Merge pull request #200 from QuantEcon/misc_edits

Misc edits

Author: jstac

lectures/business_cycle.md

@@ -11,22 +11,20 @@ kernelspec:
  name: python3
 ---
 
-+++ {"user_expressions": []}
 
 # Business Cycles
 
 ## Overview
 
-In this lecture we study business cycles
+In this lecture we review some empirical aspects of business cycles.
 
 Business cycles are fluctuations in economic activity over time.
 
-These fluctuations are in the form of expansions (booms), contractions (recessions), and recoveries.
+The include expansions (also called booms) and contractions (also called recessions).
 
-We will look into a series of economic indicators to visualize the expansions and contractions of economies using [World Bank](https://documents.worldbank.org/en/publication/documents-reports/api) and [FRED](https://fred.stlouisfed.org/) data.
+For our study, we will use economic indicators from the [World Bank](https://documents.worldbank.org/en/publication/documents-reports/api) and [FRED](https://fred.stlouisfed.org/).
 
 In addition to those installed by Anaconda, this lecture requires
-libraries to obtain World Bank and FRED data:
 
 ```{code-cell} ipython3
 :tags: [hide-output]
@@ -47,6 +45,8 @@ import wbgapi as wb
 import pandas_datareader.data as web
 ```
 
+Here's some minor code to help with colors in our plots.
+
 ```{code-cell} ipython3
 :tags: [hide-input]
 
@@ -56,14 +56,10 @@ cycler = plt.cycler(linestyle=['-', '-.', '--', ':'],
 plt.rc('axes', prop_cycle=cycler)
 ```
 
-+++ {"user_expressions": []}
 
 ## Data acquisition
 
-We will use `wbgapi` and `pandas_datareader` to retrieve data throughout this
-lecture.
-
-Let's explore how to query data first.
+We will use `wbgapi` and `pandas_datareader` to retrieve data.
 
 We can use `wb.series.info` with the argument `q` to query available data from
 the [World Bank](https://www.worldbank.org/en/home).
@@ -74,37 +70,31 @@ For example, let's retrieve the ID to query GDP growth data.
 wb.series.info(q='GDP growth')
 ```
 
-+++ {"user_expressions": []}
 
 Now we use this series ID to obtain the data.
 
 ```{code-cell} ipython3
-:tags: [hide-output]
-
 gdp_growth = wb.data.DataFrame('NY.GDP.MKTP.KD.ZG',
  ['USA', 'ARG', 'GBR', 'GRC', 'JPN'], 
  labels=True)
 gdp_growth
 ```
 
-+++ {"user_expressions": []}
 
-We can the metadata to learn more about the series.
+We can the metadata to learn more about the series (click to expand).
 
 ```{code-cell} ipython3
 :tags: [hide-output]
 
 wb.series.metadata.get('NY.GDP.MKTP.KD.ZG')
 ```
 
-+++ {"user_expressions": []}
 
-Let's dive into the data with the tools we have.
 
 (gdp_growth)=
 ## GDP growth rate
 
-First we look at the GDP growth rate. 
+First we look at GDP growth. 
 
 Let's source our data from the World Bank and clean it.
 
@@ -123,7 +113,7 @@ Here's a first look at the data
 gdp_growth
 ```
 
-Now we can write a function to generate plots for individual countries taking into account the recessions.
+We write a function to generate plots for individual countries taking into account the recessions.
 
 ```{code-cell} ipython3
 :tags: [hide-input]
@@ -199,9 +189,6 @@ t_params = {'color':'grey', 'fontsize': 9,
  'va':'center', 'ha':'center'}
 ```
 
-+++ {"user_expressions": []}
-
-Now we can plot the data as a time series.
 
 Let's start with the United States.
 
@@ -299,7 +286,7 @@ plot_series(gdp_growth, country,
 plt.show()
 ```
 
-Greece had a significant drop in GDP growth around 2010-2011, during the peak
+Greece experienced a very large drop in GDP growth around 2010-2011, during the peak
 of the Greek debt crisis.
 
 Next let's consider Argentina.
@@ -321,24 +308,18 @@ plot_series(gdp_growth, country,
 plt.show()
 ```
 
-+++ {"user_expressions": []}
-
-The figure shows that Argentina has experienced more volatile cycles than
-the economies mentioned above.
+Notice that Argentina has experienced far more volatile cycles than
+the economies examined above.
 
 At the same time, growth of Argentina did not fall during the two developed
 economy recessions in the 1970s and 1990s.
 
-+++ {"user_expressions": []}
 
 ## Unemployment
 
 Another important measure of business cycles is the unemployment rate.
 
-During a recession, it is more likely that a larger proportion of the working
-population will be laid off.
-
-We demonstrate this using a long-run unemployment rate from FRED spanning from [1929-1942](https://fred.stlouisfed.org/series/M0892AUSM156SNBR) to [1948-2022](https://fred.stlouisfed.org/series/UNRATE) with the unemployment rate between 1942 and 1948 estimated by the [Census Bureau](https://www.census.gov/library/publications/1975/compendia/hist_stats_colonial-1970.html).
+We study unemployment using rate data from FRED spanning from [1929-1942](https://fred.stlouisfed.org/series/M0892AUSM156SNBR) to [1948-2022](https://fred.stlouisfed.org/series/UNRATE), combined unemployment rate data over 1942-1948 estimated by the [Census Bureau](https://www.census.gov/library/publications/1975/compendia/hist_stats_colonial-1970.html).
 
 ```{code-cell} ipython3
 :tags: [hide-input]
@@ -358,7 +339,8 @@ unrate = web.DataReader('UNRATE', 'fred',
  start_date, end_date)
 ```
 
-Now we plot the long-run unemployment rate in the US from 1929 to 2022 with recession defined by NBER
+Let's plot the unemployment rate in the US from 1929 to 2022 with recessions
+defined by the NBER.
 
 ```{code-cell} ipython3
 ---
@@ -411,24 +393,19 @@ ax.set_ylabel('unemployment rate (%)')
 plt.show()
 ```
 
-+++ {"user_expressions": []}
-
-In the plot, we can see that the expansions and contractions of the labor
-market have been highly correlated with recessions. 
 
-However, there is often a delay in the recovery of the labor market after
-recessions.
+The plot shows that 
 
-This trend is clearly visible in the 1930s, as well as in recessions in the
-1980s. 
+* expansions and contractions of the labor market have been highly correlated
+ with recessions. 
+* cycles are, in general, asymmetric: sharp rises in unemployment are followed
+ by slow recoveries.
 
-It also shows us how unique labor market conditions have been during the
+It also shows us how unique labor market conditions were in the US during the
 post-pandemic recovery. 
 
-The labor market has recovered at an unprecedented rate, leading to the
-tightest point in the past decades after the shock in 2020-2021.
+The labor market recovered at an unprecedented rate after the shock in 2020-2021.
 
-+++ {"user_expressions": []}
 
 (synchronization)=
 ## Synchronization
@@ -577,9 +554,8 @@ plot_comparison(gdp_growth.loc[countries, 1962:],
 plt.show()
 ```
 
-+++ {"user_expressions": []}
 
-The comparison of GDP growth rates above shows that 
+The comparison of GDP growth rates above suggests that 
 business cycles are becoming more synchronized in 21st-century recessions.
 
 However, emerging and less developed economies often experience more volatile
@@ -618,42 +594,33 @@ plot_comparison(unempl_rate, countries,
 plt.show()
 ```
 
-France, with its strong labor unions, has a prolonged labor market recovery
-compared to the US and UK. 
+We see that France, with its strong labor unions, typically experiences
+relatively slow labor market recoveries after negative shocks.
 
-However, Japan has a history of very low and stable unemployment rates due to
-a constellation of social, demographic, and cultural factors.
+We also notice that, Japan has a history of very low and stable unemployment rates.
 
-+++ {"user_expressions": []}
 
-## Leading indicators and correlated factors for business cycles
+## Leading indicators and correlated factors 
 
 Examining leading indicators and correlated factors helps policymakers to
 understand the causes and results of business cycles. 
 
 We will discuss potential leading indicators and correlated factors from three
 perspectives: consumption, production, and credit level.
 
-### Consumption
 
-+++ {"user_expressions": []}
+### Consumption
 
 Consumption depends on consumers' confidence towards 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
 of Michigan.
 
-Consumer sentiment remains high during during expansion, but there are significant drops before recession hits.
-
-There is also a clear negative correlation between consumer sentiment and [core consumer price index](https://fred.stlouisfed.org/series/CPILFESL).
-
-This trend is more significant in the during [stagflation](https://en.wikipedia.org/wiki/Stagflation).
-
-When the price of consumer commodities rises, consumer confidence diminishes.
-
-We plot the University of Michigan Consumer Sentiment Index and
-Year-over-year Consumer Price Index Change from 1978-2022 in the US to show this trend
+Here we plot the University of Michigan Consumer Sentiment Index and
+year-on-year 
+[core consumer price index](https://fred.stlouisfed.org/series/CPILFESL)
+(CPI) change from 1978-2022 in the US.
 
 ```{code-cell} ipython3
 ---
@@ -715,23 +682,28 @@ ax_t.set_ylabel('CPI YoY change (%)')
 plt.show()
 ```
 
-+++ {"user_expressions": []}
+We see that 
 
+* consumer sentiment often remains high during during expansion and
+drops before a recession.
+* there is a clear negative correlation between consumer sentiment and the CPI.
 
-### Production
+When the price of consumer commodities rises, consumer confidence diminishes.
 
-Consumers' confidence often influences their consumption pattern.
+This trend is more significant in the during [stagflation](https://en.wikipedia.org/wiki/Stagflation).
+
+
+
+### Production
 
-This often manifests on the production side.
 
-The real industrial output is highly correlated with
-recessions in the economy. 
+Real industrial output is highly correlated with recessions in the economy. 
 
 However, it is not a leading indicator, as the peak of contraction in production 
-delays compared to consumer confidence and inflation.
+is delayed relative to consumer confidence and inflation.
 
 We plot the real industrial output change from the previous year 
-from 1919 to 2022 in the US to show this trend
+from 1919 to 2022 in the US to show this trend.
 
 ```{code-cell} ipython3
 ---
@@ -767,20 +739,19 @@ plt.show()
 
 We observe the delayed contraction in the plot across recessions.
 
-+++ {"user_expressions": []}
 
 ### Credit level
 
 Credit contractions often occur during recessions, as lenders become more
 cautious and borrowers become more hesitant to take on additional debt.
 
-This can be due to several factors such as a decrease in overall economic
-activity, rising unemployment, and gloomy expectations for the future.
+This is due to factors such as a decrease in overall economic
+activity and gloomy expectations for the future.
 
 One example is domestic credit to the private sector by banks in the UK.
 
-The following graph shows the domestic credit to the private sector 
-as a percentage of GDP by banks from 1970 to 2022 in the UK
+The following graph shows the domestic credit to the private sector as a
+percentage of GDP by banks from 1970 to 2022 in the UK
 
 ```{code-cell} ipython3
 ---
@@ -806,11 +777,7 @@ ax = plot_series(private_credit, countries,
 plt.show()
 ```
 
-+++ {"user_expressions": []}
 
 Note that the credit rises during economic expansion
 and stagnates or even contracts after recessions.
 
-```{code-cell} ipython3
-
-```

lectures/eigen_I.md

@@ -25,8 +25,7 @@ kernelspec:
 
 ## Overview
 
-Eigenvalues and eigenvectors are an advanced topic in linear and
-matrix algebra.
+Eigenvalues and eigenvectors are a relatively advanced topic in linear algebra.
 
 At the same time, these concepts are extremely useful for 
 
@@ -38,8 +37,8 @@ At the same time, these concepts are extremely useful for
 
 In this lecture we explain the basics of eigenvalues and eigenvectors.
 
-We assume in this lecture that students are familiar with matrices and
-understand the basics of matrix algebra.
+We assume in this lecture that students are familiar with matrices
+ and understand {doc}`the basics of matrix algebra<linear_equations>`.
 
 We will use the following imports:
 
@@ -54,7 +53,6 @@ from matplotlib.patches import FancyArrowPatch
 from mpl_toolkits.mplot3d import proj3d
 ```
 
-+++ {"user_expressions": []}
 
 (matrices_as_transformation)=
 ## Matrices as transformations
@@ -63,10 +61,10 @@ Let's start by discussing an important concept concerning matrices.
 
 ### Mapping vectors into vectors
 
-One way to think about a given matrix is as a rectangular collection of
+One way to think about a matrix is as a rectangular collection of
 numbers.
 
-Another way to think about a matrix is as a **map** (i.e., as a function) that
+Another way to think about a matrix is as a *map* (i.e., as a function) that
 transforms vectors into new vectors.
 
 To understand the second point of view, suppose we multiply an $n \times m$