New exogeneity tests and causal paths

Abstract

Abstract We modify Suppes’ probabilistic causality theory by replacing inequalities among probabilities of events by unequal residuals of flipped kernel regression conditional expectation functions, E f(Xj|Xi, Xk) and E f(Xi|Xj, Xk), allowing asymmetry. Using three criteria we aggregate evidence from four orders of stochastic dominance and new asymmetric partial correlation coefficients to develop a unanimity index: UI. The index yields a decision rule for Xi to be self-driven or exogenous, based on confirming the causal paths X i → X j . Thus UI can replace Hausman–Wu's indirect exogeneity test which diagnoses endogeneity (a disease) by showing that instrumental variables (IV) estimator remedy “works.” A simulation supports our decision rules. An illustration identifies exogenous variables which can help predict US economic recession.