Toward a human capital accounting that incorporates the individual growth trajectories
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Toward a Human Capital Accounting that Incorporates the Individual Growth Trajectories. M.CIVARDI Univ. Milano-Bicocca. E. ZAVARRONEUniv. IULM (Milano) . R.V.PANSINI Univ. Bocconi (Milano) . Agenda. HC and National Account

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Toward a Human Capital Accounting that Incorporates the Individual Growth Trajectories

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Toward a Human Capital Accounting that Incorporates the Individual Growth Trajectories

M.CIVARDI Univ. Milano-Bicocca


R.V.PANSINI Univ. Bocconi (Milano)


  • HC and National Account

  • University HC definition and measurementby latent curve approach

  • SAM for HC Accounting

HC: Human Capital

  • Classical approach: “Human Capital revolution”

  • Mincer (1958), starting from neoclassical growth model (Solow 1956), analyzed the investment in human capital as a determinant of personal earnings.

  • Schultz (1961), studied the role of knowledge and ability in accounting for productivity growth.

  • Becker (1962), considers “human capital” as an intangible asset (thought as a stock of embodied and disembodied knowledge, education, information, health, entre- preneurship, and productive and innovative skills) formed through investments in schooling, job training, health, as well as through research and development projects and informal knowledge transfers.

  • Extensions to this approach

  • (Ben Porath (1967), Heckman (1974), Rosen (1976), Willis and Rosen (1979)), explicitly treated investment decisions over the life cycle or across different schooling levels as the result of optimizing behaviour, either independently or jointly with consumption and labour supply decisions.

  • Katz and Murphy (1992) put the focus on the market for HC as a mechanism for understanding changes in income inequality and wage differentials.

  • Murphy and Welch (1992, 1993) sought to explain shifts in wage disparity by education and across race and gender as a result of changes in the supply and demand for human capital.

  • Lucas (1988), Jorgenson and Fraumeni (1992) propose evolutions of the human capital literature on the mechanics of economic growth.



Human Capital in the Accounting System 1



Human capital strongly contributes to economic growth, to society and on the life standards .


It is not yet systematically measured in NA

Economic capital represents the most important input for economic growth and it is currently evaluated in the National AccountSystems (NA)

  • A Human Capital Account (HCA) should be :

  • related to a standard macro measure (typically GDP or total population)

  • a complete system within the NA

  • linked to both nonmarket and market accounts

Human Capital in the Accounting System2

1993 UN-SNA: Human Capital is not considered

  • Consideration of human capital is ‘outside the scope of assets in the System’.

  • Expenditures on education can be considered as gross fixed capital formation but not conceived as fixed assets or as other forms of capital.

Human Capital in the Accounting System 3


2008 UN-SNA: Human Capital is only partially


  • Expenditures on education and training for the acquisition of knowledge are still not considered as investments (gross fixed capital formation) and HC is still not conceived as an asset.

  • Education services produced by schools, universities, etc. and acquired by students are treated as final consumption.

  • Costs of training given by the employer to enhance the effectiveness of staff is treated as intermediate consumption.

Human Capital in the Accounting System4

Satellite Accounts

  • Satellite Accounts for Human Capital are not explicitly considered in the SNA 1993 and 2008 .

    In the SNA 2008 satellite accounts of Tourism, Environment, Health and Unpaid Household Production are considered.

Human Capital in the Accounting System 5

Recent Applications and Studies:

  • Abraham and Mackie (2005): ideas and proposals for a framework for Nonmarket Accounting applicable to HC

  • Jorgenson and Landefeld (2006): proposal for an expansion and integration of the US accounts to nonmarket goods and services, such as HC

  • Corrado, Hulten and Sichel (2009): calculation for US of intangible investments in education and in training

  • Christian, M. (2010): Human capital accounting for US (years 1994-2006)

  • OECD (2010) the Human Capital Project: producing numerical estimates for the stock of HC for international and inter-temporal comparisons for OECD countries

  • Tartamella and Di Veroli (2010): proposal for compiling an Italian Education Satellite Account

HCA: requirements

  • Investment and stock

    -volume, value, depreciation and asset lifetime data

  • Evaluation criteria

    -intangible, not bought and sold in the market

  • Quantification of its education component

    -formal, informal, vocational, education and training

  • Starting point: a demographic account

    - Total number of people by age, sex, highest level of educational attainment, participation in the labour force

HCA: measures

  • Stock of HC

    • estimation criteria of its value

    • Since we do not have a good measure of the quantity of HC, we cannot compute the quantity“q” of HC in a similar manner as the investment literature computes the average Tobin's Q for physical capital.

    • The measure of the stock of HC would be related to its quantity in an analogous manner as the market value of physical capital (the stock price) is related to its book value.

      Several approaches to estimate the quantity or book value of HC have been proposed

      Es.:Aproxy for HCoften used is the number of years of education or educational spending.

HCA: measures2

Alternative approaches to measure nominal investments in education:

Input costs

(Kendrick, 1976; Malizia, 1998,2009; Collesi,1999; Versace, 2009)

Expected value of future returns

(Jorgenson and Fraumeni, 1989, 1992 and successive modifications: Wei, 2008, 2010; Gu and Wong, 2010, Abraham, 2010)

Use of cost-based measures is problematic when studying consumption or asset allocation decisions because these proxies ignore the cash flow streams that HC can generate.

Approach A:Components of total cost of investment in formal education

  • Market: Teacher and staff salaries, materials, capital costs.

    (Already included in existing education accounts)

  • Non-market: Student time, parent time, other volunteer time,…

    (Not included in existing education accounts)

    (Abraham, 2010)

Approach A:Estimation methods of education’value added in Italy(Malizia, 1998,1999; Collesi,1999; Versace 2009)


The measure of volume of the Education output (branch 93) refers to the different levels of teaching, distinguished into four main areas:

School system (divided into four levels: pre-primary education; primary education; lower secondary; upper secondary education).

Approach A:Estimation methods of education’ value added in Italy 2


University education (the production of services supplied by universities is split into two CPA classes: Research and Development, for the part related to research, and Education, for the part concerning didactic services).

Vocational training

Subsidiary services to education

Approach A:Estimation methods of education’value added in Italy (Malizia 2009) 3


For the School system: output method is applied

Measure of output used: the number of pupils.

For each education level changes in quality of services supplied taken into account through the “number of standard pupils” (i.e. pupils per classroom and teaching aids). The quality is therefore measured through input (classrooms and equipment) rather than on the pupils’ achievements.

Approach A: Estimation methods of education’value added in Italy4


The Laspeyres volume index for the whole school system is calculated.


  • the quantities are represented by the number of standard pupils.

  • the weights (costs to provide each of the services) are based on the Cofog classification.

Approach A:Estimation methods of education’value added in Italy(Versace, 2009)5


For the University education system: quantity

Quantity indicator : the number of students per faculty and/or group of homogenous faculties (18 faculties).

Weights: the cost per student by faculty, using a methodology based on the standard cost per student.

Approach A:Estimation methods of education’value added in Italy(Versace, 2009)6


For the University education system: quality

Quality adjustments are outcome-based.

Indicators used:

1) The ratio between “regular students” and enrolled students.

2) The reduction of the distance between the average number of years actually spent by student to achieve the degree and the theoretical length.

Same weight assigned to both indicators

Approach B:Valuing the returns to education in Jorgenson and Fraumeni model

The JF model computes expected present value of future labour income for individuals by age, sex and years of education, using data for a given cohort.

The JF model includes:

– both actual market and imputed non-market labour income;

– returns to any additional schooling the individual can be expected to acquire.

LifetimeLabourIncome (LLI) Approach

Denoting the LLI (value of HC of an individual in year y, of gender s, age a and educational attainment e) by miy,s,a,e is:

It measures HCpc for a given group (by gender, education, age) as the discounted present value of expected LLIpcfor that group.

For individuals obtaining an additional year of schooling by the next year

For individuals remaining at their current educational attainment

ymi : average labour income in the current year (including both market

and nonmarket incomes)

sr,a+1 : probability of a person at age a, surviving to age a+1

senr :school enrollment rate

g : real income growth rate

r : one year period discount rate

Our proposal1 regards a new approach to calculate the “value” of university education in HCA

  • We consider a specific dimension of HC, which refers to knowledge accumulation through the attendance of University courses (University Human Capital, shortly UHC)

  • We provide a UHC definition and a measurement in terms of knowledge accumulation through Latent Curve Model(LCM), modelled through a Gompertz function



  • UHC is characterized by :

  • Growth context:

  • enrolled students, through the university training, change

  • own initial HC in UHC

  • Individualcomponents :

  • each studentpresentsdifferent HC levels and different accumulation’

  • trajectories of UHC

  • Group components :

  • on each studenteffects induced by the "group" membership (eg cohort

  • enrolled) work

  • Systemic components :

  • on each student effects induced by the “university system" (eg degree course)


UHC : its measure

t=month of observation; t=1,2,3,…, Tl;

Tl=12 if l=1; Tl=24 if l=2; Tl=36 if l=3

l=year of enrollment

j=1,2,…., Nl

i=interval between t-1 and t


cfujl(i): credits acquired by student j, enrolled at the lth year of degree, in interval i

markjl(i): weight

uhcjl(i): increase of UHC of the student j,enrolled at the lth year of degree, at t respect to t-1.

UHC: estimation methods 1


In our proposal UHC can be estimated through a Latent Curve Model (LCM) (Tucker 1958, Rao 1958).

LCM, used for representing the structure in repeated measures data, is, at its core, a factor analysis model.

In details, we have:

UHC: estimation methods 2


In most factor analysis models the elements in L are freely estimated from the data. However, in latent curve models these elements are often fixed to predetermined values to specify a particular linear o non linear form for the growth process (Curran et al. , 2004).

Data driven choice:GompertzGrowth Curve*

(Browne, 1993; Browne &DuToit, 1991)

*Hypothesis: Given the upper limit α, time t growth rate is proportional to the difference between the maximum achievable level logarithm and the logarithm of the level achieved at time t.

UHC: estimation methods 3

The columns in matrix becomes three: one for each parameter. UHC of the first student is

The parameters can be estimated using software devoted to covariance structures (Mplus, Lisrel, and so on)

Our proposal number 1 for approach A:

In the estimate of the value added of education for the University system the weights proposed by ISTAT researchers for quality adjustments can be replaced by the estimated UHCF (T) of faculty and/or group of homogenous faculties F.

Nl :Number of students enrolled at year l in Faculty F

N :Total number of students enrolled in FacultyF

The difference between the estimated VA before and after the quality adjustments can be considered a measure of the “loss” in the UC production.

Our proposal number 1 for approach B:


With reference to individuals with educational attainment e> upper secondary education, the JF formula can be modified introducing a “learning under use rate” τel where :

Our proposal number 2: To construct a SAM for the HC Accounting

It is well know that the Social Accounting Matrix (SAM) is a flexible schema that include data related to the production side, data related to the income distribution and to consumption expenditure. These characteristics allow to consider the SAM not only as a database and as an accounting tool, but also, in a wider sense, as a macroeconomic simulation model.

We propose a SAM specifically designed for the HC Accounting.

Why to construct a SAM for the HC Accounting?


Under right hypothesis , the SAM can be used as a Leontief linear model and its solution brings to a matrix of multipliers which allows assessing the effects of changes of some of the variables (exogenous) on the others (endogenous) of the system.

Structural analyses of HC generation and accumulation become therefore possible.


Final remarks

  • The SAM including HC should be extended introducing a Satellite set of accounts for HC Stocks and Flows in Real/Physical Units.

  • These accounts in Real/Physical Units can be attached to a SAM in which only a few of the accounts traditionally introduced can be considered.

  • On the supply side, HC production will increase the disposable resources.

  • On the demand side, these resources are acquired by Institutions (first of all by households) and are used in domestic activity or in export.

  • A revaluations/ depreciation account is also necessary

Thank you for your attention

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[email protected]

[email protected]

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