Missing aggregate dynamics: on the slow convergence of lumpy adjustment models

When the microeconomic adjustment underlying an aggregate variable is lumpy, conventional VAR procedures often imply less persistence than there really is. This is relevant for non-, semi- and structural models in macroeconomics. The extent to which persistence is underestimated decreases with the level of aggregation, yet convergence is very slow and the bias is likely to be present for sectoral data in general and, in some cases, for aggregate series as well. Paradoxically, while idiosyncratic productivity and demand shocks smooth away microeconomic non-convexities and are often used as a justification for approximating aggregate dynamics with linear models, their presence exacerbates the bias. We propose procedures to correct for the bias and provide various applications. In one of them, the difference in the speed with which inflation responds to sectoral and aggregate shocks disappears once we account for the "missing aggregate dynamics" bias.