In economies with lumpy microeconomic adjustment, we establish structural relationships between the dynamics of the cross-sectional distribution of agents and its steady-state counterpart and discipline these relationships using micro data. Applying our methodology to firm lumpy investment, we discover that the dynamics of aggregate capital are structurally linked to two cross-sectional moments of the capital-to-productivity ratio: its dispersion and its covariance with the time elapsed since the last adjustment. We compute these sufficient statistics using plant–level data on the size and frequency of investments. We find that, in order to explain investment dynamics, the benchmark model with fixed adjustment costs must also feature a precise combination of irreversibility and random opportunities of free adjustment.