A Method to Estimate the Human Capital from Sample Surveys on ...

Indirect Indica<strong>to</strong>rs Γx 2 =H Gender; x 3 = H Race; x 6 = S Age; y 5 = H Yearsof Not Full-Time Work; y 7 = S Years of Not Full-Time Work; y 8 = H Job Status; y 9 = H Occupation;y 10 = H Industry; y 11 = S Job Status; y 12 = S Occupationy 13 = S IndustryFormative indica<strong>to</strong>rs F = (Ψ, y 14 )Ψ: x 1 = H Age; x 4 = Region ;x 5 = H Marital Status;x 7 = S Gender; y 1 = H Years of Schooling;y 2 = S Years of Schooling; y 3 = Number of Children;y 4 = H Years of Full-Time Work;y 6 = S Years of Full-Time Work; y 14 = HouseholdTotal Wealth; y 15 = Household Total Debts.Reflective indica<strong>to</strong>ry 17 = Household IncomeH: Household Head;S: SpouseTable 1 Observed indica<strong>to</strong>rsThe statistical definition of <strong>the</strong> LV HCWe have already stated (Dagum and Vittadini 1996)that, <strong>from</strong> <strong>the</strong> statistical point of view, HC can beexpressed as an LV. But <strong>the</strong>re are different ways an LVcan be defined. Traditionally, a variable can be definedas an LV if <strong>the</strong> equations cannot be manipulated in<strong>to</strong>expressing <strong>the</strong> variable as a function of manifestvariables (Bentler 1982). In o<strong>the</strong>r words, in thisdefinition, an LV is a fac<strong>to</strong>r that underlies and causesreflective indica<strong>to</strong>rs and accounts for <strong>the</strong>ir observedvariance in a measurement model (typically <strong>the</strong> fac<strong>to</strong>rmodel) given <strong>the</strong> effects of o<strong>the</strong>r explicative indica<strong>to</strong>rs(in this case <strong>the</strong> reflective indica<strong>to</strong>r Income, given <strong>the</strong>effect of <strong>the</strong> explicative indica<strong>to</strong>r wealth in equation(3)). O<strong>the</strong>rwise we can define HC as a latent variablecaused and measured (with errors) by a linearcombination of <strong>the</strong> formative indica<strong>to</strong>rs F in equation(2). Finally we can propose a third, more complete,definition of an LV, as in this case where it isconnected with both formative and reflectiveindica<strong>to</strong>rs in a Path Diagram. Hence <strong>the</strong> latent variableHC can be defined as a linear combination offormative indica<strong>to</strong>rs F that best fits <strong>the</strong> reflectiveindica<strong>to</strong>r earning income, as in equations (2)-(3).The proposed methodologyThis approach completes <strong>the</strong> methodology proposed byDagum and Slottje (2000) where <strong>the</strong>y combine azerodimensional latent variable approach (part A) andan actuarial ma<strong>the</strong>matical approach (part B).The Latent Variable approach proposes a newmethodology able <strong>to</strong> obtain <strong>the</strong> zerodimensional HClatent variable, <strong>the</strong>n transforms <strong>the</strong> estimated latentvariable in<strong>to</strong> an accounting monetary value, and finallyestimates <strong>the</strong> mean value of HC. The Path Analysisand <strong>the</strong> Latent Variable Approach are shown inFigure1.The Actuarial Ma<strong>the</strong>matical approach starts with <strong>the</strong>actuarial estimation, in monetary values, of <strong>the</strong> averagehuman capital by age of economic units and finallyestimates <strong>the</strong> average of <strong>the</strong> population in monetaryunits. The syn<strong>the</strong>sis gives <strong>the</strong> final HC estimation anddistribution of American Household.INDIRECTINDICATORS ΓINDICATORS OFHOUSEHOLD INVESTMENT INEDUCATION:FORMATIVE INDICATORS ΨH S YEARS OF SCHOOLING;H S YEARS OF TOTAL TIME WORK; HAGE;REGION; H MARITAL STATUS;S GENDER; NUMBER OF CHILDRENHCWEALTH y 14LATENT VARIABLE HUMAN CAPITALFigureINDICATOR OF EFFECTS OFHC: REFLECTIVEINDICATOR INCOME y 17Figure 1: Path Analysis and Latent Variablesapproachy 1 = g 1 (x 1 , x 3 , x 4 , x 5 ) + u 1y 2 = g 2 (x 1 , x 2 , x 3 , x 4 , x 5 , y 1 ) + u 2y 3 = g 3 (x 1 , x 3 , x 4 , x 5 , y 1 ) + u 3y 4 = g 4 (x 1 , x 2 , x 3 , x 4 , x 5 , y 2 , y 3 ) + u 4y 5 = g 5 (x 1 , x 2 , x 3 , x 4 , x 5 , y 1 , y 4 ) + u 5y 6 = g 6 (x 2 , x 3 , x 4 , x 5 , x 6 , y 2 , y 3 , y 4 ) + u 6y 7 = g 7 (x 2 , x 4 , x 5 , x 6 , y 2 , y 5 , y 6 )+ u 7y 8 = g 8 (x 1 , x 2 , x 3 , x 4 , x 5 , y 1 , y 3 , y 4 ) + u 8 (1)y 9 = g 9 (x 1 , x 2 , x 3 , y 8 ) + u 9(1)y 10 = g 10 (x 2 , x 3 , x 4 , y 1 , y 4 , y 5 , y 9 ) + u 10y 11 = g 11 (x 1 , x 2 , x 4 , x 5 , x 6 , y 2 , y 3 , y 6 , y 9 ) + u 11y 12 = g 12 (x 1 , x 2 , x 4 , x 5 , x 6 , y 2 , y 3 , y 9 , y 11 ) + u 12y 13 = g 13 (x 3 , x 4 , y 6 , y 12 ) + u 13y 14 = g 14 (x 4 , y 1 , y 2 , y 4 , y 7 , y 8 , y 9 , y 10 , y 11 , y 12 , y 13 )+ u 14y 15 = g 15 (x 1, x 3 , x 4 , y 1 , y 2 , y 3 , y 4 , y 9 , y 10 , y 12 , y 14 ) + u 15HC = Fg = [y 14 ,Ψ] g + u 16 (2)