Estimation of models with grouped and ungrouped data by means of "2SLS"
This paper deals with a special case of estimation with grouped data, where the dependent variable is only available for groups, whereas the endogenous regressor(s) is available at the individual level. In this situation, the solution adopted by researchers is to aggregate the individual data and then use standard 2SLS estimation. However when some data is available at the individual level, it might be possible to gain efficiency by estimating the first stage using the available individual data, and then estimating the second stage at the aggregate level. This estimation procedure yields a consistent and asymptotically normal estimator that we refer to as Mixed-2SLS. Depending on the parametric configuration of the model, the Mixed-2SLS estimator can be more or less efficient than standard 2SLS. The standard 2SLS estimator of this literature is asymptotically equivalent to the OLS estimator based on group data alone. A number of simulations are carried out that illustrate or confirm theoretical findings.
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