Johansen and Juselius (1992) estimated PPP (Purchasing Power Parity) and UIP (Uncovered Interest Rate Parity) using UK data. Theory suggests that if PPP holds in the goods market (i.e., internationally produced goods are perfect substitutes for domestic goods), we should expect to find in the long-run that price differentials between two countries are equal to differences in the nominal exchange rate (p1-p2=e), while UIP in the capital market relates the interest rates of the two countries to expected changes in exchange rates (i1-i2=ee -e). If markets are efficient, expected changes in exchange rates will be increasingly influenced by deviations from long-run PPP and thus ee =p1-p2, providing a link between the capital and the goods market. If parity holds in the long-run, we should expect i1-i2= p1-p2-e, and estimated parameter values of ±1 for all the variables in the model. The variables used are as follows: p1 (the UK wholesale price index), p2 (trade-weighted foreign wholesale price index), e (UK effective exchange rate), i1 (3-month UK Treasury bill rate), i2 (3-month Eurodollar interest rate). The data is quarterly and runs through the period 1972q1-1987q2. QUESTION. Derive the cointegrating vectors by using evidence you have found in 4b. Also, plot the residuals of the cointegrating vectors. What can you say about presence of PPP and UIP?