Macroeconomics Field Exam. August 2007

Transcription

1 Macroeconomics Field Exam August 2007 Answer all questions in the exam. Suggested times correspond to the questions weights in the exam grade. Make your answers as precise as possible, using graphs, equations, coefficient estimates with confidence intervals, etc. whenever appropriate. Include reasonably specific citations to papers when appropriate: e.g., Solow (1956). 1

2 General Questions I. Defining a competitive equilibrium. (30 minutes) Pick a growth model other than the neoclassical growth model. Define a competitive equilibrium for your choice. II. Testing the permanent income hypothesis. (30 minutes) Consider the basic permanent-income model of consumption. That is, there is a representative agent, no liquidity constraints, a real interest rate equal to the rate of time preference, and intertemporally separable, quadratic utility. Thus, the agent s objective function takes the form: V = t= 0 t [ a 2 t ] β C C, a > 0, β = 1/(1 + r), t where C is consumption and r is the real interest rate. The only uncertainty is that the path of after-tax labor income (Y) is uncertain. (a) Show that the model predicts that consumption follows a random walk: E t [C t+1 ] = C t, where E t [ ] denotes expectations given the agent s information set at time t. (b) The permanent-income hypothesis predicts that predictable changes in income do not lead to predictable changes in consumption. Unfortunately, we do not have data on expected future income or expected future consumption. (i) Suppose we instead look at the relationship between actual changes in income and actual changes in consumption. Specifically, suppose we estimate the regression: C t+1 C t = a(y t+1 Y t ) + e t by OLS. Does the permanent-income hypothesis predict that (ignoring sampling error that is, as the sample size becomes arbitrarily large) we will obtain a = 0? Why or why not? (ii) Suppose there is some variable Z t that is correlated with Y t+1 Y t and that is known by the representative agent at time t. Suppose we estimate the regression above by IV, using Z as the instrument. Does the permanent-income hypothesis predict that (again ignoring sampling error) we will obtain a = 0? Why or why not? 2

3 Field Questions III. Questions on Economic Growth (60 minutes total) 1. Growth with Intermediate Goods (20 minutes). Consider the following model of economic growth for an economy in which production involves the use of intermediate goods. An example of an intermediate good is steel or electricity: these are goods that are produced in the economy but that are then used as an input to a later stage of production, like making cars. Y t = A t (K α t L 1 α t ) 1 σ M σ t (1) Y t = C t + I t + M t (2) K t = I t δk t (3) L t = Le nt (4) A t = Āegt (5) In this model, most of the variables have the usual interpretation. I ll comment on what is different. First, M t denotes the quantity of intermediate goods ( materials ) that are used in production. Notice that according to the economy s resource constraint, intermediate goods are just units of final output. Exogenous parameters (greek letters, letters with overbars, and n and g) are assumed to be positive, and not too large when necessary. (a) (5 points) Define formally a rule-of-thumb allocation of resources in this economy. (b) (10 points) Solve for the level of output per worker along the balanced growth path for this rule of thumb allocation. (c) (5 points) Suppose Ā rises by 1 percentage point. By how much does output per worker rise in the long run? Explain why. 3

4 2. Solving the Neoclassical Growth Model in a Special Case (40 minutes) Consider the following special case of the neoclassical growth model: subject to max {C t} 0 e ρt u(c t )dt (6) u(c t ) = C t (7) K t = Y t C t δk t, K 0 given. (8) Y t = F(K t, A t L t ) = (αk t θ + (1 α)(a t L t ) θ) 1/θ (9) L t = 1, A t = e gt. (10) That is, we have a neoclassical growth model with linear utility and CES production (and no population growth). Assume θ < 0. (a) (10 points) Set up the Hamiltonian for this problem and take the first order conditions. Given these conditions, what is the economic interpretation of the Hamiltonian? (b) (10 points) Solve for the growth rate of Y t at each point in time. (c) (10 points) Solve for the saving rate s t 1 C t /Y t at each point in time. (d) (10 points) Comment on these solutions: what is going on in this economy? 4

5 IV. Question on Empirical Macroeconomics (60 minutes total) 1. Effect of Oil Price Shocks (60 minutes) One factor that has been suggested as a candidate explanation of the high inflation rates of the 1970s is adverse supply shocks, especially oil shocks. Most notably, there were very large increases in oil prices in and Yet there have been episodes of similar rises in oil prices since the 1970s, notably in and , that have not been followed by noticeable increases in inflation. (a) (25 minutes) In a recent paper (which you will almost surely not have read), Blanchard and Galí investigate the question of whether the macroeconomic effects of oil-price movements have changed over time. Simplifying slightly, their basic procedure is to run a vector autoregression (VAR) with quarterly U.S. data on oil prices, the consumer price index, the GDP deflator, wages, real GDP, and employment. Their identifying assumption is that oil prices do not respond to the other variables within the quarter. Thus, they put oil prices first in the VAR, and interpret the impulse responses to an innovation in oil prices as the casual impact of changes in oil prices. They run the VAR over two sample periods, 1970:1-1983:4 and 1984:1-2006:4. The results suggest that oil-prices movements had very large effects on output and inflation in the first period, and very small effects in the second. Discuss Blanchard and Galí s approach. Specifically: Is this a persuasive way of identifying the macroeconomic effects of changes in oil prices? Why or why not? Can you think of any reasons they might have obtained their results other than a genuine change in the macroeconomic effects of changes in oil prices? Finally, can you think of any way of improving on their procedure? That is, can you think of any variation on what they do (as opposed to an entirely different approach) that might help to remedy one or more possible problems with their procedure? (b) (25 minutes) In another recent paper (which, again, you probably will not have read), Cavallo and Wu use a narrative approach to attempt to estimate the macroeconomic effects of oil-price movements. They begin by finding the days when the price of oil changed by more than 5 percent. For each of these days, they then read the explanations given in industry publications, such as the Oil and Gas Journal, of the reasons for the large price change. It turns out that the publications almost always identify a single major cause of the large change in oil prices on a given day. Cavallo and Wu focus on the large oil-price movements that the publications attribute 5

6 to factors not directly related to the oil market. Thus, they include, for example, large oil-price movements arising from political and military developments in the Mideast and unexpected weather developments. They exclude oil-price movements arising from, for example, decisions by OPEC and announcements of data on the level of oil inventories in the U.S. They then examine the behavior of macroeconomic variables following the large oil-price changes due to factors not related to the oil market. They find that these oil-price movements are followed by very large movements in output and inflation, and that the estimated effects are much larger than what one obtains by looking at the behavior of output and inflation following generic changes in oil prices. Discuss Cavallo and Wu s approach. Specifically: Is this a persuasive way of identifying the macroeconomic effects of changes in oil prices? Why or why not? Can you think of any reasons they might have obtained their results other than genuinely large macroeconomic effects of changes in oil prices? Finally, can you think of any way of improving on their procedure? That is, can you think of any variation on what they do (as opposed to an entirely different approach) that might help to remedy one or more possible problems with their procedure? (c) (10 minutes) Barsky and Kilian (NBER Macroeconomics Annual, 2001) argue that oil-price movements were not an important reason for poor macroeconomic performance in the 1970s. Briefly summarize Barsky and Kilian s arguments and evidence. 6