Abstract
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, …, xλ) 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*, ci *, hb 1, and hci (i = 1, …, λ) such that any estimated coefficients b 1 and ci 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 ci an estimated coefficient on xi (i = 1, …, λ). The relationship discloses several important properties of k-class estimators and also suggests a series of new important Monte Carlo studies.
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