An Instrumental Variable Interpretation of k-Class Estimation

The purpose of this note is to provide an instrumental variable interpretation of Theil’s k-class of structural equation estimators. Kleins [1955] interpretation of two-stage least squares contributed to an understanding of that member of the k-class. The present extension may serve a similar function with respect to the k-class as a whole. In particular, it provides a fresh motivation for the “least variance ratio “method. 2. The k-Class And Instrumental Variables We consider a single structural equation