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‎lectures/cagan_adaptive.md

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name: python3
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---
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# A Fiscal Theory of Price Level with Adaptive Expectations
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# A Monetarist Theory of Price Level with Adaptive Expectations
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## Introduction
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As usual, we'll start by importing some Python modules.
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```{code-cell} ipython3
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import numpy as np
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from collections import namedtuple
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import matplotlib.pyplot as plt
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```
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This lecture is a sequel or prequel to this lecture {doc}`fiscal theory of the price level <cagan_ree>`.
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This lecture is a sequel or prequel to this lecture {doc}`monetarist theory of the price level <cagan_ree>`.
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We'll use linear algebra to do some experiments with an alternative "fiscal theory of the price level".
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We'll use linear algebra to do some experiments with an alternative "monetarist" or "fiscal" theory of the price level".
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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.
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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.
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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.
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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.
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It combines these components:
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Write this equation as
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$$
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A \pi^* = (1-\lambda) B \pi + \pi_0^*
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A \pi^* = (1-\lambda) B \pi + \pi_0^*
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$$ (eq:eq1)
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where the $(T+2) \times (T+2) $matrix $A$, the $(T+2)\times (T+1)$ matrix $B$, and the vectors $\pi^* , \pi_0, \pi_0^*$
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This outcome is typical in models in which adaptive expectations hypothesis like equation {eq}`eq:adaptexpn` appear as a
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component.
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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
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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
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a "perfect foresight" or "rational expectations" hypothesis.
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But now, let's dive in and do some computations with the adaptive expectations version of the model.
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As usual, we'll start by importing some Python modules.
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```{code-cell} ipython3
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import numpy as np
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from collections import namedtuple
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import matplotlib.pyplot as plt
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```
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```{code-cell} ipython3
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Cagan_Adaptive = namedtuple("Cagan_Adaptive",
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["α", "m0", "Eπ0", "T", "λ"])
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\end{cases}
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$$
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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>`.
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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>`.
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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.
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π_seq_1, Eπ_seq_1, m_seq_1, p_seq_1 = solve_and_plot(md, μ_seq_1)
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```
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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>`.
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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>`.
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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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‎lectures/cagan_ree.md

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name: python3
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---
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# A Fiscal Theory of the Price Level
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# A Monetarist Theory of the Price Level
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## Introduction
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As usual, we'll start by importing some Python modules.
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```{code-cell} ipython3
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import numpy as np
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from collections import namedtuple
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import matplotlib.pyplot as plt
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```
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We'll use linear algebra first to explain and then do some experiments with a "monetarist theory of the price level".
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We'll use linear algebra first to explain and then do some experiments with a "fiscal theory of the price level".
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Sometimes this theory is also called a "fiscal theory of the price level".
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A fiscal theory of the price level was described by Thomas Sargent and Neil Wallace in chapter 5 of
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Such a of the price level was described by Thomas Sargent and Neil Wallace in chapter 5 of
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{cite}`sargent2013rational`, which reprints a 1981 article title "Unpleasant Monetarist Arithmetic".
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Sometimes people call it a ``monetary theory of the price level'' because fiscal effects on the price level occur
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Sometimes people call it a "monetary" or "monetarist" theory of the price level because fiscal effects on the price level occur
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through the effects of government fiscal policy decisions on the path of the money supply.
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* a goverment's fiscal policies determine whether it **expenditures** exceed its **tax collections**
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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
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persistent inflation.
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The "fiscal theory of the price level" asserts that
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The "monetarist or fiscal theory of the price level" asserts that
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* to **start** a persistent inflation the government simply persistently runs a money-financed government deficit
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Let's implement and solve this model.
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As usual, we'll start by importing some Python modules.
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```{code-cell} ipython3
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import numpy as np
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from collections import namedtuple
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import matplotlib.pyplot as plt
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```
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First, we store parameters in a `namedtuple`:
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```{code-cell} ipython3
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```
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## Sequel
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This lecture {doc}`fiscal theory of the price level with adaptive expectations <cagan_adaptive>` describes an "adaptive expectations" version of Cagan's model.
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This lecture {doc}`monetarist theory of the price level with adaptive expectations <cagan_adaptive>` describes an "adaptive expectations" version of Cagan's model.
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The dynamics become more complicated and so does the algebra.
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‎lectures/inflation_history.md

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Chapter 3 of {cite}`sargent2002big` focuses on the deliberate changes in policy that Hungary, Austria, Poland, and Germany made to end their hyperinflations.
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The hyperinflations were each ended by restoring or virtually restoring convertibility to the dollar or equivalently to gold.
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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
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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
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{doc}`this lecture <cagan_adaptive>`.
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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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