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Unformatted text preview: Economics 154a Fall 2005 Bj¨orn Br¨ugemann Problem Set 6 Solution Problem 1: (Cyclical Properties of Unemployment and Output per Worker) 1. The plots are in the file http://www.econ.yale.edu/ ∼ bb338/econ154a05/ps 6 data sol.xls . The plot for this part is in the sheet BLS Data Plot . One can see that most increases in unemployment are preceded by a decrease in output per worker, so unemployment tends to be high when output per worker is low, so the two variables are negatively correlated over the business cycle, but unemployment is lagging behind by a few quarters, which brings us to part b.. 2. As already discussed, output per worker is leading the cycle in unemployment. 3. Clearly both variables exhibit some persistence. If output per worker is high this quarter, then it is likely to be high next quarter, and the same is true for unem- ployment. However, one can see that movements in unemployment are somewhat more gradual than movements in output per worker, so unemployment is somewhat more persistent. 4. The plot is in sheet BLS Data Plot . Again unemployment tends to be high when output per worker is low. 5. But in contrast to the data, now unemployment appears to be leading output per worker. As the economy moves into boom, unemployment falls very quickly. Output per worker starts to increase as the economy moves into a boom, but does so only very slowly as gradually old low productivity matches are replaced by high new productivity matches. Thus the model does a poor job at matching the business cycle fact that output per worker leads unemployment by a few quarters. 6. Because it takes time to replace old low productivity matches with new high pro- ductivity matches during a boom (or to replace old high productivity matches with new low productivity matches in a recession), output per worker is now very per- sistent. Contrary to the data, output per worker now looks more persistent than unemployment. Thus the model does a poor job at matching the business cycle fact that unemployment is more persistent than output per worker. Figure 1: G ↑ in S d IS- LM- I d diagram I d ,S d IS- LM r I d 1 S d IS- LM, 1 E 1 S d IS- LM, 2 E 2 Problem 2 (Shocks in the IS-LM Model) 1. The IS curve answers the following question: suppose current output (and thus the current income the worker receives from the firm) is equal to a hypothetical level Y , what must the real interest rate be for the goods market equilibrium to clear. Equivalently it answers the question: suppose the real interest rate is equal to a hypothetical level r , at what level of current output Y (which is also the income the worker receives from the firm) will the goods market clear. In other words, the IS curve tells you at what combinations of current output Y and the real interest rate r the goods market is in equilibrium. These combinations are determined by the following condition: S d IS- LM ( r (+) | Y (+) ,A f (- ) , K (- ) , G (- ) ,G f (+) ) = I d ( r (- ) | A f (+) , K (- )...
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