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Tom's edits of 3 intro lectures
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36 changes: 20 additions & 16 deletions lectures/cagan_adaptive.md
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name: python3
---

# A Fiscal Theory of Price Level with Adaptive Expectations
# A Monetarist Theory of Price Level with Adaptive Expectations

## Introduction

As usual, we'll start by importing some Python modules.

```{code-cell} ipython3
import numpy as np
from collections import namedtuple
import matplotlib.pyplot as plt
```

This lecture is a sequel or prequel to this lecture {doc}`fiscal theory of the price level <cagan_ree>`.
This lecture is a sequel or prequel to this lecture {doc}`monetarist theory of the price level <cagan_ree>`.

We'll use linear algebra to do some experiments with an alternative "fiscal theory of the price level".
We'll use linear algebra to do some experiments with an alternative "monetarist" or "fiscal" theory of the price level".

Like the model in this lecture {doc}`fiscal theory of the price level <cagan_ree>`, the model asserts that when a government persistently spends more than it collects in taxes and prints money to finance the shortfall, it puts upward pressure on the price level and generates persistent inflation.
Like the model in this lecture {doc}`monetarist theory of the price level <cagan_ree>`, the model asserts that when a government persistently spends more than it collects in taxes and prints money to finance the shortfall, it puts upward pressure on the price level and generates persistent inflation.

Instead of the "perfect foresight" or "rational expectations" version of the model in this lecture {doc}`fiscal theory of the price level <cagan_ree>`, our model in the present lecture is an "adaptive expectations" version of a model that Philip Cagan {cite}`Cagan` used to study the monetary dynamics of hyperinflations.
Instead of the "perfect foresight" or "rational expectations" version of the model in this lecture {doc}`monetarist theory of the price level <cagan_ree>`, our model in the present lecture is an "adaptive expectations" version of a model that Philip Cagan {cite}`Cagan` used to study the monetary dynamics of hyperinflations.

It combines these components:

Expand Down Expand Up @@ -131,7 +124,7 @@ $$
Write this equation as
$$
A \pi^* = (1-\lambda) B \pi + \pi_0^*
A \pi^* = (1-\lambda) B \pi + \pi_0^*
$$ (eq:eq1)
where the $(T+2) \times (T+2) $matrix $A$, the $(T+2)\times (T+1)$ matrix $B$, and the vectors $\pi^* , \pi_0, \pi_0^*$
Expand Down Expand Up @@ -285,9 +278,20 @@ $$ (eq:notre)
This outcome is typical in models in which adaptive expectations hypothesis like equation {eq}`eq:adaptexpn` appear as a
component.
In this lecture {doc}`fiscal theory of the price level <cagan_ree>`, we studied a version of the model that replaces hypothesis {eq}`eq:adaptexpn` with
In this lecture {doc}`monetaris theory of the price level <cagan_ree>`, we studied a version of the model that replaces hypothesis {eq}`eq:adaptexpn` with
a "perfect foresight" or "rational expectations" hypothesis.
But now, let's dive in and do some computations with the adaptive expectations version of the model.
As usual, we'll start by importing some Python modules.
```{code-cell} ipython3
import numpy as np
from collections import namedtuple
import matplotlib.pyplot as plt
```
```{code-cell} ipython3
Cagan_Adaptive = namedtuple("Cagan_Adaptive",
["α", "m0", "Eπ0", "T", "λ"])
Expand Down Expand Up @@ -427,7 +431,7 @@ $$
\end{cases}
$$
Notice that we studied exactly this experiment in a rational expectations version of the model in this lecture {doc}`fiscal theory of the price level <cagan_ree>`.
Notice that we studied exactly this experiment in a rational expectations version of the model in this lecture {doc}`monetarist theory of the price level <cagan_ree>`.
So by comparing outcomes across the two lectures, we can learn about consequences of assuming adaptive expectations, as we do here, instead of rational expectations as we assumed in that other lecture.
Expand All @@ -438,7 +442,7 @@ So by comparing outcomes across the two lectures, we can learn about consequence
π_seq_1, Eπ_seq_1, m_seq_1, p_seq_1 = solve_and_plot(md, μ_seq_1)
```
We invite the reader to compare outcomes with those under rational expectations studied in this lecture {doc}`fiscal theory of the price level <cagan_ree>`.
We invite the reader to compare outcomes with those under rational expectations studied in this lecture {doc}`monetarist theory of the price level <cagan_ree>`.
Please note how the actual inflation rate $\pi_t$ "overshoots" its ultimate steady-state value at the time of the sudden reduction in the rate of growth of the money supply at time $T_1$.
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28 changes: 16 additions & 12 deletions lectures/cagan_ree.md
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name: python3
---

# A Fiscal Theory of the Price Level
# A Monetarist Theory of the Price Level

## Introduction

As usual, we'll start by importing some Python modules.

```{code-cell} ipython3
import numpy as np
from collections import namedtuple
import matplotlib.pyplot as plt
```
We'll use linear algebra first to explain and then do some experiments with a "monetarist theory of the price level".

We'll use linear algebra first to explain and then do some experiments with a "fiscal theory of the price level".
Sometimes this theory is also called a "fiscal theory of the price level".

A fiscal theory of the price level was described by Thomas Sargent and Neil Wallace in chapter 5 of
Such a of the price level was described by Thomas Sargent and Neil Wallace in chapter 5 of
{cite}`sargent2013rational`, which reprints a 1981 article title "Unpleasant Monetarist Arithmetic".

Sometimes people call it a ``monetary theory of the price level'' because fiscal effects on the price level occur
Sometimes people call it a "monetary" or "monetarist" theory of the price level because fiscal effects on the price level occur
through the effects of government fiscal policy decisions on the path of the money supply.

* a goverment's fiscal policies determine whether it **expenditures** exceed its **tax collections**
Expand All @@ -45,7 +40,7 @@ Elemental forces at work in the fiscal theory of the price level help to underst
According to this theory, when the government persistently spends more than it collects in taxes and prints money to finance the shortfall (the "shortfall" is called the "government deficit"), it puts upward pressure on the price level and generates
persistent inflation.

The "fiscal theory of the price level" asserts that
The "monetarist or fiscal theory of the price level" asserts that

* to **start** a persistent inflation the government simply persistently runs a money-financed government deficit

Expand Down Expand Up @@ -235,6 +230,15 @@ where we require that $\vert \gamma^* \delta \vert < 1$.
Let's implement and solve this model.
As usual, we'll start by importing some Python modules.
```{code-cell} ipython3
import numpy as np
from collections import namedtuple
import matplotlib.pyplot as plt
```
First, we store parameters in a `namedtuple`:
```{code-cell} ipython3
Expand Down Expand Up @@ -673,7 +677,7 @@ The following code does the calculations and plots the results.
```
## Sequel
This lecture {doc}`fiscal theory of the price level with adaptive expectations <cagan_adaptive>` describes an "adaptive expectations" version of Cagan's model.
This lecture {doc}`monetarist theory of the price level with adaptive expectations <cagan_adaptive>` describes an "adaptive expectations" version of Cagan's model.
The dynamics become more complicated and so does the algebra.
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2 changes: 1 addition & 1 deletion lectures/inflation_history.md
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Expand Up @@ -545,7 +545,7 @@ In practice, their currencies were largely “fiat” or "unbacked", meaning th
Chapter 3 of {cite}`sargent2002big` focuses on the deliberate changes in policy that Hungary, Austria, Poland, and Germany made to end their hyperinflations.
The hyperinflations were each ended by restoring or virtually restoring convertibility to the dollar or equivalently to gold.

The story told in {cite}`sargent2002big` is grounded in a "fiscal theory of the price level" described in {doc}`this lecture <cagan_ree>` and further discussed in
The story told in {cite}`sargent2002big` is grounded in a "monetarist theory of the price level" described in {doc}`this lecture <cagan_ree>` and further discussed in
{doc}`this lecture <cagan_adaptive>`.

Those lectures discuss theories about what holders of those rapidly depreciating currencies were thinking about them and how that shaped responses of inflation to government policies.

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