[inequality] Review of lecture and incorporate updates

[mmcky]

This PR is a full review of the inequality lecture

It incorporates the following feedback from RA reading groups (#380, #379, #297, #295)

General

• review and add appropriate labels to figures x and y axis for figures
• ensure figures are captioned and numbered using mystnb metadata

Code

• write Lorenz Curve function in the lecture without the use of numba (reported to QuantEcon.py as well Fix numba deprecation notice QuantEcon.py#721) to show students what that function does. Fixes [inequality] Update lecture to include Lorenz Curve (as a function) rather than from quantecon package #379
• write gini coefficient function in the lecture without the use of numba.

Note: this has been done but it gives the lecture a long run time when calculating gini coefficients for the US data across 50 years.

• switch to compute 1 year from the data (and then import the remaining years that are pre-computed from a data file) for comparing wealth and income.
• the lecture makes use of data from https://github.com/QuantEcon/high_dim_data but that is external to the lecture. It looks like that repository makes use of git-lfs for larger file storage so there may be a good reason to keep this as a data repository. I recommend we update its name to data-lecture-python or lecture-python-data perhaps? This will be done in a separate PR due to complexity of changing names and the live site at the same time
• update this to use pandas to replace outliers as code is more intuitive.

```{code-cell} ipython3
# use an average to replace an outlier in labor income gini
ginis_li_new = ginis_li
ginis_li_new[5] = (ginis_li[4] + ginis_li[6]) / 2
```

• find out why there is such a bit outlier in 1965 in the computation of Gini from labour income for the USA

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[mmcky]

idea from @jstac re: gini coefficient and high compute costs

How about we show how to compute the gini on small simulated data and then download the gini time series from the world bank or world inequality database?
That way we could get the gini time series for the UK and one or two Scandinavian countries as discussed in the meeting, and do a cross country comparison...

• implement the above suggestion

[mmcky]

• this would need to be updated once the csv file is published on GitHub

[mmcky]

@jstac the last thing I need to do is compare USA with some other countries. This lecture is getting pretty long so I was wondering if we wanted to split this up into:

• Inequality: How do we measure inequality?
• Inequality: Closer look at income and wealth in the USA
• Inequality: Cross country comparisons of income inequality

[jstac]

Thanks @mmcky . Perhaps I'll let you make those last additions and then we can review and discuss how to slice and dice...

[mmcky]

@jstac I am about to time out in 20min for this afternoon (home duties) but wanted to give you an update.

I have added:

• cross-country comparisons in gini between US, UK and Norway
• a plot of GDP per capita vs gini (for US, UK and Normay) for all years (as a year-path scatter plot). I think it is an interesting graph as it plots a couple of dimensions but I need to declutter the labels by adding a 5 year skip on the year labelling.

No need for any detailed review but I would be interested your thoughts on the additional charts in the new sections.

Preview: https://65ea94ae2e9af43492501c44--taupe-gaufre-c4e660.netlify.app/inequality.html

I need to:

• add a 5 year skip to the year labels in the gdp per capita vs gini figure
• update new additions to make them quantecon style-guide compliant (label figures etc.)
• review all issues linked in the main comments section to make sure we address all comments
• finalise narrative additions to make the flow of the lecture more cohesive with the new sections
• proof-read.
• hand over to @jstac

[jstac]

I vote for un-hiding this. It's nice clear code and not too long.

[jstac]

(e.g., ...the following Figure below) -> , as illustrated in "Figure xx"

[jstac]

It occurred to me that the computation of the Gini coefficient could be vectorized:

def gini(y):
    n = len(y)
    y_1 = np.reshape(y, (n, 1))
    y_2 = np.reshape(y, (1, n))
    g_sum = np.sum(np.abs(y_1 - y_2))
    return g_sum / (2 * n * np.sum(y))

If that's not needed, it could still be an exercise asking the reader to produce a faster NumPy version that doesn't use loops and checking that it produces the same output.

[jstac]

Please eliminate fig 5.6 --- the lecture is already long and I don't think it adds much value over 5.8. In 5.8, please add "income" to the figure label.

Please change

"Gini coefficient for US data (income)
Now let’s look at the Gini coefficient using US data."

to

"Gini coefficient for income (US data)"
Let's look at the Gini coefficient for the distribution of income in the US."

[jstac]

I think fig 5.10 is a little confusing when it follows on from fig 5.8. Why does the Gini coefficient for total income look so different? Why are we looking at the income Gini twice? I suggest we drop the comparison and this data, and change the title and start of section 5.3.4 to

"Gini coefficient for wealth (US data)"

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

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

Please then delete

"As we have discussed the Gini coefficient can also be computed over different distributions such as income and wealth."

and suitably modify

"We can use the data collected above survey of consumer finances to look at the Gini coefficient when using income when compared to wealth data."

[jstac]

Please add "for income" to the figure titles for figs 5.12 and 5.13.

[jstac]

Hey @mmcky , many thanks. The lecture is looking very good. I have some more suggestions above. Sorry that they haven't come all at once. It's mainly a case of clarifying and cutting to emphasize the clearest results.

[mmcky]

It occurred to me that the computation of the Gini coefficient could be vectorized:

def gini(y):
    n = len(y)
    y_1 = np.reshape(y, (n, 1))
    y_2 = np.reshape(y, (1, n))
    g_sum = np.sum(np.abs(y_1 - y_2))
    return g_sum / (2 * n * np.sum(y))

If that's not needed, it could still be an exercise asking the reader to produce a faster NumPy version that doesn't use loops and checking that it produces the same output.

Thanks @jstac I think keeping the code simpler is a nice thing -- but I love the idea of making this an exercise.

[mmcky]

@jstac I wrote an exercise but it had a long run time when using us data. So I want to think about making it better using simulation data. I have opened #410 to track the addition so it doesn't have to hold this PR up.

[jstac]

I'm surprised this is green. The build is failing after the code cell starting # Fetch gini data for all countries

[mmcky]

Well that is fascinating. It is working locally -- so I suspect the wb database thought some ip was requested too much data and returned the 400. But fascinating that an API Error doesn't get recongised as a python error.

[mmcky]

@jstac the new run worked OK

https://66020e1f7cfe606404b17ca6--taupe-gaufre-c4e660.netlify.app/inequality

I have re-enabled build failure on warnings which takes an extra hardline on these types of warnings and failures so any build failures will prevent the CI from running fully.

[jstac]

Thanks @mmcky ! It's looking great. Minor comments:

• This sentence needs to be adjusted: "Let us zoom on the US data so we can more clearly observe trends."
• I wonder if we should remove the discussion starting "Looking at each data series we see an outlier in Gini coefficient computed for 1965 for labour income." It's not clear why the labor income distribution is so different to the income distribution in fig 5.7. I feel like we either need to explain that or get rid of the labor income / wealth comparison.
• "The wealth time series exhibits a strong U-shape." should probably be after fig 5.8.
• "As we saw earlier in this lecture " -> "Earlier in this lecture"
• "western economies" -> "Western economies"

[mmcky]

I wonder if we should remove the discussion starting "Looking at each data series we see an outlier in Gini coefficient computed for 1965 for labour income." It's not clear why the labor income distribution is so different to the income distribution in fig 5.7. I feel like we either need to explain that or get rid of the labor income / wealth comparison.

@jstac I would agree with this comment - I think we should get rid of the labour income comparison. I don't have a definitive reason why the series looks so different to Fig 5.7 (income). #412

[mmcky]

thanks @jstac for your review and comments. I have addressed the latest round of feedback.

[jstac]

Many thanks @mmcky . The lecture looks great. I've pushed some minor edits. If it builds correctly then please go ahead and merge.

[mmcky]

thanks @jstac

[mmcky]

thanks @jstac for all your excellent comments and feedback. Will incorporate lessons learnt re: style in the next review.