INSTABILITY OF SUNSPOT EQUILIBRIA IN REAL BUSINESS CYCLE MODELS UNDER INFINITE HORIZON LEARNING

What is it about?

Sunspot-driven equilibria in real business cycle (RBC) models have been shown to be unstable under adaptive learning, a type of expectation formation in which agents assume they know the model structure but are uncertain of the parameters. This means that when the model experiences shocks, the result deviates from the original equilibrium, even if the economy begins from it. While previous research on the expectational stability of sunspot equilibria has limited forecasting to only one period, alternative learning approaches, such as infinite-horizon learning, may yield different results. Preston (2005) and Eusepi and Preston (2011) have demonstrated that the stability and transitional dynamics of the rational-expectations equilibrium (REE) can differ under infinite-horizon learning compared to the traditional Euler-equation approach. In this paper, we investigate the expectational stability of sunspot equilibria in RBC models under infinite-horizon learning in order to gain a better understanding of the plausibility of sunspot models with boundedly rational agents. We provide general conditions for sunspot equilibria to be expectationally stable (E-stable) under infinite-horizon learning and apply these conditions to three prominent sunspot-driven one-sector RBC models: Farmer and Guo (1994), Schmitt-Grohé and Uribe (1997), and Wen (1998). Unfortunately, we find that such equilibria are generally unstable under both adaptive learning approaches. Our research makes several contributions to the literature. Firstly, we are the first to examine the stability of sunspot equilibria in RBC models under infinite-horizon learning. Secondly, we analytically derive E-stable conditions for all one-sector RBC models under infinite-horizon learning, a task that has not previously been attempted. Finally, we provide evidence that sunspot equilibria in RBC models are expectationally unstable regardless of the horizon of adaptive learning. These findings have important implications for the use of sunspot models in economic analysis and highlight the importance of considering different types of expectation formation in such models.

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Photo by Zwaddi on Unsplash

Photo by Zwaddi on Unsplash