Discussion

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THE MAJOR DECISION 23

where f and F are the pdf and cdf of the truncated exponential distribution.

Agent who are type-matched to field 1 receive value

(16)

J tm (t+H,e) =

∫ T−t−H

0

exp{−rt}[R(ǫ 1 )+P]dt

3.2.7. The optimal length of specialization. At time 1, upon beginning specialization

in field 1, the agent expects to be type-matched to field one with probability

p 1 (the first entry in the beliefs vector) and type-unmatched with probability

1 − p 1 . Given that the education stock and time are linked by the relation

e = (t/N,t/N,...,t/N), we omit the explicit dependance on e. The expected

value of specializing in field 1 writes as:

(17)

V 1 (t,p) = Max

{H≥0,H≤T}

∫ H

0

exp{−rt}zdt

+exp{−rH} [ (1−p 1 )¯J(t,e(H))+p 1 J tm (t+H,e(H)) ]

Upon finding the maximizer H ∗ (t,p), we can define the expected wage conditional

on changing fields.

(18)

ew sw,1 (t,p) = R(β(t+H ∗ (t,p))+(1−β)t/N)+P

Theexpected wageconditional onstayingin thegivenfieldistheweighted average

of the wage of initially-matched and initially-unmatched agents. The total probability

A of carrying on in field 1 is the sum of the probability of being properly

matched A 1 = p 1 and the contribution of initially unmatched agents who remain

in the field, A 2 = (1 − p 1 )(1−F (ĉ(H ∗ (t,p)))). Both groups receive as earnings

x 1 = R(β(t+H ∗ (t,p))+(1−β)(t/N +H ∗ (t,p)) while type-matched agents

receive the premium P.

(19)

ew st,1 (t,p) = (A 1 (x 1 +P)+A 2 x 1 )(A 1 +A 2 ) −1

3.2.8. Optimal experimentation and beliefs histories. Continuinginmixed-education

enables agents to periodically receive signals about their field of comparative advantage,

while increasing their stock of skills in all fields. In the discrete-time

formulation, call δ the discount rate that can be compounded into the calibrated

annual rate . 28 Recalling that a period is a third of a year, the Bellman equation

28 There are three periods per year, so δ 3 is the annual discount rate.

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