Barbara M' Fraumeni

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Muskie School of Public Service
Ph.D. Program in Public Policy
Introduction to the Lifetime Income Approach
Barbara M. Fraumeni Muskie 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 Bejing, China
June 11, 2009
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Importance of MeasuringHuman Capital
Muskie School of Public Service
Ph.D. Program in Public Policy
3
Plan
Muskie School of Public Service
Ph.D. Program in Public Policy

• Today
• Introduction to accounting system
• full J-F approach
• Another day
• Fraumeni simplified method

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

• Neoclassical theory of investment
• Human and non-human capital should be treated the
  same
• Nonmarket activities and market activities matter

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

• Jorgenson Pachon (1983a, 1983b)

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J-F (1989) The Accumulation of Human and
Nonhuman Capital
Muskie School of Public Service
Ph.D. Program in Public Policy

• Production account, GPDP and factor outlay
• Gross private national labor property income
• Gross private national receipts expenditures
• Gross private national capital accumulation
• Private national wealth

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J-F (1989) The Accumulation of Human and
Nonhuman Capital
Muskie School of Public Service
Ph.D. Program in Public Policy
8
J-F (1989) The Accumulation of Human and
Nonhuman CapitalFull Product, value, 1982
Muskie School of Public Service
Ph.D. Program in Public Policy
Nonhuman Investment
Full Consumption
Human Investment
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J-F (1989) The Accumulation of Human and
Nonhuman CapitalFull Factor Outlay, value, 1982
Muskie School of Public Service
Ph.D. Program in Public Policy
Full Property Outlay
Market Labor Outlay
Nonmarket Labor Outlay
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J-F (1989) The Accumulation of Human and
Nonhuman Capital
Muskie School of Public Service
Ph.D. Program in Public Policy
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J-F (1989) The Accumulation of Human and
Nonhuman CapitalFull Income, value, 1982
Muskie School of Public Service
Ph.D. Program in Public Policy
Full Property Income
Market Labor Income
Nonmarket Labor Income
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J-F (1989) The Accumulation of Human and
Nonhuman Capital
Muskie School of Public Service
Ph.D. Program in Public Policy
13
J-F (1989) The Accumulation of Human and
Nonhuman Capital
Muskie School of Public Service
Ph.D. Program in Public Policy
14
J-F (1989) The Accumulation of Human and
Nonhuman CapitalFull Consumer Expenditures,
value, 1982
Muskie School of Public Service
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Nonhuman Saving
Market Consumer Outlays
Human Saving
Nonmarket Consumer Outlays
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J-F (1989) The Accumulation of Human and
Nonhuman Capital
Muskie School of Public Service
Ph.D. Program in Public Policy
16
J-F (1989) The Accumulation of Human and
Nonhuman Capital
Muskie School of Public Service
Ph.D. Program in Public Policy
17
J-F (1989) The Accumulation of Human and
Nonhuman Capital
Muskie School of Public Service
Ph.D. Program in Public Policy
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J-F (1989) The Accumulation of Human and
Nonhuman CapitalFull Gross Saving, value, 1982
Muskie School of Public Service
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Full Net Saving
Depreciation
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J-F (1989) The Accumulation of Human and
Nonhuman CapitalChange in Wealth, value, 1982
Muskie School of Public Service
Ph.D. Program in Public Policy
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J-F (1989) The Accumulation of Human and
Nonhuman Capital
Muskie School of Public Service
Ph.D. Program in Public Policy
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J-F (1989) The Accumulation of Human and
Nonhuman CapitalFull Wealth, value, 1982
Muskie School of Public Service
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Human Wealth
Nonhuman Wealth
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J-F (1992) The Output of the Education Sector
Muskie School of Public Service
Ph.D. Program in Public Policy

• Constructed the full set of J-F human capital
  accounts
• Main contribution Appendix with equations

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J-F (1992) Investment in Education U.S.
Economic Growth
Muskie School of Public Service
Ph.D. Program in Public Policy

• Constructed the full set of J-F human capital
  accounts
• Looked at the sources of economic growth
• Developed an education sector, using the lifetime
  income approach
• Combined the education sector with a noneducation
  sector to determine the sources of economic
  growth for the U.S. economy

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J-F (1992) Investment in Education U.S.
Economic Growth
Muskie School of Public Service
Ph.D. Program in Public Policy

• Education sector intermediate inputs
• Capital (K), e.g., schools
• Labor (L), e.g., teachers and student time
• Intermediate inputs (X), e.g., pencils paper
• Student time as a residual in value terms
• Output (Q) is investment in education

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J-F (1992) Investment in Education U.S.
Economic Growth
Muskie School of Public Service
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• Noneducation sector only has capital and labor

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J-F (1992) Investment in Education U.S.
Economic Growth,1948-86Noneducation Sector
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Labor
Capital
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Contribution
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• Approximate
• Share weighted rate of growth
• .5 share (t) share (t-1)
• lnvolume(t) lnvolume(t-1)
• where lnvolume(t) lnvolume(t-1)
• is ROG

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Quality Decomposition
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• hours labor quality labor input
• stock capital quality capital input

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Derived Quality
Muskie School of Public Service
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• labor input
• .5 share (t) share (t-1)
• lnvolume(t) lnvolume(t-1)
• ??????
• stock capital quality capital input

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Capital Service Flows (CSF)
Muskie School of Public Service
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• Form volume index weights
• CSF net return depreciation revaluation
  property-type taxes
• Net return r(t) stock (t-1)
• Depreciation d(t) K(t-1)
• Revaluation p(t) p(t-1) K(t-1)
• Income taxes make the equation much more
  complicated

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Productivity (Translog Index)
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• rate of productivity growth ( )
• output growth (VA) input index
• where input index
• weighted rate of growth
• sum of .5 share (t) share (t-1)
• lnvolume(t) lnvolume(t-1)
• over K, L, maybe X
• Q or VA, with/without intermediate input

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J-F (1992) Investment in Education U.S.
Economic Growth,1948-86Noneducation Sector
Muskie School of Public Service
Ph.D. Program in Public Policy
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J-F (1992) Investment in Education U.S.
Economic Growth,1948-86Education Sector
Muskie School of Public Service
Ph.D. Program in Public Policy
Capital Input
Intermediate Input
Labor Input
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J-F (1992) Investment in Education U.S.
Economic Growth,1948-86Education Sector
Muskie School of Public Service
Ph.D. Program in Public Policy
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J-F (1992) Investment in Education U.S.
Economic Growth,1948-86U.S. Economy
Muskie School of Public Service
Ph.D. Program in Public Policy
Capital
Labor
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J-F (1992) Investment in Education U.S.
Economic Growth,1948-86U.S. Economy
Muskie School of Public Service
Ph.D. Program in Public Policy
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J-F (1992) Investment in Education U.S.
Economic Growth,1948-86ROG Comparison
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J-F (1992) Investment in Education U.S.
Economic Growth,1948-86Contribution Comparison
Muskie School of Public Service
Ph.D. Program in Public Policy
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J-F (1992) Investment in Education U.S.
Economic Growth,1948-86Contribution Comparison
Muskie School of Public Service
Ph.D. Program in Public Policy
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J-F (1992) The Output of the Education Sector
Muskie School of Public Service
Ph.D. Program in Public Policy

• Human capital accounting is simultaneously one
  of the easiest and most difficult exercises in
  empirical economics. It is easy in the sense that
  the statistical techniques necessary are
  relatively simple. On the other hand, getting the
  data right can be massive challenge.
• Christian (2009)

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J-F (1992) The Output of the Education Sector
Data Required for Lifetime Income
Muskie School of Public Service
Ph.D. Program in Public Policy

• By sex, individual years of age, and education
  (either highest level attained by individual
  level or enrollment by individual level)
• Population
• Enrollment
• Employment
• Labor compensation
• Hours or market works
• Survival rates
• All but survival rates are contemporary
  information

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J-F (1992) The Output of the Education Sector
Present and Future Income
Muskie School of Public Service
Ph.D. Program in Public Policy

• From contemporary information and data sets,
  assess the probabilities that persons will go to
  school, perform market work (for how many hours),
  and live
• Relative wage rates come from contemporary
  relationships
• Future wage rates are assumed to increase at a
  specified rate

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J-F (1992) The Output of the Education Sector
Methodology
Muskie School of Public Service
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• Backwards recursive
• Estimates dependent upon those older in the
  calendar year
• Stages dictated by data availability

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J-F (1992) The Output of the Education Sector
Five Stages
Muskie School of Public Service
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• Stage 1 No school or work, ages 0-4
• Stage 2 School, but no work, ages 5-15
• Stage 3 School and work, ages 16-34
• Stage 4 Work only, ages 35-74
• Stage 5 Retirement, zero income, ages 75 or
  older

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J-F (1992) The Output of the Education Sector
Equation Notation
Muskie School of Public Service
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• Mi lifetime market income
• Nmi lifetime nonmarket income
• Ymi yearly (current) market income
• Ynmi yearly (current) nonmarket income
• G real rate of growth in labor income
• R discount rate
• Sr survival rate to one year older
• s sex
• a age, by single year of age, e.g., age 0, 1, 2,
  ...74, 75
• e highest level of education attained, by
  individual level of education from grade 1, 2,
  ..., through at least one year of graduate school
• older age 1, e.g., being one year older

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J-F (1992) The Output of the Education Sector
Equations for Ages 35-74
Muskie School of Public Service
Ph.D. Program in Public Policy

• mi(s,a,E) ymi(s,a,e) sr(s,older)
  mi(s,older,e) (1g)/(1r)
• nmi(s,a,e) ynmi(s,a,e) sr(s,older)
  nmi(s,older,e) (1g)/(1r)

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J-F (1992) The Output of the Education Sector
Taxes in the Equations
Muskie School of Public Service
Ph.D. Program in Public Policy

• Yearly ( lifetime) market labor income excludes
  labor income taxes
• The wage rate used to compute yearly ( lifetime)
  nonmarket labor income excludes labor income
  taxes at the average marginal tax rate
• Accordingly, the wage rate from the nonmarket
  computations is gross taxes paid on market labor
  income (1tax), then net the average marginal
  rate (1-taxam)

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J-F (1992) The Output of the Education Sector
What Is Yearly Nonmarket Income?
Muskie School of Public Service
Ph.D. Program in Public Policy

• Assumed 10 hours per day is spent sleeping and in
  maintenance
• Assumed students spend 1600 hours per year in
  formal education activities
• 14 hours per day available to go to school,
  perform market work and engage in nonmarket
  activities, including nonmarket work and leisure
• Opportunity cost methodology is used to value
  nonmarket activities

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J-F (1992) The Output of the Education Sector
Equations for Ages 0-4
Muskie School of Public Service
Ph.D. Program in Public Policy

• mi(s,a,E) sr(s,older) mi(s,older,e)
  (1g)/(1r)
• nmi(s,a,e) sr(s,older) nmi(s,older,e)
  (1g)/(1r)

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J-F (1992) The Output of the Education Sector
More Equation Notation
Muskie School of Public Service
Ph.D. Program in Public Policy

• Senr school enrollment rate
• enr grade level enrolled, by individual level of
  education, grade 1, 2, through at least one year
  of graduate school
• e1 the next higher level of education
  completed, from grade 1, 2, ..., through at most
  one year of graduate school

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J-F (1992) The Output of the Education Sector
Market Equations for Ages 5-34
Muskie School of Public Service
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• mi(s,a,e) ymi(s,a,e) sr (s,older)
• senr(s,a,enr) mi(s,older,e1)
• (1 - senr(s,a,enr)) mi(s,older,e)
• (1g)/(1r)
• nmi(s,a,e) ynmi(s,a,e) sr (s,older)
• senr(s,a,enr) nmi(s,older,e1)
• (1 - senr(s,a,enr)) nmi(s,older,e)
• (1g)/(1r)

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J-F (1992) The Output of the Education Sector
Muskie School of Public Service
Ph.D. Program in Public Policy

• Lifetime income is the sum of market and
  nonmarket lifetime income
• Life(s,a,e) mi(s,a,e) nmi(s,a,e)

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Jorgenson-FraumeniInvestment in Human Capital
Muskie School of Public Service
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• From births, is the expected future lifetime
  income of that individual
• From schooling, investment is produced when
  individuals are enrolled in school
• Is the impact of completing another year of
  school on expected future lifetime income
• Si(s,a,e) senr(s,a,e) life(s,a,e1
  life(s,a,e)

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J-F (1992) The Output of the Education Sector
Valuation Summary
Muskie School of Public Service
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• Market hours At after average labor income tax
  rate
• Nonmarket hours excluding school hours At after
  average marginal labor income tax rate
• School hours Total amount is investment in
  education

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J-F (1992) The Output of the Education Sector
Data Issues
Muskie School of Public Service
Ph.D. Program in Public Policy

• Is population and other variables as of July 1,
  January 1, or what?
• If July 1, which is normally school vacation
  time, is enrollment for the Fall or the past
  Spring?

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J-F (1992) The Output of the Education Sector
Data Issues
Muskie School of Public Service
Ph.D. Program in Public Policy

• Rose-colored glasses effect, e.g., does the
  educational attainment data line-up with the
  enrollment data?
• Drop-outs?
• Students talking more than 5 years to complete a
  4 year college degree?
• Graduate degree completion and degree-type labor
  information?

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J-F (1992) The Output of the Education Sector
Choice of Rates
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• G Real rate of growth in labor income
• R Discount rate

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J-F (1992) The Output of the Education Sector
Data Estimation Issues
Muskie School of Public Service
Ph.D. Program in Public Policy

• Labor data with different marginal information,
  e.g., wages by sex and age (1 margin) and by sex
  and education (another margin), but none by sex,
  age, and education
• RAS or maximum likelihood techniques
• Data from different years with zeroes in
  different places
• Standard demographic techniques to convert
  categorical to single
• Waves problem
• Value-added information

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Jorgenson-FraumeniVolumes
Muskie School of Public Service
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• Translog indexes, where the weights are lifetime
  income or investment shares
• Volumes in the index are population or numbers of
  persons enrolled in school
• For example
• Lifetime income volume (year,s,a,e)
• .5 share(year,s,a,e) share(year-1,s,a,e)
• lnpopulation(year,s,a,e)
  lnpopulation(year-1,s,a,e)

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J-F (1992) The Output of the Education Sector
Volumes
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• For total human capital and by male vs. female
  will be relatively flat in the aggregate as the
  growth rates are population growth rates
• Sub-indices by sex and highest level of education
  attained will show growth over time if
  enrollments in higher levels have been increasing
• In that case, investment in education indices
  would show growth also

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J-F (1992) The Output of the Education Sector
Appreciation/Depreciation
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• At first lifetime income increases Appreciation,
  with education
• Then lifetime income decreases Depreciation, as
  aging dominates the education affect

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J-F (1992) The Output of the Education Sector
Revaluation
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• Hold category constant e.g., sex, age,
  education
• Then determine lifetime income in year t versus
  year t-1 for that category
• Depreciation allows an individual to become
  older, but holds the year t constant

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J-F (1992) The Output of the Education Sector
Nonmarket Component
Muskie School of Public Service
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• Recommend starting with a market only set of
  accounts
• Preserving separate estimates for comparability
  even after a nonmarket component is added

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J-F (1992) The Output of the Education Sector
Result Changes Expected
Muskie School of Public Service
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• ??? Geneva paper and results from this paper

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J-F (1992) The Output of the Education Sector
Per Person capita (Student) Estimates
Muskie School of Public Service
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• Estimating per person (student) is advisable as
  it facilitates checking
• Wage rates should be higher for those with more
  education
• Lifetime incomes should initially rise, then fall
  at some point between 18 and at most 30
• Typically (U.S.) men still spend more time in
  market work than females

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Canadian Decomposition Approach is
AttractiveCharts, tables, etc.
Muskie School of Public Service
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67
Document, document, document!In computer
files as well as in separate documentation
filesDocument assumptionsDocument strange
dataCookbook for someone new to the project
Muskie School of Public Service
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Look at your dataDoes it make sense?(But it
will never be perfect.)Check control totals
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Mistakes will be made!Admit them!
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70
Take time to learn and teachYou are creating
human capital
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Muskie School of Public Service
Ph.D. Program in Public Policy

• Economic success crucially depends upon human
  capital the knowledge, skills, competencies and
  attributes that allow people to contribute to
  their personal and social well-being, as well as
  that of their countries. (Keeley, 2007)