The Human Capital Model.docx

The Human Capital Model The human capital model establishes link between the observed wages and the quantity of the skills owned by a worker, these are unobserved. The labour market is competitive. Wt = PtHt Wt is the market wage rate Pt is the price of a unit of skills The Ht is the total quantity of skills lnWt = lnPt + lnHt Ct =ktEt The Et is potential earnings at t or the human capital at t The Ct is the investment in human capital The kt is the time spent investing in human capital, if the person is in school then kt is 1 Et+1 = Et + ctρt The t is the returns to the investment in human capital Et+1 = Et + ktEtρt Et+1 = Et(1 + ktρt) Et = π(1 + iki)E0 The π is the product and the E0 is the human capital when t is 0 The horizon can be divided into 2 periods, the period of schooling and the period of training Period 1 is schooling, the t is equal to the s Period 2 is training, the t is equal to the 0 The schooling period: Es = (1 + kts)sE0 Es = (1 + s)sE0

Et = π(1 + iki)Es Et = π(1 + iki)(1 + s)sE0

lnEt = lnE0 + sln(1 + s) + ln(1 + ki0) lnEt = lnE0 + ss + 0ki The lnEt is the log of human capital, the lnE0 is the human capital when t is 0, it can be the innate ability. The s is the years of schooling and the s is the returns to schooling. The s is constant. The 0 is the returns to training and the ki is the investment in training The 0 is constant The experience period: Kt = k(1 – xt/T) The k is post schooling investment in human capital which is declining over time The k could be less than or equal to 1 The x is on the job experience, it is 0 when person is in school The x increases when the person is out of school Xt = t – s The t is the total time until retirement The s is the years of schooling The equation shows that the person puts less investment in Et as he gets more xt and as T decreases The equation assumes the person finds a job straight after schooling

The k is 1 when in school. After school the k declines with every increase in x The k is the portion of time spent on human capital accumulation The T is the total working life lnEt = lnE0 + ss + 0k(1 – xt/T) (1 – xt/T) = 1 – x – (x(x – 1)/2T)

𝑙𝑛𝐸𝑡 = 𝑙𝑛𝐸0 + 𝑠𝜌𝑠 + 𝜌0 𝑘(𝑥 − 1 −

𝑥 2 −𝑥 2𝑇

𝑙𝑛𝐸𝑡 = (𝑙𝑛𝐸0 − 𝜌0 𝑘) + 𝑠𝜌𝑠 + (𝜌0 𝑘 +

)

𝜌0 𝑘 2𝑇

)𝑥 −

𝜌0 𝑘 2𝑇

𝑥2

The lnEt are potential earnings but the person only works a fraction of his time. The person speds an amount of time doing the kt. Wt = (1 – kt)Et Mincer wage regression: The Mincer wage regression is the relationship between wages, education and experience. lnwt = β0 +β1St +β2Xt +β3Xt2 +εt The S is the years of schooling The X is the years of experience The X2 is the possible decline in post schooling human capital acquisition The εt is the unobserved things that affect the wage such as gender The β0 is the product of the log price of skills and the initial ability. The β1 is the percentage wage increase for an additional year of schooling. The β2 is the percentage wage increase for an additional year of experience. In the absence of direct information on experience Mincer proposed to use years of potential experience The number of years person with age A could have worked if she went to school at 6 and did S years Then after the S years the person works immediately from then X=A–S–6 The 0 is the product of the log price of skills and E0 The 1 is equal to the s because they show the returns to an additional year of schooling and are constant

The model assumptions: There is no optimal years of schooling There is an exogenously determined rate of human capital accumulation The rate of returns to schooling is constant The rate of returns to experience is constant There is no interaction between schooling and training, there is no possibility the schooling is going to change the on the job human capital accumulation process.

Individual investment decision: The S is 1 if person decides to attend college, the S is 0 if person does not attend college The college education pays premium WE > WN The individual’s lifetime wealth is equal to the discounted value of his earnings stream net of his educational cost

VS – The lifetime value of schooling w’ – The wage earned while in school r – the discount rate The c is the cost of schooling The individual that does not choose to attend college has a wage that is w0 There is no cost to schooling as he does not attend the college

If VS is larger than V0 then the individual chooses to attend the college The working life span T is an important determinant in the value of education. The young are more likely to enroll in college than the old as the young have larger T. An increase in T can induce individuals to decide to increase educational attainment. The opportunity cost of going to college increases with the length of schooling is also important. The benefits of education increase with the college wage premium and decrease with the interest rate.

Problems with the model: The S is the rate of return to the schooling In the model the S is constant Including dummy variables for the different levels of education can solve it The εt measures the random shock affecting W. It also picks up unmeasured differences in ability. The correlation between S and the εt is not 0 so there is upward bias in the 1 There is correlation because the residual picks up unobserved characteristics such as cognitive ability, the ability can be correlated with S because smarter people will usually do more schooling because their costs are lower. There needs to be a control for innate ability Using an instrumental variable for innate ability such as IQ tests can solve it. There are other IV possibilities such as family background, wealth, gender etc. If there is no variable that controls for innate ability then the model will overestimate the returns to school The more talented individuals choose to go to school as their costs are lower e.g. effort and tuition The more talented individuals are more likely to have higher wages even if they didn’t have schooling The children from richer backgrounds have lower costs to schooling than others The richer children are more likely to have higher wages If talent and wealth are not controlled for then the returns to schooling are overestimated There is positive ability bias and wealth bias leading to an overestimated 1

Empirical evidence is consistent with the model as wages are increasing in schooling and life cycle profile of wages is increasing and concave. The main criticism of the model is that schooling choices are assumed to be exogenous The OLS estimate of the returns to schooling β1 suffers from the selection (ability) bias There is a large literature that tries to estimate the causal effect of schooling using IV methods or variables controlling for ability. Returns to schooling are found to be in the amount of 5-10% (for OLS and IV).