The Use of Internal Instruments for Errors in Variables and Missing Cross Products.

Theoretically, the most satisfying technique for dealing with errors in variables is the use of instrumental variables. However, the operational difficulty of finding an appropriate instrument is so great that theoretical discussions of errors in variables are even disappearing from the texts. This paper develops a method of constructing instruments whenever one set of independent variables is measured without error and one set is measured with error. This method, which relies upon the internal structure between the independent variables in different subaggregates of the data, also provides a specialized method of dealing with missing data problems. In this latter problem, when variables are measured without error, there is an efficiency loss relative to OLS for complete data. The efficiency loss is such that the technique is more appropriate for dealing with misspecification bias in the "known" portion of the model than with parameter estimation for the "missing" portion of the model. (For publication in the Journal of the American Statistical Association.)