Theory of Purchasing Power Parity - Essay Example

QUANTITATIVE METHODS. by Theory of Purchasing Power Parity. Theory of purchasing Power Parity says that exchange rates of two different country currencies’ are in equilibrium when they have the same purchasing power. Therefore, the exchange rates of two countries are equal to the price level ratio of the two countries. The price level should be of fixed collection of goods and services. When the domestic price level of a country increases, the exchange rate in that country must depreciate in order to maintain the Purchasing Power Parity. The Purchasing Power Parity acts on the basis of “law of one price” when the costs of transportation and other transaction costs are absent. The competitive markets will equalize the price of a similar good in the two countries when prices are expressed in similar currencies. For instance, a certain Television Set priced at 750 Dollars in Canada should cost 500 Dollars in United States when the exchange rate between the two countries is 1.50. Economists use two Purchasing Power Parity versions: Relative Purchasing Power Parity and Absolute Purchasing Power Parity. Absolute PPP is when the price level across countries is equalized. For instance, the exchange rate of Canada and US is computed by dividing the price level of Canada by that of the US. Assuming the exchange rate is 1.3 CAD per USD from 1.5 CAD per USD today. PPP theory implies the Canadian dollar will appreciate as USD depreciated. The relative Purchasing Power Parity refers to the degree of changes in the price level commonly known as the inflation rate. It says that appreciation rate of a currency is similar to the difference in the rate of inflation between the home and the foreign country. Assuming the inflation rate for Canada and US are 1% and 3% respectively, The US currency will depreciate against the Canada Dollar by 2% annually. Relative PPP withstands when the difference in inflation is very large. Law of one price. The concept is related to effect of trade and market arbitrage on the prices of similar products exchanged in multiple markets. In markets that are efficient, there must be a single price of those commodities in respective of their trading areas. The law of one price is also applicable to factor market. However, since the costs of the transaction and transport are positive, the law needs reformulation when applicable to spatial trade. Assuming we have two markets (Liverpool and Chicago) trading wheat and the wheat are transported from Chicago to Liverpool. The difference in the prices of wheat between the two markets should be similar to the cost of the transaction and transportation from Chicago to Liverpool. Meaning ratio of the price in Liverpool to Chicago price plus the costs in the transaction and transportation should be one. If the differential in prices exceeds the costs of the transaction and transport, it means the ratio in prices is greater than one, and then well informed and self-interested traders take the chance to earn profits by transporting wheat to Liverpool from Chicago. The price gap is closed by arbitrage because it raises supply and in result causes a decrease in price in Liverpool as well as demand and price in Chicago. If the differential in prices exceeds the costs of the transaction and transport, it means the ratio in prices is greater than one, then well informed, and self-interested traders take the chance to hold wheat from Liverpool warehouse and thus reduce shipment demand of wheat from Chicago. The reactions normally trigger off price increase. This is because there is a fall in supply in Liverpool and reduced price in Chicago because there will be a fall in demand. Empirical (Econometric) Tests for PPP. Purchasing Power Parity is believed to be holding relationship for long-run equilibrium. However, PPP’s empirical support when using unit root tests is not appealing. The unit root tests suggest that the real exchange rates are not stationary when applied to statistics of previous eras. The finding is attributed to inability of cointegration test and standard unit root to lack power in smaller samples against certain alternatives that are non-stationary. The lack of power has been surmounted by various strategies that have been devised such as using long span data and employing panel unit root tests. Using long spans of data means mixing statistics from nominal (floating) and fixed exchange rate eras. Seemingly, real exchange rates behave differently under the two exchange rate regimes. Panel unit root rests do not correct real exchange rates comovements in the panels employed. Consequently, the panel unit root tests misleads because when null hypothesis is rejected, it means the considered smaller series number is stationery. There are various explanations explaining the failure of finding the empirical evidence that favours PPP (Manzur, 2008). The most common one is the presence of trade barriers for example the cost of transportation and tariffs. Various theoretical models have come up showing that the frictions in the market results to nonlinear adjustments in rates of real exchange and PPP equilibrium. The strength and power of mean reversion raises with parity deviation , as profits from the arbitrage of goods which is believed to be the final force behind PPP maintenance. Additionally, another explanation is the presence of non-traded products in the price index that constructs real exchange rates. US-China Case Study. Specifying PPP relationship and Testing. PPP outlines that qt =S Pt*/P where Pt is the price index of the domestic country while Pt * is the price index of the foreign country and S is the nominal exchange rate . The nominal exchange rate S is computed as domestic currency per foreign currency unit. qt is the real exchange rate and t is a given point in time. According to Purchasing Power Parity, qt should be one. Therefore, if qt =1 then S = Pt /Pt * Hence %∆s = %∆P - %∆P* The above equation is PPP relative version that relates the change in exchange rate with changes in the price level of the two countries. The relative PPP will be tested through the estimation of %∆s = β0 + β1 %∆P – β2 %∆P* + u β0 , β1 ,β2 represents the constant terms and the regressros coefficient while u is a residual term. The equation is a linear model, therefore the Ordinary Least Square is applied. The above equation makes use of the multivariable regression. The relative PPP is tested by employing bivariate regression analysis and also estimating %∆s = β0 + β1 (%∆P – %∆P*) + u Additionally, the relative PPP is investigated in its absolute version, by transforming equation S = Pt /Pt * logarithmically, we arrive at et = pt – pt * et =ln(Et ) pt =ln(Pt ) pt * = ln(Pt *) Using OLS to find out the multivariate and bivariate regression analyses the equation can be estimated using the linear models: st = β0 + β1 (pt – pt *) + u st = β0 + β1 pt – β2 pt * + u Based on law of one price concept, β0 =0. The regressors coefficient in the two models should be one. Whereby β0 = 0, β1 =1, and β2 =1. Additionally, the regressor’s coefficient is tested. When the null hypothesis is rejected then the PPP theory holds for the tested data (Manzur, 2008). US-China Analysis. Equation %∆s = %∆P - %∆P* approves the monetary approach of determining PPP. This exchange rate’s rate of change can be termed as the nominal exchange rate depreciation. The difference in the price level’s rate of change is the inflation differential this is because the CPI is referred to as the inflation rate. This brings us to the following equation: %S  *   Where %S is the nominal exchange rate’ depreciation, is the US inflation rate while China’s inflation rate is * The difference in the inflation rate of the two countries is termed as the inflation differential. Therefore, the countries’ analysis while using the OLS model is as shown below: %S  0  (*  )  u In the long-run Purchasing Power Parity predicts 0 t to be zero while β1 would be 1 Tests. Relative PPP. % ΔS ΔP ΔP* Δ(P-P*) Average 0.00131 0.00211 0.0028 -0.0007 S.E 0.0002 0.0003 0.0007 0.0007 Med. 0.0000 0.0021 0.0010 -0.0009 Mode 0.0000 0.0000 0.0000 #N/A SD 0.0030 0.0036 0.0095 0.0097 S V 0.0000 0.0000 0.0001 0.0001 Kurtosis 9.0816 6.6663 1.1718 0.6767 Skewness 2.9007 -1.3423 0.8274 -0.5012 Range 0.0192 0.0314 0.0525 0.0579 Min -0.0020 -0.0192 -0.0140 -0.0358 Max 0.0171 0.0122 0.0385 0.0221 Sum 0.2426 0.3912 0.5268 -0.1356 Count 228 228 228 228 Confidence Level (95.0%) 0.00044 0.0005 0.0014 0.0014 Relative PPP Bivariate Regression Analysis %∆ E     (%P  %P* )  u %ˆ E  bˆ  bˆ (%P  %P* )  u t 0 1 t t t ******* H0 : β0 = 0 Ha : β0 ≠ 0 t* =( b0 - β0 ) / Sb0 = (0.001271564 – 0)/ 0.00022176 = 5.7340442 P = TDIST (|t*|, n -2, 2) = TDIST (5.7340442, 185, 2) = 3.932E-08 ≈ 0 P < α, reject H0 ******* H0 : β1 = 1 Ha : β1 ≠ 1 t* =( b1 - β1 ) / Sb1 = (-0.035383806 – 1)/ 0.02287805 = -45.25664582 P = TDIST (|t*|, n -2, 2) = TDIST (45.25664582, 185, 2) = 5.3035E-102 ≈ 0 P < α, reject H0 Absolute PPP. s at time t p at time t p* at time t p - p* Mean Standard Error -2.0893 4.5139 4.5601 -0.0462 0.0044 0.0085 0.0073 0.0043 Median -2.1135 4.5108 4.5524 -0.0291 Mode -2.1135 4.4439 4.5436 #N/A Standard Deviation 0.0607 0.1159 0.0995 0.0594 Sample Variance 0.0037 0.0134 0.0099 0.0035 Kurtosis 2.5133 -1.1442 2.5039 -0.4873 Skewness 1.8998 0.1124 -0.9697 -0.2886 Range 0.2431 0.4085 0.5419 0.2807 Minimum -2.1637 4.3157 4.1974 0.1625 Maximum -1.9206 4.7241 4.739 0.1182 Sum -392.7878 848.6204 857.3056 8.6853 Count 228 228 228 228. Confidence Level(95.0%) 0.0087 0.0167 0.0143 0.0086 Hypothesis testing. For the two countries hypothesis, we set H0 : β0 = 0 & Ha ≠ 0 for intercept & H1 : β1 = 1 and Ha : β1 ≠ 1 for slope. The c- value and p-value approaches are used at significance level of 5 per cent as shown below: %∆ E  0   (*   )  u %ˆ E  bˆ  bˆ (*   )  u 0 1 ******* H0 : β0 = 0 Ha : β0 ≠ 0 t* =( b0 - β0 ) / Sb0 = (1.61 – 0)/ 4.8463- 1014 = 33221216516827.00 P = TDIST (|t*|, n -2, 2) = TDIST (33221216516827.00, 72-2, 2) = 0 P < α, reject H0 ******* H0 : β1 = 1 Ha : β1 ≠ 1 t* =( b1 - β1 ) / Sb1 = (1– 1)/ 1.8461  10 = 0 P = TDIST (|t*|, n -2, 2) = TDIST (0, 79-2, 2) = 1 P > α, fail to reject H0 %∆ s  0   (*  )  u %ˆ E  bˆ  bˆ (*   )  u t 0 1 ******* H0 : β0 = 0 Ha : β0 ≠ 0 t* =( b0 - β0 ) / S b0 = (1.61 – 0)/ 4.8463-10 = 33221216516827.00 c = TINV (α, n -2,) = TINV (0.05, 77) = 1.99 |t*| > c, therefore reject H0 ******* H0 : β1 = 1 Ha : β1 ≠ 1 t* =( b1 - β1 ) / S b1 = (1– 1)/ 1.8462  1017 = 0 c = TINV (α, n -2,) = TINV (0.05, 77) = 1.99 |t*| < c, therefore fail to reject H0 Based on the literatures, there no agreement on the PPP validity. The monthly data do not support the PPP theory therefore there should be a single relationship between changes in differential of US and China inflation rates and the nominal exchange rates. However, after analyzing the data, there is a rejection. The test results shows that the exchange rate policy can be affected in terms of trade between them. Failing to find the PPP evidence means that the exchange rate between china and United States is not at its correct value. More detailed analysis is required to review this. Analysis between China and USA suggests that the inflation differential relative to the United States is equivalent to depreciation rate relative to United States. Eviews: Bivariate Model Regression Statistics Multiple R 0.112882184 R Square 0.012864974 Adjusted R Square 0.007828568 Standard Error 0.003523981 Observations 228 ANOVA Significance df SS MS F F Regression 1 2.1374E-05 2.1834E-05 2.395054708 0.12366217 Residual 227 0.001641725 9.16446E-06 Total 228 0.001743599 Coefficients Standard Error t Stat P-value Intercept 0.005271564 0.000621757 5.734744232 3.93701E-08 %∆(P-P*) -0.035383806 0.02277805 -1.54672688 0.12368217 ANOVA df SS MS F Significance F Regression 2 0.000151386 6.06631E-05 7.0136400890.001659997 Residual 226 0.001592213 8.65343E-06 Total 228 0.001713699 Coefficients Standard Error t Stat P-value Lower 95% Intercept 0.000845447 0.000252668 3.266817606 0.001299085 0.000329947 %∆P 0.152496616 0.05975134 2.553123068 0.01148782 0.034698071 %∆P* 0.054340095 0.022849371 2.369567941 0.018864216 0.00920235 Absolute PPP Bivariate Model Regression Statistics Multiple R 0.196234428 R Square Adjusted R Square 0.035339544 0.06216395 Standard Error 0.056704794 Observations 228 ANOVA Significance df SS MS F F Regression 1 0.02471741 0.02571741 7.214542966 0.0078854923 Residual 227 0.665027217 0.003464662 Total 228 0.687744628 Standard Coefficients Error t Stat P-value Lower 95% - Intercept -2.08418037 0.005520911 376.782438 4.2258E-270 -2.091342024 p - p* 0.197331448 0.07336693 2.6856690128 0.004585923 0.052378884 Multivariate Model Regression Statistics Multiple R 0.8056558192 R Square 0.6537645349 Adjusted R Square 0.674023283 Standard Error 0.035894764 Observations 228 ANOVA df SS MS F Significance F Regression 2 0.4556780610.22575903 174.6866293 2.5641E-43 Residual 226 0.238846567 0.009689008 Total 228 0.680346528 Coefficients Standard Error t Stat P-value Lower 95% Intercept -4.265665567 0.120394561 -35.42422048 2.26748E-84 -4.500459273 p at time t 0.197238613 0.044175464 4.478599663 1.7426E-05 0.11644025 p* at time t 0.280963705 0.051842984 5.462985746 1.50249E-07 0.17880339 Reference. Manzur, M. 2008. Purchasing power parity. Cheltenham, UK: Edward Elgar. Read More