1 economic models of discrimination sendhil mullainathan economics 1035 fall 2007
Post on 21-Dec-2015
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TRANSCRIPT
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Overview
• Describe a simple labor model
• Incorporate discrimination into the model
• Use this model to interpret audit studies
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Setup
• Production Firm:– Employs E workers– Suppose all workers earn the same amount– Quantity Produced is a function of the number
of workers: q=f(E)
– Pays wage w– Therefore Profits are:
p·q – wE = p·f(E) - w·E
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Optimization
• Again, Profits are:
p·f(E) - w·E
• First order condition for optimal E, E* p·f’(E*) = w
• Interpretation?– Firms hire workers until their marginal product
(the extra units they would produce) equals their cost
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Two types of workers
• Now suppose there are two types of workers A and D, advantaged and disadvantaged– Suppose the market pays the same wage for
both workers– A and D are substitutable
• Firms Maximize Profits: p·f(A+D) - w·(A+D)
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Optimum
• Again total employment is such that:p·f’(E*)=w
• How many A and D workers will a given firm hire?– The model does not say. They will be indifferent. – A firm could hire all of one or all of another.
• How many A and D workers would the market as a whole hire? – Determined by their labor supply curve. – But there is nothing here to encourage discrimination
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Some room for discrimination
• Suppose now that the market wage is different: wA and wD
• What would happen now?
• Optimization: – wA < wD Hire all A
– wA > wD Hire all D
• Why no discrimination?– Firms have no motive.
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How to model discrimination
• Possibilities:
– Firms only want to hire A. What’s the problem here?• No ability to make tradeoffs. Economics is most useful when
there are smooth tradeoffs
– Discriminatory firms have a “preference” for hiring A. How to model?
• Easy way of doing it: Include a cost of hiring D. • Profits:
p·f(A+D)- wA·A - wD·D – d·D• Here d is the strength of the firm’s discriminatory preference
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Optimization
• What will the firm do? Recall profit function:p·f(A+D)- wA·A - wD·D – d·D
• Depends on wages:– wA < wD · (1+d) Hire only As– wA > wD · (1+d) Hire only Ds– wA = wD · (1+d) Indifferent
• Even discriminatory firms hire D’s. Why?– If they are sufficiently cheap. – The required discount for D rises with d– But will they hire the same number?
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Observations
• Firms that hire all A’s– Lose money because they are paying for
more expensive workers– Inefficient scale
• Firms that hire all Ds – Still can lose money if d > 0. Inefficient scale.– They hire too few Ds. Why?
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Discriminatory Firm’s Profits
• Questions– Why are profits initially falling?– Why a discrete drop?– What is this point?– Why is it flat
thereafter?
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• Why are profits falling?– A firm with greater discrimination is inefficiently hiring
• Why a discrete drop at a point?– At d = wA/wD – 1, the firm is indifferent between D and
A. When it switches to A’s, profit falls.– But why is it discrete? Compensating differential
• Why is it flat?– Once hiring all A workers, greater d doesn’t affect
behaior
• What happens to high d employers?– They earn less profits
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Profits as a function of wages
• Questions– Why are profits falling initially?– Why a discrete drop?– What is this point?– Why is it flat
thereafter?
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• Why are profits falling?– When hiring all D workers, as their wage rises, profit
falls.
• Why a discrete drop at a point?– This is the point at which wA =wD (1+d). So the firm is
indifferent between the two workers. – When it switches to As, profit falls.– But why is it discrete? Compensating differential
• Why is it flat?– Once hiring all A workers, the wage of D does not
matter
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Key Insight
• Wage differential is determined by the nature of the marginal firm, not the average firm
• What does this mean?– All the D workers sorted to firms with low d,
the non-discriminators.– If there are enough them, there will be no
wage impact.
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Other observations
• There will be segregation• Profit of discriminators will be the same as non-
discriminators if there are enough non-discriminators
• If there are not, discriminators will pay a “price”• What should happen to them in the long-run?
– They will not be able to compete with non-discriminators and should leave the industry.
• Assumes there are enough non-discriminators to run the firms
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Critique of Audit Studies
• They only measure average discrimination.
• Not what happens in wages.
• Responses?– Market sorting is not perfect. – Job search is an inefficient process.
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Statistical DiscriminationA Different Model
• Employers are profit maximizing
• Workers have productivity p.
• Firms would like to hire any worker and pay wage w=p.
• But productivity is uncertain. – They see a signal s.
• So they will pay w=E[p|s]
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Race might matter
• Case 1: Suppose that average productivity of D is lower than A.– Then they will pay E[p|s,D] or E[p|s,A]– So even with the same signal, D’s can get
paid less
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Race might matter
• Case 1: Suppose that average productivity of D is lower than A.– Then they will pay E[p|s,D] or E[p|s,A]– So even with the same signal, D’s can get
paid less
• Case 2: Average productivity is the same but Firms “understand” s less for D’s– So will put less weight on s signal for D. – Key insight: Low performing D will do better
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Testing for these models
• How would you test for these models?• As information increases, gap decreases
– Any evidence you’ve seen– Recall resume audit study. What was found there?
Increasing gap– Altonji-Pierre: Race gap shortest at entry into job
• How else to test?– What if you could vary how much information is seen?