# LABOR ECONOMICS Lecture 7: Human Capital and Distribution of Earnings Prof. Saul Hoffman Université de Paris 1 Panthéon-Sorbonne March, 2013.

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LABOR ECONOMICS Lecture 7: Human Capital and Distribution of Earnings Prof. Saul Hoffman Université de Paris 1 Panthéon-Sorbonne March, 2013

Human Capital Basics Investment Approach Private v social Forms of Human Capital General v Specific Rate of Return Analysis 2

Rate of Return Analysis: Details  Notation: r = interest rate; Y t = amount of \$ available in year t  Compounding: FV t (Y 0 )= Y 0 x (1+r) t. Or in continuous time: = Y 0 e rt  Discounting - compounding in reverse. Present value of some future amount of money is amount of money which if available today and invested at interest rate r would just equal that amount in that future year. Y 0 is PV of Y t if Y 0 x (1+r) t = Y t.  PV 0 (Y t ) =Y t /(1+r) t or in continuous time Y t e -rt  PV capitalizes stream of future incomes into a single #.  Loss of life settlements: present value of lost future income = ΣY t /(1+r) t.  Value of long-term contracts. 3

Computing Internal Rate of Return  IRR (r*) = interest rate at which PV of Benefits, discounted at r*, = costs. Find r* such that ΣB t /(1+r*) t = C.  Mechanics of finding r*  Interpretation: larger is r*, the better is investment; if r* > r (rate at which can borrow), investment is worth making.  Yields rule for optimal human capital investment: Invest in HC until for last unit, r* = r. As amount of HC ↑, r*↓, b/c T↓, and costs ↑ b/c opportunity cost (foregone earnings) ↑. 4

Equilibrium Return to Human Capital How large do earnings need to be to elicit investment in human capital? Yields predictions about occupational wage differences.  Benefits just large enough to make marginal person indifferent between acquiring and not acquiring HC  r* ≈ equal to rate of return on alternative investments (R). Very simple, but powerful idea.  Operates via labor supply  Compare rates of return, not earnings.  Parallel idea to zero profit long run competitive equil. 5

Education and Earnings Econometric Problem: classic omitted variables problem. “Ability” bias in return to schooling Y i = α + βYrsEduc + δZ + ε, where Z is “ability” If ability is unmeasured, estimate Y i = α + θYrsEduc + ε* E(θ) = β + δ x Effect of ability on educational attainment Rate of Return Studies Econometric Approaches Fixed Effect (twins), Natural Experiment (Indonesia) IV 6

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