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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

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

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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

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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

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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

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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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