Minsu Chang

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 coefficients. 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 shocks tends to increase the fraction of individuals earning less than the labor share of per capita GDP, and shocks that raise the inequality of earnings have ambiguous effects on per-capita GDP.

Most economic data are multivariate and so estimating multivariate densities is a classic problem in the literature. However, given vector-valued data, the curse of dimensionality makes nonparametrically estimating the data’s density infeasible if the number of series D is large. Hence, we do not seek to provide estimators that perform well all of the time (it is impossible), but rather seek to provide estimators that perform well most of the time. We adapt the ideas in the Bayesian compression literature to this environment by randomly binning the data. The binning randomly determines both the number of bins and which observation is placed in which bin. This novel procedure induces a simple mixture representation for the data’s density. For any finite number of periods T, the number of mixture components used is random. We construct a bound for this variable as a function of T that holds with high probability. We adopt the nonparametric Bayesian framework and construct a computationally efficient density estimator using Dirichlet processes. Since the number of mixture components is the key determinant of our model’s complexity, our estimator’s convergence rates — √log(T)/√T in the unconditional case and log(T)/√T in the conditional case — depend on D only through the constant term. We then analyze our estimators' performance in a monthly macroeconomic panel and a daily financial panel. Our procedure performs well in capturing the data’s stylized features such as time-varying volatility and fat-tails.