We argue that dynamic indeterminacy in structural models can help rationalize statistical regularities regarding higher-order properties of macroeconomic time series. Without departing from the Gaussian rational expectations paradigm, we formally establish that any indeterminate equilibrium model admits a linear recursion with multiplicative noise representation. This allows self-fulfilling expectations (sunspots) to enhance endogenous propagation forces that trigger high-probability extreme changes in model variables, while also inducing time variation in conditional volatilities. As a result, even modest, short-lived exogenous shocks can produce large and persistent macroeconomic effects. Using a workhorse New Keynesian framework, we investigate the ability of such a general mechanism to account for observed fat-tailed behavior and volatility clusters in the inflation series over the Great Inflation period of US macroeconomic history.
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