Let st be the log of the nominal exchange rate pt be the

Question

Answer ALL sub-questions:

Question -

A basic proposition is that exchange rates adjust so as to maintain the purchasing power parity (PPP): the price of a bundle of goods, expressed in common currency, should be the same across countries. That is taking into consideration the exchange rate between two countries, a good in country A should be sold at the same price in country B.

The aim of this exercise is to test whether PPP theory holds between UK and US in the long-run. The data for this exercise are contained in the file Coursework_data.xlsx, where CPIUK is the United Kingdom Consumer Price Index, CPIUS is the US Consumer Price Index and GBPUS is the United Kindom Pound to US dollar nominal exchange rate (i.e. how many pounds you need to buy one US$). UK is the domestic country and US is the foreign country. Data have a monthly frequency and span from 1995 to 2007 (source: IFS).

Let s_t be the log of the nominal exchange rate, p_t be the log of the CPIUK, p_t* be the log of CPIUS.

a) Generate an appropriate Eview work file and comment briefly on the series provided;

b) Generate the real exchange rate q_t, by applying the following formula:

q_t = s_t + p_t* - p_t

For the variable q_t graph the series and briefly comment;

c) Test if there is autoregressive conditional heteroscedasticity in the real exchange rate series q_t, and briefly comment;

d) Test whether the real exchange rate is a random walk or a martingale and briefly comment;

e) If the PPP theory holds then the real exchange rate should not deviate persistently from its average. Investigate the order of integration of the real exchange rate and briefly comment;

f) Frenkel (1978) suggests that an alternative way to check for the validity of PPP theory consists of estimating the nominal exchange rate versus the differences in prices. More specifically, he suggests to estimate the following equation

s_t = α + β(p_t - p_t*) + ε_t

And to test whether α = 0 and β = 1.

Thus, estimate the above equation, test whether α = 0 and β = 1 and perform the joint hypothesis test, comments on your results;

g) Verify whether the two series s_t and (p_t - p_t*) have a unit root, and then test for cointegration, and comments on your results;

h) Assuming that the two series s_t and (p_t - p_t*) are cointegrated, following Edison (1987), estimate the following simple first-order error correction model (ECM) and comments on your results:

?s_t = β₁ + β₂[s_t-1 - α - β(p_t-1 - p_t-1*)] + β₃(?p_t-1 - ?p_t-1*) + ε_t