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Revert checked emphasis comments back to italic (batch 3)
Based on PR review feedback with checked [x] emphasis comments, reverted
the following terms from bold back to italic (emphasis, not definitions):
- linear_models.md: ergodicity (concept emphasis)
- markov_asset.md: tree, fruit, shares, dividend (metaphorical emphasis)
- mccall_model.md: values (concept emphasis)
- mle.md: parametric class (emphasis not definition)
- morris_learn.md: prior/posterior distributions, speculative behavior,
ex dividend, Short sales, Harsanyi Common Priors Doctrine (emphasis)
- ols.md: exogenous, marginal effect (emphasis not definitions)
- rational_expectations.md: rational expectations equilibrium (intro emphasis),
perceived/actual law of motion (intro emphasis, formal definitions come later)
- samuelson.md: second-order linear difference equation, national output identity,
consumption function, accelerator, accelerator coefficient, aggregate demand/supply,
random, stochastic, shocks, disturbances (emphasis not definitions)
These are emphasis on concepts or references, not formal definitions.
Copy file name to clipboardExpand all lines: lectures/markov_asset.md
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@@ -451,8 +451,8 @@ Lucas considered an abstract pure exchange economy with these features:
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* a single non-storable consumption good
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* a Markov process that governs the total amount of the consumption good available each period
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* a single **tree** that each period yields **fruit** that equals the total amount of consumption available to the economy
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* a competitive market in **shares** in the tree that entitles their owners to corresponding shares of the **dividend** stream, i.e., the **fruit** stream, yielded by the tree
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* a single *tree* that each period yields *fruit* that equals the total amount of consumption available to the economy
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* a competitive market in *shares* in the tree that entitles their owners to corresponding shares of the *dividend* stream, i.e., the *fruit* stream, yielded by the tree
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* a representative consumer who in a competitive equilibrium
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@@ -50,12 +50,12 @@ Key features of the environment in Morris's model include:
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* A single parameter indexes the set of statistical models
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* All traders observe the same dividend history
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* All traders use Bayes' Law to update beliefs
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* Traders have different initial **prior distributions** over the parameter
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* Traders' **posterior distributions** over the parameter eventually merge
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* Traders have different initial *prior distributions* over the parameter
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* Traders' *posterior distributions* over the parameter eventually merge
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* Before their posterior distributions merge, traders disagree about the predictive density over prospective dividends
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* therefore they disagree about the value of the asset
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Just as in the hard-wired beliefs model of Harrison and Kreps, those differences of opinion induce investors to engage in **speculative behavior** in the following sense:
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Just as in the hard-wired beliefs model of Harrison and Kreps, those differences of opinion induce investors to engage in *speculative behavior* in the following sense:
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* sometimes they are willing to pay more for the asset than what they think is its "fundamental" value, i.e., the expected discounted value of its prospective dividend stream
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As in Harrison-Kreps:
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* The asset is traded **ex dividend**
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* The asset is traded *ex dividend*
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* An owner of a share at the end of time $t$ is entitled to the dividend at time $t+1$
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* An owner of a share at the end of period $t$ also has the right to sell the share at time $t+1$ after having received the dividend at time $t+1$.
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**Short sales are prohibited**.
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*Short sales are prohibited*.
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This matters because it limits how pessimists can express their opinions:
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A set of statistical models that has a particular geometric structure is called a [manifold](https://en.wikipedia.org/wiki/Manifold) of statistical models. Morris endows traders with a shared manifold of statistical models.
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```
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Proceeding in this way adheres to the **Harsanyi Common Priors Doctrine**.
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Proceeding in this way adheres to the *Harsanyi Common Priors Doctrine*.
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## Overview
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This lecture introduces the concept of a **rational expectations equilibrium**.
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This lecture introduces the concept of a *rational expectations equilibrium*.
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To illustrate it, we describe a linear quadratic version of a model
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due to Lucas and Prescott {cite}`LucasPrescott1971`.
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We will learn about how a representative agent's problem differs from a planner's, and how a planning problem can be used to compute quantities and prices in a rational expectations
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equilibrium.
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We will also learn about how a rational expectations equilibrium can be characterized as a [fixed point](https://en.wikipedia.org/wiki/Fixed_point_%28mathematics%29) of a mapping from a **perceived law of motion** to an **actual law of motion**.
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We will also learn about how a rational expectations equilibrium can be characterized as a [fixed point](https://en.wikipedia.org/wiki/Fixed_point_%28mathematics%29) of a mapping from a *perceived law of motion* to an *actual law of motion*.
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Equality between a perceived and an actual law of motion for endogenous market-wide objects captures in a nutshell what the rational expectations equilibrium concept is all about.
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