Skip to content

Misc edits #200

New issue

Have a question about this project? Sign up for a free GitHub account to open an issue and contact its maintainers and the community.

Sign up for GitHub

By clicking “Sign up for GitHub”, you agree to our terms of service and privacy statement. We’ll occasionally send you account related emails.

Already on GitHub? Sign in to your account

Merged
merged 2 commits into from
May 30, 2023
Merged

Misc edits #200

Show file tree
Hide file tree
Changes from all commits
Commits
Show all changes
2 commits
Select commit Hold shift + click to select a range
83b8218
misc
jstac May 30, 2023
997c3fb
misc
jstac May 30, 2023
File filter

Filter by extension

Filter by extension
Conversations
Failed to load comments.
Loading
Jump to
Jump to file
Failed to load files.
Loading
Diff view
Diff view
131 changes: 49 additions & 82 deletions lectures/business_cycle.md
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -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]
Expand All @@ -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]

Expand All @@ -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).
Expand All @@ -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.

Expand All @@ -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]
Expand Down Expand Up @@ -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.

Expand Down Expand Up @@ -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.
Expand All @@ -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]
Expand All @@ -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
---
Expand Down Expand Up @@ -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
Expand Down Expand Up @@ -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
Expand Down Expand Up @@ -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
---
Expand Down Expand Up @@ -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
---
Expand Down Expand Up @@ -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
---
Expand All @@ -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

```
12 changes: 5 additions & 7 deletions lectures/eigen_I.md
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -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

Expand All @@ -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:

Expand All @@ -54,7 +53,6 @@ from matplotlib.patches import FancyArrowPatch
from mpl_toolkits.mplot3d import proj3d
```

+++ {"user_expressions": []}

(matrices_as_transformation)=
## Matrices as transformations
Expand All @@ -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 $n \times m$
Expand Down
Loading