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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 finite-dimensional representation in terms of macroeconomic aggregates and sieve coefficents. We use this model to study the joint dynamics of technology shocks, per capita GDP, employment rates, and the earnings distribution. We find 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 significant increase in GDP.