Signaling in Education ECON 381

Signaling in education Suppose there are two types of workers – low productivity workers and high productivity workers. Individual workers know their own type, but employers cannot costly observe a workers type What will employer do? Hire workers and pay them a wage equal to their average productivity. If high productivity workers make up half of the population, the wage will be (MP h +MP l )/2 This will be nice for low productivity workers, but high productivity workers will not like it. They will have an incentive to try to signal to employers that they are in fact high productivity workers.

Signaling in education How could they do this? What if they could take some action that would be visible to employers? For example, they could all get their hair dyed pink. Would this work? No, because all the low productivity workers would dye their hair pink and then they would all look the same to the employer For high productivity workers to signal their type, they need to find some action that they can take that low productivity workers will choose not to imitate

Signaling in education Some people have suggested that this is the primary function of formal education Let’s see how this could work. In order to make a nice diagram, let’s assume that high productivity workers are exactly twice as productive as low productivity workers. Productivity is innate. Education does not increase productivity.

Signaling in education MP l MP h =2MP l Years of education $ Education does not increase productivity. h types productivity is twice as high as l types

Signaling in education Now let’s make some assumptions about costs. Suppose it costs a low-ability person $C to complete a year of education, but it costs a high ability only $C/2. For example a low ability person might have to duplicate courses to raise their GPA, spend more time studying, etc. Suppose the high ability decide that they will get a degree in order to signal to firms that they are high ability. Will the low ability people imitate them? It depends.

Signaling in education C C/2 MP l MP h =2MP l Years of education $ Firms can tie wages to education levels. If they promise to pay W h =MP h to workers with a given level of education, the benefit to workers of getting that level of education is MP h -MP l =MP l. Note that the magnitude of this benefit does not depend on the worker’s type. What about the cost?

Signaling in education C C/2 MP l MP h =2MP l e* Years of education $ Suppose the firm says it will pay W h =MP h to all workers with an education level of e 0 <e*. High ability workers will go to school because the benefit (=MP l ) is greater than the cost. But so will low ability workers. So this won’t work. e0e0

Signaling in education C C/2 MP l MP h =2MP l Years of education e** $ Suppose the firm says it will pay W h =MP h to all workers with an education level of e 1 >e**. High ability workers will not go to school for this long because the benefit (=MP l ) is less than the cost. So this won’t work e1e1

Signaling in education C C/2 MP l MP h =2MP l e* Years of education e** $ But, for any level of education such that e*<e 2 <e**, the benefit to high ability workers exceeds their cost, and the benefit to low ability workers is less than their cost. So high ability workers get the signal, and low ability workers choose not to. Firms will pay wages that depend on education levels, even though education does absolutely nothing to make workers more productive. e2e2

Empirical evidence A number of studies have tried to test the signaling hypothesis. It’s not easy to do. One example of an empirical test: Consider three types of workers, and three levels of schools (high school dropout, high school completion and college). Now consider two towns. Town A has a college nearby, and Town B is a long way from any college The costs of attending college in Town A is therefore lower than the cost of attending college in Town B.

Empirical evidence When the cost of attending college is lower, more people choose to attend college. The marginal person who attends college in Town A is not as smart as the marginal person in Town B who attends college. This means that the marginal person who completes high school but does not continue on in Town B is smarter than the same person in Town A.

Empirical evidence Now consider the decision of someone who is at the margin of dropping out or completing high school. If education acts as a signal, he will earn a wage equal to the average productivity of workers who complete high school but don’t go on to college. This average ability level is higher in Town B, because lots of smart people in Town B don’t go to college (because it’s so far away). So the really low ability guys have a greater incentive to complete high school in the Town B than Town A.

Empirical evidence A prediction of the signaling model is that high school drop-out rates will be lower in communities that are a greater distance from colleges. This seems counterintuitive. It’s hard to think of any other theory that would predict this. When researchers went out to test this hypothesis, they found it was supported in the data: drop-out rates are higher when the costs of attending college are lower and vice versa.

Empirical evidence Other empirical evidence is less supportive of the signalling model. Role of signalling may differ at different levels of education. e.g. the return to a high school diploma may reflect a signalling components, but the return to a medical degree likely reflects valuable human capital.