### Schooling as a Signal

```Schooling as a Signal
1
The Schooling Model we saw in a previous section assumed that education
really increases a worker’s productivity.
Here we will study an alternative idea – schooling does not increase productivity,
but sends a “signal” that a worker can handle a certain type of work. Table of info
Type of worker
proportion in population
Low-productivity
q
\$200,000
High-productivity
1-q
\$300,000
In the table here low-productivity workers make up q percent of the population
and earn \$200,000 over their lifetime (in present value terms), while highproductivity workers make up 1-q percent of population and they earn \$300,000
The problem for a firm in this is that it is not cheap to figure out if a worker can
handle a job or not. So, the firm would prefer the workers send signals about
their ability to do the work.
Low productivity workers may not even know they are low productivity, so they
would probably say they should get the \$300,000 jobs!
2
If there is no signal the firm will not know which worker is which and will thus
pay an “expected wage” to both and that wage is
q(200,000) + (1-q)(300,000) = 300,000 – 100,000q.
Now, since q can range from 0 to 1, the earnings will range from 200,000(like
when q =1) to 300,000(when q = 0).
When the firm can not distinguish between the types of workers the firm just
“pools” them and pays the one wage to all. As an example, say q = .5. Then all
would make \$250,000.
The low-productivity worker would like this because of being paid more than
what they should be paid. The high-productivity workers will not like this
because of getting paid too low. The firm will not like it either because they
would find they are mismatching workers with jobs and this would lead to lower
efficiency.
So the high-productivity worker has an incentive to send a signal and the firm
has an incentive to require that a signal be sent. It helps both. When you think
about it the low-productivity workers are helped as well because if they get into
high-productivity job they will not perform and they will get fired.
3
Let’s say that the signal required is for workers to reveal their level of schooling
and the firm requires ybar years of college to get the high-productivity job.
Major assumption: high-productivity workers and low-productivity workers do not
have the same cost of getting a year of education. The tuition and fees are the
same, but the logic is the low-productivity worker will have to spend more time
studying and may have to buy tutors, study guides and special classes.
Let’s say the high-productivity worker can get a year of schooling for \$20,000,
while the low-productivity worker can do it for \$25,001.
A low-productivity worker will make \$200,000 (over their lifetime in present value
terms) if they get less than ybar years of school. If they get ybar years of school
they will make \$300,000, but they will have to pay 25,001 per year to do it. The
net income then would be 300,000 – 25,001ybar
The low-productivity worker will not go to college if
200,000 > 300,000 – 25,001ybar, which means if
ybar >100,000/25,001= 3.999
So, if the firm requires more than 3.999 years of schooling the low-productivity
workers will find it too expensive to get the high productivity job and will in fact
not go to college at all because even some college will not change earnings.
4
If the firm requires more than 3.999 years of schooling the low-productivity
workers will “signal” to the firm their low-productivity skill level.
The high-productivity worker will go to college if
200,000 < 300,000 – 20,000ybar, which means if
ybar < 100,000/20,000= 5
So, high-productivity workers will go to college as long as they do not have to get
too much schooling, here less than 5 years.
So when firms say the signal for schooling is not less than 3.999 but not more
than 5 the workers will be separated into their own groups.
5
Public Policy
The human capital model suggested education increased productivity and thus
accounted for the higher income of more educated people. The signaling
model also says more educated get more income, but for a different reason – it
signals the worker’s innate ability that is otherwise difficult to see.
The human capital model would suggest government intervention in the form of
educational assistance can lift people to higher wages, whereas the signaling
model indicates the education won’t really change the wages of workers, but
will just get the right workers into the right jobs.
6
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