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Lecture6_pt1_Externalities.pdf
Lecture 6
Secondary and Post-Secondary Education
Joseph Rossetti
Dept. of Economics, the Ohio State University
06-18-2017
Today
What is education? Why is education subsidized?
discounting positive externalities
What are the returns to schooling for individuals? Can education be improved by more investment?
Role of Education
Education generates Human Capital It is not the only way, but it is certainly one of the major ways
Human Capital is the ability of people to create goods and services Skill biased technological change
Technology changed the demand for different types of human capital
Role of Education
This gives the first answer to the question: what is education?
Education is an investment Workers, parents, or firms invest in education and training
because the net present value is positive
Net Present Value = Present Value Benefits �Present Value Costs
Detour to Discounting
When thinking about the value of things in the future economists use a discount factor:
The discount factor represents how much more valuable something is today than it is tomorrow A simple example of a discount factor is an interest rate:
Lets compare $50 today with $100 ten years from now Suppose we have a savings account with a 1% interest rate Two options:
Take the money now and put it in savings account Or wait for the $100
Detour to Discounting
When thinking about the value of things in the future economists use a discount factor:
The discount factor represents how much more valuable something is today than it is tomorrow A simple example of a discount factor is an interest rate:
Lets compare $50 today with $100 two years from now Suppose we have a savings account with a 1% interest rate Two options:
Take the money now and put it in savings account Or wait for the $100
Detour to Discounting
When thinking about the value of things in the future economists use a discount factor:
How much money would we need now to get $100 in two years? Lets suppose we have x dollars today then in two years we will have:
FV2 = x + xr + (x + xr)r = x(1 + 2r + r2) = x(1 + r)2
This pattern generalizes of course: FVn = PV (1 + r)n
If we want FV2 = 100 then PV = 100(1+0.01) . = 98.03
Detour to Discounting
When thinking about the value of things in the future economists use a discount factor:
We would have to give someone $98.03 today to give them the same value in the present as they get from waiting The cost of waiting is $50 (opp. cost) and this is a present value The benefit of waiting is $100 in the future which is equivalent to $98.03 dollars today The Net Present Value is 98.03 � 50 = 48.03 > 0
The decision maker chooses to wait
Detour to Discounting
When thinking about the value of things in the future economists use a discount factor:
Would you wait? I probably would not wait
For most people the relevant discount rate is greater than the interest rate
PV = FV
(1 + r)n
Increasing r lowers the PV
Detour to Discounting
When thinking about the value of things in the future economists use a discount factor:
What r is needed to make not waiting rational?
50 = 100
(1 + r)2
) r = r
100 50
� 1 . = 0.4
Detour to Discounting
When thinking about the value of things in the future economists use a discount factor:
Now finally lets re-write this in the form of a discount factor rather than an interest rate: Suppose peoples utility from consumption/money overtime is:
U = nX
t=0
�tu(xt)
� is the discount rate u() is a utility function lets say u(x) = x xt is the amount of money that person has in period t
Detour to Discounting
When thinking about the value of things in the future economists use a discount factor:
If the person waits two years to get $100 then his total utility would be:
0 + � · 0 + �2 · 100
If the person takes the money now then he gets utility 50 The � required to make the two equal is given by the equation: 100 · �2 = 50
Detour to Discounting
When thinking about the value of things in the future economists use a discount factor:
The � required to make the two equal is given by the equation: 100 · �2 = 50 Note the similarity to the equation for the interest rate to make the two equal:
50 = 100 (1+r)2 = 100 ·
1 (1+r)2
So the � that would make our utility function make the same choices as the person with a savings account with interest rate r is:
� = 11+r . = 0.71
So things one period the future are worth about 30% less to us than things today
Applying this to education
What is the net present value of education?
Parents or prospective students face costs today (and during the period of education)
Tuition, fees, and books Opportunity costs: if you don’t send you kid to school you will need daycare or to stay at home
Students when the graduate receive wages and income proportional to the value of their human capital
Lifetime earning potential
If the discounted value of their lifetime earning potential is larger than the discounted costs of education
Then they will invest in education
In a few slides we will try to get an idea at least what the lifetime earning potential is in order to understand the value of education
Applying this to education
One key point about these discount factors:
Individuals will do this discounting according to their personal discount factor If individuals are too impatient they may not invest enough in education
what does it mean to be too impatient?
We can think about a social discount factor–the way that society as a whole would choose to discount the future
i.e. this is part of the social choice function depends on values of society So a statement like “people are too impatient” is inherently subjective
Applying this to education
The U.S. government actually uses a social discount factor when it does policy evaluations
The social discount factor is recommended to be between approximately 0.93 and 0.97 depending on how it is calculated
2003 Office of Management and Budget guidelines
This is based on rates of return on capital and government bonds
Which in competitive markets are related to individual discount factors
Experimentally and from microeconomic studies economist estimate that people often are much less patient, however, it is unclear how this generalizes to other decisions like the decision to invest in education
Applying this to education
So it may be possible that society provides subsidies to education because it values the future more than individuals It is also possible that there is a positive externality from schooling that makes society want to subsidize schooling
Positive Externality
When I gain education (say an additional year) I get a return My wages rise over my lifetime
But other people may also experience rising wages and non-pecuniary returns when I gain education
Positive Externality
This may occur through several channels: My human capital may complement other’s productivity
e.g. by exchanging ideas and working together
Positive Externality
This may occur through several channels: If human capital and physical capital are complements
Firm’s need skilled workers to use their physical capital and they must search for these workers If the average/expected human capital of a worker rises then firms will invest in more physical capital They will invest even in advance of finding the worker since physical capital takes time to build The increase in physical capital raises the productivity of workers and therefore their wages
Positive Externality
This may occur through several channels: Wage and education data may get use an idea of these first two channels (perhaps not seperately) But there are other channels:
Educated people may make better citizens across several dimensions
Returns to Education
In order to evaluate the positive externalities to schooling and estimate its value to individuals we face a problem:
Since individuals choose their level of education there are many confounding effects Also workers who are more educated may choose to live in places that are more productive We cannot easily compare the wages of two people with different number of years of education
Returns to Education
Acemoglu and Angrist (2000) use variation in compulsory schooling laws to solve this problem:
A compulsory schooling law (CSL) requires children to stay in school an additional year CSLs are correlated with the amount of schooling that people achieve, but do not represent individual choices Basically we compare people who had no choice but to get an additional year of schooling with those who did not
Returns to Education
They estimate the following equation:
ln Wijt = �0 + �1S̄jt + �2⌘isi + ujt
Want to estimate �1 the coefficient on average schooling �2⌘i is the effect of individual schooling si But S̄jt is in part determined by the selection effect discussed above
Also people may choose to live in places with higher S̄ unobserved state specific effects may drive migration and returns to education
state booms and recessions are correlated with funding for education
Returns to Education
They use two options to correct for the possible correlation/selection effects:
State of Residence CSL The CSL that was active when you were 14 in the state you currently live in Uncorrelated with state specific effects Is not the CSL that was binding on you if you moved to the state
Returns to Education
They use two options to correct for the possible correlation/selection effects:
State of Residence CSL The CSL that was active when you were 14 in the state you currently live in Uncorrelated with state specific effects Is not the CSL that was binding on you if you moved to the state
Returns to Education
The idea is to divide the variation in average years of education S̄jt into two parts:
The part that is driven by CSLs The part that is driven by unobserved state specific effects and migration Replace S̄jt with the predicted S̄jt using CSLs
Returns to Education
Acemoglu and Angrist (2000) use variation in compulsory schooling laws to solve this problem:
Data comes from 1950-1980 census focus on males age 40-49 Estimate external return to individuals from living in a state with higher levels of required secondary education They find modest external returns
Estimates lie between 1% and 3%
These kinds of returns are significant enough to justify subsidization
Returns to Education
Median wage: $17.091
2008 working hours in 2015 gives an annual income of: $34,316.72
If your wage goes up by 2% due to an increase in the average level of schooling
Thats a new annual income of $35,003.05
So the external benefit gives you on average a $686.33 raise in a given year
This raise occurs in each year of your working life
1May 2015, BLS
Returns to Education
If you work for 50 years you would get a total $34,316.72 from this external benefit
Discounting the stream of $686 payments to the present at discount factor 0.95 Present value is $12,529
Per student spending has risen from $3,408 in 1960 to $12,957 in 1990 So by this back of hand calculation we can already see why states might subsidize
Note these are my calculations based on Acemoglu and Angrist (2000)
Returns to Education
They also report the private returns from increasing schooling They estimate this to be between 6% and 10%
If we take it to be 7% and repeat the previous calculation Leads to a yearly raise of $2402.17 PV is $43,853 (OSU costs ~$25,00 per year)
Returns to Education
Moretti (2004) uses a similar approach with both panel data and census data:
Finds the following effect of increasing the number of college graduates in a city
1.9% increase in wages for high-school dropouts 1.6% increase in wages for highs-school graduates 0.4% increase in wages for college graduates
Returns to Education
Oreopoulos (2006) uses a change in British schooling laws to measure the returns to schooling:
In 1947 Britain raised the minimum age at which someone could leave school to work from 14 to 15 This did more than just add a year of school, as it made the 1st year of high-school (secondary school) mandatory The problem with previous studies may have been that the changes in compulsory schooling were not affecting a large group of students The 1947 change had an impact on the majority of students as leaving school at 14 was normal
From 1945-1948 the percentage of students leaving school at 14 fell from 59.7% to under 10%
He finds a total return between 10-14% on average wages in Britain
Returns to Education
Oreopoulos and Salvanes (2011) survey some non-pecuniary benefits from schooling:
Results are mostly correlational rather than causal
Returns to Education
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Milligan, Moretti, and Oreopoulos (2003) examine whether or not more educated people make better citizens:
Education may effect the quality of participation and the level of participation They focus on the level of participation
High school graduation increases the probability of a voter voting by 0.34 This number is lower around 0.15 when conditioning on registration Indicates registration for voting is a major channel for how education can alter participation
They predict that voter participation could have been around 10% lower in 2000 had the number of high school graduates not risen since 1964
Returns to Education
Oreopoulos (2007) studies whether or not high school drop out behavior is consistent with discounting:
Basically he calculates the return to schooling as being well above the returns from dropping out
Discounted at levels above 0.9 (like the typical social discount rate)
Conclusion something is forcing dropouts to use a much lower discount factor He concludes based on survey evidence that this is not likely to be a general dislike of high school or concerns about risk aversion Whether this reflects emergency situations or psychology or both is unclear
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