.Provide adequate solutions to these questions.

You are given the following information. The current dollar-pound exchange rate is $2 per pound. A representative basket of goods and services costs $100 in the US and $120 (dollars, not pounds) in the United Kingdom. For the next year, the Fed is predicted to keep U.S. inflation at 2%, and the Bank of England is predicted to keep U.K. inflation at 3%. The speed of convergence to absolute PPP is 20% per year. That is, if the real exchange rate today is 1.4 and the speed of convergence to absolute PPP is 15% per year, the real exchange rate in one year will be 1.4-0.30*0.4=1.28).

1. What is the expected U.S. minus U.K. inflation differential for the coming year?

2. What is the current U.S. real exchange rate qUS/UK with the United Kingdom? (recall that qUS/UK is defined as the ratio of prices in the UK to the US, both expressed in a common currency).

3. By what percentage is the dollar overvalued or undervalued relative to its absolute PPP level

4. What do you predict the U.S. real exchange rate with the United Kingdom will be in one year's time?

5. What is the expected rate of real depreciation for the United States (versus the United Kingdom)?

6. What is the expected rate of nominal depreciation for the United States (versus the United Kingdom)?

7. What do you predict will be the dollar price of one pound a year from now?

3.8.1 White Noise Observed through Matched Filters 3.8.7 Example. Consider a matched filter h(t) for a real signal S(t) at time T. The impulse response of that filter is h(t) = S(T -t). Let & denote the energy of S(t). Assume that the input to the matched filter is a zero mean white Gaussian noise W(t) with power spectral density of No/2. This system is shown in Fig. 3.8.1. Let Z denote the output of the filter at time WH ) h(t= S(T-t) t= T Figure 3.8.1: Matched filter with white noise input. T. Using the convolution integral, OO Z = W ( T )h ( T - T) dT - 0o roo (3.8.8) = W (T ) S(t) dT. -CO1. A bit of practice with dummy variables and heferoskedasficify: Consider the following model for the logarithm of wage given years of university education and gender of person 1' : log(wage;) = g + oqfenmle, + lronmi; + lfemale; x 10mm,- + u; # where log is the natural logarithm, femlei is a dummy variable that is equal to 1 if person i is female is 0 otherwise, and 10mm",- is the number of years of university education that person 1' has. Based on a random sample of 6763 individuals, we have estimated this model using OLS and obtained the following estimated equation: _--_-__-_ log(wage,z) =3.289 0.360fenmle; +0. 050 forum,- +0.0309maie, x forum}, (0011) (0.015) (0.003) (0.005) 1':l,2,...,67l63,1l22 = 0.202. a. Explain how you would test the hypothesis that the conditional expectation of log(wage) conditional on years of university education is exactly the same for men and women. You need to specify the null and the alternative, the test statistic and its distribution under the null, the regression that you should run so that you can compute the test statistic, and the rule for rejection or non-rejection of the null hypothesis. c. Using the estimated equation, nd the value of tomni (total number of years in university) such that the predicted values of log(wage) are the same for men and women. Can women realistically get enough years of university education so that their earnings catch up to those of men? Explain. d. Suppose we suspect that the variation of Iog(wage) around its conditional mean is larger for women than it is for men. That means that in the