1. Methodology for New Measurement of Human Capital at World Bank
Gang Liu
Statistics Norway
Presentation at the Fifth World KLEMS Conference
Harvard University, June 4-5, 2018

2. Presentation outline 1. Background 2. Database
3. Lifetime income (Jorgenson-Fraumeni) approach
4. Deriving wage profiles
5. Other variables/parameters needed
6. Population
7. Inter/extrapolation for missing years
8. Concluding remarks

3. 1. Background
Comprehensive wealth accounting at World Bank (World Bank, 2006, 2011)
OECD human capital project (Liu, 2014)
Cooperation between World Bank and OECD (Hamilton and Liu, 2014)
Residual approach vs. Lifetime income (Jorgenson-Fraumeni) approach
I2D2 database (International Income Distribution Database)
Leading to new measurement of human capital (World Bank, 2018)

4. 2. Database
One primary database: I2D2 (International Income Distribution Database), developed by the World Bank and covers 141 economies and 920 harmonized household surveys (up to 2014).
The I2D2 database was once employed for making estimates of the private rate of return to schooling around the world for the period (Mortenegro and Patrinos, 2014)
By using the standard Mincer equations, the M&P paper gives rise to a number of results that can be utilized for measuring human capital.
In addition, ILO employment data, PWT compensation data, UN population database

5. 3. Lifetime income (Jorgenson-Fraumeni) approach
Two stages assumed in a working-age life-cycle: and For the subpopulation (25-65), the lifetime income ( 𝑙 𝑎,𝑒 ) of an individual with certain age of ‘a’ and education of ‘e’ is estimated as:
𝑙 𝑎, 𝑒 = 𝑝 𝑎,𝑒 𝑤 𝑎,𝑒 +𝑑∗ 𝑣 𝑎+1 ∗ 𝑙 𝑎+1,𝑒 ,
where 𝑝 𝑎,𝑒 is employment rate; 𝑤 𝑎,𝑒 is current wages when employed;
𝑑 = (1+growth rate)/(1+discount rate), is discount factor; 𝑣 𝑎+1 is survival rate.
As for the subpopulation (15-25), the lifetime income is estimated as:
𝑙 𝑎, 𝑒 = 𝑝 𝑎,𝑒 𝑤 𝑎,𝑒 + 1− 𝑟 𝑎,𝑒 𝑒+1 ∗𝑑∗ 𝑣 𝑎+1 ∗ 𝑙 𝑎+1,𝑒 + 𝑟 𝑎,𝑒 𝑒+1 ∗𝑑∗ 𝑣 𝑎+1 ∗ 𝑙 𝑎+1,𝑒+1 ,
where 𝑟 𝑎,𝑒 𝑒+1 is school enrolment rate for taking one more year’s education from education
of ‘e’ to one-year higher level of ‘e+1’.
With the estimated lifetime income for a representative individual in each age/gender/education category, the total stock of human capital (ℎ𝑐) is computed as:
ℎ𝑐= 𝑎 𝑒 𝑙 𝑎, 𝑒 𝑛 𝑎,𝑒 ,
where 𝑛 𝑎,𝑒 is the total number of people in group of age ‘a’ and education ‘e’.

6. 4. Deriving wage profiles - Mincer equations
The standard Mincer equation for making estimates of private returns per year of schooling is the following log earnings equation (see Mincer, 1974):
𝐿𝑛(𝑤 𝑖 )=𝛼+ 𝛽 1 𝑆 𝑖 + 𝛽 2 𝑋 𝑖 + 𝛽 3 𝑋 𝑖 2 + 𝜇 𝑖 ,
where 𝐿𝑛(𝑤 𝑖 ) is natural log earnings for individual 𝑖; 𝑆 𝑖 is years of schooling (as a continuous variable); 𝑋 𝑖 is labor market working experience (estimated as 𝐴𝐺𝐸 𝑖 - 𝑆 𝑖 - 6); 𝑋 𝑖 2 is working experience-squared; and 𝜇 𝑖 is a random disturbance term reflecting unobserved abilities.
Suppose all the above estimates are statistically significant, then for an individual 𝑗 in a specific economy/year with 𝑆 𝑗 years of schooling, and age of 𝐴𝐺𝐸 𝑗 , the wage 𝑤 𝑗 will be estimated as follows:
If 𝑋 𝑗 = 𝐴𝐺𝐸 𝑗 − 𝑆 𝑗 −6<0, then 𝑤 𝑗 = 0, else
𝑤 𝑗 = exp ( 𝛼 𝑀 + 𝛽 1 𝑀 𝑆 𝑗 + 𝛽 2 𝑀 𝑋 𝑗 + 𝛽 3 𝑀 𝑋 𝑗 2 ) for male;
𝑤 𝑗 = exp ( 𝛼 𝐹 + 𝛽 1 𝐹 𝑆 𝑗 + 𝛽 2 𝐹 𝑋 𝑗 + 𝛽 3 𝐹 𝑋 𝑗 2 ) for female.
By applying the two equations, the (relative) wages/earnings profile by age, education and gender can be readily derived for each economy/year given the corresponding data availability.

7. 4. Deriving wage profiles - Benchmarking to control totals
Wage versus labor compensation
Using control variables, e.g. ILO total employment by gender, to scale down/up I2D2 sample employment by age/gender/education.
Then using control variables, e.g. UN compensation of employees data, to scale down/up wages/earnings profiles.

8. 5. Other variables/parameters needed
Other variables that are derived from I2D2 database: Employment rate by age/gender/education; Enrolment rate by age/gender/education.
Survival rates: based on country life tables from e.g. UN, WHO databases
Discount factor = (1+real income growth rate)/(1+real discount rate)
In the field of human capital measurement, real income growth rate is usually approximated by the growth rate of the average labor productivity.
The choice of real discount rate varies, as large as 8.26% (World Bank, 2011) and as low as 3.5% (Liu and Greaker, 2009).
As a first try for the new measurement of human capital at World Bank: a uniform discount factor (= 1/1.015) = 0.985, applied for all countries and over years.

9. 6. Population - Benchmarking to control totals
UN population data, only by age group/gender, rather than by single year of age/gender/education
One option: using Barro and Lee datasets (by age group/gender/education) to break down UN population data into population by age/gender/education
Another option: using I2D2 sample distribution to break down UN population data into population by age/gender/education

10. 7. Inter/extrapolation for missing years
Issue: Mincer parameters and other key parameters can only be drawn at some single observed years, while no I2D2 data exist for the years in between, as well as those before, and/or after the single observed years.
Three suggested options: first option is to use other sources, data-demanding
Second option: average of forward and backward interpolation
Third option: linear interpolation

11. 8. Concluding remarks Version zero is a good try.
Methodologies and data, to be updated: e.g. current HC estimation for self-employed
Current status of HC measurement in international organizations: Lifetime income approach already applied by OECD, World Bank, UNECE (Guide)
Any short-term and long-term plan in World Bank?