4. Assume that the following regression model was applied to historical annual d
ID: 396276 • Letter: 4
Question
4. Assume that the following regression model was applied to historical annual data: where e, is the percentage change in exchange rate of the USD/JPY in period t, INT, is the interest rate differential between Japan and the U.S. in period t, INC, is the income growh rate differential between Japan and the U.S. in period t, BOT, is the U.S. balance of trade (in USD billions), and e, is an error term. Assume that the regression coefficients were estimated as B-30 t .65 8-0025 In addition, we have the following data: ElINTJ-2%. . This year BOT, is forecasted as follows: BOT -70 -100 Probability .60 40 This year INC, is forecasted as follows: INC 2% 3% Probability .70 .30 Now, you have to answer the following questions: iUsing the above information, what will be your forecast for e? i. Suppose that S.. .01 USD/JPY, provide a confidence interval for SExplanation / Answer
i) Expected BOT= -70*0.6+(-100)*0.4=-82
Expected INC= 2*0.7+3*0.3=2.3%
Putting the values to the regression equation
et=0.01+(-0.03)*2+0.65*2.3+(-0.0025)*(-82)=0.01-0.06+1.495+0.205=1.65%
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