Estimating aggregate autoregressive processes when only macro data are available

The aggregation of individual random AR(1) models generally leads to an AR(∞) process. We provide two consistent estimators of aggregate dynamics based on either a parametric regression or a minimum distance approach for use when only macro data are available. Notably, both estimators allow us to recover some moments of the cross-sectional distribution of the autoregressive parameter. Both estimators perform very well in our Monte-Carlo experiment, even with finite samples.