# Slutsky Equation - Labour Economics - Past Exam, Exams for Economics. Veer Bahadur Singh Purvanchal University

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Slutsky Equation, Two Good Model, Dramatic Decline, Budget Share, Wealth and Wages, Economic Downturn, Payroll Taxes, Constant Returns, Scale Technology, International Capital Markets are some points from questions of th...
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University of California Department of Economics Field Exam August 2010

Labor Economics

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 minutes. 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.

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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′) 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

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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 is happening. 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 minutes. 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

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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 the disadvantages? 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 neighborhood choice.