Human Capital
Optimal Decisions over the type of OTJ Training
*Assume 2 time periods* 1. working with OTJ training (OTJ training is costly) 2. working
Schooling as a Signal
*Assumptions*: -Two types of workers 1. High Productivity (prop. (1-q), PDV $300k) 2. Low Productivity (prop. q, PDV $200k) -The workers know their type but the firms don't (asymmetric information)
The Schooling Model
*Decision:* after completing HS, go to work or acquire higher education? *Cost* -OC: forgo WHS for four years -Direct Cost: pay H dollars for four years *Benefit* -Earn WCol > WHS from age 22 until retirement
OTJ Training
*Definition:* HC acquired while (and because) you are working at a given job -General: useful at all firms/jobs -Specific: useful only at a specific job and firm
(Marginal) Rate of Return to Schooling
*Definition:* The MRR to schooling is the % increase in earning resulting from an additional year of school *Property:* given the concavity of the wage-schooling locus, the MRR is positive but decreasing as year of schooling increases
Pooling Equilibrium
*High type acquires S* if:* 300k - 20k(S*) >= 200k *Low type acquires S* if:* 300k - 25k(S*) >= 200k -Pooling equilibrium possible if S* = 4 *Conclusion:* if firms pay 300k to those with at least 4 years of schooling, they induce a pooling equilibrium
Separating Equilbrium
*High type acquires S* if:* 300k - 20k(S*) >= 200k *Low type does not acquire S* if:* 300k - 25k(S*) < 200k -Separating equilibrium is possible if S* = 5 *Conclusion:* if firms pay WH=300k to those with at least 5 years of schooling, they induce a separating equilibrium
The Schooling Model: PV of Age-Earnings Profiles
*How should the agent decide between going straight to work or acquiring higher education?* -By comparing the PV of the 2 alternatives and picking the higher one -If PVHS > PVC stop at high school -If PVHS < PVC stop at college or later
Heterogeneity in Discount Rates
*Implications* -More "impatient" agents acquire less schooling earn permanently lower wages -The relative different in wages between WHS and WDrop is the return to the 12th year of schooling *Policy Implication* -Can use this information to estimate the impact of a policy increasing HS grad. rates because the relative difference in wages is due to the 12th year of schooling (same W-S locus)
Asymmetric Information with Schooling as a Signal
*Schooling is such that:* 1. It is costly to acquire 2. More costly to acquire for low prod. types 3. It has no impact on prod. (types assigned at birth) 4. It is fully observed by firms
Definition of HC
*Standard approach:* any investment perceived to have a direct impact on labor market productivity 1. General HC (schooling) 2. Specific HC (OTJ training)
MRR to Schooling Cont.
*Suppose that:* -the only cost of schooling is the OC of foregone wages -Intertemporal discount rate = market return -When should you stop acquiring schooling? : when MRR = r *Proof* -Suppose you make w at schooling level S and if you invest w in the market you receive a return r, while if you invest w in schooling you receive a return MRR -MRR > r, acquire more schooling -MRR < r, do not acquire more schooling -MRR = r, indifferent, stop acquiring schooling
General OTJ Training
*Worker is more productive in P2 in all firms* -They quit if not paid marginal productivity -Firms provide general training in t=1 only if the worker pays for it by accepting lower wages than marginal productivity in t=1
Specific OTJ Training
*Worker is more productive in P2 only at that firm* -If they quit, they lose the training and neither the worker nor the firm have an incentive to cover all the costs -However, if they share in the costs they may also share in the benefit -An appropriate salary package over the two periods may achieve that
Optimal Decisions with Schooling as a Signal
-Firms can hope to identify type by observing schooling only if they pay different wages to different schooling levels -i.e. they have to give an incentive to acquire costly schooling *Since there are only 2 types, they need to pay only 2 wages:* -If schooling >=S*, then WH = 300K -If schooling <S*, then WL = 200K
Asymmetric Information without Signal
-Firms don't know if they are hiring a high or low productivity worker, so they pay each worker the expected value of their productivity - w = (1-q)(300k) + (q)(200K) -Example of pooling equilibrium, since all workers are paid the same regardless of status -Good for low prod. workers, but bad for high prod. workers and firms
Heterogeneity in Ability
-In this case B is more "able" to earn higher wages than A as his schooling increases *Implications* -More "able" agents acquire more schooling and earn higher wages -However, the relative wage difference between WHS and WDrop is not the return to the 12th year of schooling (i.e. Ace would get WA not WHS) *Policy Implication* -Cannot be used to estimate the impact of a policy increasing grad. rates because the z curve has no implicit meaning
Optimal Decisions over the life cycle
-Looking at schooling decisions, we saw it is optimal to acquire schooling earlier in life so that they are enjoyed over a longer period of time -OTJ training HC investments follow the same optimal strategy -As a result, agents invest less and less in OTJ training as they age -This may provide an explanation for the flattening age-earnings profiles we see in the data
Optimal Decision Rule
-MRR schedule decreasing due to technology -Assumption: discount rate is constant and equal to market return -Assumption: Only OC is cost of schooling *Conclusion* -a worker maximizes the PV of lifetime earnings by going to school until MRR = discount rate (S*)
Schooling as a Signal: Conclusion
-Schooling as a signal means schooling acquisition does not really increase productivity (not really a HC investment) -Even under this assumption, schooling may be useful to reveal productivity when asymmetric information is present -For the mechanism to work, firms must set wages conditional on the "right" level of schooling
Issue with the Schooling Model
-Schooling is typically acquired before enjoying its benefits *It is a dynamic decision*: use PDV to account giving up income today for higher income in the future
Equilibrium
-Separating equilibrium: when the types are perfectly separated (i.e. high types acquire S* and low types acquire 0) -Pooling equilibrium: when the types are not separated (i.e. both types acquire either S* or 0)
Main Idea
-Since labor is tied together with capital, an input in the production process, we can find an analogy between physical and human capital *Implication* -just as we invest in physical capital and expect returns, we can invest in human capital and expect returns -we can use a similar framework to make and evaluate these two different decisions
The Wage-Schooling Locus
-The combination of wages that firms are willing to pay at different levels of schooling is defined as the wage-schooling locus *Properties* -Upward sloping (+ returns to schooling) -Slope is the marginal increase in earnings associated with an additional year of schooling -Concave (diminishing returns to schooling)
Impact of Interest Rates in HC Decisions
-The general result is that the higher the discount rate, the lower the HC investment (it is more costly) -Important: the intertemporal discount rate of a specific agent may be higher/lower than the interest rate determined in the labor market
The Stopping Rule
-The optimal decisions method is very convenient when individuals are faced with few discrete choices -However, HC investments may be about a larger set of choices (e.g. how many years of schooling to complete) -When this is the case, a stopping rule may generate a better optimal decision method *Definition* -Used to determine at which years-of-schooling level the agent should stop accumulating them
Optimal Decisions with Schooling as a Signal Cont.
-Workers acquire schooling to earn higher wages, and since there is only one threshold (S*), they will decide to either acquire schooling to S* or 0 *Assume* -Low type cost of schooling = 25,000 -High type cost of schooling = 20,000