From 3825e85fec9ab2b18deb72a19a442050bc5d1dec Mon Sep 17 00:00:00 2001 From: John Stachurski Date: Fri, 15 Mar 2024 06:27:52 +1100 Subject: [PATCH] misc --- lectures/cagan_adaptive.md | 14 +++++++------- 1 file changed, 7 insertions(+), 7 deletions(-) diff --git a/lectures/cagan_adaptive.md b/lectures/cagan_adaptive.md index 6ecb5a1b..88d13626 100644 --- a/lectures/cagan_adaptive.md +++ b/lectures/cagan_adaptive.md @@ -16,13 +16,13 @@ kernelspec: ## Introduction -This lecture is a sequel or prequel to another lecture {doc}`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. -Like the model in this lecture {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. +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}`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: @@ -36,7 +36,7 @@ It combines these components: Our model stays quite close to Cagan's original specification. -As in the {doc}`pv` and {doc}`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. @@ -278,7 +278,7 @@ $$ (eq:notre) This outcome is typical in models in which adaptive expectations hypothesis like equation {eq}`eq:adaptexpn` appear as a component. -In this lecture {doc}`cagan_ree`, we studied a version of the model that replaces hypothesis {eq}`eq:adaptexpn` with +In {doc}`cagan_ree` we studied a version of the model that replaces hypothesis {eq}`eq:adaptexpn` with a "perfect foresight" or "rational expectations" hypothesis. @@ -431,7 +431,7 @@ $$ \end{cases} $$ -Notice that we studied exactly this experiment in a rational expectations version of the model in this lecture {doc}`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. @@ -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}`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 $T_1$.