Estimation across Data Sets: Two-Stage Auxiliary Instrumental Variables Estimation (2SAIV)

In each of these cases our ability to estimate the theoretically determined equation is limited by the data that are available. In many cases there is simply no solution, and theory must await new opportunities for testing. Under certain circumstances, however, we may still be able to estimate relationships between variables even though they are not measured on the same set of observations.

This technique, which I call two-stage auxiliary instrumental variables (2SAIV), provides some new leverage on such problems and offers the opportunity to test hypotheses that were previously out of reach. T his article develops the 2SAIV estimator, proves its consistency and derives its asymptotic variance. A set of simulations illustrates the performance of the estimator in finite samples and several applications are sketched out.