1. 1 Economic Models of Discrimination Sendhil Mullainathan Economics 1035 Fall 2007

2. 2 Overview Describe a simple labor model Incorporate discrimination into the model Use this model to interpret audit studies

3. 3 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

4. 4 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

5. 5 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)

6. 6 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

7. 7 Some room for discrimination Suppose now that the market wage is different: w A and w D What would happen now? Optimization: –w A < w D  Hire all A –w A > w D  Hire all D Why no discrimination? –Firms have no motive.

8. 8 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)- w A ·A - w D ·D – d·D Here d is the strength of the firm’s discriminatory preference

9. 9 Optimization What will the firm do? Recall profit function: p·f(A+D)- w A ·A - w D ·D – d·D Depends on wages: –w A < w D · (1+d)  Hire only As –w A > w D · (1+d)  Hire only Ds –w A = w D · (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?

10. 10 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?

11. 11 Discriminatory Firm’s Profits Questions –Why are profits initially falling? –Why a discrete drop? –What is this point? –Why is it flat thereafter?

12. 12 Why are profits falling? –A firm with greater discrimination is inefficiently hiring Why a discrete drop at a point? –At d = w A /w D – 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

13. 13 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?

14. 14 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 w A =w D (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

15. 15 Equilibrium There will be a gap. Is this always true? What does this graph assume?

16. 16 Equilibrium There is still a gap Is this always true?

17. 17 Equilibrium No longer a gap How many d=0 firms are needed?

18. 18 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.

19. 19 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

20. 20 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.

21. 21 Statistical Discrimination A 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]

22. 22 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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24. 24 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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26. 26 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?

27. 27 Conclusion Simple economic models of discrimination depend on preference –Employers, workers, customers –Basic insight is sorting to lessen impact of discrimination –Discriminators can pay a tax Statistical discrimination models emphasize using group membership as a signal