There are two forms of purchasing power parity. The first one is according to the theory of law of one price which states that, the cost of an identical products sold in different countries should be the same expressing a common currency. The other one is the relative version of PPP, assumption of transport costs and imperfect competition are being considered in this version. Gustav Cassel started the first research on PPP in 1918, nowadays, the theory of PPP have applied on international finance widely. Policy maker viewed PPP as a significant indicator regard to the performance of domestic currency against the foreign currencies and used it to forecast the movement of exchange rate in long run. The purchasing power parity theory acts a key part in macroeconomic policy decision made by government. Within the project, the Purchasing Power Parity for Hong Kong, Japan and South Korea will be analysis, where Hong Kong is the domestic country.
The economy of Hong Kong itself heavily depends on trade and financial services, base on her well known free trade and low tax rate system. Hong Kong nowadays was developed as the financial, trading and shipping centre of Asia. Besides of Mainland China, Japan is one of the largest trading partners with Hong Kong. Therefore, I will test Hong Kong against Japan. In order to make a comparison, I will also test Hong Kong against South Korea. The reason that I chose South Korea is because both economies are the member of Four Asian Tigers, they maintaining exceptionally high growth rates and rapid industrialization between the early 1960s and 1990s. Therefore I will test Hong Kong against South Korea, base on the similar nature of the economy between two regions. Nevertheless, according to studies did in the recent past, the topic itself showed different results. But, most of the studies do agreed that real exchange rates can be generally estimated in long run. Through the stationarity analysis and cointegration analysis, I can show whether PPP holds between Hong Kong and Japan, as well as Hong Kong and South Korea.
The University of Pennsylvania (commonly referred to as Penn) documented a series of studies on a modern relationship between income and price known as Penn Effect  . The main findings shows that, between high and low income countries, the real income ratios are systematically exaggerated by gross domestic product (GDP) conversion at market exchange rates. . This is because; countries with higher incomes consistently had higher prices of domestically produced goods relative to prices of goods included in the exchange rate. Applying this logic to the project, PPP of the countries with similar income are more likely to hold. Therefore, PPP for Hong Kong and South Korea should hold in the long run. The Big Mac Index  is an example for explaining the concept of purchasing power parity in an informal way and economists widely cite the index as a ‘reasonable’ real world measurement of PPP. The method of obtaining the Big Mac PPP exchange rate is dividing the price of a Big Mac in the home country (in its currency) by the price of a Big Mac in the foreign country (in its currency). If the value is lower than the actual exchange rate, it implies that the home currency is under-valued, compared with the foreign. In the other hand, if the value is high than the actual exchange rate, it means that the home currency is over-valued. Through the Big Mac Index we may know how well each currency against the dollars, nevertheless, the performance of PPP between the home currencies against dollar itself was not been showed. The reason for this can be the ingredient of making a Big Mac. As both traded and non-traded goods are used in the process, but in different countries, non-traded goods such as labour cost may various. At McDonald UK, a working staff may receive higher wage than a working stuff in China, which means other input cost for the Big Mac may have variation; therefore, the Big Mac price is different in two countries.
By applying Purchasing Power Parity (PPP) theory, policy makers are able to make forecasts of the long run trend of exchange. There are two different forms of Purchasing Power Parity, which is absolute and relative version. According to the basic theorem of purchasing power parity, which states that one unit of home currency could purchase the same amount of goods in both domestic and foreign country. It ignored some distortions such as transport costs and imperfect competition which implies that absolute PPP are unlikely to hold. The law of one price is derived from the idea of perfect arbitrage. It states that all identical goods should have equal amount of price in a competitive market. Base on the PPP theory, arbitrage will occur due to an agent try to construct a profit through exchange rate transaction. For instance, a can of coke worth 50p in Britain and in France is AA1, and then the exchange rate is AA.5/AA1. Nevertheless, if the exchange rate is lower, means that sterling has appreciated against Euros. As a result, sterling is more valuable, and people can use the same amount of pounds to consume more coke in France. As people try to make yield through buying sterling, the exchange rate will move back to the original equilibrium level in long run. That is recognized as the absolute PPP. The absolute PPP: S represent nominal exchange rate, p for domestic price and p for the foreign price. The relative price of the two currencies is represented by the nominal exchange rate. Absolute PPP are unlikely to hold because of several assumptions such as the existence of administrative cost and different types of imperfect competitions are being ignored. This is the reason for the existence of other version of PPP called the relative PPP. Some of the distortions such as transportation costs were taken into account by the theory of relative PPP. In the recent past, some studies showed that, even taking distortions into consideration, the relative version do hold in the long run.
The relative PPP: In the relative version of PPP, S stand for the change of the nominal exchange rates in percentage; P for the change in price of domestic country in percentage and P for the change in price of foreign country in percentage. According to the relative PPP formula above, adjustment of the exchange rates will be made due to the inflation discrepancy between the two countries. The common model for testing PPP through regression study: St = logged exchange rate, Pt= logged domestic price Pt= logged foreign price Ut= error term showing deviation from PPP. In a short conclusion, the theory of PPP show the way of determining exchange rate by checking the percentage change in domestic price and foreign price. The exchange rate performance within two economies is tracked by the economic modeling of purchasing power parity. The country’s performance on trade can be estimated by policymaker if they understand how the PPP theory works. Beside of that, up to date monetary and fiscal policies could be made.
The data I used in the project are mainly collected from GMID (Global Market Information Database) and Hong Kong Census and Statistics Department. The exchange rate and the Consumer Price Index (CPI) of both home and foreign country are the main variables of the PPP Econometric model. I have collected the exchange rate as well as the Consumer Price Index from Hong Kong, South Korea and Japan. The time period of the data is 1980-2009, all of the figures are annual average. The data in monthly and quarterly was not being used due to seasonality and avoiding dishonesty in my findings. In order to make sure the fairness of the test, all the annual data of CPI was being adjusted and the base year of it was set as 2005 automatically. From the Figure 1 of appendix, the actual value of the consumer price index for all three economies is being described. The Hong Kong economy achieved a rapid growth from 1980-1997. Start from 1980s, Hong Kong focus in developing services sector such as financial services, real estate, insurance, brokering and banking, in late 1980, Hong Kong is being one of the largest financial markets in the world. Nevertheless, in 1997, Hong Kong is in the same situation like many other South East Asian countries which suffered in the financial crisis.
Consumer confidence is being damaged significantly which reflect by the plunge in the consumer price index. Up until the end of 2003, the consumer price index starts to rebound. The CPI of Japan increased steadily from 1981 to 1990, but in late 1990s, the growth slowed obviously. Some economists believe that it is because the failure of bank of Japan cut interest rates rapidly enough to offset after-effects of burst of investment bubble during the late of 1980s. Start from the late 80s, Japan mainly specialized in developing manufacturing industry such as electronic and car industry. Until 90s, the developments of its manufacturing industry are highly successful. From the figure 1.2, we can see that Japan’s economy affected by the Asian financial crisis is far from the other South East Asian countries. From figure 1.3, the South Korea consumer price index maintains a steady growth throughout 1980 to 2009, even though it has been suffer in financial crisis in 1997. South Korea experienced a rapid industrialization since 1980s, therefore we believe that the main force for supporting its growth is by attracting huge amount of foreign direct investments and a large volume of trade. Nowadays, the economy of South Korean is ranked the fourth in Asia and 15th of universe. Figure 2 shows the fluctuation of the exchange rates within Hong Kong and Japan, and also Hong Kong and South Korea.
From Figure 2.1, since 1980 to 1995, the Hong Kong dollar had continued to depreciate against the Japanese dollar reaching HK$0.08/YenAA In 1995, when the yen strike an all time peak the dollar, valuing Japan’s economy slightly larger than the United States in nominal GDP. Japan becomes the largest economy in world for just a short period of time due to that. The Japanese dollar started to depreciate in order to aid its export. In 1997, Hong Kong had suffered in the financial crisis, the Hong Kong dollar depreciated against Japanese dollar. From 2000-2009, the Hong Kong dollar against the Japanese dollar had fluctuated between 0.65 to 0.80 From Figure 2.2, since 1980-1989, the Hong Kong dollar against the South Korea Won had continued to depreciate reaching HK$0.012/SKW 1. After 1990, Hong Kong dollar began to appreciate up till 1997. In 1997, Both Hong Kong and South Korea were suffered in Asia financial crisis. After that, the South Korea Won had appreciated again as its economy started to recuperate.
The theory of stationarity states that if the process of stochastic is strictly stationary, the probability law of the data is not time dependent. It means if any consecutive subset of the time series is being taken, its joint distribution function is identical to any other subsets. This implies a stationary series will have both finite variance and constant mean. Therefore, the time series mean will be independent to time t. If we use the non-stationary time series data to compute the analysis, spurious regression will be given by the misleading result. From Figure 3.1, 3.2 &3.3, analysis within my data are showed by the correlogram. The data is being logged in order to check for randomness. I run the analysis with 3 lag values. If the data exceeds the critical value of 0.36, then the data itself is non-stationary All my data showed in above figure are being logged and non-stationary. If the data is stationary, the correlogram and its lag value will come up with close to zero. The graphs of spectral density from figure 4.1, 4.2 &4.3, showed that there is a non-stationary sign such as zero peak and had dramatically decline from 0 to 0.5 within three countries. These imply that all the logged variables for CPI are non stationary. As seen in Figure 5, the correlogram analysis of CPI showed the logged variables of exchange rates are non-stationary because all the values are exceed the critical value line. The spectral density for the exchange rates in Figure 6 shows that there is also non-stationary sign such as zero peak, and radically decline from 0.0 to 0.5. Therefore, through correlogram and spectral density analysis, all the logged data for Consumer Price Index and the foreign exchange rates could be concluded as non-stationary.
In appendix Table 1, all the data are gathered and analysis by the software PC GIVE. For the log variable of Hong Kong CPI, the lowest AIC value is -7.413 and its corresponding t-adf value is -1.787 at lag 1. That is not within the 5% critical value, therefore, my null hypothesis cannot be rejected. Thus, the data itself is said to be non-stationary. For the log variable of Japan CPI, the lowest AIC value is -9.322 and its corresponding t-adf value is -2.000 at lag 1. That is not within the 5% critical value and that means I cannot reject the null hypothesis. Thus, the data itself is also said to be non-stationary. For the log variable of South Korea CPI, the lowest AIC value is -7.980 and its corresponding t-adf value is -1.718 at lag 1. My null hypothesis cannot be rejected because the t-adf value is not within the 5% critical region, therefore, the data itself is said to be non stationary. Throughout the unit root analysis above, Both Hong Kong, Japan and South Korea have non-stationary data. This is same as the visual analysis. Nevertheless, I will still using further plot to check whether the data are stationary or not. According to Figure 7, all the logged variables of CPI are being plotted. All of them are seem to be converged around 2005.
The reason for that is because the CPI is all adjusted to a base year equal to 2005. The definition of stationarity states that the mean should independent to time t. Therefore, the result of the unit-root test in previous should be rejected because all values are showed to be non-stationary at I (0). For the exchange rate LHKD/YEN, the lowest AIC value is -4.682 and its corresponding t-adf value is -3.264. the result is within the 5% critical value. Therefore, the LHK per Yen is said to be stationary. That is contradicting with the visual judgment I worked in previous. For the exchange rate LHKD/WON, the lowest AIC value is -4.214 and its corresponding AIC value is -1.081. This shows that it is not within the 5% critical value region, therefore, data is said to be non-stationary. This is same as the visual analysis I did before. All my variables are showed to be non-stationary through the unit root test and the graphical analysis,. In order to precede the further analysis of stationarity, I should carry on the test on the first difference of the data.
From Appendix Table 2, it shows the result of first differencing with 4 lag values in the unit root test. The null hypothesis is showed to be larger than -3.00 at 5% critical value, and my alternative hypothesis will be showed to be lower than -3.00 at 5% critical value. Base on the result for first difference of log value of Hong Kong CPI, the least AIC value is -7.438 and its corresponding t-adf value is -0.9655 at 0 lag. This value is not within the 5% critical value region. Thus, my null hypothesis cannot be rejected which implies that my log data for Hong Kong CPI is still non-stationary at first difference level. From Figure 8, it shows the analysis of the variable for log Hong Kong CPI in first difference level in correlogram and the spectral density. Both of the analysis support the previous unit root test result, therefore, the variable is still to be showed as non-stationary. From Figure 9, the actual value of the HK CPI at first difference level is plotted. There is not much fluctuations were showed in the graph within the series, therefore, the previous result of unit root test is supported by that.
Within the graph, we may see that the Asia financial crisis in 1997 is being reflected by the outlier. Base on the result for first difference of log value of Japan CPI, the least AIC value is -9.201 and its corresponding t-adf value is -2.125. The value is not within the 5% critical value region. Thus, my null hypothesis cannot be rejected and the data is said to be still non-stationary. From Figure 10, it shows the analysis of the variable of log Japan CPI in first difference level in correlogram and the spectral density. Both of the analysis support the previous unit root test result, therefore, the variable is still to be showed as non-stationary. In figure 11, the actual value plot of the DLJAPCPI shows that the variable has some characteristics of stationarity as there is several degree of fluctuation around the mean. Base on the result for first difference of log value of South Korea CPI, the least AIC value is is -7.902 and its corresponding t-adf value is -2.863 at lag 0. The value is not within the 5% critical value region. Thus, my null hypothesis cannot be rejected and the data is said to be still non-stationary. Nevertheless, from Figure 12, characteristic of stationarity are showed in my correlogram and the spectral density analysis, this contradicts my previous unit root test result.
The actual value of the DLSKRCPI is plotted in Figure 13, characteristics of stationarity are showed in the graph as several fluctuations are around the mean. It contradicts the unit root test I worked in previous. Therefore, second difference level of the data is needed to be analysed in order to check whether the variable are stationarity or not. For the log exchange rate for HKD/YEN in first difference level, the lowest AIC value is -4.345 and its corresponding t-adf value is -3.540at lag 0. The value is within the 5% critical value, Therefore the null hypothesis is needed to be rejected, implies that the HKD/YEN is stationary. The correlogram and the spectral density in Figure 14 both support the result above, as characteristic of stationarity is showed to be within the variable. Figure 15, is the actual value plot of the DLHKD/YEN. Characteristics of stationarity are shown in the graph as we can see there are several degrees of fluctuations around the mean. Thus, the previous result of the unit root test are being supported. In order to check the stationarity, further analysis is needed to carry on the second difference level for the variable. For the log exchange for HKD/KRW in first difference level, the lowest AIC value is -4.151 and its corresponding t-adf value is -3.875. Again, I need to reject my null hypothesis which means the HKD/KRW is stationary.
In Figure 16, it shows the analysis of the I(1) of the variable of log HKD/KRW in first difference level in correlogram and the spectral density. Characteristics of stationarity within the variable are shown in graph. Therefore, the previous result for unit root test is being supported. The actual value of DLHKD/KRW is being plotted in Figure 17, The plot showed some characteristics of stationarity as there is several degree of fluctuations around the mean. There is a noticeable shock exists within the data which started from 1995 up until 1998, which can be explained the Asian Financial crisis.
From Appendix Table 3, all the log variables are being analyses in second difference level through unit root test. For the log variables of CPI for Hong Kong in second difference level, the lowest AIC value is -7.376 and its corresponding t-adf value is -3.340. It means I could reject my null hypothesis and accept the alternative one as the value is within the 5% critical value region. Thus, the log variable of CPI for Hong Kong at second difference level is shown to be stationary. In Figure 18, the log variables in second differencing are shown in the correlogram and the spectral density graph. It shows stationarity within the graph, and this supported the previous result of the unit root test. In Figure 19, the actual value of the variable are plotted. The graph showed some characteristics of stationarity as there is several degrees of fluctuations around the mean. Nevertheless, two excessive shocks were shown within the graph. The first one exists from 1997-1999, which can be explained the Asian Financial crisis. The other one exist start from 2007, which can be explained the worldwide financial crunch. For the log variables of Japan CPI in second difference level, the lowest AIC value is -9.049 and its corresponding t-adf value -4.226. It means I could reject my null hypothesis and accept the alternative one as the value is within the 5% critical value region. Thus, the log variable of CPI for Japan at second difference level is shown to be stationary. In Figure 20, the log variable of Japan CPI in second difference level is shown in the correlogram and the spectral density graph. Characteristic of stationarity exists in both graphs within the second differencing.
My previous result for unit root test is being supported. In Figure 21, is the actual value of the variable are being plotted. There are several fluctuations shown around the mean. Within the plot, we may discover that there is one excessive shock. Japan suffered considerably from a recession in 2007 and its consumer confidence is being affected significantly, which is reflected by the actual value plot. For the log variable of South Korea CPI in the second difference level, the lowest AIC value is -7.711 and its corresponding t-adf value is -6.907. It means I could reject my null hypothesis and accept the alternative one as the value is within the 5% critical value region. Thus, the log variable of CPI for South Korea at second difference level is shown to be stationary. In Figure 22, the log variables of South Korea CPI are shown in the correlogram and the spectral density graph. Characteristic of stationarity do exists in both graphs within the second differencing. It means my previous result for unit root test is being supported. In Figure 23, the log variable of South Korea CPI in second difference level is being plotted. Within The graph, we may also discover that several fluctuation are around the mean, this is the characteristic of stationarity. Nevertheless, there is one outlier we believe that is caused by Asia Financial Crisis that occurred in 1997. In that year, the economy of South Korea was suffered significantly from a recession. For the analysis of the exchange rates in second difference level, the lowest AIC value for HKD/YEN is -4.622 and its corresponding t-adf value is -6.008. This is within the 5% critical value region.
Therefore I can reject my null hypothesis, therefore the data is said to be stationary. In Figure 24, the log variables of exchange rate for HKD/YEN in second difference level are shown in the correlogram and the spectral density. Stationarity are existed within the both graphs and these do support my unit test result. In Figure 25, the actual value of the exchange rate in second difference level is plotted, Characteristic of stationarity are shown within the series as there is several degree of fluctuations around the mean. I believe that the excessive shocks were caused by the Asia Financial Crisis which happened in 1997 and this also support my previous result. For the the log variables of exchange rate HKD/KRW in second difference level, the lowest AIC value is -3.779 and its corresponding t-adf value is -5.497. I could reject my null hypothesis and accept the alternative one as the value is within the 5% critical value region. Thus, the data at second difference level is shown to be stationary. In Figure 26, the correlogram and the spectral density graphs shows analysis for the variable for the exchange rate. As the variable are shown to be stationary with both graphs, which support my previous analysis in the unit root test In Figure 27, the actual value of the exchange is being plotted. Several degrees of fluctuations were shown around the mean. Thus, exchange rate is said to be stationarity. Same as the previous actual value plot, one excessive shock was showed within the graph. Through the analysis of the log variable in second difference level, all the data are shown to be stationary at I(2).
In this section, the performance of the PPP will be analysed by the econometric modelling. The tool which will be used is the Cointegration analysis, in concurrence with the residual from the Ordinary Least Square estimation. Cointegration may be formally defined as: The components of the vector Xt are said to be cointegrated of order d,b (denoted Xt (I(d,b)) if: All components of Xt are I(d) There exists a vector AA±(A”°A 0) such that t = A± Xt I(d-b) b>0 For instance, if a set of variables are said to be time dependent. However, through cointegration analyse, it can be said that they are cointegrated at the order of (d,b) if a stationary error term is given out. Take the above equation as an example, Yt and Xt can be non-stationary variable. Nevertheless, in case both Yt and Xt are cointegrated, the error term ut can still be stationary. Through the cointegration process, the non-stationary degree will be eliminated. This implies that misleading analysis will not be given out. My testable hypothesis: In logs: Strong form (absolute PPP) AA±=0 AA²1=1 AA²2=-1 Weaker form: AA±A”°A 0 AA²1= AA²2A”°A 1 so that: Weak form AA±A°A 0 AA²1A”°A AA²2A”°A 1 so that: With ut such that the relationship is stable in time. Through augmented Dickey-Fuller test, Durbin-Watson test, MacKinnon critical values and several graphical analysis, the residual from the OLS estimation will be exanimate. Thus, if the residual is stationary, we can assume the theory of PPP is being supported by the regression in long run. In order to ensure my accuracy of the analysis, the cointegrating regression Durbin-Watson (CRDW) test is introduced .
The CRDW test suggests that if the series with no autocorrelation, then the DW value will go to two. In roughly speaking, if the Durbin-watson statistic is substantially less than 2, it shows there is a positive correlation of the data; If the value is substantially larger than 2, It shows there is successive error terms which are negatively correlated. In regressions, this mean there is an underestimation of the statistical significance level.
In Table 4, the results for Hong Kong against Japan through the OLS estimation are showed. The result of DW statistic is 0.718. The regression may contain autocorrelation. Therefore, we may know the price and the exchange rate is not co-integrated. The R-square of the regression is 0.853751. The regression may have perfect predictability if it contains with a R-square equal to 1. So, in this table, 0.853751 implies that PPP is well predicting in these two countries. The coefficient of log variable for CPI of Hong Kong (AA²1) and CPI of Japan (AA²2) is -0.0919722 and 4.62565 respectively. However, the domestic economy Hong Kong shows the positive signs of coefficient and the coefficient of Japan is negative. A weak form of PPP IS appeared as AA²1A”°A -AA²2A”°A 1. In Table 5, the result of the ADF test is showed. The lowest AIC value is -4.526 and its corresponding t-adf value is -3.674. This means it failed to reach the 1% critical region, therefore it seems to have stationary within analysis. In order to check whether there is cointegration for the level terms. Additional graphical analysis is needed. In Figure 28, the test for the residual at I(0) is shows by the correlogram and the spectral density. Although characteristics of stationary are shown in the results of the ADF test, that is contradicted by the graphical analysis. Base on the correlogram graphical analysis, the first lag is above the critical value. In the ADF test, the correspondent t-adf value in lag 0 is -2.183, which is within the 5% critical value.
Thus, the regression shows weak stationarity and co-integration do not exists between the consumer price index and the exchange rate. From Figure 29, The actual value of the residual at I(0) is plotted. There are not much fluctuations around the mean in the plot and also showed that there is no cointegration within the level terms, The ADF test and the graphical analysis do support that result. Therefore, The Ordinary Least Square estimation is needed to carry out at first difference level I(1). In Table 6, the OLS results for Hong Kong and Japan at first difference level I(1) is showed. It may contain autocorrelation within the regression as the result of DW statistic is 1.64. Nevertheless, through the CRDW test, there is a possibility of cointegration at I(1). The R-Square is 0.229002, which means the analysis is not a high-quality indicator for tracking the the performance of the PPP for Hong Kong and Japan. The coefficient of log variable of Hong Kong CPI (AA²1) and the log variable of Japan CPI DLJAP CPI (AA²1) is 0.377666 and -0.640497 respectively. In this analysis, the sign of the coefficient matched my expectation as a positive coefficient is given out by the domestic economy Hong Kong and a negative coefficient is given out by the foreign country Japan. For Table 7, the unit root test showed the result for residuals of Hong Kong against Japan at first difference level, the lowest AIC value is -4.335 and its corresponding t-adf value is -3.579. As the t-adf value is within the 5% critical value. Thus, Xt and Yt are showed to be cointegrated in the unit root test. Further graphical analysis will carry out as follow. In figure 30, the regression for Hong Kong against Japan is showed to be cointegrated at first difference level through the correlogram and the spectral density graph.
This graphical analysis do support my previous result of augmented Dickey-Fuller test. In Figure 31, the actual value of the residual at first difference level is plotted. Several degrees of fluctuations are shown around the mean within the plot. Which implies that there is a cointegration.
In Table 8, the results for Hong Kong against South Korea through the OLS estimation are showed. The result of the DW statistics is 0.485. the estimation may contain autocorrelation. Through the interpretation of the CRDW test, there is no cointegration among the two variables within the figure. In Table 9, the unit root test shows the result of the residual that Hong Kong against South Korea. The lowest AIC value is -4.386 and its corresponding t-adf value is -2.345. I cannot reject the null hypothesis and accept the alternative as the value is within the 5% critical value. Thus, no cointegration is shown within the estimation. The R-square of the regression is 0.712697. As I mentioned in previous part, if a regression contain a R-square that close or equals to 1, it implies the regression itself may have a higher predictability. In this analysis, the R-square is closer to 1, Therefore, the regression is believed to be consistent.
The coefficient of log variable of HK CPI (AA²1) and log variable of South Korea CPI (AA²2) is 0.386482 and -0.680975 respectively. In this time, the signs of the coefficients matched my expectation as the domestic economy shows the positive sign and the foreign economy shows the negative sign. A weak form of PPP is appears as AA²1A”°A -A²2A”°A 1. In Figure 32, the correlogram and the spectral density graph shows the analysis of the the residual from cointegration analysis of Hong Kong against South Korea. My previous result for ADF test is being supported by the correlogram, It shows that the exchange rate and consumer price index is not cointegrated. Nonetheless, according to the analysis of the spectral density graphical, characteristic of non-stationary are shown, In Figure 33, the actual value for the residual of Hong Kong against South Korea is plotted. As several degrees of fluctuations were shown around the mean which implies that there is cointegration within the data. As the graphical analysis contradict the the OLS estimation at level terms I(0), thus, further analysis in first difference level is needed to carry out.
Table 10 shows the OLS estimation of Hong Kong and South Korea at I(1). The result of Durbin-Watson statistics is 1.51 which suggests that autocorrelation may exists within the regression. In Table 11, The unit root test showed the result for the residual of Hong Kong against South Korea at first difference level. The least AIC-value is -4.267 and its corresponding t-adf value is -3.718. It is within the5% critical value. Therefore, the exchange rate and the consumer price index for Hong Kong and South Korea may exist cointegration. In figure 34, the analysis of correlogram and the spectral density graph shows that there are signs of cointegration for the residual for Hong Kong against South Korea at first difference level. From Figure 35, the actual value of the residuals is plotted.
The regression itself may contain cointegration as there is some degree of fluctuations around the mean. I believe that the residual at I(0) is affected by the Asian Financial crisis happened in 1997, as one outlier is showed in the actual value plot. According to the analysis we did in table 6, the form of PPP between Hong Kong against Japan is showed to be weak. The constant (AA±) is 0.0342385, the slope coefficient (AA²1) is 0.377666 and (A²2) is -0.640497. (AA²1) is not near to 1 and (AA²2) does not reach to -1. As a result, in a situation that the weak form of PPP exists, given a unchanged HK CPI and a increasing CPI of Japan. The exchange rate of Hong Kong dollar against Japanese Yen will increase. The currency of Hong Kong will stronger than the currency of Japan. For instance, Hong Kong has an inflation, the purchasing power for the Hong Kong currency will reduce. Meanwhile, with the same amount of HKD, fewer amounts of goods and services can be consumed in Japan. The exchange rate of HKD/JPY must increase to maintain the purchasing power of Hong Kong Dollar in Japan. For the other test we did in table 10, the constant (AA±) is 0.0205733, the slope coefficient (AA²1) is 0.452422 and (A²2) is -1.08451. (AA²1) is far away from 1 but (AA²2) is much closer to -1. Due to the AA²1 A”°A -AA²2 A”°A 1, thus the obtained performance for the PPP between Hong Kong and South Korea is still a weak form.
Frenkel  (1981) states that two countries are geographically close together, their PPP should also be relatively close. It is due to the low barrier of trade. According to the econometric modelling, the coefficients of the OLS estimation showed that my analysis for the PPP of Hong Kong against Japan and Hong Kong against South Korea is not a good indicator for predicting the long run exchange rate. Even though the exchange rate and consumer price index did exist cointegration relationship, however both the value of AA±, AA²1 and AA²2 is unsuccessful to match strong and the weaker form of PPP. Referring to the PPP in weak form, in the case for Hong Kong against Japan and Hong Kong against South Korea, both value of AA± was close to 0. Nevertheless, AA²1 for both regressions were not near to +1 and the R-squares of both analyses were comparatively low. That may be caused by some sort of error within the economic modelling. Through the actual value plot, we may discover that the Asian Financial crisis which happened in 1997 had played a major role in creating outliers within my residuals.
This may explain the poor performance of my PPP analysis. Also, as the exports markets for Hong Kong, Japan and South Korea are likely to be the same, for instance, the mainland China and the USA. In recent past, the service sector within the GDP of Hong Kong, Japan and South Korea has accounts for 88%, 73.1% and 67.7% respectively  . The key components of service sector are included shipping, wholesale & retail trade and financial services. When you compare the relationship between the main industries in Hong Kong against Japan and Hong Kong against South Korea, it is no doubt to say that they are electronics, chemicals and textiles. Nevertheless, when constructing the price indices, different countries are always using various of goods and services. It means that the fairness of price index of two economies may be low, as they constructed by several of goods and services. Thus, a weak form of PPP is obtained in these three economy.
The error-correction model is based on the theorem of Granger representation. The model itself shows the crucial connection between cointegration and the error correction model. The reason is that when there is connection between the exchange rate and consumer price index in long run, a mechanism should be there to coordinate the exchange rate and the consumer price index back to their equilibrium level. Testable hypothesis: A”St = a + but-1 + c1A”pt-1+ c2A”p*t-1 + AAµt Where: ut = st – AA±- AA²1Pt +AA²2Pt As series st, pt and pt* are usually non-stationary, so PPP implies cointegration. In Tables 12 and13, the trial and error process are showed. The parsimonious model for Hong Kong against Japan can be found by eliminating the larger t-probs. According to table 13, the parsimonious model from ADL modelling is being achieved. In theory, similar result would be given out even the methods of deriving the error correction model are different. Therefore, Engle and Granger two-step procedure is introduced to derive the parsimonious model. In order to test whether the error correction model are hold, OLS estimation is applied again . Through the OLS estimation, all the variables I tested are in log form and first difference level. Secondly, as the above estimation of OLS, I let the log variable of Hong Kong dollars against Japanese Yen be the St value. And in order to make my analysis be more accurate, the lag length for both log HK CPI and log Japan CPI in first difference level are changed to be 4. According to Table 14, we can see that the t-probs of numerous variables are greater than 0.05. As DLHKCPI_4 is 0.693.
Therefore, those larger t-prob variables are needed to be eliminated and re-run the OLS estimation. In Table 15, the coefficient value of DLHK CPI_1 is -1.96949 and the t-prob is 0.006, and the DLJapan CPI_1 with the coefficient value is 8.76664 and the t-prob is 0.002. The test summary in Table 16 shows all pass result for AR1-2 test, ARCH 1-1 test, normality test and the RESET test as no asterisk is present. The value of Durbin-Watson test is 1.44 with 25 observations and 4 parameters. For the 5% significant leve, the lower bounds dL=1.04 and upper bounds dU =1.77. The value is within the lower and upper bounds. Therefore, the exchange rate and the consumer price index are shown to contain serial correlation. Let St be the log value of exchange rate in first difference level and ut-1be the lag value of residual. For the C1 should be DLHK CPI_1 and C2 be DLJapan CPI_2. Also, in the St (exchange rate) in one period corrected in next period, the proportion of the disequilibrium is showed by the value b. Hence, insert all variables within the formula, we may have; A-A³St= 0.0512308+0.464698ut-1-1.96949A-A³pt-1+8.76664A-A³pt-1+AAµt According to the result of the equation above, positive coefficients for the CPI have shown in the short-run, and for the b value is 0.464698, inconsistency is showed between the actual value relationships in long run. Base on all passed tests result, we may conclude that the PPP tracks well within Hong Kong against Japan. In Table 17 and 18, the ADL Modelling results of the trial and error process ofHong Kong against South Korea are showed. Again repeating the same process for Hong Kong against Japan, the parsimonious model for Hong Kong against South Korea is derived.
Through the result, it shows that further derivation of the model can be made in short run. Nevertheless, in order to check whether my ADL modelling is valid, Engle and Granger two step procedure is introduced for analysis. In Table 19, the regression result for the OLS model of the DLHKD/KRW in first difference level is showed. By taking the same step I used in the above analysis. We eliminate larger t-prob value and run the OLS estimation again. Therefore, DLHK CPI 2,3 and 4, also the DLSKR CPI 2,3and 4are being delected. From Table 20, The DW value is 1.19 with 25 observation and 4 parameters. From the Durbin-Watson significance table, we may find that the dL = 1.04 and the dU = 1.77. The DW value is within the lower and upper bounds. As a result, I believe that the data itself may contain serial correlation. Finally, the result for the Table 21 is being analysis. It shows that AR 1-2 test, the normality test and RESET test are all passed excepted the ARCH 1-1 test. Moreover, when all coefficients are inserted into the formula, we got; A-A³St = -0.0425611+ 0.589508 ut-1-1.31079 A-A³pt-1+ 1.81169A-A³pt-1+AAµt The results shows that there is a negative coefficients for the CPI in short- run, and the b-value is 1.81169,it shows inconsistency between the actual value relationships in long run.
Base on the econometric testing above, even though my data showed characteristics of nonstationarity and cointegrated. In long run, it is obvious that there is no relationship between Hong Kong and South Korea in purchasing power parity, according to my error correction model analysis; and also Hong Kong and South Korea. Therefore I need to examine the quality of the data and also some of the assumption. The consumer price index and the exchange rate of Hong Kong and Japan are showed to be cointegrated in the section of cointegration analysis, nevertheless, the error correction model had confirmed that the two countries do not contain long run relationship. As a result, the data itself cannot be used for forecasting and analysis. For Hong Kong against Japan, there may be flaws within my data due to the negative 1 coefficient. However, all variables in my project showed that the second differencing in the stationary analysis is the signs of stationary; which implies my regression could not assume as a spurious regression. Therefore, there could be a high possibility of the existence of other reasons which would affect the coefficients.
Base on the same test I worked for Hong Kong against Japan, the exchange rate and consumer price index of Hong Kong and South Korea are showed to be cointegrated in the section of cointegration analysis, nevertheless, the error correction model also proved that the two countries do not contain long run relationship. From the first difference of actual value plot of residual, there were one major structural break within the data; we may consider that as the consequence of Asian Financial crisis in 1997. For these events, I believe that is the main reason for my failure of Error Correction Model. In order to improve the quality of the analysis, there is a need to increase the series length and identify the flaws of the data. Nevertheless, more structural breaks may result due to the extension of time period. Therefore, we should adding dummy variables within the analysis in an attempt to smooth out the outliers. Hence, to construct a more efficient research.
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