diff --git a/lectures/ar1_processes.md b/lectures/ar1_processes.md index 34b93ae7..1a041a52 100644 --- a/lectures/ar1_processes.md +++ b/lectures/ar1_processes.md @@ -356,7 +356,7 @@ In this equation, we can use observed data to evaluate the left hand side of {eq And we can use a theoretical AR(1) model to calculate the right hand side. -If $\frac{1}{m} \sum_{t = 1}^m X_t$ is not close to $\psi^(x)$, even for many +If $\frac{1}{m} \sum_{t = 1}^m X_t$ is not close to $\psi^*(x)$, even for many observations, then our theory seems to be incorrect and we will need to revise it. diff --git a/lectures/business_cycle.md b/lectures/business_cycle.md index 5e7174bb..89f72d7f 100644 --- a/lectures/business_cycle.md +++ b/lectures/business_cycle.md @@ -211,7 +211,7 @@ plt.show() GDP growth is positive on average and trending slightly downward over time. -We also see fluctuations over GDP growth over time, some of which are quite large. +We also see fluctuations in GDP growth over time, some of which are quite large. Let's look at a few more countries to get a basis for comparison. @@ -608,7 +608,7 @@ perspectives: consumption, production, and credit level. ### Consumption -Consumption depends on consumers' confidence towards their +Consumption depends on consumers' confidence in their income and the overall performance of the economy in the future. One widely cited indicator for consumer confidence is the [consumer sentiment index](https://fred.stlouisfed.org/series/UMCSENT) published by the University diff --git a/lectures/cagan_adaptive.md b/lectures/cagan_adaptive.md index f3d48c34..db4335a9 100644 --- a/lectures/cagan_adaptive.md +++ b/lectures/cagan_adaptive.md @@ -437,8 +437,8 @@ We invite you to explain to yourself the source of this overshooting and why it ### Experiment 2 -Now we'll do a different experiment, namely, a gradual stabilization in which the rate of growth of the money supply smoothly -decline from a high value to a persistently low value. +Now we'll do a different experiment, namely, a gradual stabilization in which the rate of growth of the money supply smoothly +declines from a high value to a persistently low value. While price level inflation eventually falls, it falls more slowly than the driving force that ultimately causes it to fall, namely, the falling rate of growth of the money supply. diff --git a/lectures/long_run_growth.md b/lectures/long_run_growth.md index d9a5ef57..e21bee1c 100644 --- a/lectures/long_run_growth.md +++ b/lectures/long_run_growth.md @@ -57,7 +57,7 @@ These graphs will portray how the "Industrial Revolution" began in Britain in th In a nutshell, this lecture records growth trajectories of various countries over long time periods. -While some countries have experienced long-term rapid growth across that has lasted a hundred years, others have not. +While some countries have experienced long-term rapid growth that has lasted a hundred years, others have not. Since populations differ across countries and vary within a country over time, it will be interesting to describe both total GDP and GDP per capita as it evolves within a country. @@ -181,7 +181,7 @@ gdp_pc[country].plot( [International dollars](https://en.wikipedia.org/wiki/international_dollar) are a hypothetical unit of currency that has the same purchasing power parity that the U.S. Dollar has in the United States at a given point in time. They are also known as Geary–Khamis dollars (GK Dollars). ::: -We can see that the data is non-continuous for longer periods in the early 250 years of this millennium, so we could choose to interpolate to get a continuous line plot. +We can see that the data is incomplete for longer periods in the early 250 years of this millennium, so we could choose to interpolate to get a continuous line plot. Here we use dashed lines to indicate interpolated trends diff --git a/lectures/lp_intro.md b/lectures/lp_intro.md index 102ad4fd..52504a5a 100644 --- a/lectures/lp_intro.md +++ b/lectures/lp_intro.md @@ -34,7 +34,7 @@ Linear programs come in pairs: If a primal problem involves *maximization*, the dual problem involves *minimization*. -If a primal problem involves *minimization**, the dual problem involves **maximization*. +If a primal problem involves *minimization*, the dual problem involves *maximization*. We provide a standard form of a linear program and methods to transform other forms of linear programming problems into a standard form. diff --git a/lectures/supply_demand_heterogeneity.md b/lectures/supply_demand_heterogeneity.md index 347294be..2672cda1 100644 --- a/lectures/supply_demand_heterogeneity.md +++ b/lectures/supply_demand_heterogeneity.md @@ -36,7 +36,7 @@ import numpy as np from scipy.linalg import inv ``` -## An simple example +## A simple example Let's study a simple example of **pure exchange** economy without production. diff --git a/lectures/tax_smooth.md b/lectures/tax_smooth.md index 0ba1095f..128541de 100644 --- a/lectures/tax_smooth.md +++ b/lectures/tax_smooth.md @@ -19,7 +19,7 @@ kernelspec: This is a sister lecture to our lecture on {doc}`consumption-smoothing `. -By renaming variables, we obtain a version of a model "tax-smoothing model" that Robert Barro {cite}`Barro1979` used to explain why governments sometimes choose not to balance their budgets every period but instead use issue debt to smooth tax rates over time. +By renaming variables, we obtain a version of a model "tax-smoothing model" that Robert Barro {cite}`Barro1979` used to explain why governments sometimes choose not to balance their budgets every period but instead issue debt to smooth tax rates over time. The government chooses a tax collection path that minimizes the present value of its costs of raising revenue. @@ -49,7 +49,7 @@ from collections import namedtuple A government exists at times $t=0, 1, \ldots, S$ and faces an exogenous stream of expenditures $\{G_t\}_{t=0}^S$. -It chooses chooses a stream of tax collections $\{T_t\}_{t=0}^S$. +It chooses a stream of tax collections $\{T_t\}_{t=0}^S$. The model takes a government expenditure stream as an "exogenous" input that is somehow determined outside the model. diff --git a/lectures/unpleasant.md b/lectures/unpleasant.md index 0891036c..2edde85e 100644 --- a/lectures/unpleasant.md +++ b/lectures/unpleasant.md @@ -36,7 +36,7 @@ by printing money at times $t \geq T$. These outcomes are the essential finding of Sargent and Wallace's "unpleasant monetarist arithmetic" {cite}`sargent1981`. -That lecture described supplies and demands for money that appear in lecture. +That lecture described supplies and demands for money that appear in that lecture. It also characterized the steady state equilibrium from which we work backwards in this lecture.