Lecture_Notes_Human_Capital_October_15

# Lecture_Notes_Human_Capital_October_15 - Economics 140...

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Economics 140 Human Capital Michael Rothschild October 15 2009

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Human Capital 2 Human Capital 1 Outline 1. The Basic Idea – the standard model (a) Mincer’s Equation (b) Explaining differences in earnings (i) Ability (ii) Credit Constraints (c) Timing and fungibility – transition to a richer model (i) Does it matter when you get human capital? (ii) Are there different kinds of human capital? 2. The Heckman model of human capability formation Economics 140
Human Capital 3 2 The Basic Idea 1. Wage depends on schooling, s , and experience, x ; is a function of form W ( s; x ) . 2. Generally written in log form: w ( s; x ) = ln W ( s; x ) (a) Biggest argument for: (i) Relationship should be proportional. Why? (ii) This fits. (iii) Not such a great argument as can think of this as an atheoretical linear approximation. (b) Theory . Education is an investment. Ignore experience for the time being. Speak of rate of return. Simplest (linear) form w ( s ) = bs W ( s ) = e bs Economics 140

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Human Capital 4 (c) PDV at birth of earnings of someone who is born at 0 ; starts school at 6 ; gets s years of schooling and lives T years: V ( s ) = exp(( b ° r ) s ) Z T ° ( s +6) 0 exp( ° rt ) dt = e ( b ° r ) s 1 ° e r ( T ° ( s +6)) r (1) and the first derivative with respect to s is V 0 ( s ) = ( b ° r ) r (1 ° e ° r ( T ° 6) ) ° e bs e ° r ( T ° 6) (2) (i) No education if b < r: If the rate of return on education is less than the discount rate there is no point in investing in education. (a) Implicit assumption here that you can borrow and lend at the discount rate r . There are perfect capital markets.. Economics 140
Human Capital 5 (ii) The first term in (2) is positive if b > r: The second term is negative and decreasing (in absolute value) in T: If b > r; then getting more education is a trade off between earning more and having less time to earn more. (a) Note that if b > r; the trade off does not involve deferring consumption – because you can borrow. (b) Assuming perfect credit markets then one can borrow against future earnings. (c) But lost wages are the opportunity cost of schooling. (d) When b > r lim T !1 V (0) = 1 : Economics 140

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Human Capital 6 3 Mincer equation 1. Experience. As you get older you get more productive – but there are decreasing returns. Experience, x; is what’s picked up on the job and is generally presumed to be age ° ( s + 6) . The wage of someone who has s years of schooling and is of age a > s + 6 is w ( s; a ) = b 0 + b 1 s + b 2 ( a ° ( s + 6)) + b 3 ( a ° ( s + 6)) 2 (3) 2. Not much theory just an approximation. 3. For diminishing returns to experience (and age) we must have b 3 < 0 : 4. This is known as Mincer’s equation and has been estimated, with various wrinkles millions of times.
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