Distinguishing cause from effect based on exogeneity

Recent developments in structural equation modeling have produced several methods that can usually distinguish cause from effect in the two-variable case. For that purpose, how- ever, one has to impose substantial structural constraints or smoothness assumptions on the functional causal mod- els. In this paper, we consider the problem of determining the causal direction from a related but different point of view, and propose a new framework for causal direction de- termination. We show that it is possible to perform causal inference based on the condition that the cause is “exoge- nous” for the parameters involved in the generating pro- cess from the cause to the effect. In this way, we avoid the structural constraints required by the SEM-based ap- proaches. In particular, we exploit nonparametric methods to estimate marginal and conditional distributions, and pro- pose a bootstrap-based approach to test for the exogeneity condition; the testing results indicate the causal direction between two variables. The proposed method is validated on both synthetic and real data.