Joint Dynamics of Inflation and Unemployment: A Copula-Based Study

Abstract This paper investigates the nonlinear dependence structure between inflation and unemployment in the United States by employing copula models. Using monthly data from 2000 to 2024, we apply the Inference Functions for Margins method to model marginal distributions separately from their dependence structure. Eight copula families—including Gaussian, Clayton, Gumbel, Student-t, Frank, Joe, BB1, and BB7—are estimated and compared using AIC, BIC, Vuong tests, and goodness-of-fit measures. Results indicate that the Gaussian copula provides the best overall fit, effectively capturing moderate and symmetric co-movements in stable macroeconomic conditions. However, tail-dependent copulas such as Student-t and BB7 show superior ability to model joint extreme events, such as stagflation or synchronized downturns. This dual insight emphasizes the importance of aligning model choice with policy objectives—whether focused on central trends or stress scenarios. Our copula-based simulation of joint distributions highlights risks often overlooked by traditional linear models, offering a more nuanced foundation for macroeconomic risk assessment and robust policy formulation, with potential future applications in tail-sensitive risk forecasting and early warning systems.