If firms can not tell them apart pay their expected

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If firms can not tell them apart pay their expected worth Expected productivity = 0.50*200,000 + 0.50*300,000 = $250k High types are “underpaid” Job match greater productivity, good for H and firms
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    If H types can signal their ability, firms can pay both types according to their productivity What are the requirements for such a signal? It must separate – H finds it worthwhile to do it, but L does not Signal has Benefit (higher pay) and Cost For H: PV of Signal > PV of Not signal For L: PV of Signal < PV of Not signal Educational attainment can be this signal!
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    Assume school costs H-type $20,000/year and L-type $30,000/year Assume firm pay both types their PV of productivity if it can separate Step 1: How much schooling must be required so L-type won’t go? $200,000 > $300,000 - $30,000*S S min = 3.33 years Step 2: Is this small enough that the H-type will go? $200,000 < $300,000 - $20,000*S ? Yes! + $33,333.. Step 3: What is the maximum amount of schooling so H-type will go? $200,000 > $300,000 - $20,000*S S max = 5 Years
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    Separating Equilibrium: 3.33 years < S < 5 years H-type will go to school and L-type will not H-type pay = $300k, L-type pay = $200k If S is lower or higher, back to pooling equilibrium
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    Firms respond to existence of signal – pay $100,000 premium if complete 3.33 years of school L-type: Attend no school get $200,000 L-type worse off in separating eql.– getting $200k instead of $250k Can not free ride on H-type H-type: Attend 3.33 years get $300,000-$20,000*3.33 = 233,333 H-type also worse off! 233k vs. 250k in pooling case
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    If school is “harder” for low ability than high ability it can serve as a signal Given the signal exists, H type are forced to increase education (given believe another will do so) H type may be worse off in the separating equilibrium! Only a few L-type More costly is schooling No productivity increases from job match
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   Alternative approach: Does school quality matter? Be careful – prestige could also be a signal Possible measures of school quality (increase learning) More attention - small class sizes? More experienced teachers? More resources – computers?
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    Experiment in 79 Tennessee public schools began 1985 11,600 K-3 students randomly assigned to small classes (13-17) regular (22-25) and reg + aide Teachers also randomly assigned**
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 Krueger and Whitmore (2001) 5 percentile point difference on test scores for K small class vs. regular Greatest difference for disadvantaged and minority students Gap closes somewhat after experiment ends – all go to regular classes ACT/SAT taking increases for those that had small classes: 3.7 percentage pts. overall, 10 pct. pts. for black students
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 Chetty, Friedman, Hilger, Saez, Schanzenbach, Yagan (2010) Link STAR data to tax returns for 95% of sample
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     Schooling has potential to Increase human capital – provide with skills rewarded Reveal human capital – in markets with imperfect information Schooling is rewarded Gain more if PV of Benefits > PV of costs Discount rate < Marginal rate of return Evidence schooling is productive
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