Information Content of Inflation Expectations: A Copula-Based Model

Abstract

This paper introduces a holistic framework that integrates copula modeling and information-theoretic measures to examine the information content of inflation expectations. Copulas are used to capture the dynamic dependence between inflation and expectations, accounting for extreme events and tail dependence. Information-theoretic measures are employed to quantify the information that expectations provide about inflation. Theoretical results establish a link between copula entropy and mutual information, propose a lower bound for copula entropy, and provide a practical tool for central banks to anchor expectations to achieve inflation targets. Empirical findings reveal higher uncertainty in the tails of the joint distribution and underscore the meaningful information carried by expected inflation for forecasting inflation, particularly with shorter-term expectations.