Signalling and Spence model Flashcards
what is the signal in the spence model
firms may not observe ability but they observe education (the signal)
what is the single crossing property *
increasing the level of education is more difficult for low-ability workers,
cost is greater
what are the simplifying assumptions for the simple spence model *
out of work utility = 0 regardless of type,
cost of education proportional to level of education,
productivity depends only on ability not education
explain assumption for the spence model ‘productivity depends only on ability not education’
signal about underlying ability but is pure signal as education does not affect your underlying productivity
what does y(e) represent for the simple Spence model
the firm’s expectation of the worker’s productivity given their level of education e
what are the four stages of the simplified Spence model **
the worker’s ability is drawn at random,
the worker (who knows ability) chooses an education level e,
the firm makes a take it or leave it offer to the worker,
the worker decides whether to accept
what is the payoff for the worker in the simplified spence if the worker accepts the job
the wage from the job minus the cost of education
what is the payoff for the worker in the simplified spence if the worker doesn’t accept
0 minus the cost of education
what is e for simplified spence model
level of education
in the simplified spence model what is the pure strategy PBE characterised by *
education levels eh and el (education levels chosen given their ability high or low),
wage offer function (w(.)),
the firm’s belief function (u(.))
what is a separating equilibrium
where the two different types choose different levels of education
what happens if there is a separating equilibrium in the simplified spence game
the firm will be able to tell which workers are high or low productivity based on their education level
for a separating equilibrium for the simplified spence game when does the firm know a workers ability
when they observe his education
what does a separating equilibrium imply for simplified spence model
there is no point of the low ability workers choosing any level of education because they will be offered the same wage
what is the condition characterising a separating equilibrium for the simplified spence game
need to prevent low types from taking high type education,
need low type to be better off by taking no education than masquerading to pretend to be high type
what is signalling
informed individuals may send signals about the hidden characteristic to the uninformed party
when does the worker and firm move in the spence model
the worker moves at step 2 (chooses edu) and step 4 (decides whether to work),
firm moves at step 3 by making a wage offer
under asymmetric information in the spence model what does the firm know
the firm does not know the worker’s ability, only his education
what is μ in the spence model
μ is the firm’s belief function
what is w in the spence model
wage offer function
what is cl and ch in the spence model
cost of education for type l and type h workers respectively
in a separating PBE what education do type l and h workers take
l-type workers choose el=0 and h-type workers choose eh (ehmin,ehmax)
how does each of the infinite available PBE compare to the perfect information equilibrium
each of the PBE is less efficient than under perfect information, wages are the same but some resources are devoted to producing a signal -education- that does not increase productivity
what is the most efficient (least costly) separating PBE where the high type chooses education
most efficient are the ones where eh=ehmin
what is a pooling equilibrium
a pooling equilibrium is a PBE where the workers choose the same education level, say e’ regardless of ability
where do you start when working out what the equilibrium is for pooling
we start with the firm’s belief about the worker’s productivity when e=e’
in a pooling equilibrium what is firm’s belief about the productivity of the workers
the probability that a worker with education e’ has high ability is equal to the proportion of high-ability workers in the whole population θ
what is the pooling equilibrium wage when e=e’
E(y) = θyh + (1-θ)yl
which equilibrium is better out of any pooling pbe or the no-signalling equilibrium
any pooling pbe is weakly pareto dominated by the no-signalling equilibrium
when is a pbe achieved
each worker chooses the optimal signal given his type and the firm’s beliefs and choices,
firm sets optimal wage rates given worker’s signal and beliefs,
firm’s beliefs follow bayes’ rule on the equilibrium path
what does it mean for signalling if the market is perfectly competitive full information (ELQ1)
firms know worker’s productivity and have to offer wage equal to this productivity,
several different outcomes depending on whether the reservation wage is met
stages you go through to work out least cost saving separating equilibrium when can choose education (ELQ1)
in separating type a will take e- and b will take e_,
firms beliefs must be such that Pr(a|e-)=1 and Pr(a|e_)=0,
so a types get offered whigh and b wlow,
it is then optimal for b to choose edu=0,
work out ehmin and ehmax by doing incentive constraints for a and b,
incentive for b is utility from not signalling has to be greater than if they were to masquerade so would be higher wage - cost of edu,
incentive for a is utility from signalling has to be greater than utility if no signal (baring in mind if no signal then will be taken as low type),
then check reservation values
in a pooling equilibrium what is the wage the same as (ELQ1)
in a pooling equilibrium the wage is the same as in the no-signalling case, however if resources spent on signalling then welfare is lower in pooling than no signalling
draw the belief functions and derive and draw the corresponding wage offer functions (what do you do ELQ1)
y=Pr(a|e),
x=e,
draw belief function going through (0,0),
then wage offer function is now based on the firm’s expectations of their type based on their education,
wage offer functions are on graph
y=y(e),
x=e
what graph do belief functions go on (ELQ1)
y=Pr(a|e),
x=e
what graph do the wage offer functions go on (ELQ1)
y=y(e),
x=e
