Identification and Inference for Causal Effects in Extremes under General Conditions

Abstract: Understanding the propagation of extreme events is important in many economic and environmental applications, yet most econometric methods for causal inference focus on average effects rather than tail behavior. This paper studies the identification of causal relations in extremes and derives resulting estimators and their asymptotic inference. As measure of causal dependence between extreme realizations of variables, we analyze the asymptotic behavior of the Causal Tail Coefficient (CTC) within a linear structural causal model with heavy-tailed regularly varying innovations. In contrast to the existing literature, we allow the variables in the system to exhibit heterogeneous tail indices and consider the presence of potentially heavy-tailed confounders. We derive theoretical results assessing the limiting behavior of the CTC under these conditions and show how differences in tail behavior can help to reach identification of the causal structure. Light-tailed confounders are asymptotically negligible, but sufficiently heavy-tailed confounders can induce extremal dependence patterns that are observationally indistinguishable from direct causal effects. When suitable proxy information is available, identification can be recovered using an adjusted Causal Tail Coefficient. Based on these results, we develop estimation and inference procedures for causal relations in extremes under general conditions. We establish asymptotic properties of the proposed estimators and derive tests for the causal direction and heavy-tailed confounding. Simulation evidence examines their finite-sample performance and provides guidance on their implementation. Applications to climate and financial extremes illustrate how the proposed methods can uncover causal relations that may remain undetected by approaches targeting average dependence.