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Where Et is the exchange rate between Dollars and Pounds, PtUS is CPI for U.S and PtUK is CPI for UK. By taking logs for Equation (1), the nominal exchange rate will be subsequently reduced to a linear equation of the domestic (UK) and foreign (U.S) price levels, as shown in equation (2) below.

As a result, the estimated model will be;

Where α is intercept, β is slope and εt is the residuals.

3.2.1 “Strong” PPP

In this section, I will seek to investigate whether the “strong form” of PPP exist for the U.S and the UK. There are two main methodology to analyse whether the most direct relationship of PPP holds for the subject countries.

Ordinary Least Square Regression

This method involves performing a regression on equation (3) and testing the null hypothesis that and If the null hypothesis cannot be rejected, it meant that PPP holds in the long run but instead the null hypothesis is rejected, PPP theory does not hold. From the descriptive statistic (Figure 1), it is seen that the exchange rate and relative price of U.S and UK are trended. This observed fact meant that Ordinary Least Square (OLS) estimator might not be suitable for the analysis as non-stationary time-series variables tend to produce spurious regression due to problems of hetereoskedasticity and serial auto-correlation, which will eventually lead to misleading and biased estimation results.

Stationarity of Real Exchange rate

Instead, to examine the basic relationship of PPP between U.S and UK, I have opted to test for unit root in the real exchange rate to determine the validity of PPP in the long run. To achieve this, the real exchange rate will first be determined, as shown in equation (4).

Where denotes the real exchange rate, denotes logarithm of nominal exchange rate whereas and denotes logarithm of CPI for U.S and UK respectively. Follow on, I will test the null hypothesis that the time series of real exchange rate remain stationary and does not follow a random walk. If this occurs, it will be concluded that PPP holds in the long run. Alternatively, if the real exchange rate does not follow a random walk, On the contrary, if real exchange rate does follow a random walk, PPP does not hold. Subsequently, this could be explained some shocks or factors i.e extreme fall in production or productivity, in the economy due to unforeseen circumstances. Linear unit root test could be used to detect the existence of unit root in time-series. More specific, Augmented Dickey-Fuller (ADF), which is a test of unit root, will be performed;

Where Δyt is the 1st difference of log(Et); are the optional exogenous regressors which might include a constant or a constant and trend, α and δ represents the parameters that are to be estimated, represents the residuals.

3.2.2 Co-integration Test

Co-integration test involves testing the null hypothesis that the variables are co-integrated and alternative hypothesis that they are not co-integrated as shown below.

: And are cointegrated

: Andare not cointegrated

Before begining the co-integration analysis, it will have to determine whether the two time series are stationary or does not have a unit root. This involves testing the null hypothesis of non-stationary in the variables. To test the assumption of non-stat