1.4 Show the steps necessary to obtain relative PPP in growth rates.

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1 Kiel Institut für Weltwirthschaft Advanced Studies in International Economic Policy Research Spring 2005 Menzie D. Chinn Problem Set 1 Answers Exchange Rate Economics 1. Purchasing power parity. 1.1 Write out the expression absolute PPP. S = P/P* or in logs s = p p* 1.2 Explain why one cannot typically test for absolute PPP. One does not typically have data on prices for identical bundles of goods. Instead, one has access to price indices, which typically refer to differing bundles of goods, and are based on different base years. 1.3 For what data series can one test for absolute PPP? Penn World Tables data (the price level variable. Big Macs Starbucks coffee (Ikea goods really a test for Law of One Price. 1.4 Show the steps necessary to obtain relative PPP in growth rates. Take first differences of the answer to 1.1. s = p p* 1.5 If relative PPP holds, is this a necessary and/or sufficient condition for absolute PPP to hold? It is a necessary, but not sufficient, condition. Relative PPP in growth rates implies relative PPP in levels, in a deterministic setting. [Extension: But in a stochastic setting, if there are errors in the growth rate version of the relative PPP expression, then integrating up to the levels, even relative PPP may not hold (i.e., if log spot rates and log price levels are not cointegrated, then the real exchange rate may drift. ] 1.6 Show why mean reversion in the real exchange rate is consistent with relative PPP holding. If qt = α + ϕqt 1 + ut, 1< ϕ < 1 then the real exchange rate reverts to mean α /( 1 ϕ. But the real * exchange rate is merely qt st pt + pt, so in the steady state s= p p + α /( 1 ϕ which is relative PPP in levels.

2 2. Covered and uncovered interest parity. 2.1 Assume that covered interest parity holds, so (1+i = (F/S(1+i*. Fill in the following grid (carry your answer out to three decimal places, for (a and (b. 2.2 Assume that uncovered interest parity holds, so (1+i = (S e /S(1+i*. Fill in the following grid (carry your answer out to three decimal places, for (c and (d. i i* F S a b i i* S e S c d Using real data to evaluate PPP and UIP. Consider the tables drawn from the Economist, April 10 th, 2004 edition, on the attached pages. Answer these questions using equations. (You can use the most recent edition (March 5-11 th, 2005 if you have access to a copy. 3.1 Using the 3 month interest rates, and assuming UIP holds, calculate the expected change in the dollar/euro exchange rate over the next three months. Be sure to state what the rate will be, in annualized terms, and what will be the actual percentage change in the dollar/euro exchange rate. The interest rates are expressed in annual terms, so the differential that one obtains is for the annualized depreciation. e US St + 1 ( 1+ it = EU S ( 1+ i t e S t + 1 t ( = 121. ( S t e+ 1 = which is consistent with -096 or about 1 percent appreciation. Notice that this is for one year. The actual change over three months is given by: 312 / = or 0.25 percent Given the empirical evidence on the relationship between exchange rate changes and interest differentials provided in the table in the handout on CIP and UIP, what do you expect to happen to the dollar/euro rate. Explain. Inspection of the regression results in the table indicate that at the 3 month horizon, a one percentage point interest differential causes a 0.65 percentage point appreciation, on an annualized basis. So, instead of the ¼ percentage point appreciation over three months, on average, one would see a 1/6 (= 1/ percentage point depreciation.

3 3.3 Using 10 year bonds, calculate what the implied change in the dollar/pound exchange rate is, over the next ten years. Using the approximation: e US UK st + 1 = ( it it = ( or 0.91 percentage point appreciation. This is the depreciation over one year; over ten years, multiply this amount by 10 to obtain the total depreciation expected over ten years. This figure is 9.1 percentage points. 3.4 Given the inflation rates over the past year, what should have been the rate of change in the US dollar/canadian dollar exchange rate if relative purchasing power parity held? Relative PPP is: US Can s t = ( π t π t = ( so the US dollar should have depreciated by 1 percent against the Canadian dollar over the past year. 3.5 Interpret the Economist poll of expected inflation rate for 2004 as the expected change from December 2003 to December What is the expected change in the US dollar/australian dollar? (If you use the March 5-11, 2005 edition of the Economist, answer the question, using the measure of expected inflation for 2005 to answer the question. e US, e Aus, e s t + 1 = ( πt + 1 π t = ( or a percentage point appreciation of the US dollar against the Australian dollar is implied by the expected rates of inflation. 4. [Optional] Using real world data to test for uncovered interest parity. Download the data available at: If the software you are using can do it, plot the forward premium (assuming covered interest parity holds and ex post depreciation USD/DEM ex post depreciation GRDEP3M GR3MDIF(-1

4 4.2 Estimate the Fama regression for all the USD/DEM and USD/JPY, and the DEM/JPY, at the three months horizon. Dependent Variable: GRDEP3M Date: 03/10/05 Time: 13:31 Sample (adjusted: 1979:2 2000:4 Included observations: 87 after adjustments C GR3MDIF( R-squared Mean dependent var Adjusted R-squared S.D. dependent var S.E. of regression Akaike info criterion Sum squared resid Schwarz criterion Log likelihood F-statistic Durbin-Watson stat Prob(F-statistic Dependent Variable: JADEP3M Date: 03/10/05 Time: 13:32 Sample (adjusted: 1979:2 2000:4 Included observations: 87 after adjustments C JA3MDIF( R-squared Mean dependent var Adjusted R-squared S.D. dependent var S.E. of regression Akaike info criterion Sum squared resid Schwarz criterion Log likelihood F-statistic Durbin-Watson stat Prob(F-statistic 13765

5 Dependent Variable: -(GRDEP3M-JADEP3M Date: 03/10/05 Time: 13:33 Sample (adjusted: 1979:2 2000:4 Included observations: 87 after adjustments C (GR3MDIF(-1-JA3MDIF( R-squared Mean dependent var Adjusted R-squared S.D. dependent var S.E. of regression Akaike info criterion Sum squared resid Schwarz criterion Log likelihood F-statistic Durbin-Watson stat Prob(F-statistic What do the residuals from this regression look like? RESID RESID USD/DEM 1.2 USD/JPY - RESID

6 4.3 Estimate the Fama regression for all the USD/DEM and USD/JPY, and the DEM/JPY, at the 10 year horizon. Below is the DEM/JPY regression. The other ones are reported in Chinn & Meredith (2004. Dependent Variable: -(GRDEP10Y-JADEP10Y Date: 03/10/05 Time: 13:39 Sample (adjusted: 1980:1 2000:4 Included observations: 84 after adjustments C (GR10YDF1(-1-JA10YDF1( R-squared Mean dependent var Adjusted R-squared S.D. dependent var S.E. of regression Akaike info criterion Sum squared resid Schwarz criterion Log likelihood F-statistic Durbin-Watson stat Prob(F-statistic C:\user\kiel\ps1a_s05.doc

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