Labor Field Exam January 2012
Answer three of the following four questions. You have three hours. Try to
explain your reasoning wherever possible.
1. Consider a simple search model applied to an experiment on the labor supply of
undergraduates. You take a random sample of 100 undergraduates. For each such
undergraduate, you explain that they will receive a series of wage offers that will
vary from day to day. Each offer can be accepted or not and acceptance or
rejection of a day’s offer does not affect subsequent wage offers. Each such task
takes 10 minutes to accomplish and can be done over the internet. Wage offers
will be given daily at 6am over the internet by e-mail; the task can be
accomplished any time prior to 5:59am the next day. You do not specify a final
period to the experiment and describe it as being an open-ended arrangement.
Students are indexed by s, and let their wage offers be distributed exponential
with parameter λs. You randomly assign the parameters from a list of possible
parameters. Let Bst denote the random variable associated with the wage offer
student s on day t. You inform students of the range of offers they are likely to get
by giving them 100 examples of draws from their wage distribution. Assume that
the students are able to infer the parameters from the list. Assume that
undergraduates have utility of zero associated with not working for you on the
menial task. Assume linear utility.
a. Write down the Bellman equation for this problem.
b. Give a formula for the expected value of the value function associated
with a random draw Bst. Your formula may depend on the reservation
wage.
c. Give a formula for the reservation wage. Your formula may depend on the
expected value of the value function associated with a random wage offer.
d. Derive the log-likelihood function for the set of binary labor supply
decisions recorded by the experiment, as a function of the discount factor.
e. Would the model be identified if you only gave one wage offer to the
undergraduates?
