University of California Department of Economics
Field Exam August 2010
There are three parts in the exam. Each part will be weighted equally and
should take approximately one hour. Make sure you allocate your time
carefully, answering all parts as fully as possible given the time constraint. Use
equations and graphs whenever possible to clarify your reasoning.
WRITE YOUR ANSWERS FOR EACH QUESTION IN A SEPARATE BOOK
PART I Answer both questions in this part. Each question should take about 30
Question 1: LABOR SUPPLY
a) Derive the Slutsky equation for hours of work in a standard two-good model with
leisure and consumption. Be sure to define your notation, and carefully state any
assumptions that you have used in your derivation.
b) The recent financial crisis led to a dramatic decline in the net worth of many American
households. Suppose that for a representative household the elasticity of hours worked
per year with respect to income is −0.1 and that the budget share of earned income in
total consumption is 0.8. How much of an increase in hours worked should we expect if
the crisis destroyed ten percent of lifetime wealth and wages remained constant? Using a
reasonable estimate of the compensated elasticity of labor supply, how much would
wages need to fall for total hours worked to be unaffected by the crisis?
Question 2: LABOR DEMAND
A pair of well known economists proposed cutting payroll taxes during the recent
economic downturn in order to boost employment. Note: Payroll taxes are federal taxes
levied on wages paid by firms to workers (e.g. firms pay an after tax wage of w(1+τ)).
a) Suppose firms produce output using a constant returns to scale technology F(K,L)
taking capital (K) and labor (L) as inputs. Assume the rate of return on capital r is fixed
exogenously by international capital markets. Derive an expression for the employment
effects of a 10% decrease in the federal payroll tax τ. Be sure to state any additional
assumptions needed to derive your answer, and discuss their plausibility.
b) Now consider a representative firm facing the following dynamic objective:
Π(A,K,L)= max AF(K′,L′) − c1 1[L′<L] − c2(K′-(1-δ)K) − wL′ + β E Π (A′,K′,L′)
where A is the firm's total factor productivity, which follows some stochastic process, F
is a production function, c1 represents the fixed cost of firing workers, 1[.] is an indicator
function for the expression in brackets being true, c2 is the cost of new capital, w is the
wage rate, and β<1 is a discount factor.
Using this model, discuss the dynamic effects of a small, temporary cut in the payroll tax
(e.g., a reduction in the tax rate that will last for 1 year).
c) How does your answer to b) depend on the firm's level of uncertainty regarding next
period's level of productivity A′?
PART II Answer all parts of this question. The question is designed to take 1 hour. Use
equations and graphs whenever possible to clarify your reasoning.
In this question you will develop a variant of the Roback (JPE, 1982) model of the joint
determination of wages and cost of living. In particular, consider the case where there are
2 cities (A and B) and 2 skill groups: skilled workers and unskilled workers. Skilled and
unskilled workers are imperfect substitutes. Variation in the cost of living depends only
on variation in cost of land which is assumed to be the same for all workers in the same
city, irrespective skill.
1) State all the assumptions of the Roback model. (for example: what are you assuming
about workers' and firms' mobility? Which goods are traded and which goods are local?
What are you assuming about firms' profits?) . Full credit will be awarded for a full
description of all the assumptions.
2) Assume for now that the two cities are identical in terms of amenities and production
technology, and there are no externalities. Describe the equilibrium in words. Now,
describe the equilibrium graphically. (Hint: Draw two graphs side by side. The left
graph is for the skilled workers. The right graph is for the unskilled workers. Label the
axis and all the curves and explain in detail why each curve looks the way it does.)
3) Now suppose that city A is less attractive than city B because schools have lower
quality. For simplicity, assume that school quality directly enters workers' utility
functions. Assume also that schools are not financed locally and that skilled and
unskilled workers value schools equally. In a graph, show what happens to wages and
rents in equilibrium. Label all the curves. Explain what is happening in words.
4) In equilibrium, both skill groups are present in both cities. Since workers are free to
migrate from city B to city A, why are equilibrium wages---net of any differentials
associated with the quality of schools ---not driven to equality?
5) Assume now that schools are financed locally through a tax on land. Discuss in detail
whether and how this changes the equilibrium prices and wages.
6) Now let's go back to the case where schools are not financed locally. A graduate
student is writing a dissertation on whether school quality affects property values. She
regresses property values on school quality. Explain whether in this context her estimates
of the effect of school quality are correct, too large or too small, and why. If they are not
correct, explain how to obtain correct estimates. (Recall that the two cities are identical
with the exception of school quality)
7) Assume as before that city A is less attractive than city B because it has schools of
lower quality. But now assume that skilled workers value school quality more than
unskilled workers. Further, assume now that there are human capital externalities, so that
workers' productivity depends on the share of skilled workers in the city, as well as on
their own human capital. In a graph, show what happens to wages and rents in
equilibrium. Make sure to distinguish the effect of imperfect substitutability between
skilled and unskilled workers from the effect of human capital externalities. Explain what
8) A graduate student wants to empirically tests for human capital externalities. She runs
a regression of wages on the share of skilled workers in each city, by skill group. Based
on point 7 above, explain how to interpret the estimates from this regression.
PART III Answer BOTH questions in this part. Each question should take about 30
Question 1: Option Value and the Returns to Schooling
This question concerns the interpretation of estimates of the “return” to post-secondary
(i.e., college-level) education. An analyst estimates a model of wages for men between
the ages of 40 and 45 with at least 12 years of schooling of the form
log w = α0 + α1 X + Σj βj Dj + εj
where X is a vector of controls (including potential experience), Dj is a dummy equal to 1
for people whose highest level of schooling is the jth year of college (j=1, …. 10), and εj
is a residual. The analyst calls β1 the “return” for the 1st year of college, and βj − βj−1 the
return for each of the subsequent years of college (j=2, 3…).
a) For purposes of this question, assume that the estimates of β1, β2 and β3 are all very
close to 0, while β4 = 0.6 and is highly significant. Discuss how the concept of option
value can explain why some people go to college for 1-3 years and drop out, even though
people without a degree earn about the same wages as those who only finished high
school and never went to college.
b) An analyst has argued that low returns to the first three years of college arise because
students like to go to college, even though college has no effect on productivity, and
employers use a college degree as a signal of inherent ability. Does this “signaling”
explanation make sense? (Note: you may have to add some additional assumptions).
c) Discuss how you would test between the option value explanation and the signaling
explanation. What kinds of data would you need to conduct the test?
Question 2: School and Neighborhood Choice
This question concerns the economic and econometric issues that arise in estimating the
valuations that different families place on alterative neighborhoods and schools. For
purposes of this question, assume that each neighborhood has its own school.
a) What types of data would you need to estimate a model of neighborhood choice that
would allow you to derive the willingness to pay for higher school quality? Assuming
you have access to the appropriate data, discuss how you would specify a multinomial
logit model that could be used for such an exercise. (Be specific about the kinds of
neighborhood and school characteristics you would like to include).
b) Two co-authors are discussing the issues of model specification for a study of school
quality and neighborhood choice. One wants to use a multinomial logit model, the other
wants to use a mixed logit model. What are the advantages of the mixed logit? What are
c) Suppose that school quality is measured by student test scores, which are determined
in part by family characteristics like income, race, and parental education. Discuss the
econometric and conceptual problems that arise in trying to value school quality.
Hint: think of the equilibrium sorting that arises in model of school and