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ansen test has significant power superiority over the residual-based test like co-integration. Moreover, as the Johansen test only involves one step as compared to three steps under co-integration, there will be less probability for errors in the application process. Therefore, Johansen test will be utilized for robustness.

4. Empirical Results

4.1 “Strong” form PPP Results

Table 1 shows the results from the unit root test for real exchange rate. The ADF test on the real exchange rate shows that the null hypothesis of unit root cannot be rejected at the 95% confidence level. As expected, the results show that real exchange rate is non-stationary and there is no statistical evidence to support the existence of a convergence to PPP in the long run for the “strong” form.

4.2 Co-integration Results

As mentioned previously, the initial screening for co-integration tests involves determining whether the variables are stationary. Augmented Dickey-Fuller unit root test was performed and it was found that nominal exchange rate, CPI for both U. S and UK and difference between the CPI for both countries are non-stationary or has unit root at the 95% confidence level. (See table 2)

After determining that the variables are non-stationary and follows a random walk, I will specify the amount of lags that will be included into the ADF regression to prevent the problem of serial correlation in our respective variables. The ADF results which includes the minimum Schwarz information criterion is presented in table 3. The results show that both variables are made stationary when integrated to the order of I(1), with the inclusion of the lags with minimum Schwarz information for each variable.

It will be feasible to carry on testing for co-integration when the variables are found to be non-stationary and could be integrated to the same order. However, it will not be possible to carry on testing for co-integration if variables are integrated to different order or when either one of the variables (Independent and dependent) or both exhibits stationary time series in the unit root test. The results till now have shown the null hypothesis of non-stationary or unit root cannot be rejected for both the variables at 95% confidence level. Furthermore, both variables could be integrated to the order of one, I(1). As a result, I will proceed with the results from co-integration.

The co-integration test has carried out performing a regression on the following co-integrating regression

The results for the co-integration regression are as follows:

Furthermore, the R2 and Adjusted R2 are 0.581843 and 0.581014 respectively. This result shows that the coefficient for the independent regressor (difference in CPI) is positive and significant. Following on, the residual of the co-integrated regression will be determined and subjected to the ADF test. This will test the null hypothesis of unit root and stationary for the residual. If the null hypothesis of unit root cannot be rejected, I will conclude that the variables are not co-integrated and PPP does not hold in the long run. Conversely if null hypothesis is rejected, it will conclude that the evidence seems to infer that the variables are co-integrated and PPP theory holds for U.S and UK in the long run equilibrium. The ADF test on the residual has given us a test sta