A Theory of Dichotomous Valuation with Applications to Variable Selection

An econometric or statistical model may undergo a marginal gain when a new variable is admitted, and marginal loss if an existing variable is removed. The value of a variable to the model is quantified by its expected marginal gain and marginal loss. Under a prior belief that all candidate variables should be treated fairly, we derive a few formulas which evaluate the overall performance of each variable. One formula is identical to that for the Shapley value. However, it is not symmetric with respect to marginal gain and marginal loss; moreover, the Shapley value favors the latter. Thus we propose a unbiased solution. Two empirical studies are included: the first being a multi-criteria model selection for a dynamic panel regression; the second being an analysis of effect on hourly wage given by additional years of schooling.