L16 - Asymmetric Information: Signalling II

Question 1

Where did the theory of signalling in the labour come from?

Answer 1

• This was the original setting for Spence’s Nobel prize winning work on signalling, link.
• Workers differ in productivity levels. Employers do not observe productivity levels of prospective workers.
• The existence of low productivity workers dampens the equilibrium wage rate.
• High productivity workers want to persuade employers of their high productivity to gain a higher wage rate.
• They may attempt to do this by using education as a signal.#
• Studying this topic can help us understand some of the issues regarding university tuition fees. However, in all that follows, contrary to reality, we assume that education has no effect on productivity.
• This is for simplicity, but any resulting policy conclusions must bear this limitation in mind. Richer models can incorporate additional productivity effects if desired

Question 2

How is Spence’s Signalling Model set up?

Answer 2

Let a worker of type i with wage w have a payoff, U_i = w - Ci, for i=L,H.

By which I mean low workers have U_L=w-C_L and high workers have U_H=w-C_H.

Let total firm profits be denoted by π.

Game:

• Stage 0: Workers each learn own type, private information
• Stage 1: Workers each choose an education level, y
• Stage 2: Firms observe education levels and each decide on a wage offer schedule, w(y), simultaneously.
• Stage 3: Workers each choose wage offer or exit

Question 3

How can we analyse the signalling model given we have full information?

Answer 3

Full Information Benchmark

If productivity is common knowledge, clearly competition for the workers pushes the wage for each type up to their productivity levels. –> paying the wage equal to the productivity

wH = 2 and wL = 1

Firms do not earn any profits, π =0.

Workers do not incur any education and so U_H = 2, U_L = 1

Question 4

How can we analyse the signalling model given we have asymmetric information and no signalling?

Answer 4

• f productivity is asymmetric information and there is no education, then the firms cannot distinguish between workers.
• There can only be one wage rate and competition between the firms pushes the wage rate up to the expected level of productivity

Wage rate equals w = 2 - q. (average wage rate where probability of q low types and 1-q high types)

We assume both types of workers have a zero outside option and so both types are willing to work here as 2-q>0. (This keeps things simple and avoids any extreme adverse selection problems related to market breakdown).

Hence, welfare can be described by: U_H = U_L = 2-q, π=0 –> profits are still zero as wages are still paid up to the level of the expected productivity of workers

high types arent happy because they are getting paid a lot lower than they think they are worth

Question 5

What properties does the signalling equilibrium need to have?

Answer 5

Clearly high types would like to distinguish themselves from the low types. Without signalling, they earn w = 2 – q, but there true productivity equals 2.

Can we construct a separating equilibrium, where the two types select different education levels that allow the firms to distinguish between them?

Informally, any equilibrium must have the following properties otherwise a player would wish to change their behaviour:

• i) workers must select their education optimally, given other players’ behaviours and firms’ beliefs
• ii) firms must select wage offers optimally, given other players’ behaviours and firms’ beliefs
• iii) firms must hold correct beliefs about each worker’s productivity given their education level –> if they weren’t correct there would be a reason to change their behaviour and the eqm wouldn’t be stable

Question 6

What does the equilibrium wage schedule look like with signalling under asymmetric information?

Answer 6

• Imagine both firms hold the following beliefs about education levels, y:
• If y ≥ y*, a worker is a high type and if y < y* a worker is a low type
• The resulting eqm wage schedule describing how w* varies with y is below
  
  • e.g. Oxford could be above y* and get 2, whereas Stafford Uni would be below y* and thus pay 1
• Consequently, workers find any education levels other than 0 and y* to be dominated
  
  • no point working any harder to get a better education if you are only going to get one the two different points

Question 7

How can we analyse the signalling model with asymmetric information given that signalling is possible?

Answer 7

• Y* cost needs to be between the two productivity levels
  
  • not too small that low types can/wants to mimic equally not two high that it puts high type off as well

Question 8

What is the non-uniqueness issue within our signalling models over the last 2 lectures?

Answer 8

• eqm can occur anywhere between the range (uncertainty in the predictions)
• Note that the separating equilibrium is not unique. It can exist here (with the lecture example) for any 1 < y*≤ 2. (Similar issues in last lecture, with levels of advertising and low prices.)
• Non-uniqueness is very common in signalling games but is a bit uncomfortable. Can we think of a ‘refinement’ – a way of selecting one equilibrium above the others?
• One candidate, (among many), is Pareto dominance – the eqm with the highest social welfare.
• Here, this would suggest that the ‘least cost separating eqm’ with y* = 1 is the most sensible because education is costly. High types engage in just enough education to deter low types

This least cost separating eqm is drawn below:

• distance a and b maybe equal and the high types just engage in just enough education to deter low types

Question 9

Welfare comparison under no signalling and signalling (separating equilibrium)?

Answer 9

• Without signalling, everyone gets the pooled wage rate
• low types prefer low signalling as they get more money (2-q > 1)
• Following from the previous slide, how can it be that the high types may not prefer the signalling outcome relative to the no signalling outcome?
• Surely, this cannot hold given the way we constructed the separating equilibrium which required high types to want to signal
• Not quite – there is a difference in beliefs:
  
  • To construct the separating eqm, we required high types to prefer to signal relative to being treated as a low type, with 2 – (y*/2) ≤ 1.
  • However, in the comparison of signalling versus no signalling, we are comparing the payoffs from signalling relative to the payoffs in the pooling equilibrium, with 2 – (y*/2) versus 2 – q.
  • These are not the same comparisons.
    
    • signalling may is rational in the model but it might not be social welfare enhancing under the adverse selection equilibrium

Question 10

How does this signalling apply to current tuition fees?

Answer 10

• • Is education just a way of high types earning better wages?
    
    • Signalling may actually damage social welfare and make society more unequal
• Does it just increase inequality?
  
  • Under the current system, high and low productivity workers pay the same. Are there some high productive workers that are forced to not attend university cause its not optimal to pay
• If so, would society be better off without education? Why should society pay for the education of the high types?
  
  • The original plan was good as the benefit was shared between the graduate (with better pay overtime) and society with hopefully advance in tech etc. –> hopefully help society and the economy in some way.
  • Issue now is that because everyone is paid a maintenance loan (on the flip side to the above point) there is a pooling equilibrium –> if everyone is going to university how can employers tell the difference?
    
    • Is it grades? What about grade inflation with oxford and Cambridge now handing out the lowest amount of first and around 90% of students were given a 2:1 or above (Weale, 2020)
  • Does this interpretation of education help justify tuition fees?
    
    • No there is no way to tell the difference, probably why, especially in Finance brand name, and extra circular activities set you apart over
• How would your answers change if education acted to improve productivity?
  
  • But if education enhanced productivity then the model and signalling prove that although they are getting paid more the high types will be providing more to society –> enhancing social welfare
  • (Kampelmann and Rycx, 2018) –> firms profitability found to rise when lower-educated workers replaced with higher –> educational credentials have a stronger impact on productivity than on wage costs
• • Do you become a better citizen too?
• Would your answers depend upon the type of education the workers engaged in?
  
  • Some subjects are more productivity-enhancing than others –> STEM is often seem as more economically beneficial
  • But could the arts be better for social welfare in a way that cannot be quantified –> COVID showed how necessary the arts were for mental health
    
    • Imagine it without it

Question 11

How does Culture influence signalling?

Answer 11

• ADD to this slide
• In some cultures, “Acting White” by gaining education is associated with stigma.
• This may damage the incentives for some types to use education as a signal.
• By introducing stigma, equilibria can be found where ‘middle’ types reduce their education to avoid stigma, but high types continue to engage in signalling.
• • See the award-winning work of Roland Fryer, as surveyed by Katz (2016),.