Estimating Aggregate Relationships in Panel Data via the LASSO

This article is concerned with the estimation of aggregate relationships among a potentially large number of panel data variables in the presence of unobserved heterogeneity in the form of interactive effects, an empirically very relevant scenario that has not been considered before. One of our findings is that if the regressors load on the same set of latent factors as the dependent variable, which seems a priori likely since many variables are co-moving, the aggregation automatically accounts for the unobserved heterogeneity. In order to also account for the many regressors, the aggregate model is estimated using a version of LASSO. It is shown that under suitable regulatory conditions, the estimator is oracle efficient and selection consistent, properties that are verified in small samples using Monte Carlo simulations. The empirical usefulness of the estimator is illustrated using as an example the gravity equation of trade.