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We propose two metrics for asset pricing models and apply them to representative agent models with recursive preferences, habits, and jumps. The metrics describe the pricing kernel's dispersion (the entropy of the title) and dynamics (time dependence, a measure of how entropy varies over different time horizons). We show how each model generates entropy and time dependence and compare their magnitudes to estimates derived from asset returns. This exercise — and transparent loglinear approximations — clarifies the mechanisms underlying these models. It also reveals, in some cases, tension between entropy, which should be large enough to account for observed excess returns, and time dependence, which should be small enough to account for mean yield spreads.
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Identification problems arise naturally in forward-looking models when agents observe more than economists. We illustrate the problem in several macro-finance models with Taylor rules. When the shock to the rule is observed by agents but not economists, identification of the rule's parameters requires restrictions on the form of the shock. We show how such restrictions work when we observe the state directly, indirectly, or infer it from observables.
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We inject aggregate uncertainty – risk and ambiguity – into an otherwise standard business cycle model and describe its consequences. We find that increases in uncertainty generally reduce consumption, but they do not account, in this model, for either the magnitude or the persistence of the most recent recession. We speculate about extensions that might do better along one or both dimensions.
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