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Unformatted text preview: = wage, X= years of education. One component of u could be unobserved ability. Ability affects wage, but it is
also correlated with education attainment. So ability varies with education level. For example, we expect that individuals with 16 years of education (college graduates) on average have higher ability than individuals with 12 years of education (HS graduates), i.e., E (u | X = 16) ≠ E (u | X = 12) . When we observe that the average wage of individuals who has 16 years of educations is higher than those with 12 years of education, we do not know it is because of the 4 extra years of education or because of the higher innate ability as implied by the higher education level. In particular, If X and u are positively correlated, then when X increases by one year, u is also expected to be higher. As a result, the increase in wage, Y, may come from both a higher education level and also higher ability. In short, if u and X are correlated, then X can affect Y directly, but at the same time, X can also move u and thereby affect Y (you do not hold u constant in this case). For example, if u and X are positively corrected and u has positive 13 ˆ
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