First scenario: You are considering the impact of a public policy antipoverty intervention on a health outcome. You have a range of potential control variables: other policies, community level macroeconomic variables, and individual demographics, income, and education. a In an OLS regression setting, some argue for controlling for as much as possible. "When in doubt, put it in the regression". Explain, as precisely as possible, the rationale for this argument. b. Under what circumstances do you want to not include a potential control variable? Be as comprehensive and precise as possible. Second scenario: You are estimating an OLS regression where you expect the bias to be positive (such as in a regression of earnings on education). You find a plausible instrument, perform IV, and to your surprise the coefficient goes up, not down! C. List four to six (or more) categories of reasons that can explain this, and briefly explain the issue for each. d. Also, explain as carefully as possible what sort of ancillary evidence you can use to distinguish amongst them or further diagnose the situation. Third scenario: Experiments are often considered the "Gold Standard' of evidence for assessing public policy. e. What have been the most important (actual) experiments in the US public policy context? Give a few details about each one that you discuss. f. What do we know about the ability of nonexperimental methods to get at the results that an experiment would have found? Be as specific and comprehensive as possible regarding particular methods, the relevant literature, and other relevant issues. Question 2. Willingness to Pay: The Certainty and Uncertainty Cases Suppose that there are n goods, the first of which serves as the numeraire. While income is fixed at yo, a public project changes consumer prices from qa to q which results in an increase in utility from u to u a. Use the expenditure function to write down an expression for equivalent variation (EV), defined in such a way that it is positive in this case. b Now write down an expression for equivalent surplus (ES), also defined so as to be positive. C. Draw a diagram which compares EV to ES. Use your diagram to show that EV 2 ES, and explain. d. Prove algebraically that EV > ES. Now suppose instead that the benefits of the public project depend on which of two states of nature occurs. There are n consumers, each consumer experiences the same state of nature, and there are no insurance markets (no risk sharing). Consumer i's willingness-to-pay locus is the set of pairs (xiyil, where x; is the amount to be paid in the event the first state of nature occurs and yi is the amount to be paid if the second state of nature occurs. The probability of the each state of nature occurring is 1/2. For positive values of x; and vi the locus satisfies x2 + y/ =8. e. What is the option price for consumer i? F. What is the fair bet point? What is the appropriate notion of aggregate willingness to pay in this case? Explain. h. Suppose the probability of the first state of nature occurring increases to 2/3, In which direction would the intercept of the willingness to pay locus with the x- axis move? Explain how you know.1) Willingness to Pay for Pollution Control Under Income Uncertainty. Suppose that a consumer's utility depends on income (c) and whether regional air quality is improved (8=1) or the air is left polluted (8=0), according to the utility function u(c,6) = c"+8. Note that for a given air quality level the consumer is risk averse, but that the marginal utility derived from air quality improvement is the same regardless of income. The consumer's exogenous income is uncertain: it is e, with probability p, and ez with probability p2. Although elce2, the utility function is the same in both states. a) Write down an equation which defines the willingness-to-pay locus in (11,y2) space. b) Use the implicit function theorem to find the slope of the willingness-to-pay locus, and determine whether it is concave or convex. Then illustrate the locus in a figure having y1 on the horizontal axis and 2 on the vertical axis. c) Write down an equation for the line of the points having an expected value equal to a constant A. d) Taking A=OP (the option price), prove that the willingness-to-pay locus at the 450 line is steeper than is the locus of points with expected value equal to OP. Then illustrate the locus of points with expected value OP in your figure. e) Give an intuitive interpretation of your result in part (d).3. Monetary policy in the overlapping generations model with ex ante heterogeneity Time: discrete, infinite horizon, t = 1, 2, 3... Demography: A mass 2/ of newborns enter in every period. Everyone lives for 2 periods except for the first generation of old people who live for 1 period. Within the population there are two types of household A and B who differ according to their endowments (see below). The population is split exactly in half between the groups. Preferences: for the generations born in and after period 1; 1 = A, B where c , is consumption in period t and stage s of life for type i = A. B individuals. For the initial old generation U(G ]) = In(c ) for i = A, B Endowments: Except for the initial old, in the first period of life type A people receive 1 unit of the consumption good and type B people receive 2 units. No one gets any endowment in their second period of life. In period 1 the first generation of old are endowed with Ho units of money spread equally among them which can be stored but provides no utility in consumption. The money supply grows each period so that the aggregate money supply in period t is Ho(1 + ). The new money transfers occur by helicopter drop (i.e. lump sum) to each old person at the beginning of the period in which they are old. Information: There is complete information with perfect foresight. Solution concept: Competitive equilibrium. Each period there are markets for the con- sumption good and money. Let, pr, be the price for goods in terms of money in period t which is taken as given by every participant. (a) Write out and solve the problem faced by the members of each type in each generation t. Use My to represent the nominal money demand of each type i = A, B individual born in period t. (Hint: If pr+1 drops out of your first order condition equation don't worry about it.) (b) Write down the market clearing conditions and define a competitive equilibrium. (c) We will focus on a steady state monetary equilibrium. Obtain an expression for the transfers made to each household. (d) Solve for money demand in each period in terms of the current price of goods, pr, and the transfer amount. You do not have to solve for pr. (e) Solve for the amount of consumption in each period of life for each generation also in terms of p, and the transfer amount (f) By comparing consumption of type A individuals with that of type B, comment on the extent to which money growth, o > 0 has a redistributive effect. Briefly interpret the result.2) Optimal Public Utility Pricing A new town is considering building a hydroelectric plant. There are two goods (electricity and labor), and this plant would incur a large fixed cost and then produce electricity at a small (but increasing) marginal cost. All consumers have identical preferences for electricity and can therefore be represented by a single consumer; they have no non-wage income. The consumers' preferences are such that it is Pareto optimal to build the plant, using Ly units of labor to produce EA units of electricity. Unfortunately, pricing at (the low) marginal cost would generate negative profits. a) Write down the government's simple "first-best" optimization problem (where the government controls production and consumption directly rather than through the market). Illustrate the problem in a clearly labeled diagram, showing that the Pareto optimum described above is the solution. b) Use your diagram to illustrate the situation where marginal cost pricing would not be a viable way to achieve the Pareto optimum in a market economy because a competitive firm would make negative profits. Explain. c) Show in your diagram that average cost pricing (zero profits) would also not be a viable way to achieve the Pareto optimum. Explain. d) Now write down a market-based optimization problem in this situation, where the government affects consumption only by its choice of prices and a lump-sum tax on the consumer (which covers the utility's losses). Illustrate the problem in a clearly labeled diagram, showing that the Pareto optimum described above is the solution. e) Finally, write down a market-based problem in which the government sets prices but cannot charge a lump-sum tax. Illustrate the problem in a clearly labeled diagram, showing why the Pareto optimum is not achieved