cant increase in GDP.