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Working Paper
Diagnosing and treating bifurcations in perturbation analysis of dynamic macro models
In perturbation analysis of nonlinear dynamic systems, the presence of a bifurcation implies that the first-order behavior of the economy cannot be characterized solely in terms of the first-order derivatives of the model equations. In this paper, we use two simple examples to illustrate how to detect the existence of a bifurcation. Following the general approach of Judd (1998), we then show how to apply l'Hospital's rule to characterize the solution of each model in terms of its higher-order derivatives. We also show that in some cases the bifurcation can be eliminated through ...
Working Paper
When it Rains it Pours: Cascading Uncertainty Shocks
We empirically document that serial uncertainty shocks are (1) common in the data and (2) have an increasingly stronger impact on the macroeconomy. In other words, a series of bad (positive) uncertainty shocks exacerbates the economic decline significantly. From a theoretical perspective, these findings are puzzling: existing benchmark models do not deliver the observed amplification. We show analytically that a state dependent precautionary motive with respect to uncertainty shocks is required. Our derivations suggest that the state dependent precautionary motive only shows up at fourth ...