A Simple Mathematical Relationship amongk-Class Estimators

Abstract

A simple mathematical relationship among k -class estimators is demonstrated when a regression equation in a simultaneous system involves the regression of an endogenous variable ( y 0 ) on exogenous variables ( x 1 , …, x λ) and on a single endogenous “independent” variable ( y 1 ). The relation is that given any set of observations on the relevant variables, we can calculate a constant k * and set of constants b 1 *, c i *, h b 1 , and h ci ( i = 1, …, λ) such that any estimated coefficients b 1 and c i are related to the value of k corresponding to the estimating procedure by rectangular hyperbolas and where b 1 is an estimated coefficient on y 1 and c i an estimated coefficient on x i ( i = 1, …, λ). The relationship discloses several important properties of k -class estimators and also suggests a series of new important Monte Carlo studies.