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[unpleasant] Address Comments on Styles and Improve Citation Style (#495)
* add admonitions, unbold emphasis, and clean the citation style * address comments
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lectures/unpleasant.md

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## Overview
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This lecture builds on concepts and issues introduced in our lecture on **Money Supplies and Price Levels**.
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This lecture builds on concepts and issues introduced in {doc}`money_inflation`.
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That lecture describes stationary equilibria that reveal a [*Laffer curve*](https://en.wikipedia.org/wiki/Laffer_curve) in the inflation tax rate and the associated stationary rate of return
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on currency.
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And the larger is $T$, the higher is the gross-of-interest government deficit that must be financed
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by printing money at times $t \geq T$.
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These outcomes are the essential finding of Sargent and Wallace's **unpleasant monetarist arithmetic** {cite}`sargent1981`.
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**Reader's Guide:** Please read our lecture on Money Supplies and Price levels before diving into this lecture.
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These outcomes are the essential finding of Sargent and Wallace's "unpleasant monetarist arithmetic" {cite}`sargent1981`.
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That lecture described supplies and demands for money that appear in lecture.
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It also characterized the steady state equilibrium from which we work backwards in this lecture.
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In addition to learning about ''unpleasant monetarist arithmetic", in this lecture we'll learn how to implement a **fixed point** algorithm for computing an initial price level.
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In addition to learning about "unpleasant monetarist arithmetic", in this lecture we'll learn how to implement a [*fixed point*](https://en.wikipedia.org/wiki/Fixed_point_(mathematics)) algorithm for computing an initial price level.
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## Setup
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Let's start with quick reminders of the model's components set out in our lecture on **Money Supplies and Price Levels**.
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Let's start with quick reminders of the model's components set out in {doc}`money_inflation`.
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Please consult that lecture for more details and Python code that we'll also use in this lecture.
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## Monetary-Fiscal Policy
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To the basic model of our lecture on **Money Supplies and Price Levels**, we add inflation-indexed one-period government bonds as an additional way for the government to finance government expenditures.
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To the basic model of {doc}`money_inflation`, we add inflation-indexed one-period government bonds as an additional way for the government to finance government expenditures.
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Let $\widetilde R > 1$ be a time-invariant gross real rate of return on government one-period inflation-indexed bonds.
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This equation says that the government (e.g., the central bank) can *decrease* $m_0$ relative to
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$\check m_0$ by *increasing* $B_{-1}$ relative to $\check B_{-1}$.
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This is a version of a standard constraint on a central bank's **open market operations** in which it expands the stock of money by buying government bonds from the public.
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This is a version of a standard constraint on a central bank's [**open market operations**](https://www.federalreserve.gov/monetarypolicy/openmarket.htm) in which it expands the stock of money by buying government bonds from the public.
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## An open market operation at $t=0$
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Following Sargent and Wallace (1981), we analyze consequences of a central bank policy that
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Following Sargent and Wallace {cite}`sargent1981`, we analyze consequences of a central bank policy that
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uses an open market operation to lower the price level in the face of a persistent fiscal
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deficit that takes the form of a positive $g$.
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p_T = \frac{m_0}{\gamma_1 - \overline g - \gamma_2 R_u^{-1}} = \gamma_1^{-1} m_0 \left\{\frac{1}{R_u-\lambda} \right\}
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$$ (eq:pTformula)
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**Remark:**
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```{prf:remark}
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We can verify the equivalence of the two formulas on the right sides of {eq}`eq:pTformula` by recalling that
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$R_u$ is a root of the quadratic equation {eq}`eq:up_steadyquadratic` that determines steady state rates of return on currency.
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```
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## Algorithm (pseudo code)
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Now let's describe a computational algorithm in more detail in the form of a description
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that constitutes ''pseudo code'' because it approaches a set of instructions we could provide to a
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that constitutes pseudo code because it approaches a set of instructions we could provide to a
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Python coder.
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To compute an equilibrium, we deploy the following algorithm.
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```{prf:algorithm}
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Given *parameters* include $g, \check m_0, \check B_{-1}, \widetilde R >1, T $.
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We define a mapping from $p_0$ to $\widehat p_0$ as follows.
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* Compute $R_u, p_T$ from formulas {eq}`eq:up_steadyquadratic` and {eq}`eq:LafferTstationary` above
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* Compute a new estimate of $p_0$, call it $\widehat p_0$, from equation {eq}`eq:allts` above
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* Compute a new estimate of $p_0$, call it $\widehat p_0$, from equation {eq}`eq:allts` above
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* Note that the preceding steps define a mapping
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$$
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where $\theta \in [0,1)$ is a relaxation parameter.
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```
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## Example Calculations
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Since the public has less currency (it's supply has diminished) it is plausible to anticipate that the price level at time $0$ will be driven downward.
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But that is not the end of the story, because this ''open market operation'' at time $0$ has consequences for future settings of $m_{t+1}$ and the gross-of-interest government deficit $\bar g_t$.
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But that is not the end of the story, because this **open market operation** at time $0$ has consequences for future settings of $m_{t+1}$ and the gross-of-interest government deficit $\bar g_t$.
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Let's start with some imports:
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from collections import namedtuple
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```
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Now let's dive in and implement our ''pseudo code'' in Python.
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Now let's dive in and implement our pseudo code in Python.
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```{code-cell} ipython3
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# Create a namedtuple that contains parameters
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return p0
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```
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Let's look at how price level $p_0$ in the stationary $R_u$ equilibrium depends on the initial
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money supply $m_0$.
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Notice that the slope of $p_0$ as a function of $m_0$ is constant.
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This outcome indicates that our model verifies a ''quantity theory of money'' outcome,
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This outcome indicates that our model verifies a quantity theory of money outcome,
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something that Sargent and Wallace {cite}`sargent1981` purposefully built into their model to justify
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the adjective **monetarist** in their title.
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the adjective *monetarist* in their title.
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```{code-cell} ipython3
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plot_path([80, 100], msm)
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```
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{numref}`fig:unpl1` summarizes outcomes of two experiments that convey messages of {cite}`sargent1981`.
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{numref}`fig:unpl1` summarizes outcomes of two experiments that convey messages of Sargent and Wallace {cite}`sargent1981`.
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* An open market operation that reduces the supply of money at time $t=0$ reduces the price level at time $t=0$
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