Incorporating micro data into macro models using pseudo VARs

This paper develops a method to incorporate micro data, available as repeated cross-sections, into macro VAR models to understand the distributional effects of macroeconomic shocks at business cycle frequencies. The method extends existing functional VAR models by "looking within" the micro distribution to identify the degree to which specific types of micro units are affected by macro shocks. It does so by creating a pseudo-panel from the repeated cross-section and adding these pseudo individuals into the macro VAR. Jointly modeling the micro and macro data leads to a large (pseudo) VAR, and we use Bayesian methods to ensure shrinkage and parsimony. Our application revisits Chang et al. (2024) and compares their functional VAR-based distributional impulse response functions with our proposed pseudo VAR-based ones to identify what types of individuals' earnings are most affected by business-cycle-type shocks. We find that the individuals exhibiting the strongest positive cyclical sensitivity are those in the lower tail of the earnings distribution, particularly men and those without a college education, as well as young workers.