Estimating aggregate autoregressive processes when only macro data are available

- The aggregation of individual AR(1) models is an infinite AR process.
- We estimate the aggregate process when only macro data is available.
- A parametric and a minimum distance estimator for the aggregate dynamics are proposed.
- The estimators recover the moments of the distribution of the AR parameters.
- The estimators perform very well, even with finite samples.

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.