# Signalling (economics)

In contract theory, signaling (or signalling: see American and British English differences) is the idea that one party (termed the agent) credibly conveys some information about itself to another party (the principal). For example, in Michael Spence's job-market signalling model, (potential) 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 greater ability and difficult for low ability employees to obtain. Thus the credential enables the employer to reliably distinguish low ability workers from high ability workers.

Self-signaling is a form of signaling that conveys information about an actor to herself.[1] Betting that a team will win or lose can send a signal to the bettor about her own identity (e.g., serve as an indicator that she is or is not a fan of that team).[2]

## Introductory questions

Signalling took root in the idea of asymmetric information (a deviation from perfect 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.[3] That party would then interpret the signal and adjust 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 (agent) spend on sending the signal?
• How can the receiver (the principal, who is usually the buyer in the transaction) 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

In the job market, potential employees seek to sell their services to employers for some wage, or price. Generally, employers are willing to pay higher wages to employ better workers. While the individual may know his or her own level of ability, the hiring firm is not (usually) able to observe such an intangible trait—thus there is an asymmetry of information between the two parties. Education credentials can be used as a signal to the firm, indicating a certain level of ability that the individual may possess; thereby narrowing the informational gap. This is beneficial to both parties as long as the signal indicates a desirable attribute—a signal such as a criminal record may not be so desirable.

### Spence 1973 "Job Market Signaling" paper

#### Assumptions and groundwork

Michael Spence considers hiring as investment under uncertainty,[3] analogous to buying a lottery ticket. Of the observable attributes on an applicant, the observable attributes are called indices, while the signal refers to attributes that are manipulable by the applicant.[clarification needed] Applicant age is thus an index, since it does not change at the discretion of the applicant. On the basis of previous experience of the market the employer is supposed to have conditional probability assessments over productive capacity given a certain combination of indices and signals.[clarification needed] The employer updates his beliefs regarding his upon observing the employee characteristics.[clarification needed]

The paper is concerned with a risk-neutral employer. The offered wage is the expected marginal product. Signals may be acquired by sustaining signaling costs (monetary and not). If everyone invest in the signal in the exactly the same way, then the signal can't used as discriminatory, therefore a critical assumption is made: the costs of signaling 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 signaling and recruitment takes place.

The differing cost structure need not preclude "bad" workers from obtaining the credential. All that is necessary for the signal to have value (informational or otherwise) 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 (or is created), "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”,[4] 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 to 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.

One of the consequences of the existence of a pure signalling value to education is that public funding of education, especially higher education, is questioned. The debate is not so much about whether there should be any public funding at all; but what the correct level of funding should be. In purely economic terms, the optimal level of public funding would equal the total public benefits from the educated population—the private value of the signal would be excluded.

#### 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:

Data of the Model
Group Marginal Product Proportion of population Cost of education level y
I 1 ${\displaystyle q_{1}}$ y
II 2 ${\displaystyle 1-q_{1}}$ 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(y) will be:

${\displaystyle W(y)={\begin{cases}1,&yy*\end{cases}}}$

Working with these hypotheses Spence shows that:

1. There is no rational reason for someone choosing a different level of education from 0 or y*.

2. 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.

3. 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.

4. Therefore, putting the previous two inequalities together, if 1<y*<2, then the employer initial beliefs are confirmed.

5. There are infinite equilibrium values of y* belonging to the interval [1,2], 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.

6. If no signaling takes place each person is paid his unconditional expected marginal product ${\displaystyle 2-q_{1}}$. Therefore, Group I is worse off when signaling is present.

In conclusion, even if education has no real contribution to the marginal product of the worker, the combination of the beliefs of the employer and the presence of signaling transforms the education level y* in a prerequisite for the higher paying job. It may appear to an external observer that education has raised the marginal product of labor, without this necessarily being true.

### 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 (the observable signal) 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*:

Summary of the outcome for l and h with and without S*
Person Without Signal With Signal Will the person obtain the signal S*?
l Wo W* - C'(l) No, because Wo > W* - C'(l)
h Wo W* - C'(h) Yes, because Wo < W* - C'(h)

The structure is as follows: There are two individuals with differing ability (productivity) levels.

• A higher ability / productivity person: h
• A lower ability / productivity person : l

The premise for the model is that a person of high ability (h) has a lower cost for obtaining a given level of education than does a person of lower ability (l). Cost can be in terms of monetary, such as tuition, or psychological, stress incurred to obtain the credential.

• 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*

For the individual:

Person(credential) - Person(no credential) Cost(credential) Obtain credential
Person(credential) - Person(no credential) < Cost(credential) Do not obtain credential

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(credential) and Person(no credential) are not clear.

For the employers:

Person(credential) = E(Productivity | Cost(credential) Person(credential) - Person(no credential))
Person(no credential) = E(Productivity | Cost(credential) > Person(credential) - Person(no credential))

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.[5]

## Signalling and IPOs

Leland and Pyle (1977) analyse the role of signals within the process of IPO. The authors show how companies with good future perspectives and higher possibilities of success ("good companies") should always send clear signals to the market when going public (e.g. the owner should keep control of a significant percentage of the company). To be reliable, the signal must be too costly to be imitated by "bad companies". If no signal is sent to the market, asymmetric information will result in adverse selection in the IPO market.

## Brand and Signaling

Waldfogel and Chen (2006)[6] demonstrate the importance of brands in signaling quality in online marketplaces.

## Signalling and eBay Motors' Price Premium

Signaling has been studied and proposed as a means to address asymmetric information in markets for Lemons.[7] Recently, signaling theory has been applied in used cars market such as eBay Motors. For example, Lewis (2011)[8] examines the role of information access and shows that the voluntary disclosure of private information increases the prices of used cars on eBay. Further, Dimoka et al. (2012)[9] analyzed data from eBay Motors on the role of signals to mitigate product uncertainty. Extending the information asymmetry literature in consumer behavior literature from the agent (seller) to the product, authors theorized and validated the nature and dimensions of product uncertainty, which is distinct from, yet shaped by, seller uncertainty. Authors also found information signals (diagnostic product descriptions and third-party product assurances) to reduce product uncertainty, which negatively affect price premiums (relative to the book values) of the used cars in online used cars markets.

## Signalling outside options

Most signalling models are plagued by a multiplicity of possible equilibrium outcomes.[10] In a study published in the Journal of Economic Theory, a signalling model has been proposed that has a unique equilibrium outcome.[11] In the principal-agent model it is argued that an agent will choose a large (observable) investment level when he has a strong outside option. Yet, an agent with a weak outside option might try to bluff by also choosing a large investment, in order to make the principal believe that the agent has a strong outside option (so that the principal will make a better contract offer to the agent). Hence, when an agent has private information about his outside option, signalling may mitigate the hold-up problem.

## (Self-)Signaling and gambling

Signaling influences bettors in domains that are relevant to their identity or commitments. When betting on or against a group, belief, or ideal, such as a favorite sports team or politician, the choice of bet (i.e., for or against) sends a signal to the bettor about his or her identity. Betting on the outcome seems to send a reaffirming signal to the bettor about her identity, whereas betting against the outcome seems to send a signal to the bettor that the outcome is less important than before. As a result, bettors are reluctant to bet against such identity-relevant outcomes, even when bets against identity-relevant outcomes are more favorable than bets on identity relevant outcomes. When presented real gambles of equal expected value (ev = $7.50) on the 2000 US Presidential election, for example, both supporters of George W. Bush and Al Gore were more likely to bet their candidate to win (74%) the election than to lose the election (26%). As further evidence, more than 45% of N.C.A.A. basketball and hockey fans turned down a free chance to earn$5 if their team lost its upcoming game.[2]

## References

1. ^ McKay, Ryan; Mijović-Prelec, Danica; Prelec, Dražen (2011-02-01). "Protesting too much: Self-deception and self-signaling". Behavioral and Brain Sciences. 34 (1): 34–35. doi:10.1017/S0140525X10002608. ISSN 1469-1825.
2. ^ a b Morewedge, Carey K.; Tang, Simone; Larrick, Richard P. (2016-10-12). "Betting Your Favorite to Win: Costly Reluctance to Hedge Desired Outcomes". Management Science. doi:10.1287/mnsc.2016.2656. ISSN 0025-1909.
3. ^ a b c Michael Spence (1973). "Job Market Signaling". Quarterly Journal of Economics. 87 (3): 355–374. doi:10.2307/1882010. JSTOR 1882010.
4. ^ Hungerford, Thomas; Solon, Gary (1987). "Sheepskin Effects in the Returns to Education". Review of Economics and Statistics. 69 (1): 175–177. JSTOR 1937919.
5. ^ http://economics.mit.edu/files/552
6. ^ Waldfogel, Joel; Chen, L. "Does Information Undermine Brand? Information Intermediary Use and Preference for Branded Web Retailers". Journal of Industrial Economics. 54 (4): 425–449. doi:10.1111/j.1467-6451.2006.00295.x.
7. ^ Akerlof, G. A. (1970). The market for" lemons": Quality uncertainty and the market mechanism. The Quarterly Journal of Economics, 488-500.
8. ^ Lewis, Gregory. "Asymmetric Information, Adverse Selection and Online Disclosure: The Case of eBay Motors". American Economic Review. 101 (4): 1535–1546. doi:10.1257/aer.101.4.1535.
9. ^ Dimoka, Angelika; Hong, Yili; Pavlou, Paul. "On Product Uncertainty in Online Markets: Theory and Evidence". MIS Quarterly. 36 (2): 395–426.
10. ^ Fudenberg, Drew; Tirole, Jean (1991). Game Theory. MIT Press.
11. ^ Goldlücke, Susanne; Schmitz, Patrick W. (2014). "Investments as signals of outside options". Journal of Economic Theory. 150: 683–708. doi:10.1016/j.jet.2013.12.001.