摘要:本文是旨在对美元和英镑的汇率分析的留学生论文,本文试图参考关于购买力平价的丰富的文献资料,分别调查世界上最发达的两个经济体——美国和英国长期购买力平价的总体情况。
ionarity of variables, Augmented Dickey-Fuller test will be used.
Once settled on the status of stationary of the variables, the adequate number of lags (p) that should be integrated in the ADF regression will next determined, so as to avoid the problem of serial correlation in the residuals. This could be determined by choosing the amount of lags that minimizes the standard information criterion (Schwarz Information Criterion). So, if both the variables are non-stationary and integrated to the same order, it will be deemed possible to carry on using co-integration to test the long run relationship of the variables and convergence to PPP. On the contrary, if the variables cannot be integrated to the same order or that either one or both of the variables are stationary; it would not feasible to carry on with the testing.
Engle and Granger (1987) mentioned that two non-stationary variables when integrated to the same order, will be co-integrated if their residual is stationary. Putting into application, if two non-stationary time series and that are both integrated to the same order, produces a stationary variable after the regression, it can be inferred that the variables are co-integrated.
The test of co-integration involves two main procedures. First, the following regression equation (3) will be estimated, so as to get the estimated error term or residual (equation 6)
Next, Augmented Dickey-Fuller will be used to test the null hypothesis that the estimated error term has a unit root or is non-stationary. By comparing the t-stats with the Dickey-Fuller t-Statistics (spurious co-integrating regression), the variables are co-integrated if we cannot reject the null hypothesis that the residual has a unit root or non-stationary. But if we reject the null hypothesis of unit root, the variables will be co-integrated.
H0: PPP does not hold in the long run
H1: PPP hold in the long run
Finally based on our empirical hypothesis, if the variables are found to be co-integrated, the null that PPP does not hold in the long run will be rejected and I can conclude there exist an equilibrium relationship between the exchange rate and relative price levels in the long run. Alternatively, the null hypothesis cannot be rejected if the variables are not co-integrated.
3.3 Robustness Test
To ensure that the results from the co-integration test is robust, I will employ another methodology for the examining the long run equilibrium relationships of the variables and whether PPP holds. The Johansen maximum likelihood (ML) test is proposed to carry out the analysis.
Johansen (1988, 1991) came out with the maximum likelihood (ML) method for estimating the equilibrium relationships in the long run or co-integrating vectors. He derives a likelihood ratio (LR) test for co-integration in a Gaussian vector error correction model.
The likelihood ratio (LR) test statistic for the hypothesis of at most r co-integrating vectors is;
Where are the smallest eigenvalues of S21S11-1 S12 with respect to S22.
Gonzalo (1989) argued that for the finite sample properties of the ML estimator are very consistent with the asymptotic results. Stock and Watson (1991) used the monte carlo to substantiate the unbiased property of the ML estimator. Cheung and Lai (1993) also concluded that the Joh
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