Introduction to signaling

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• Introduction to signaling

2
Models of Adverse Selection

• 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)

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• 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

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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 workers ability)

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Education as a Signal (Spence, 1973)

• Time dedicated to study y
• Cost of studying y for low ability individuals y
• Cost of studying y for high ability individuals
  y/2
• It is commonly known that companies follows this
  scheme
• a threshold of education time y, such that
• They pay w2, if the individual has yy
• They pay w1, if the individual has ylty
• Individuals optimal response is to choose y0,
  or yy
• (it does not make sense to study more because
  studying is costly and the wage will not be
  larger than 2, anyway)

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Education as a Signal (Spence, 1973)

• Who will choose y0, or yy?
• 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
• Lets look for the value(s) of y that give us a
  separating equilibrium

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• Lets 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
• 1-02-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

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• 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.

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• 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.