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Tweaks to inequality lecture
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9 changes: 9 additions & 0 deletions lectures/_static/quant-econ.bib
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QuantEcon Bibliography File used in conjuction with sphinxcontrib-bibtex package
Note: Extended Information (like abstracts, doi, url's etc.) can be found in quant-econ-extendedinfo.bib file in _static/
###
@article{levitt2019did,
title={Why did ancient states collapse?: the dysfunctional state},
author={Levitt, Malcolm},
journal={Why Did Ancient States Collapse?},
pages={1--56},
year={2019},
publisher={Archaeopress}
}


@book{Burns_2023,
title={Milton Friedman: The Last Conservative by Jennifer Burns},
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106 changes: 61 additions & 45 deletions lectures/inequality.md
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## Overview

In this section we
In the lecture {doc}`long_run_growth` we studied how GDP per capita has changed
for certain countries and regions.

Per capital GDP is important because it gives us an idea of average income for
households in a given country.

However, when we study income and wealth, averages are only part of the story.

For example, imagine two societies, each with one million people, where

* in the first society, the yearly income of one man is $100,000,000 and the income of the
others is zero
* in the second society, the yearly income of everyone is $100

These countries have the same income per capita (average income is $100) but the lives of the people will be very different (e.g., almost everyone in the first society is
starving, even though one person is fabulously rich).

The example above suggests that we should go beyond simple averages when we study income and wealth.

This leads us to the topic of economic inequality, which examines how income and wealth (and other quantities) are distributed across a population.

In this lecture we study inequality, beginning with measures of inequality and
then applying them to wealth and income data from the US and other countries.


* provide motivation for the techniques deployed in the lecture and
* import code libraries needed for our work.

### Some history

Many historians argue that inequality played a key role in the fall of the
Roman Republic.
Many historians argue that inequality played a role in the fall of the Roman Republic (see, e.g., {cite}`levitt2019did`).

Following the defeat of Carthage and the invasion of Spain, money flowed into
Rome from across the empire, greatly enriched those in power.

Meanwhile, ordinary citizens were taken from their farms to fight for long
periods, diminishing their wealth.

The resulting growth in inequality caused political turmoil that shook the
foundations of the republic.
The resulting growth in inequality was a driving factor behind political turmoil that shook the foundations of the republic.

Eventually, the Roman Republic gave way to a series of dictatorships, starting
with Octavian (Augustus) in 27 BCE.
Eventually, the Roman Republic gave way to a series of dictatorships, starting with [Octavian](https://en.wikipedia.org/wiki/Augustus) (Augustus) in 27 BCE.

This history is fascinating in its own right, and we can see some
parallels with certain countries in the modern world.
This history tells us that inequality matters, in the sense that it can drive major world events.

Let's now look at inequality in some of these countries.
There are other reasons that inequality might matter, such as how it affects
human welfare.


### Measurement
With this motivation, let us start to think about what inequality is and how we
can quantify and analyze it.


Political debates often revolve around inequality.

One problem with these debates is that inequality is often poorly defined.

Moreover, debates on inequality are often tied to political beliefs.
### Measurement

This is dangerous for economists because allowing political beliefs to shape our findings reduces objectivity.
In politics and popular media, the word "inequality" is often used quite loosely, without any firm definition.

To bring a truly scientific perspective to the topic of inequality we must start with careful definitions.
To bring a scientific perspective to the topic of inequality we must start with careful definitions.

Hence we begin by discussing ways that inequality can be measured in economic research.

Expand All @@ -77,6 +91,8 @@ import wbgapi as wb
import plotly.express as px
```



## The Lorenz curve

One popular measure of inequality is the Lorenz curve.
Expand Down Expand Up @@ -197,7 +213,7 @@ households own just over 40\% of total wealth.
---
mystnb:
figure:
caption: Lorenz curve of simulated data
caption: Lorenz curve of simulated wealth data
name: lorenz_simulated
---
n = 2000
Expand All @@ -212,13 +228,16 @@ ax.plot(f_vals, f_vals, label='equality', lw=2)
ax.vlines([0.8], [0.0], [0.43], alpha=0.5, colors='k', ls='--')
ax.hlines([0.43], [0], [0.8], alpha=0.5, colors='k', ls='--')
ax.set_xlim((0, 1))
ax.set_xlabel("share of households (%)")
ax.set_xlabel("share of households")
ax.set_ylim((0, 1))
ax.set_ylabel("share of income (%)")
ax.set_ylabel("share of wealth")
ax.legend()
plt.show()
```




### Lorenz curves for US data

Next let's look at US data for both income and wealth.
Expand Down Expand Up @@ -304,8 +323,8 @@ ax.plot(f_vals_nw[-1], l_vals_nw[-1], label=f'net wealth')
ax.plot(f_vals_ti[-1], l_vals_ti[-1], label=f'total income')
ax.plot(f_vals_li[-1], l_vals_li[-1], label=f'labor income')
ax.plot(f_vals_nw[-1], f_vals_nw[-1], label=f'equality')
ax.set_xlabel("share of households (%)")
ax.set_ylabel("share of income/wealth (%)")
ax.set_xlabel("share of households")
ax.set_ylabel("share of income/wealth")
ax.legend()
plt.show()
```
Expand All @@ -316,14 +335,15 @@ One key finding from this figure is that wealth inequality is more extreme than





## The Gini coefficient

The Lorenz curve is a useful visual representation of inequality in a distribution.
The Lorenz curve provides a visual representation of inequality in a distribution.

Another way to study income and wealth inequality is via the Gini coefficient.

In this section we discuss the Gini coefficient and its relationship to the
Lorenz curve.
In this section we discuss the Gini coefficient and its relationship to the Lorenz curve.



Expand Down Expand Up @@ -354,21 +374,19 @@ The idea is that $G=0$ indicates complete equality, while $G=1$ indicates comple
---
mystnb:
figure:
caption: Shaded Lorenz curve of simulated data
caption: Gini coefficient (simulated wealth data)
name: lorenz_gini
---
fig, ax = plt.subplots()
f_vals, l_vals = lorenz_curve(sample)
ax.plot(f_vals, l_vals, label=f'lognormal sample', lw=2)
ax.plot(f_vals, f_vals, label='equality', lw=2)
ax.vlines([0.8], [0.0], [0.43], alpha=0.5, colors='k', ls='--')
ax.hlines([0.43], [0], [0.8], alpha=0.5, colors='k', ls='--')
ax.fill_between(f_vals, l_vals, f_vals, alpha=0.06)
ax.set_ylim((0, 1))
ax.set_xlim((0, 1))
ax.text(0.04, 0.5, r'$G = 2 \times$ shaded area')
ax.set_xlabel("share of households (%)")
ax.set_ylabel("share of income/wealth (%)")
ax.set_ylabel("share of wealth (%)")
ax.legend()
plt.show()
```
Expand Down Expand Up @@ -399,16 +417,16 @@ ax.set_ylim((0, 1))
ax.set_xlim((0, 1))
ax.text(0.55, 0.4, 'A')
ax.text(0.75, 0.15, 'B')
ax.set_xlabel("share of households (%)")
ax.set_ylabel("share of income/wealth (%)")
ax.set_xlabel("share of households")
ax.set_ylabel("share of wealth")
ax.legend()
plt.show()
```



```{seealso}
The World in Data project has a [nice graphical exploration of the Lorenz curve and the Gini coefficient](https://ourworldindata.org/what-is-the-gini-coefficient)
The World in Data project has a [graphical exploration of the Lorenz curve and the Gini coefficient](https://ourworldindata.org/what-is-the-gini-coefficient)
```

### Gini coefficient of simulated data
Expand Down Expand Up @@ -527,7 +545,7 @@ To get a quick overview, let's histogram Gini coefficients across all countries
---
mystnb:
figure:
caption: Histogram of Gini coefficients
caption: Histogram of Gini coefficients across countries
name: gini_histogram
---
# Fetch gini data for all countries
Expand Down Expand Up @@ -585,21 +603,20 @@ As can be seen in {numref}`gini_usa1`, the income Gini
trended upward from 1980 to 2020 and then dropped following at the start of the COVID pandemic.

(compare-income-wealth-usa-over-time)=
### Gini coefficient for wealth (US data)
### Gini coefficient for wealth

In the previous section we looked at the Gini coefficient for income using US data.
In the previous section we looked at the Gini coefficient for income, focusing on using US data.

Now let's look at the Gini coefficient for the distribution of wealth.

We can use the {ref}`Survey of Consumer Finances data <data:survey-consumer-finance>` to look at the Gini coefficient
computed over the wealth distribution.
We will use US data from the {ref}`Survey of Consumer Finances<data:survey-consumer-finance>`


```{code-cell} ipython3
df_income_wealth.year.describe()
```

**Note:** This code can be used to compute this information over the full dataset.
This code can be used to compute this information over the full dataset.

```{code-cell} ipython3
:tags: [skip-execution, hide-input, hide-output]
Expand Down Expand Up @@ -666,7 +683,6 @@ plt.show()
The time series for the wealth Gini exhibits a U-shape, falling until the early
1980s and then increasing rapidly.


One possibility is that this change is mainly driven by technology.

However, we will see below that not all advanced economies experienced similar growth of inequality.
Expand All @@ -677,7 +693,8 @@ However, we will see below that not all advanced economies experienced similar g

### Cross-country comparisons of income inequality

Earlier in this lecture we used `wbgapi` to get Gini data across many countries and saved it in a variable called `gini_all`
Earlier in this lecture we used `wbgapi` to get Gini data across many countries
and saved it in a variable called `gini_all`

In this section we will use this data to compare several advanced economies, and
to look at the evolution in their respective income Ginis.
Expand Down Expand Up @@ -821,7 +838,6 @@ the US exhibits persistent but stable levels around a Gini coefficient of 40.

Another popular measure of inequality is the top shares.


In this section we show how to compute top shares.


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