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[cagan_adaptive] update the editorial suggestions #399

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Update cagan_adaptive.md
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24 changes: 12 additions & 12 deletions lectures/cagan_adaptive.md
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Expand Up @@ -16,13 +16,13 @@ kernelspec:
## Introduction


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

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

Like the model in this lecture {doc}`monetarist theory of price levels <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 {doc}`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}`monetarist theory of price levels <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 {doc}`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 All @@ -36,7 +36,7 @@ It combines these components:

Our model stays quite close to Cagan's original specification.

As in the {doc}`present values <pv>` and {doc}`consumption smoothing<cons_smooth>` lectures, the only linear algebra operations that we'll be using are matrix multiplication and matrix inversion.
As in the lectures {doc}`pv` and {doc}`cons_smooth`, the only linear algebra operations that we'll be using are matrix multiplication and matrix inversion.

To facilitate using linear matrix algebra as our principal mathematical tool, we'll use a finite horizon version of
the model.
Expand All @@ -54,7 +54,7 @@ Let
* $\pi_0^*$ public's initial expected rate of inflation between time $0$ and time $1$.


The demand for real balances $\exp\left(\frac{m_t^d}{p_t}\right)$ is governed by the following version of the Cagan demand function
The demand for real balances $\exp\left(m_t^d-p_t\right)$ is governed by the following version of the Cagan demand function

$$
m_t^d - p_t = -\alpha \pi_t^* \: , \: \alpha > 0 ; \quad t = 0, 1, \ldots, T .
Expand Down Expand Up @@ -88,7 +88,7 @@ $$ (eq:adaptexpn)
As exogenous inputs into the model, we take initial conditions $m_0, \pi_0^*$
and a money growth sequence $\mu = \{\mu_t\}_{t=0}^T$.

As endogenous outputs of our model we want to find sequences $\pi = \{\pi_t\}_{t=0}^T, p = \{p_t\}_{t=0}^T$ as functions of the endogenous inputs.
As endogenous outputs of our model we want to find sequences $\pi = \{\pi_t\}_{t=0}^T, p = \{p_t\}_{t=0}^T$ as functions of the exogenous inputs.

We'll do some mental experiments by studying how the model outputs vary as we vary
the model inputs.
Expand Down Expand Up @@ -278,7 +278,7 @@ $$ (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}`monetarist theory of the price level <cagan_ree>`, we studied a version of the model that replaces hypothesis {eq}`eq:adaptexpn` with
In {doc}`cagan_ree` we studied a version of the model that replaces hypothesis {eq}`eq:adaptexpn` with
a "perfect foresight" or "rational expectations" hypothesis.


Expand All @@ -296,7 +296,7 @@ import matplotlib.pyplot as plt
Cagan_Adaptive = namedtuple("Cagan_Adaptive",
["α", "m0", "Eπ0", "T", "λ"])

def create_cagan_model(α, m0, Eπ0, T, λ):
def create_cagan_adaptive_model(α, m0, Eπ0, T, λ):
return Cagan_Adaptive(α, m0, Eπ0, T, λ)
```
+++ {"user_expressions": []}
Expand All @@ -314,7 +314,7 @@ m0 = 1
μ0 = 0.5
μ_star = 0

md = create_cagan_model(α=α, m0=m0, Eπ0=μ0, T=T, λ=λ)
md = create_cagan_adaptive_model(α=α, m0=m0, Eπ0=μ0, T=T, λ=λ)
```
+++ {"user_expressions": []}

Expand Down Expand Up @@ -431,7 +431,7 @@ $$
\end{cases}
$$

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>`.
Notice that we studied exactly this experiment in a rational expectations version of the model in {doc}`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 @@ -442,7 +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 another lecture {doc}`monetarist theory of price levels <cagan_ree>`.
We invite the reader to compare outcomes with those under rational expectations studied in {doc}`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 $T_1$.

Expand Down