Chapter 4 introduces asymmetry properties of error distributions of competing causal models. In a way similar to distributional features of observed variables, distributional characteristics of model errors offer valuable information about the underlying causal flow of variable relations. It presents marginal and joint measures that use higher than second moments of error, discusses methods of statistical inference, and summarizes decision guidelines for causal model selection. Further, results of a Monte-Carlo simulation are presented to characterize the behavior of the discussed DDA measures. Simulated as well as real-world data examples illustrate causal model selection based on third and fourth moment properties of model errors.