developments in the estimation of human capital

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Barbara M. FraumeniMuskie School of Public Service, USM, Portland, ME & the National Bureau of Economic Research, USA,

China Center for Human Capital and Labor Market Research,Central University of Finance and Economics, Beijing, China

Italian Statistical Agency (Istat), Rome, ItalyNovember 17, 2010

Developments in the Estimation

of Human Capital

Muskie School of Public Service Ph.D. Program in Public Policy

Human Capital Developments

Methodology overview & adaptations

Rates

Volume indices

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Human Capital as Capital

• Seminal: Becker (1964), Mincer (1974), Schultz (1961)

• More recent– OECD Human Capital Consortium– “Stiglitz” Commission: Commission on Economic

Performance and Social Progress– World Bank Wealth report– Task Force on Measuring Sustainability


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Theoretical BasisJorgenson‐Fraumeni

• Neoclassical theory of investment (Jorgenson)

• Investment amount as the price you would pay for a business machine that would help you earn future income


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Jorgenson‐Fraumeni (1989, 1992a, 1992b)

• Lifetime income projections

• Depend upon education, age, and survival as well as income earned

• Present discounted values adjusted for future expected income changes with contemporaneous information

• Backwards recursive


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Jorgenson‐Fraumeni Market Equations for Ages 5‐34(those who could be in school)

mi(s,a,e) = ymi(s,a,e) + sr (s,older) * [senr(s,a,enr) * mi(s,older,e+1) + (1 ‐ senr(s,a,enr)) *mi(s,older,e)] * (1+g)/(1+r)


J‐F/OECD Paper Assumptions

• Cannot achieve > highest educational level• No quitting or delaying during whole study

period• Can only enroll in a higher grade than the

one you are in• Data availability (J‐F)

– Determines ages you can be in school– Retirement at age 75

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Adaptations

• Fraumeni simplified method (2006, 2008a, 2008b)

• China– Mincer equations

– Contemporaneous information and expected future enrollment rates

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OECD PaperAssumptions

• Parabolic curve used to determine earnings by individual year of age from 5‐year age group earnings

• Enrollment (employment) rates by single year of age assumed to be equal to the enrollment (employment) rates for 5‐year age groups

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Real Rates

• J‐F approach (rates from Jorgenson & Yun, 1991)– Discount rate

• Long‐run rate of return for the private sector of the economy (4.58%)

– Growth rate of real labor incomes• Growth rate of Harrod neutral productivity growth (1.32%)

• World Bank Wealth Reports (2006, forthcoming)– Discount rate

• Ramsey equation formulation for a social discount rate

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Ramsey EquationWorld Bank, 2006

• World Bank’s Where is the Wealth of Nations (2006, p. 144)

r = ρ + η ∗ ∆ c/c• r = social rate of return on investment• ρ is pure rate of time preference assumed = 1.5• η is the elasticity of utility with respect to

consumption assumed = 1.0• ∆ c/c is the rate of change in per capita

consumption, 1970‐2008? from the World Bank wealth data set

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Ramsey Equation

• “…implicitly assumes that consumption is on a sustainable path, that is, the level of saving is enough to offset the depletion of natural resources.”

• “…the discount rate used is the one a government would choose in allocating resources across generations.”

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J‐F

• Long‐term rate of return for the private sector

• Private (not social) rate, from the point of view of individuals

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What Matters

• Ratio (1+g)/(1+r)

• Rates over the relevant time horizon

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Discount Rate ComparisonsChina

• In the October 2009 paper, 3.14% was used

• Computations of a real discount rate from the 10‐year bond secondary market bracketed 4.58% (the J‐F & OECD rate)

• In the October 2010 paper, 4.58% was used

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Ramsey Equation Result for China

• World Bank methodology resulted in a discount rate of 8.26%

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Real Rate of Growth in Labor IncomeChina

• Computed as labor productivity over past 30 years

• Urban 6.00%– Ratio of real GDP of the secondary and tertiary

industries to the number of persons employed in these industries

• Rural 4.11%– Ratio of real GDP of the primary industries to the

number of persons employed in these industries

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How Do the China Ratios Differ?

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Scenario 80/20 55/45 Discount Labor Income

J‐F & OECD .969 .969 4.58 1.32

World Bank .965 .970 8.26 4.11/6.00

Oct. 2010 .999 1.004 4.58 4.11/6.00

Oct. 2009 1.013 1.018 3.14 4.11/6.00

Ratio of October 2010 scenario ratio to World Bank scenario ratio 1.031 1.040

How Do the China Ratios Differ?Nominal Total Human Capital, 2007

Trillons of RMB

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Scenario IARIW Li et. al. paper

Discount Labor Income

J‐F & OECD 163.74 4.58 1.32

World Bankupdated

176.16 8.14 4.11/6.00

Oct. 2010 322.48 4.58 4.11/6.00

Oct. 2009 437.55 3.14 4.11/6.00

Volume Indices

• China– Moving from a CPI deflated value to a Divisia

index volume measure

• Excellent presentation of Divisia index analysis in Gu and Wong (2008)– Overall index and major aggregate index

– Contribution indices

– Plus a total human capital decomposition

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IARIW CHLR Human Capital in China PaperLi, Liang, Fraumeni, Liu, & Wang (2010)


% Rate of Growth of

Real Measures

Total Human Capital

Human Capital per

CapitaPopulation

1985‐2007 2.35 .78 (33%) 1.57 (67%)

1985‐1995 2.42 .49 (20%) 1.93 (80%)

1995‐2007 2.28 1.02 (45%) 1.27 (55%)

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Gu and Wong 2008Turin Canada Human Capital Paper


% Rate of Growth of

Real Measures

Total Human Capital

Human Capital per

CapitaPopulation

1970‐2007 1.7 .2 (12%) 1.5 (88%)

1970‐1980 3.0 .9 (30%) 2.1 (70%)

1980‐2000 1.2 .0 (0%) 1.2 (100%)

2000‐2007 1.1 ‐.2 (‐18%) 1.3 (118%)

Volume Indexes

• Paasche, Laspeyres, Fisher, Divisia (Thornqvist, translog)

• Chain indices

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Divisia Indexes

• Starts with weighted growth rates

• Weights are average share (over t and t‐1) of nominal human capital in total human capital for that category, e.g., male and female

• Growth rates are population growth rates from t‐1 to t

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Overall Divisia Index

• Total – a Divisia with individual weights and growth rates by characteristic– OECD – by gender, age, & education– China (CHLR) human capital – by gender, age,

education and location– Canada – by gender (2), age (3), and

education (5) – 30 components– J‐F – by gender (2), age (75), and education

(18) – 2700 components

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Partial Human Capital Indexes

• Weights and growth rates only for the type of partial index being constructed– For gender, add up nominal human capital for

male and female separately to create share weights and take the population growth rates for male and female separately

– Same idea for any subcomponent– Can do partial indexes for any combination of

characteristics, e.g., gender and age, or gender, age, and educational attainment

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Partial Indexes & Perfect Substitutes

• In the previous example, males and females can be heterogeneous, but it is assumed there are no differences between males (females) having different age or educational attainment characteristics

• It makes no difference what your age is or what your highest level of education attained when a partial index is being constructed for gender

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Quality (Composition) Decomposition

• Any volume index can be decomposed into an additively aggregated part and a quality (or composition) part

• Additive aggregation – homogeneity assumed

• Quality (or composition) captures heterogeneity

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Quality (Composition)

• Overall index = Additively aggregated part

* Quality index• Overall index to be determined with a

Divisia index in this example• Quality index = Overall index

/ Additively aggregated part

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Quality (Composition)Human Capital

• Homogeneity (additively aggregated) part is population

• Quality index = overall HC index/population• By definition is human capital per capita

• Overall index uses nominal lifetime income shares as weights and population growth rates

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Contributions

• Contributions are the weighted growth rates which comprise a Divisia index

• Contributions by characteristic type always sum by construction to the overall rate of growth of human capital

• For example, the sum of the male and female contribution or the sum of young, prime age, and older age groups (Canada)

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Gu and Wong 2008Turin Canada Human Capital PaperContribution to the Annual Growth of Human Capital


% Rate of Growth of

Real Measures

(roundings)

1970‐2007 1970‐80 1980‐2000 2000‐7

Total 1.7 3.0 1.2 1.1

Young .7 (41%) 2.3 (77%) .0 (0%) .6 (55%)

Prime Age .9 (53%) .7 (23%) 1.2 (100%) .3 (27%)

Older .1 (6%) .1 (3%) .1 (8%) .2 (18%)

Partial Indices for Human Capital Per Capita

• Equations exist which allow the identification of the separate contributions of one vs. two vs. any number of combination of characteristics in an index

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Contributions from Partial Indices for Human Capital Per Capita

• The sum of contributions for one characteristic indices, plus two order indices, … up to the max number of characteristics index, equal the total rate of growth

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Contributions from Partial Indices for Human Capital Per Capita

• The individual indices (say 2nd order: gender and age) subtract the higher order indices (1st order: gender alone and age alone) and the population growth rate for human capital per capita contributions, for example:

dlnHKPKg,a = dlnHKg,a – dlnPOP – dlnHKPKg ‐ dlnHKPKa

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Li et. al. 2010 IARIW PaperContribution to the Average Annual Growth

of Human Capital per Capita, 1986‐2007


Total .81st order age ‐.70

1st order education .86

1st order gender ‐.0006

1st order location 1.05

All 2nd order indices (6) ‐.38

All 3rd order indices (3) ‐.03

4th order index ( 1 ‐ a,e,g,l) .0005

Refinements and TweaksAdaptations for Emerging and Developing

Countries• As time goes on the methodology will be

refined and modified as the number of involved researchers has grown

• Use of Divisias will facilitate comparisons• Thoughts about methodology and possible

refinements are in Christian (2009, 2010) and Abraham (2010)

• Research into rates needs to go forward• The biggest challenge is for the countries for

whom these efforts have not yet begun

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developments in the estimation of human capital

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