Economic Models of Discrimination

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

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

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. 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. 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. 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. Some room for discrimination • Suppose now that the market wage is different: wAand wD • What would happen now? • Optimization: • wA< wD  Hire all A • wA> wD  Hire all D • Why no discrimination? • Firms have no motive.

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)- wA·A - wD·D – d·D • Here d is the strength of the firm’s discriminatory preference

9. 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?

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

12. 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

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. 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

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

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

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

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. 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. 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. 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]

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

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

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. 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