Political Analysis, 1:1
© by the Society for Political Methodology
research-article |
Estimation across Data Sets: Two-Stage Auxiliary Instrumental Variables Estimation (2SAIV)
Theories demand much of data, often more than a single data collection can provide. For example, many important research questions are set in the past and must rely on data collected at that time and for other purposes. As a result, we often find that the data lack crucial variables. Another common problem arises when we wish to estimate the relationship between variables that are measured in different data sets. A variation of this occurs with a split half sample design in which one or more important variables appear on the "wrong" half. Finally, we may need panel data but have only cross sections available. 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.
This 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.