Midterm 2 Practice - Statistical Discrimination

PRACTICE QUESTIONS > Midterm 2 Practice - Statistical Discrimination

University of Missouri, Columbia ECONOM 4311 Econ 4311 - Labor Economics Practice Problem: Statistical Discrimination Suppose there are two types of workers: lifelong criminals and non-criminals. Lifelong criminals, if hired, will steal company property and be worth x = 0 to the firm. Noncriminals, if hired, will not steal company property and will ...[Show More]

University of Missouri, Columbia
ECONOM 4311
Econ 4311 - Labor Economics

Practice Problem: Statistical Discrimination

Suppose there are two types of workers: lifelong criminals and non-criminals. Lifelong

criminals, if hired, will steal company property and be worth x = 0 to the firm. Noncriminals, if hired, will not steal company property and will be worth x = 1 to the firm.

Some lifelong criminals already have a criminal record, while others have never been caught.

Some non-criminals have never committed a crime, and therefore do not have a record, while

others do have a criminal record but have been completely reformed. For lifelong criminals,

let p = probability that they have a record and 1 - p = probability that they do not have a

record. For non-criminals, let p = probability that they do not have a record and 1 - p =

probability that they do have a record. It is common knowledge that a fraction π of workers

in the overall population are non-criminals and 1 - π are lifelong criminals. Suppose p = 0:9

and π = 0:8.

1. Suppose companies can perfectly observe whether a worker is a lifelong criminal or a

non-criminal. What wage will each type of worker earn?

2. Suppose that companies can only observe whether a worker has a criminal record.

What wage will workers with criminal histories earn? How about workers without

records?

Hint: prob(non-criminal conditional on not having a record) = pπ

pπ+(1-p)(1-π)

prob(non-criminal conditional on having a record) = (1-p(1 )π-+pp)(1 π -π)

3. Suppose the government \bans the box" so that companies cannot observe criminal

histories. However, companies can observe some other signal ~ p < p that gives information about the likelihood that a worker is a lifelong criminal. Let ~ p = 0:6. What

wage will workers with good signals earn? How about workers with bad signals? How

would criminals and non-criminals view the \ban the box" policy?

Hint: prob(non-criminal conditional on good signal)