Testing The Two Forms Of Purchasing Power Parity Finance Essay
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.
In this project I will try and test Purchasing Power Parity for Hong Kong, Japan and South Korea, 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 in the long run, real exchange rates can be generally estimated. 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.
Theory of Purchasing Power Parity
The study of the Purchasing Power Parity (PPP) helped policy maker 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 domestic currency should be able to 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 in the presence of a competitive market, all identity goods must have same price. Base on the PPP theory, arbitrage will occur due to an agent tries to make a profit through exchange rate.
For instance, a can of coke worth 50p in Britain and in France is $1, and then the exchange rate is £0.5/$1. 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 the assumptions of ignoring the existence of administrative cost and different types of imperfect competitions. 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
P*t= 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 performance of the exchange rate between two countries is tracked by the economic modelling 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, it may help to make informed monetary and fiscal policies.
Descriptive Data analysis
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. Monthly and quarterly data were not collected due to seasonality and avoiding dishonesty in my findings. In order to make sure the fairness of the test, the annual data of CPI has all been adjusted to base year of 2005 automatically.
From the Figure 1 of appendix, the trends of the consumer price index for all three countries are 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’s 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抯 economy affected by the Asian financial crisisp 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, As the largest of the Four Asian Tigers, the South Korean economy is the fourth largest in Asia and 15th largest in the world
Figure 2 shows the trend of the exchange rates between 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/Yen?. 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 become 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, they showed the correlogram analysis of my data set. 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 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 rapid 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.
Stationarity analysis at I(0)
In appendix Table 1, all the results from the software PC GIVE are showed.
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, the actual plots for all the logged CPI variables are showed together. 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.
Stationarity analysis I(1)
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 I(1) of the variable of 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 I(1) 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 there is some degree of fluctuations around the mean. It contradicts the unit root test I worked in previous.
Therefore, second difference level of the data are needed to be analysed in order to check whether the variable are stationarity or not.
For the first difference of the log exchange rate for HKD/YEN, 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 . The graph itself shows characteristics of stationarity due to its fluctuations around the mean. Therefore, this support the unit root test. As a result, I will also look for the second difference in order to find stationarity for the variable.
For the first difference of log of the HKD/KRW, the lowest AIC value is ?.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.
Figure 16 shows the correlogram and the spectral density analysis. Both graph shows thhat there are some characteristics of stationarity within the variable. So, this support the unit root test result.
Figure 17 is the actual value plot of DLHKD/KRW, The graph itself shows characteristics of stationarity due to its 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.
Stationarity Analysis for I(2)
Table 3 in the appendix showed the unit root test results for the second differencing of log variables.
For the second difference of the log of Hong Kong CPI, the lowest AIC value is -7.376 and its corresponding t-adf value is -3.340. This is within the 5% critical value region. This also means that I can reject my null hypothesis and accept the alternative hypothesis. Therefore, the log of Hong Kong CPI at I(2) is stationary.
Figure 18 shows the correlogram and the spectral density of the second differencing. The graphs supported the unit root test which shows stationarity within the variable.
Figure 19 is the actual value plot of the variable. The graph also showed many fluctuations around the mean. This means it is also another characteristics of stationarity. However, It shows two excessive shock. 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 second difference of the log of Japan CPI, the lowest AIC value is -9.049 and its corresponding t-adf value -4.226. This is within the 5% critical value region. Therefore, I can reject my null hypothesis and this means the log of Japan CPI at I(2) is stationary.
Figure 20 shows the correlogram and the spectral density of the Japan CPI. Both graphs show that stationarity exists within the second differencing. This means it supports my unit root test.
Figure 21 is the actual value plot of the variable which shows fluctuations around the mean. There is one excessive shock within the graph and that happened in 2007. Japan suffered considerably from a recession. This had led to the drop of the consumer confidence and reflected from the actual value plot.
For the second difference of the log of South Korea CPI the, the lowest AIC value is -7.711 and its corresponding t-adf value is -6.907. This is within the 5% critical value region. Therefore I can reject my null hypothesis and this means the log of US CPI at I(2) is stationary.
Figure 22 shows the correlogram and the spectral density of the second difference of the South Korea CPI. Both graphs support the unit root test which means there is stationarity within the variable.
Figure 23 is the actual value of the CPI. The graph shows there is fluctuation around the mean, this means there is another sign of stationarity. However, there is one outlier which occurred in 1997. In 1997 the South Korea economy suffered considerably from a recession. This had reflected from the actual value plot.
For the second difference of the exchange rates, the lowest AIC value for HKD/YEN is -4.622 and its corresponding t-adf value is -6.008. This is also within the 5% critical value region. Therefore I can reject my null hypothesis, thus the data is stationary.
Figure 24 shows the correlogram and the spectral density of the exchange rate HKD/YEN. Both graphs supports my unit root test, therefore stationarity exists within the data.
Figure 25 is the actual value plot of the exchange rate, the graph also shows fluctuations around the mean. This implies that there is stationarity within the series. The excessive shocks which happened in 1997 also support previous analysis.
For the second difference of HKD/KRW, the lowest AIC value is -3.779 and its corresponding t-adf value is -5.497. This is within the 5% critical value region. Therefore I can reject my null hypothesis and this means the data is stationary.
Figure 26 shows the correlogram and the spectral density graphs, both graphs support the unit root test which means the variable is stationary.
Figure 27 is the actual value plot which shows fluctuations around the mean, this also support the theory of stationarity. In the actual value plot, there is one excessive shock which is also appeared in previous differencing.
Through the second differencing of the log variable, it showed that all the data are stationary at I(2).
Ordinary Least Square Estimation and Cointegration Analysis and its interpretation
In this section of the project, the performance of the PPP will be analysed by the econometric modelling. Cointegration analysis is also another tool which will be use in conjunction 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 α(≠0) such that Zt = α Xt ~ I(d-b) b>0
It means that if a set of variables are time dependent, however, through cointegration analyse, a stationary error term is given out, then it can be said that they cointegrated at the order of (d,b)
Take the above equation as an example, Yt and Xt can be non-stationary data. However, if Yt and Xt are both cointegrated, then the error term ut can still be stationary. The non-stationary degree will be eliminated through the cointegration process. This implys the analysis itself will not be misleading.
My testable hypothesis: In logs:
Strong form (absolute PPP) α=0 β1=1 β2=-1
Weaker form: α≠0 β1= β2≠1 so that:
Weak form α≠0 β1≠ β2≠1 so that:
With ut such that the relationship is stable in time.
By testing the residual from the OLS estimation through augmented Dickey-Fuller test, cointegrating regression Durbin-Watson test, MacKinnon critical values and other graphical analysis, Thus, if the residual is stationary, we can assume that the regression support the long run theory of PPP.
The introduction of the cointegrating regression Durbin-Watson (CRDW) test can ensure my accuracy on my analysis. 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朩atson 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 ecrror terms which are negatively correlated. In regressions, this mean there is an underestimation of the statistical significance level.
Analysis for Hong Kong and Japan
Table 4 shows the results of the OLS estimation on level terms for Hong Kong against Japan. The result of DW statistic is 0.718. It shows that regression may contain autocorrelation and which is not reach to the critical value. Thus we know that the regression is not co-integrated between the price and the exchange rate.
The R-square of the regression is 0.853751. If the R-square is equals to 1, this implies the perfect predictability of the regression. So, in this table, 0.853751 is an accurate sign of predicting that if the PPP track well in these two countries. The coefficient of LHK CPI (β1) is -0.0919722, and the coefficient of LJapan CPI (β2) is 4.62565. However, the signs of coefficient of the domestic economy Hong Kong should be positive and Japan should be negative. It appears to be a weak form of PPP as β1≠-β2≠1.
Table 5 shows the ADF test results. 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. Further graphical analysis is required to check whether there is cointegration for the level terms.
Figure 28 shows the correlogram and the spectral density test for the residual at I(0). Although the results of the ADF test have appeared to be stationary, the graphical analysis contradicts the unit-root test. As we can see from the correlogram graphical analysis, the first lag is above the critical value. In the ADF test, the t-adf value in the lag 0 is -2.183, which larger than the 5% critical value. Therefore, it is weak stationarity and co-integration do not exists within the regression.
The results show that there is no cointegration exists between the consumer price index and the exchange rate. Figure 29 is the actual value plot for the residual at I(0). The plot itself did not show many fluctuations around the mean, this is also a sign of the two variables not cointegrating. Both graphical analysis and the ADF test showed that no cointegration within at level terms.
Therefore, we need to carry out the Ordinary Least Square estimation at first difference I(1).
Table 6 shows the OLS results at I(1) for Hong Kong and Japan. The result of DW statistic is 1.64, which still shows that the regression itself may contain autocorrelation. Nevertheless, under the criteria of CRDW test, there is a possibility of cointegration at I(0). The R-Square is 0.229002, which means it may not be a good indicator for tracking the performance of the PPP for Hong Kong and Japan.
The coefficient of DLHK CPI (β1) is 0.377666, and the coefficient of DLJapan CPI is (β2) is -0.640497. In this time, the signs of coefficient are right as the domestic economy Hong Kong is positive and for the foreign country Japan is negative. The sign of the coefficient matched my expectation.
From the unit root test on table 7, the lowest AIC value is -4.335 and its corresponding t-adf value is -3.579. The t-adf value is within the 5% significance level, therefore, the unit root test shows that the Xt and Yt are cointegrated. I will now test this with graphical analysis.
From figure 30, both correlogram and the spectral density graph shows that the regression is cointegrating at I(1) for Hong Kong and Japan. This means, my graphical analysis for cointegration at I(1) support the augmented Dickey-Fuller test.
Figure 31 shows the actual value plot of the residual at I(1). The plot shows fluctuations around the mean which means there is cointegration.
Analysis for Hong Kong and South Korea
Table 8 shows the OLS estimation results of the cointegration analysis for Hong Kong against South Korea at level terms I(0). The result of the DW statistics is 0.485. It shows that there is autocorrelation within the estimation. From the interpretation of the CRDW statistics, the figure also represents no cointegration between the two variables. Table 9 is the unit root test of the residual. The lowest AIC value is -4.386 and its corresponding t-adf value is -2.345. This means it failed to reach the 5% critical value region, therefore I could not reject the null hypothesis of that there is no cointegration within the estimation.
The R-square of the regression is 0.712697. As I mentioned in previous part, if the R-square is close or equals to 1, it means that the regression with a higher predictability. In this analysis, the R-square is nearly to 1, thus the regression should be reliable.
The coefficient of LHK CPI (β1) is 0.386482 and the foreign country L South Korea CPI (β2) is -0.680975. In this time, the signs of the coefficients within my expectation asthe domestic country should be positive sign and for South Korea should be negative sign. It appears to be a weak form of PPP as β1≠-β2≠1.
Figure 32 shows the results of the correlogram and the spectral density analysis. The correlogram did support my ADF test, which means there is no cointegration between the exchange rate and the consumer price index. However, from the spectral density graphical analysis, it shows a sign of non-stationary, cause of the dramatically decline.
Figure 33 shows the actual value plot of The plot shows fluctuations around the mean which means there is cointegration.
As the graphical analysis contradict the the OLS estimation at level terms I(0), thus, we need to carry out the OLS estimation at the first differences I (1).
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 there is still serial correlation exists within the regression but also the regression may contain cointegration.
Table 11 shows the unit root test for the residual Hong Kong and South Korea at I(1). The lowest AIC-value is -4.267 and its corresponding t-adf value is -3.718. This is larger than 5% critical value region. This means that there is a sign of cointegration exists between the exchange rate and the consumer price index for Hong Kong and South Korea.
From figure 34, both the correlogram and the spectral density shows that there are characteristics of cointegration for the residual at I(0). The actual value plot (figure 35) of the cointegration shows that there are fluctuations around the mean. This means the regression itself may contain cointegration. The actual value plot also showed that there is one outlier which happened around 1997, this means the residual at I(0) is affected by the Asian Financial crisis.
According to the analysis we did in table 6, it shows a weak form of PPP between Hong Kong and Japan. The constant (α) is 0.0342385, the slope coefficient (β1) is 0.377666 and (β2) is -0.640497. (β1) is not near to 1 and (β2) does not reach to -1. As a result, if the CPI of Japan increases, presuming the CPI of Hong Kong remains unchanged. Given the weak form of PPP holds, the exchange rate of HKD/JPY will rise. The Hong Kong Dollar will become stronger while JPY will become weaker. For example, if there is inflation in Hong Kong, the purchasing power parity will reduce in Hong Kong. The goods and services which HKD can consume in Japan will decrease as well. 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 (α) is 0.0205733, the slope coefficient (β1) is 0.452422 and (β2) is -1.08451. (β1) is far away from 1 but (β2) is much closer to -1. Due to the β1 ≠ -β2 ≠ 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 had failed to track the performance of the long run exchange rate. This was because, although the exchange rate and consumer price index did exist cointegration relationship, however both the value of α, β1 and β2 failed to match strong and the weaker form of PPP.
Referring back to the weak form of PPP, although in both cases (Hong Kong and Japan, Hong Kong and South Korea) the α was close to 0. But β1 for both regression were not near to +1. The R-squares for both analyses were also relatively low. This may imply that there may be some sort of error which existing in my modelling. From the actual value plot of each cointegration analysis, the Asian Financial crisis in 1997 had continuously played a role in creating outliers within my residuals. That could be one of the reasons in explaining the 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 of Hong Kong, Japan and South Korea has accounts for 88%, 73.1% and 67.7% of the GDP respectively. The major components of service trade are shipping, wholesale & retail trade and financial services. When you compare for the similarity of 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, countries are usually attaching different weights of goods and services when constructing their own price indices. It means that the fairness of price index of two economies may not fair enough to compare, as they states for several of goods and services. Thus, PPP obtained a weak form in these three regions.
Error Correction Model
The error-correction model is derived from the Granger representation theorem. It shows the important link between the error correction model and cointegration. The reason is that when there is relationship between the exchange rate and consumer price index in long run, a mechanism should be there which takes the exchange rate and the consumer price index back to their equilibrium, hence, the derivation of the error correction model and the short run model.
ΔSt = a + but-1 + c1Δpt-1+ c2Δp*t-1 + εt
Where: ut = st – α– β1Pt +β2Pt*
As series st, pt and pt* are usually non-stationary, so PPP implies cointegration.
Tables 12, 13 shows the trial and error process by eliminating the larger t-probs, therefore I can try and find the parsimonious model for Hong Kong and Japan analysis. According to table 13, I have achieved the parsimonious model from ADL modelling. In theory, different methods of deriving the error correction model should give similar results. This means I have to use the Engle and Granger two-step procedure to derive the parsimonious model.
I have used the OLS estimation again to test whether the error correction model hold. The variables which I tested by the OLS estimation all at first difference log forms, it means they stayed at I(1). Secondly, as used OLS estimation above, I let LHKD/JPY be the 慡t?value. And then, I changed the lag length of 4 for both DLHK CPI and DLJapan CPI to make more accurate. From the results of the Table 14, we can see t lhat many variables` t-probs are larger than 0.05. Like DLHKCPI_4 is 0.693. Therefore, we need delete those larger t-prob variables and run the OLS again. From the Table 15, we can see the results clearly. The DLHK CPI_1 with the coefficient value 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 that AR1-2 test, ARCH 1-1 test, normality test and the RESET test are all passed as there is no asterisk (*) present. It means all the tests are passed. The Durbin-Watson value is 1.44with 25 observations and 4 parameters, its 5% significant level dL=1.04 and dU =1.77. The value is between the lower bounds and upper bounds` values, thus means that it probably has serial correlation between the exchange rate and the consumer price index.
Let St be the log of first difference of exchange rate, and ut-1 is the lag residual. For the C1 should be DLHK CPI_1 and C2 is DLJapan CPI_2, also the value of b can shows the proportion of the disequilibrium in the St (exchange rate) in one period corrected in next period. Therefore, put all variables into the formula, we can got;
The result shows that the coefficients for the CPI have positive short-run, and for the value of b is 0.464698 of the inconsistency between the long-run and the actual value relationships. Due to all tests passed, this in a sense and also support the fact that PPP performs and tracks well between Hong Kong and Japan.
Table 17 and 18 shows the results of the trial and error process for the ADL modelling for Hong Kong against South Korea. Again repeating the same process for Hong Kong against Japan, I have derived the parsimonious model for Hong Kong against South Korea. The results shows that further derivation of the short run model can be made. However, I have to also check it with Engle and Granger two step procedure whether my ADL modelling valid.
Table 19 shows the results of the regression of the OLS model of the first difference of DLHKD/KRW. Same steps like I mentioned for the DLHKD/JPY. We need find out the larger t-prob value and then delete them for the second time OLS estimation. Thus, I have deleted the DLHK CPI 2,3 and 4, also the DLSKR CPI 2,3and 4.. From Table 20, The DW value is 1.19 with 25 observation and 4 parameters. Look at the Durbin-Watson table, we can see that the dL = 1.04 and the dU = 1.77. The value is between the lower bounds and upper bounds value. Thus it probably has serial correlation. At last, we see the result for the Table 21. It shows that AR 1-2 test, the normality test and RESET test are all passed excepted the ARCH 1-1 test.
Moreover, we put all coefficients into the formula, it got;
△St = -0.0425611+ 0.589508 ut-1-1.31079 △pt-1+ 1.81169△p*t-1+εt
The results shows that the coefficients for the CPI have negative short- run, and the b-value is 1.81169 of the inconsistency between the long-run and the actual value relationships.
Base on the econometric testing above, even though my data showed characteristics of nonstationarity and cointegrated, it is obvious that there is no long run relationship for the purchasing power parity of Hong Kong and South Korea, 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, as to conduct a more efficient research..
. http://en.wikipedia.org/wiki/Penn_effect The Penn Effect
www.economist.com The Big Mac Index
Frenkel (1981) The collapse of PPP during the 1970s, European Economic Review, Vol 16, pp.145-165
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