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Tom's edit of another lecture, Dec 30
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lectures/calvo.md

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@@ -42,7 +42,7 @@ This lecture describes a linear-quadratic version of a model that Guillermo Calv
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used to illustrate the **time inconsistency** of optimal government
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plans.
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Like Chang {cite}`chang1998credible`, we use the model as a laboratory in which to explore the consequences of
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Like Chang {cite}`chang1998credible`, we use the model as a laboratory in which to explore consequences of
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different timing protocols for government decision making.
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The model focuses attention on intertemporal tradeoffs between
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The model features
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- rational expectations
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- costly government actions at all dates $t \geq 1$ that increase household
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utilities at dates before $t$
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- two Bellman equations, one that expresses the private sector's expectation of future inflation
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- costly government actions at dates $t \geq 1$ that increase household
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utilities at all dates before $t$
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- two Bellman equations, one that expresses the private sector's forecast of future inflation
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as a function of current and future government actions, another that
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describes the value function of a Ramsey planner
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(When there is no uncertainty, an assumption of **rational expectations** simplifies to **perfect foresight**).
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(See {cite}`Sargent77hyper` for a rational expectations version of the model when there is uncertainty)
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(See {cite}`Sargent77hyper` for a rational expectations version of the model in which there is uncertainty)
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Subtracting the demand function at time $t$ from the demand
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function at $t+1$ gives:

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