14.661 F17 Lecture Note: Schooling, Experience, and Earnings

Schooling, Experience, and Earnings MIT 14.661 (FALL 2017) • We learn much of what we know “on the job” – We punish you with problem sets, but on the job you’ll eventually learn to teach, maybe even to write • The Mincer framework puts experience and schooling on a continuum – Becker also asks: who pays for your OJT? Lets Get Specific About General HK • The distinction can be drawn in two periods ⇡(L) = pf0 (L) + pf1 (L) 1+r (w0 + c)L w1 L 1+r where c is training cost and w0 , w1 are wages in periods 0 and 1 – Assume f10 (L) > f00 (L) by virtue of OJT paid for by c • f.o.c. pf00 (L) + pf10 (L) w1 = (w0 + c) + 1+r 1+r which we can write M P0 + M P1 w1 = (w0 + c) + 1+r 1+r • How will wages evolve? – If training raises my M P to M P1 for all employers, my OJT is said to produce general HK ⇤ In general, you better pay me what I’m worth: w1 = M P1 – This implies: w0 = M P0 pay for general HK c, from which we conclude that workers 1 – If training is specific, that is, when the employer that provides OJT benefits uniquely from the resulting productivity boost, the period 1 wage need only clear M P1 elsewhere (this might be equal to M P0 ), hence he may share the costs of my OJT, paying w0 > M P0 c • The notion that most HK is general (and therefore paid for by workers) can explain why wages increase with experience (not the only possible explanation for that, of course) – Mincer gives us a functional form that captures this • Note policy implications of general HK: min wage is double bad, yo! • Acemoglu and Pischke (1998, 1999) and Autor (2001) question the Beckerian conclusion that workers pay for general skills training. As an empirical matter, many firms pay for what looks like general skills training. The explanation, as with many such puzzles, revolves around worker heterogeneity and market structure. The Mincer Earnings Function • Mincer (1974) asks – How do schooling and OJT generate wages over a working life? • Assumptions – HK production technology is given – The investment path is exogenous; Ben-Porath (1967) does the endogenous case, not empirically very tractable; but Mincer can be interpreted as choosing a specification suggested by the YBP analysis • Details – k(t) = fraction of earnings capacity devoted to investment in HK, fraction 1 k(t) can be consumed – The rate of return on HK is fixed at ⇢ for all workers, a parameter determined by market forces (equalizing differences, perhaps) – Earnings are given by y(t) = (1 k(t))E(t) where E(t) is “earnings capacity”, my marginal product, which determines my pay if I don’t spend anything on OJT – Assuming I reap the rewards to my OJT in continuous (is that real?) time, this implies E 0 (t) = ⇢k(t) · E(t) = g(t) · E(t) 2 where g(t) = ⇢k(t). Equivalently, d ln E(t) = g(t) dt Assuming g(0) = k(0) = 0, this simple differential equation has solution ´t E(t) = E(0)e 0 g(⌧ )d⌧ (1) • Schooling – For the first s years of life, set k(t) = 1, with k(t) = 0 for t > s – This implies 0⌧ s otherwise g(⌧ ) = ⇢k(⌧ ) = ⇢ =0 so for t > s, y(t) = E(s) ⌘ E(0)e⇢s and ln y(t) = ln y(0) + ⇢s as in the eq. diffs. story (What about t < s?) • Experience – For t > s, let x = t s and set k̃(x) = k0 (1 Tx ) for 0  x  T and 0 otherwise: investment declines linearly from k0 to 0. – This comes from YBP-67 in the sense that he shows: (a) some postschooling investment is optimal; (b) investment should decline with age because the payoff horizon shrinks – Break (1) up to write earnings as a function of schooling and time E(s, t) = E(0)e ´s 0 g(⌧ )d⌧ + ´t s – next, change vars from t to x ⌘ t g(⌧ )d⌧ ´t = E(s)e s g̃(⌧ )d⌧ (2) s: ´x E(s, x) = E(s)e 0 g(⌧ )d⌧ (3) where g̃(x) = ⇢k̃(x) describes investment as a function of potential experience, x = t s – Sub using k̃(x) = k0 (1 x T) to find E(s, x) = E(s)e ´x 0 ⌧ ]d⌧ [⇢k0 ⇢k0 T Integrate and log to find ln E(s, x) = = ⇢k0 2 x 2T ⇢k0 2 ln E(0) + ⇢s + ⇢k0 x x 2T ln E(s) + ⇢k0 x 3 (4) – Finally, using y(s, x) = [1 k(x)]E[s, x] and the fact that ln(1 k(x))⇠ = k(x) = k0 (1 Tx ), we get the Mincer wage equation ln y(s, x) = ln E(0) + ⇢s + ⇢k0 x = [ln E(0) ⇢k0 2 x  2T k0 ] + ⇢s + ⇢k0 + k0 (1 k0 x T x ) T ⇢k0 2 x 2T Heckman (1976) found that this does well against a more rigorously YBP-founded spec – When do earnings peak? Solve for x⇤ in x⇤ = ⇢k0 + kT0 = T + 1/⇢ ⇢k0/T which equals 40 for T = 30 and ⇢ = .1 ⇤ I’m not yet over the hill (in this model, earnings peak after investment stops - whew!) – Mincer also computes the over-taking age: the age (or experience level) at which the earnings of someone with schooling s + pass the earnings of someone with school s. Note that we need the quadratic term for this to happen in our lifetimes! • Questions – Why is this a model of general HK? – In what sense does Mincer place schooling and experience on a continuum? Wage ’Metrics • Mincer functional forms put to the test in Murphy and Welch (1990) • Experience vs seniority in Altonji and Shakotko (1987) and Topel (1991) • Causality, as always, at issue Angrist 1990: The price of service • Draftees suffer a loss of earnings and, not coincidentally, perhaps, a loss of experience • Other experience experiments: plant closure and layoffs 4