Introduction to signaling

1. Introduction to signaling

2. 1 Principal With SI: Both types got their U With AS: B got his U G got more than U Agents are better with AS than with SI They do not have incentives to disclosure any information Many Ps competing for A Type B gets the same utility with SI than with AS Type G gets less utility with AS than with SI Type G has incentives to reduce the information asymmetry (convey credibly that he is G type) Models of Adverse Selection

3. There are circumstances where some individuals are worse off because there is some information that is not public • This is the case of Type G when Principals are competing for agents. • It is realistic to expect that, in reality, type G will carry out an activity (“send a signal”) to convey that he is type G • In order for this to work, we need that: • The P observes the signal • The signal is informative (that is, P knows that this signal cannot come from a type B) • Hence, type B should be worse off carrying out the activity (sending the signal) than not carrying it out • Types will self-select into whether or not send the signal

4. Education as a Signal (Spence, 1973) • The model assumes that even if education does not increase workers’ productivity. • The important result is that individuals will get education just to signal that they are high ability workers • Two types of workers: • “Good” or “high ability”, production equals to 2 • “Bad” or “low ability”, production equals to 1 • Company profits: • 2-w, or • 1-w (depending on the worker’s ability)

5. Education as a Signal (Spence, 1973) • Time dedicated to study = y • Cost of studying y for low ability individuals: y • Cost of studying yfor high ability individuals: y/2 • It is commonly known that companies follows this scheme: • a threshold of education time y*, such that: • They pay w=2, if the individual has y≥y* • They pay w=1, if the individual has y<y* • Individuals’ optimal response is to choose y=0, or y=y* • (it does not make sense to study more because studying is costly and the wage will not be larger than 2, anyway)

6. Education as a Signal (Spence, 1973) • Who will choose y=0, or y=y*? • Each type of individual will choose the education level that maximizes his surplus • A separating equilibrium will be one such that each type gets a different contract (wage) • Whether or not a separating equilibrium exists depends on the value of y* • Let’s look for the value(s) of y* that give us a separating equilibrium

7. Let’s look for the value(s) of y* that give us a separating equilibrium • High ability prefers to study y* to study 0: • 2-y*/2 ≥ 1-0. This means that: y* ≤2 • Low ability prefers to study 0 to study y*: • 1-0≥2-y*. This means that: y* ≥1. • As long as firms choose y* between 1 and 2, we will have that high ability will select into studying and low ability no • In the model, individuals take this education decisions even if education does not improve productivity. Only as a signalling device

8. Very Important: The cost of education was different according to the type. • This is very important !!!! Otherwise, they will not self-select into whether or not sending the signal • If they had the same education cost, so all of them would have done the same: either education or not. Then, the P will not have been able to separate them.

9. Other examples of signalling: • Offer products with large guarantee periods. This will only be profitable for the high quality manufacturer because he knows that he will hardly have to repair the product. However, low quality manufacturers will find that unprofitable !! • Buying a car that cannot take high speed… we are signalling that we do no like driving at high speed. This would be very costly for a individual that enjoys driving at high speed.