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Differences Between the Models of Education

- Education as signaling model
- Education as human capital investment

Education as Signaling Model

- Assumes the existence of differences in innate abilities (productivity types) of individuals and that these innate abilities are observable only by the worker
- Underlines the role of education as a signaling device, used for the high type worker to obtain the desired type of job and earnings

Education as Signaling Model

- Abstracts for the role of education on productivity enhancement
- Remember that it assumes that the firm gets the same profits from educated or non-educated workers
- What matters for the firm is the productivity type or innate abilities of the worker

Human Capital Investment Model

- Underlines the role of education on human capital enhancement (i.e., increase of productivity through education)
- Abstracts for differences in innate abilities of individuals, and therefore, it does no consider the role of education as signaling

Human Capital Investment Model

- Our discussion of the human capital theory is based on the work of Gary Becker (Nobel Prize in Economics, 1992)

“Investment in Human Capital: A Theoretical Analysis,” Journal of Political Economy, 1962

Human Capital Investment Model

- The essence of the human capital theory is that investments are made in human resources so as to improve their productivity and therefore, their earnings
- Costs are incurred by potential workers in the expectation of future benefits. For this reason, the term “investment in human resources” is used

Human Capital Investment Model

- Is investment in human capital economically worthwhile for an individual?
- The answer depends on whether or not the benefits from the investment exceed the costs incurred

Economic Analysis of Investment in Human Capital

- We will perform an inter-temporal analysis of economic costs and benefits of acquiring education
- This framework is analogous to the one used in the investment in physical capital decision

Economic Costs of Human Capital Acquisition

- In calculating the costs of human capital acquisition, we will need to use the “economic cost” concept
- Explicit costs incurred in acquiring education (books, tuition fees, etc.)
- The opportunity cost or income forgone while people acquire education (while people enhance their human capital)

Economic Benefits of Human Capital Acquisition

- Economic benefits from human capital acquisition are represented by the higher wages related to the higher educational attainment
- The higher wages are not seen as a payment for innate ability but merely as a compensation to the individual for making the investment in education (for the resources spent in education cost), which enhances his/her productivity

Economic Benefits of Human Capital Acquisition

- Only the outcome of the educational process,

i.e., productivity enhancement and therefore, increase in earnings, is important in the analysis

- The individual does not receive any direct utility or disutility from the educational process

Stream of Costs and Benefits

- The model assumes that there is no uncertainty involved in the inter-temporal decision making
- The lifetime earnings and costs associated with the different amounts of education are known with certainty

Stream of Costs and Benefits

- The model assumes that individuals can always borrow and lend at the real interest rate “r”

Inter-temporal Choice

- To make decisions that involve different periods of time, we need first to set the quantities in the same period of time
- The present value (PV) concept is the way to convert a stream of payment into today’s value

Present Value Concept

- X dollars invested today at an annual interest rate “r” would increase in value

to X (1 + r) dollars in one year

to [X(1 + r)] (1 + r) = X (1 + r)2 in two years

to X(1 + r)t in t years

Present Value Concept

- Let Q = X(1 + r)t

Hence, the PV of Q dollars received t years from now is

Q/(1 + r)t = Qt = X

- Note that = 1/(1 + r) is the discount factor we have used previously to compute the PV of a stream of payments in infinitely repeated games

Inter-temporal Choice

- Similarly, the promise (from a bank, for example) to pay Y dollars t years from today has a present value

PV = Y/(1 + r)t = Y t

Inter-temporal Choice

- Suppose we have more than 2 periods, starting with the current period, called “period 0”
- Suppose that we receive V0 in period 0, V1 in period 1, …, Vt in period t

Inter-temporal Choice

- Then, the PV of receiving V0 in period 0, V1 in period 1, …, Vt in period t

PV = V0/(1 + r)0 +V1/(1 + r)1 +V2/(1 + r)2 + . . . +Vt/(1 + r)t

where

Vi = value on period i

i = 0,1,…t (period number; from period 0 to period t)

Inter-temporal Choice

- Assume now that we receive V0 in period 0, and V1 in period 1 to period t
- Then, the PV of the stream of payments V1 received during t periods is

V1 + 2 V1 + 3 V1 + … + t V1

This sum of finite terms can be seen as

( V1 + 2 V1 + 3 V1 + …+ t V1 + t+1 V1 + …) –

(t+1 V1 + t+2 V1 + … + …)

Inter-temporal Choice

- Where, the first sum of infinite terms

( V1 + 2 V1 + 3 V1 + …+ t V1 + t+1 V1 + …)

=

V1 ( 1 + +2+ 3+ …+ t+ t+1 + …)

=

V1/(1 – )

Inter-temporal Choice

- And the second sum of infinite terms

(t+1 V1 + t+2 V1 + … + …)

=

t+1 V1 ( 1 + +2+ 3+ …+ t+ t+1 + …)

=

t+1 V1/(1 – )

Inter-temporal Choice

- Then, the PV of the stream of payments V1 received during t periods

V1 + 2 V1 + 3 V1 + … + t V1

=

V1/(1 – ) – t+1 V1/(1 – )

=

V1 ( 1 – t)/(1 – )

Inter-temporal Choice

- Given that = 1/(1+ r), then the PV of the stream of payments V1 received during t periods is

V1 + 2 V1 + 3 V1 + … + t V1

=

V1 {1 – [1/(1+r)]t}/r(annuity formula)

Inter-temporal Choice

- Hence, the PV of the payments received from period 0 to period t, assuming that we receive V0 in period 0 and V1 in period 1 through period t is

PV = V0 +V1 {1 – [1/(1+r)]t}/r

An Application of the Education as Human Capital Investment Model

- Suppose an 18-year-old high-school graduate needs to decide whether to pursue a university degree
- Assume that our 18-year-old person knows that she will work until age T. So, she has a maximum of T – 18 remaining working years (or T – 18 + 1 total periods)

An Application of the Education as Human Capital Investment Model

- The decision about pursuing a university degree implies
- To compare the lifetime stream of net benefits from not pursuing and from pursuing higher a university degree

Or

- To compare the lifetime stream of costs and benefits from education
- We will then use the concept of inter-temporal choice (PV)

An Application of the Education as Human Capital Investment Model

- If the person doesn’t pursue the university degree, the PV of the stream of earnings of a high school degree (H) is

PV(H) = Y18H / (1 + r)0 + Y19H / (1 + r)1 + … + YTH / (1 + r)T-18,

where Y18H, Y19H are the earnings after high school degree at age 18, at age 19, etc.; T is the age of the individual at the last working year; T -18 is the maximum number of remaining working years

An Application of the Education as Human Capital Investment Model

- Using the summation notation, the stream of earnings of a high school degree (H) is

PV(H) = t=0T-18 [Yt+18 H / (1 + r)t]

Aside: A Numerical Example to Clarify Notation

- Suppose that the person starts working at age 18 and can work at most for 5 years (i.e., until age 22)
- Working years: year 1 at age 18, year 2 at age 19, …, year 5 at age 22
- T = 22 represents the age of the individual during the last working period

Aside: A Numerical Example to Clarify Notation

- T -18 = 4 represents the maximum number of remaining working years (not including year 1 at age 18)
- T-18 + 1 = 5 represents the total number of working years (including year 1 at age 18)

Aside: A Numerical Example to Clarify Notation

- Then, PV of income stream of earnings of a high school degree (H) is

PV(H) = Y18H/(1+r)0+Y19H/(1+r)1+Y20H/(1+r)2+Y21H/(1+r)3+Y22H/(1+r)4

- Using the summation notation,

PV(H) = t=04 [Yt+18 H/(1 + r)t]

An Application of the Education as Human Capital Investment Model (cont.)

- If the person gets the university degree
- She will earn nothing for 4 years during studies and incur in explicit cost D (D18 … D21) each year she is in the university
- However, her earnings YU (Y22U…YTU) will be higher when she graduates

An Application of the Education as Human Capital Investment Model

- Then, the PV of net earnings (PV of the stream of earnings and costs) of a university degree (U) is

PV(U) = (-D18)/(1+r)0 + (-D19)/(1+r)1 +…+ (-D21)/(1+r)3

+ Y22U /(1+r)4 + … + YT U / (1+r)T-18

Using the summation notation,

PV(U) = t=0 3 {[-Dt+18/(1 + r)t]} + t=4T-18 {[Yt+18U/(1 + r)t]}

An Application of the Education as Human Capital Investment Model

- The rational investment decision is to pursue the university degree if

PV(U) = t=0 3 {[-Dt+18/(1+r)t]} + t=4T-18 {[Yt+18U/(1+r)t]}

>

PV(H) = t=0T-18 [Yt+18 H / (1 + r)t]

An Application of the Education as Human Capital Investment Model

- Alternatively, this decision can be expressed in terms of benefits and costs of the university degree, where costs include both the explicit costs and opportunity costs

An Application of the Education as Human Capital Investment Model

- The benefit (B) of pursuing the university degree is the increase in earnings from age 22

PV(B) = t=4T-18 { [Yt+18U -Yt+18H ] / (1 + r)t }

An Application of the Education as Human Capital Investment Model

- The cost (C) of pursuing the university degree is the explicit cost of university, plus the opportunity cost (forgone earnings while attending university) during 4 four years until age 21

PV(C) = t=0 3 { [Yt+18H + Dt+18 ] / (1 + r)t }

An Application of the Education as Human Capital Investment Model

- The high-school graduate should pursue the university degree if

PV(B) > PV(C)

- Obviously, both decision criteria

PV(B) > PV (C) and PV(U) > PV(H)

are identical

Optimal Human Capital Investment

- The optimal human capital investment is the educational attainment that maximizes the lifetime net earnings
- The optimal educational attainment can be obtained in two equivalent rules
- Marginal Cost and Benefit Rule
- Internal Rate of Return of the Investment Rule

Marginal Cost and Benefit Rule

- A rational individual chooses the human capital investment that maximizes the net PV of her/his lifetime earnings
- The net PV of her lifetime earnings is maximized when

Marginal Benefit (Mg B) = Marginal Cost (Mg C)

Marginal Cost and Benefit Rule

- The individual should increase the number of years of education until the PV of the benefits of an additional year equals the PV of the costs of an additional year
- Mg B generally declines with years of education due to a diminishing return to education and to the shorter period over which higher income accrues
- Mg C rises with years of education because forgone earnings increase with educational attainment

Internal Rate of Return of the Investment Rule

- For any specific amount of education, the internal rate of return “i” can be defined as the implicit rate of return earned by an individual acquiring that amount of education

Internal Rate of Return of the Investment Rule

- The internal (implicit) rate of return “i” of the investment on a level of education “j” is computed by calculating the discount rate that yields a Net PV of zero for the investment on level of education “j”
- ij s.t. Net PV = PV(B)j - PV(C)j = 0

or

- ij s.t. PV(B)j = PV(C)j

Internal Rate of Return of the Investment Rule

- The rational individual will continue investing in education as long as the internal rate of return “i” exceeds the market interest rate “r” (that represents the opportunity cost of financing the human capital investment)

Internal Rate of Return of the Investment Rule

- That is, if at specific level of education i > r, the individual can increase the net present value of lifetime earnings by acquiring more education, which may involve borrowing at the market interest rate r, or allocating his own funds in education investment instead of lending the funds at the market interest rate r
- That is, investing in education is the best investment alternative for the individual

Internal Rate of Return of the Investment Rule

- Remember that PV of the Mg B is a decreasing function of education and the PV of the Mg C is an increasing function of education
- Then, the internal rate of return (that reflects the net return to the individual from the investment on education) falls as educational attainment rises

Internal Rate of Return of the Investment Rule

- The optimal level of investment in education is achieved when

(internal rate of return) i = r (market interest rate)

Graphically,

- MgB = MgC at the optimal
- level of educational
- attainment

MgB,

MgC

MgC

MgB

Years of education (E)

E*

(b) Internal rate of return i =

market interest rate r

at the optimal level of

educational attainment

i, r

r

i

Years of education (E)

E*

Predictions of the Education as Human Capital Investment Model

- The most obvious implication of the theory is that human capital investments should be made early in one’s lifetime

Educational investments made at later stages earn a lower financial returns

- Because forgone earnings increase with work experience
- Because of the shorter period over which higher income is earned

Predictions of the Education as Human Capital Investment Model

- So, we should expect that most college students will be young
- Given similar yearly benefits of going to college to young and old people, young people have a larger PV of benefits than older people because they have a longer remaining work life after finishing college

Predictions of the Education as Human Capital Investment Model

2) Human capital investment will decrease if the costs of education rise.

We should expect that (other things equal)

- If the explicit cost of college increases, total cost of education increases and then, attendance will decrease

Predictions of the Education as Human Capital Investment Model

- If opportunity cost of college increases, we will also expect lower attendance

This is another reason for which older people

(who are more experienced and therefore,

have higher opportunity cost of wage forgone

during studies) are less likely to attend

college than younger people

Predictions of the Education as Human Capital Investment Model

3) Human capital investment will increase if the earnings gap between educational attainment levels widen. So, we should expect that (other things equal)

- If the gap between earnings of college graduates and high school graduates widen, college attendance will increase. This is due to the increase in the benefits from college attendance

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