Signalling (economics)
In contract theory, signalling is the idea that one party credibly conveys some information about itself to another party. Although signalling theory was initially developed by Michael Spence based on observed knowledge gaps between organisations and prospective employees, its intuitive nature led it to be adapted to many other domains, such as Human Resource Management, business, and financial markets.
In Michael Spence's job-market signaling model, employees send a signal about their ability level to the employer by acquiring education credentials. The informational value of the credential comes from the fact that the employer believes the credential is positively correlated with having the greater ability and difficulty for low ability employees to obtain. Thus the credential enables the employer to reliably distinguish low ability workers from high ability workers. The concept of signaling is also applicable in competitive altruistic interaction, where the capacity of the receiving party is limited.
Introductory questions
Signalling took root in the idea of asymmetric information, which says that in some economic transactions, inequalities in access to information upset the normal market for the exchange of goods and services. In his seminal 1973 article, Michael Spence proposed that two parties could get around the problem of asymmetric information by having one party send a signal that would reveal some piece of relevant information to the other party. That party would then interpret the signal and adjust his or her purchasing behaviour accordingly—usually by offering a higher price than if she had not received the signal.There are, of course, many problems that these parties would immediately run into.
- How much time, energy, or money should the sender spend on sending the signal?
- How can the receiver trust the signal to be an honest declaration of information?
- Assuming there is a signalling equilibrium under which the sender signals honestly and the receiver trusts that information, under what circumstances will that equilibrium break down?
Job-market signalling
Spence 1973 "Job Market Signaling" paper
Assumptions and groundwork
Michael Spence considers hiring as a type of investment under uncertainty analogous to buying a lottery ticket and refers to the attributes of an applicant which are observable to the employer as indices. Of these, attributes which the applicant can manipulate are termed signals. Applicant age is thus an index but is not a signal since it does not change at the discretion of the applicant. The employer is supposed to have conditional probability assessments of productive capacity, based on previous experience of the market, for each combination of indices and signals. The employer updates those assessments upon observing each employee's characteristics. The paper is concerned with a risk-neutral employer. The offered wage is the expected marginal product. Signals may be acquired by sustaining signalling costs. If everyone invests in the signal in the exactly the same way, then the signal can't be used as discriminatory, therefore a critical assumption is made: the costs of signalling are negatively correlated with productivity. This situation as described is a feedback loop: the employer updates his beliefs upon new market information and updates the wage schedule, applicants react by signalling, and recruitment takes place. Michael Spence studies the signalling equilibrium that may result from such a situation. He began his 1973 model with a hypothetical example: suppose that there are two types of employees—good and bad—and that employers are willing to pay a higher wage to the good type than the bad type. Spence assumes that for employers, there's no real way to tell in advance which employees will be of the good or bad type. Bad employees aren't upset about this, because they get a free ride from the hard work of the good employees. But good employees know that they deserve to be paid more for their higher productivity, so they desire to invest in the signal—in this case, some amount of education. But he does make one key assumption: good-type employees pay less for one unit of education than bad-type employees. The cost he refers to is not necessarily the cost of tuition and living expenses, sometimes called out of pocket expenses, as one could make the argument that higher ability persons tend to enroll in "better" institutions. Rather, the cost Spence is referring to is the opportunity cost. This is a combination of 'costs', monetary and otherwise, including psychological, time, effort and so on. Of key importance to the value of the signal is the differing cost structure between "good" and "bad" workers. The cost of obtaining identical credentials is strictly lower for the "good" employee than it is for the "bad" employee. The differing cost structure need not preclude "bad" workers from obtaining the credential. All that is necessary for the signal to have value is that the group with the signal is positively correlated with the previously unobservable group of "good" workers. In general, the degree to which a signal is thought to be correlated to unknown or unobservable attributes is directly related to its value.The result
Spence discovered that even if education did not contribute anything to an employee's productivity, it could still have value to both the employer and employee. If the appropriate cost/benefit structure exists, "good" employees will buy more education in order to signal their higher productivity.The increase in wages associated with obtaining a higher credential is sometimes referred to as the “sheepskin effect”, since “sheepskin” informally denotes a diploma. It is important to note that this is not the same as the returns from an additional year of education. The "sheepskin" effect is actually the wage increase above what would normally be attributed to the extra year of education. This can be observed empirically in the wage differences between 'drop-outs' vs. 'completers' with an equal number of years of education. It is also important that one does not equate the fact that higher wages are paid to more educated individuals entirely to signalling or the 'sheepskin' effects. In reality, education serves many different purposes for individuals and society as a whole. Only when all of these aspects, as well as all the many factors affecting wages, are controlled for, does the effect of the "sheepskin" approach its true value. Empirical studies of signalling indicate it as a statistically significant determinant of wages, however, it is one of a host of other attributes—age, sex, and geography are examples of other important factors.
The model
To illustrate his argument, Spence imagines, for simplicity, two productively distinct groups in a population facing one employer. The signal under consideration is education, measured by an index y and is subject to individual choice. Education costs are both monetary and psychic. The data can be summarized as:| Group | Marginal Product | Proportion of population | Cost of education level y |
| I | 1 | y | |
| II | 2 | y/2 |
Suppose that the employer believes that there is a level of education y* below which productivity is 1 and above which productivity is 2. His offered wage schedule W will be:
Working with these hypotheses Spence shows that:
- There is no rational reason for someone choosing a different level of education from 0 or y*.
- Group I sets y=0 if 1>2-y*, that is if the return for not investing in education is higher than investing in education.
- Group II sets y=y* if 2-y*/2>1, that is the return for investing in education is higher than not investing in education.
- Therefore, putting the previous two inequalities together, if 1
- There are infinite equilibrium values of y* belonging to the interval , but they are not equivalent from the welfare point of view. The higher y* the worse off is Group II, while Group I is unaffected.
- If no signaling takes place each person is paid his unconditional expected marginal product. Therefore, Group, I is worse off when signaling is present.
Another model
For a signal to be effective, certain conditions must be true. In equilibrium, the cost of obtaining the credential must be lower for high productivity workers and act as a signal to the employer such that they will pay a higher wage.In this model it is optimal for the higher ability person to obtain the credential but not for the lower ability individual. The table shows the outcome of low ability person l and high ability person h with and without signal S*:
| Person | Without Signal | With Signal | Will the person obtain the signal S*? |
| l | Wo | W* - C' | No, because Wo > W* - C' |
| h | Wo | W* - C' | Yes, because Wo < W* - C' |
The structure is as follows:
There are two individuals with differing abilities levels.
- A higher ability / productivity person: h
- A lower ability / productivity person : l
- Wo is the expected wage for an education level less than S*
- W* is the expected wage for an education level equal or greater than S*
Thus, if both individuals act rationally it is optimal for person h to obtain S* but not for person l so long as the following conditions are satisfied.
Edit: note that this is incorrect with the example as graphed. Both 'l' and 'h' have lower costs than W* at the education level. Also, Person and Person are not clear.
Edit: note that this is ok as for low type "l": , and thus low type will choose Do not obtain credential.
Edit: For there to be a separating equilibrium the high type 'h' must also check their outside option; do they want to choose the net pay in the separating equilibrium over the net pay in the pooling equilibrium. Thus we also need to test that: Otherwise high type 'h' will choose Do not obtain credential of the pooling equilibrium.
For the employers:
In equilibrium, in order for the signalling model to hold, the employer must recognize the signal and pay the corresponding wage and this will result in the workers self-sorting into the two groups. One can see that the cost/benefit structure for a signal to be effective must fall within certain bounds or else the system will fail.