Question

4. Discuss how differences in discount rates or in ability across workers lead to differences in earning and schooling. Under what conditions can the rate of return to schooling be estimated?

Answer 1

Introduction
• W i d b diff k l diff b f Wages received by different workers not only differ because of
compensating wage differentials, but also because different
workers bring into the labour market unique sets of abilities and
acquired skills known as human capital.
• Workers add to their stock of human capital throughout their
lives (“life-long g ), p y g learning”), especially through formal and
informal education and job experience.
• How do workers choose what skills to acquire, and how
does that affect earnings?

• Basic trade-off: People receive lower or no earnings during

education and training, but hope to receive higher earnings later

due to their increased human capital. But is it a good

investment?

• Basic assumption: A person chooses the level of human capital

investments that maximises the present value of lifetime

earnings.

• Note that this is not the only determinant of a person’s income.

Human capital cannot explain everything (but possibly a lot).

Luck also plays a role in ‘real life’.

6-1 Education in the Labour Market: Some

Stylized Facts

• education is strongly correlated with:

- Labour force participation rates.

- Unemployment rates.

- Earnings.

This applies to NZ as well as the US.

• Some NZ statistics from Statistics NZ’s “Labour

Market Statistics 2007” where shown in class.

6-2 Present Value

• Present value (PV) allows comparison of dollar amounts spent Present value (PV) allows comparison of dollar amounts spent

and received in different time periods.

PV = y/(1+r)t

- PV is the present value of y dollars received t years from now.

- r is the discount rate.

6-3 The Schooling Model

• The basic assumption (i.e. maximisation of the PV of lifetime

earnings) is quite strong! Education & training are valued earnings) is quite strong! Education & training are valued only

because they increase earnings!

- Non-monetary rewards of ‘schooling’ are neglected for

simplicity. But there are many of these!

• A simple model:

- 18 year old who finished high-school: To go or not to go to

university for four years?

- Assume for simplicity there is no on-the-job training if s/he joins

the workforce instead of going to university. Also, assume skills

learned at school do not depreciate over time. In that case, the

person’s productivity does not change after leaving school and

his/her real income stays constant over the life-cycle.

• Real earnings (earnings adjusted for inflation) Real earnings (earnings adjusted for inflation).

• Going to university involved two types of costs:

- Foregone earnings (opportunity costs of 4 years wages at wHS).

- Direct costs while studying (H): Fees, books etc.

• Calculate the PVs of the person’s two potential lifetime income

streams.

• WCOL has to be greater than wHS or no person would go to

university (the higher wage is like a compensating

differential for the higher training costs).

Equation (6.6): Go to College if PVCOL > PVHS

• The discount rate is usually crucial: The higher the discount

rate, the less likely someone will invest in education (since

th l f t i t d) they are less future oriented).

• The discount rate depends on:

- The market rate of interest.

- The individual’s “time preference” (how a person feels about

giving up today’s consumption in return for future rewards).

The Wage-Schooling Locus

• The comparison of PVs can be generalized to more than two options, e.g.

high school undergraduate versus graduate degree, or each year of

schooling.

• Another approach to determine the optimal length of schooling is to draw a

wage-schooling locus. This locus shows what salary firms are willing to pay

a particular worker for given levels of schooling. It is market determined!

• Three properties of the wage-schooling locus:

- It is upward sloping (more educated workers earn more) It is upward sloping (more educated workers earn more).

- The slope of the wage-schooling locus indicates the increase in earnings

associated with one more year of schooling.

- The wage-schooling locus in concave (diminishing returns to education

are assumed).

• Do you think these properties always apply?

The Marginal Rate of Return to Schooling

• The slope of the wage The slope of the wage-schooling locus ( schooling locus (?w/ ?s) tells us the tells us the

increase in earnings for one more year of schooling.

• The marginal rate of return (MRR) to schooling is the

percentage change in earnings resulting from one more year of

schooling.

MRR: (?w/w)*100

The MRR declines with more years of schooling.

The MRR gives the percentage increase in earnings per $ spent in e ducational investment

6-4 Education and Earnings

• Observed data on earnings and schooling do not allow us to

estimate returns to schooling.

• In theory, a more able person gets more from an additional year

of education.

• Ability bias – the extent to which unobserved ability differences exist affects estimates on returns to schooling (since  

the ability differences, and not the length of schooling, may be

the true source of the wage differentials). If there is an ability

bias, different workers have different wage-schooing loci.

MRR if Workers Differ Only in Terms of

Their Discounts Rates

• Case 1: Case 1:

If workers differ only in terms of their discount rates,

it is easy to estimate the returns to schooling:

- They lie on different points of the same wage-schooling

locus and have the same MRR schedule (Figure 6-4)

- We can use the observed wage differential wHS – wDROP to

calculate the MRR:

MRR = (wHS – wDROP) / wDROP

Figure 6-4: Schooling and Earnings When Workers

Have Different Rates of Discount (Case 1)