Estimation of models with grouped and ungrouped data by means of "2SLS"

This paper deals with a special case of estimation with groupeddata, where the dependent variable is only available for groups,whereas the endogenous regressor(s) is available at the individuallevel. In this situation, the solution adopted by researchers is toaggregate the individual data and then use standard 2SLS estimation.However when some data is available at the individuallevel, it might be possible to gain efficiency by estimating the firststage using the available individual data, and then estimating thesecond stage at the aggregate level. This estimation procedureyields a consistent and asymptotically normal estimator that werefer to as Mixed-2SLS. Depending on the parametric configurationof the model, the Mixed-2SLS estimator can be more or lessefficient than standard 2SLS. The standard 2SLS estimator of thisliterature is asymptotically equivalent to the OLS estimator basedon group data alone.A number of simulations are carried out that illustrate or confirmtheoretical findings.