The Algebra of a Class of Transformations with Applications to Log-Log Models of School Spending

Abstract

A transformation is defined and algebraic relatconships developed between the least squares coefficients, standard errors, and R² in the original and transformed models. This complete analysis is then used to explain the impact on these quantities of different measures of the tax price and dependent variable in log-log school spending models. More generally, it is shown that the different specifications are linked to each other through this transformation so that they have a common fundamental structure. The results should be interpreted in this light. Other applications are described briefly.