From 359caaaa79523cb0bfa05e650d6ebe39e80d0c53 Mon Sep 17 00:00:00 2001 From: John Stachurski Date: Thu, 6 Jun 2024 12:21:17 +1000 Subject: [PATCH] misc --- lectures/_static/quant-econ.bib | 9 +++ lectures/inequality.md | 106 ++++++++++++++++++-------------- 2 files changed, 70 insertions(+), 45 deletions(-) diff --git a/lectures/_static/quant-econ.bib b/lectures/_static/quant-econ.bib index 409748aa..ce5c6e1c 100644 --- a/lectures/_static/quant-econ.bib +++ b/lectures/_static/quant-econ.bib @@ -2,6 +2,15 @@ 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}, diff --git a/lectures/inequality.md b/lectures/inequality.md index acfded55..f6c0ff67 100644 --- a/lectures/inequality.md +++ b/lectures/inequality.md @@ -15,15 +15,35 @@ kernelspec: ## 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. @@ -31,30 +51,24 @@ 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. @@ -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. @@ -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 @@ -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. @@ -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() ``` @@ -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. @@ -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() ``` @@ -399,8 +417,8 @@ 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() ``` @@ -408,7 +426,7 @@ 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 @@ -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 @@ -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 ` to look at the Gini coefficient -computed over the wealth distribution. +We will use US data from the {ref}`Survey of Consumer Finances` ```{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] @@ -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. @@ -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. @@ -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.