misc

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 $T_1$.