Practice Final Exam Answers Revised: January 9, 2008

Transcription

1 Practice Final Exam Answers Revised: January 9, 2008 You have 120 minutes to complete this exam. There are 3 questions for a total of 120 points. You should budget your time at about 1 minute per point. Please answer each question in the Booklet provided. You may consult two double-sided pages of notes and a calculator, but devices capable of wireless transmission are prohibited. Please read the following and sign below: I understand that the honor code applies: I will not lie, cheat, or steal to gain an academic advantage, or tolerate those who do. (Name and Signature)

2 Practice Final Exam Answers 2 A. Short answer questions (40 points). 1. Explain the concept of total factor productivity (TFP). How is it distinct from labor productivity? How might we try and measure it using data on observable inputs and outputs? Give three examples of ways that a country might increase its TFP (15 points). 2. Explain whether each of the following macroeconomic variables is (i) pro- or counter-cyclical and (ii) whether they are more or less volatile than real GDP: consumption of services investment employment hours per worker Which of these is most likely to be useful in forecasting quarterly changes in real GDP? Which of these is least likely to be useful? (15 points) 3. Explain the concept of an individual s reservation wage. How does it relate to their labor supply? How is the reservation wage likely to change depending on an individual s (i) willingness to work and (ii) non-labor income? Give intuition. How is the reservation wage affected by an increase in labor income taxes? What about corporate income or property taxes? (10 points) Answers. 1. TFP is the amount of output left unexplained after inputs from all other factors of production have been accounted for (labor, capital and possibly other things like human capital and land). It s the residual that s left once we have accounted for other inputs. Labor productivity is a narrower notion of productivity that does not take into account for example that two otherwise identical workers might have different productivities because one uses more capital than the other. A typical way to measure TFP is (a) to take a stand on how inputs map to outputs via a production function, e.g., Y = AK α L 1 α where A is the TFP term, and then (b) to use measures of Y, K, L to infer A. Notice that we cannot use measures of Y, K, L to infer A without taking a stand on the nature of the production function. Three possible ways a country might increase A: (i) R&D and innovation; (ii) more competition between firms; (ii) freer international trade. Four points for the right idea about TFP. Four points for the right comparison with labor productivity. Four points for describing how to infer TFP. One point each for examples of ways to increase TFP. To count these have to involve genuine increases in productivity/efficiency, not just increases in output that might come from increase in input use.

3 Practice Final Exam Answers 3 2. Consumption of services is pro-cyclical and less volatile than real GDP. Investment is procyclical and more volatile than GDP. Employment is pro-cyclical and more volatile than GDP. Hours per worker is pro-cyclical and less volatile than GDP. Investment is most likely to lead the cycle while employment is most likely to lag the cycle and in that sense investment is most likely to be useful for forecasting while employment is least likely to be useful. Oneand-a-half points for getting the right correlation and volatility of each of the variables (a total of 12 points). Two points for getting that employment is least likely to be useful and one point for getting that investment is most likely to be useful. 3. An individual s reservation wage is the lowest wage at which she is willing to work (for any lower wage, she would prefer not to work). An individual s reservation wage is likely to be higher if her willingness to work is intrinsically low or if her non-labor income is high (meaning that she has good outside opportunities). An increase in labor income taxes is likely to increase an individual s reservation wage because it makes the return from working lower. A higher corporate income or property tax is likely to decrease non-labor income and thereby decrease her reservation wage making her more likely to work (of course, these taxes may have other adverse consequences on savings and capital accumulation, say). Two points for the right definition, two points each for the effects of willingness to work and non-labor income, and two points each for the effects of labor income and corporate/property income taxes. B. Labor market dynamics (40 points). You are told the following data for a large North American economy. The labor force is 150 million people. Everybody is either employed or unemployed. The job finding rate is f = per quarter. The job separation rate is s = per quarter. 1. What is the steady state unemployment rate? How many people are unemployed in steady state? How many are employed? How many unemployed people find a job each quarter in steady state? How many employed people lose their job each quarter? (10 points) 2. By contrast, in a medium-sized European economy, the job finding rate is f = per quarter and the job separation rate is s = per quarter. How does the European steady state unemployment rate compare to the North American steady state unemployment rate? (5 points) 3. Suppose that a global recession increases unemployment from steady state to u 0 = 0.10 (or 10%) in both economies. What is the unemployment rate in the North American economy

4 Practice Final Exam Answers 4 after 4 quarters? What about in Europe? Does the European economy respond more or less quickly to unemployment shocks? Explain (10 points). 4. Suppose the European government decides to attack long run (i.e., steady state) unemployment by imposing a tax that firms have to pay if they fire a worker. As a consequence, the separation rate falls to s = 0.01 per quarter. Explain how this might reduce unemployment. But political opponents argue that if it is harder for firms to fire workers, firms will also be less willing to hire workers and so the job finding rate f will fall as well. How large would the fall in f have to be for the government s new policy to have no effect on long run unemployment. Even if f does not actually fall this much, what other possible consequences is a tax on firing likely to have? (15 points) Answers. 1. The steady state unemployment rate is u = s s + f = = 0.05 or 5%. Since the labor force is 150 million, this means = 7.5 million people are unemployed in steady state. The rest, = million people are employed. The steady state flow into unemployment each quarter is s(1 u) = 0.025(1 0.05) = of 150 million, so million people lose jobs each quarter. This is matched by a steady state flow out of unemployment each quarter of fu = 0.475(0.05) = of 150 million, so million people find jobs each quarter. Two points for each of these. 2. The European steady state unemployment rate is u = s s + f = = 0.05 or 5% (again). So the steady state unemployment rate is the same. Four points for the right number, one point to note that it s the same as in the North American economy. 3. The dynamic response of unemployment to a shock is given by u t = u + λ t (u 0 u) where λ = 1 (s + f). So after 4 quarters, the unemployment rate in North America is given by u 4 = (0.50) 4 ( ) 0.053

5 Practice Final Exam Answers 5 which uses λ = 1 ( ) = By contrast, after 4 quarters the unemployment rate in the European economy is given by u 4 = (0.75) 4 ( ) which uses λ = 1 ( ) = Since the two economies have the same steady state unemployment rate, the only reason why unemployment is 5.3% in North America vs. 6.6% in Europe is that the labor market is less fluid in Europe. Two points for the right formula to use, three points for getting each number right, and two points for the right analysis. 4. If the European government reduces the separation rate to s = 0.01 and nothing else happens, then steady state unemployment falls to u = s s + f = = But if the job finding rate f falls too, then steady state unemployment may not change after all. How much would f have to fall? The new f would have to solve f = 0.05 so that at the new separation rate of s = 0.01 we would get the old steady state unemployment rate of Doing the algebra shows that this will happen when f = = so f would have to fall from to Even if f doesn t fall this much (or doesn t change at all), then the fall in the job separation rate will make the labor market less fluid (will make λ larger, e.g., λ = 1 ( ) = if f doesn t change) and so will mean that the economy will take longer to respond to shocks. Whether this is a worthwhile trade-off against a lower steady state unemployment rate depends on your preferences. Two points for the new steady state, four points for the argument for finding the right change in the finding rate and four points for the right number, three points for noting that a reduction in s will reduce labor market fluidity as measured by λ and two points for discussing the implicit trade-off between steady state unemployment and labor market fluidity. C. Yield curve and the Taylor rule (40 points). Suppose current forward rates f m and averages over the last 25 years f m were

6 Practice Final Exam Answers 6 Maturity (m) Forward Rate (f m 1 ) Mean Forward Rate (f m 1 ) Maturity is measured in years and forward rates are annually compounded percentages. 1. Compute zero-coupon prices p m and yields y m for maturities between 1 and 3 years (10 points). 2. Use the forward rate curve to construct forecasts of future 1-year yields. How do you see the 1-year rate evolving over the next two years? What does this suggest for output growth? (10 points) 3. Describe the Taylor Rule. Under what economic conditions would it lead to the path of short term interest rates you described above? (10 points) 4. We can measure inflation expectations using the yield on TIPS (Treasury Inflation Protected Securities) bonds of various maturities. Suppose that the bond market expects inflation to be 4% this year, 4.5% next year and 5% the year after that. Based on these inflation forecasts and the expected future interest rates calculated above, is the economy in good shape? Why or why not? What does the yield curve suggest the Fed is going to do? Do you think this is a good response to the expected state of the economy? Why or why not? (10 points) Answers. 1. The bond prices p m, zero coupon yields y m, etc, are given in the following table. Maturity Bond Price Yield Term Risk Premium Future Short Rate These calculations repeatedly use y 1 = f 0 and the formulas p m = p m f m 1, y m = ( ) 1/m Two points for using the right formulas (either the ones given above or equivalent ones from the notes) to calculate prices, three points for getting the price numbers right. Two points for using the right formulas for yields (and again, either the ones given above or equivalent ones from the notes) and three points for getting the numbers right. p m

7 Practice Final Exam Answers 7 2. The future short rate is the current forward rate less the term risk premium, that is f m 1 f 0 as in the table above. The expected future short rates are decreasing, which suggests that future output growth (and/or inflation) will be relatively weak. Three points for the right term premium calculations, three points for the right future short rate calculations and four points for the right interpretation in terms of future output growth and inflation. 3. The Taylor rule relates the fed funds rate to inflation and output relative to trend. Something like: i t = r + π t + a 1 (π t π) + a 2 (y t y t ) The rule suggests that the Fed will raise short term interest rates if inflation is above target or if output is above trend. The data in this example are consistent with the Taylor rule in that lower future output or inflation is associated with lower future short rates. Five points for the right formula, five points for the right discussion connecting the expected future short rates above to future output and inflation. 4. If expected inflation is rising and nominal interest rates are falling, then real interest rates are falling in the face of increased inflation. Roughly we have expected real rates of = 2.1% next year, = 0.9% the year after and = 0.0% the year after that. This is a clear violation of the Taylor principle which would have nominal rates rising more than one for one with inflation so that real rates also rise and if so the Fed is probably not doing enough to fight inflation. The Fed is in a somewhat invidious position though, since this data is suggests the economy is about to experience stagflation in the sense that the economy seems to be about to experience simultaneously weaker economic activity and higher inflation. If so, the economy is not in good shape. Three points for realizing that real rates must be falling even as inflation rises, four points for connecting this to the Taylor principle (or otherwise explaining why this policy might not be a good one) and three points for noting that the data suggests the economy is not in good shape. c 2008 NYU Stern School of Business