Compute lifetime earnings profiles

[SeaCelo]

Preparing the lifetime earnings profiles for ZAF using data from the Luxembourg Income Study (LIS), available in their LISSY portal.

For South Africa, the LIS has a survey from 2017 which includes total wages as well as hours worked for each individual. Their description of the data is available in their METIS site.

The strategy is to use wages/hour as a measure of productivity, and reporting it by age (s) and by income group (j).

The computation generally follows the procedure described in the OG-USA calibration of lifetime earnings profiles.

1. Download wage/hour in SxJ dimensions
2. Normalize them by the mean of each J income group
3. Take natural log
4. Fill in missing values by regressing ln(productivity) on age, age^2 by each J income group

This is all done with Stata code in the LISSY interface, and manually formatted into a simple CSV with SxJ dimensions.

I'm attaching the results:
productivity_modelled.csv

The .do file is attached (as a zip). lissy2.do.zip

@rickecon Let me know if you think this calculation is reasonable. In the US calibration you do more to compute present value and your range looks different, so we would probably have to adjust this further.

[SeaCelo]

Adding productivity compared to means (the result of step 2 above)
productivity_to_mean.csv

[SeaCelo]

An alternative approach is to use the coefficients computed for the OG-USA calibration as the general structure, and shift them according to the national means available in the NTA database.

[SeaCelo]

After extensive testing with the LIS dataset I don't think it will be possible to compute well-behaved productivity curves for individual countries.
It is possible to estimate national curves by age, but not at the level of the 7 groups ("j"). There is not much to be gained from pursuing this, in my opinion.

My suggestion then is to use the productivity curves created for the OG-USA calibration as standard structural productivity for every country. In other words, keep the current default matrix as is.

[SeaCelo]

I think we have a viable path by adjusting the OG-USA curves with ZAF data. I'm reopening this issue

[SeaCelo]

Reshape lifetime earning profile curve

Method to adjust the shape of the lifetime earning profile curve to better match the country calibration
The OG-USA calibration uses micro data of incomes to estimate the "e" matrix. For most other countries, this level of data is not readily available from public sources or surveys.

We start from the proposition that the estimated USA curves represent a generalized relationship between age and lifetime income. We then propose to adjust this generalized shape in two ways:

1. adjust the shape of all the USA curves to match the target country's national distribution of income per capita for each age year
2. adjust the gaps between the USA curves to match the target country's distribution between the J-income groups

This code addresses only the first. The second is left to a future adjustment

Strategy

Our approach is to apply the national distribution of income by age of the target country (from NTA dataset) to the estimated USA data on income by age (from OG-USA), and then use this re-distributed data to re-estimate the earning profile curves and use them for the target country (ZAF).

Data

We use data from NTA project to compare the differences in income per capita for each age between the target country and the USA. This ratio is the "factor" adjustment at each age.

We use the nearest year available. For South Africa the latest year is 2005. For the USA we use 2006 as the nearest comparator

*Source: https://ntaccounts.org/web/nta/show/Browse%20database

*Notes: We use "Smooth Mean: Per capita, smoothed values."

The adjustment of the USA National data using these factors looks like this:

[SeaCelo]

@rickecon and @sarvonz: this is the result of applying this adjustment to "reshape" of the OG-USA curve using NTA data. Let's discuss at our next meeting.

The original OG-USA curve

The new adjusted curve that applies the ZAF distribution to the USA curve. This would be the OG-ZAF curve (without the inequality adjustment that would shift the differences between the curves).

[SeaCelo]

Here is the Jupyter notebook showing each step
lifetime_income_curve_reshape.ipynb.zip

Population data needed to run the notebook:
un_zaf_pop.csv