【正文】 ng power parity (PPP) was raised by Cassel (1918). The theory holds that the value of a country’s money depends on its purchasing power, which in turn determines its exchange rate vs. another currency. II. The Law of One Price in an Open Economy Assumptions ?Homogeneity of modities ?Price flexibility ?No transaction costs 52 The Law of One Price (LOOP) LOOP states that in petitive markets free of transportation costs and official barriers to trade, identical goods sold in different countries must sell for the same price when their prices are expressed in terms of the same currency (Krugman and Obstfeld, 2020, pp. 389). Let pi denote the home price of a certain tradable goods (i) in home country and pi*, the foreign price of the same goods in another country, then the law of one price can be expressed as follows, pi=Spi* Where, as before, S denotes the exchange rate. ?Purchasing Power Parity 53 III. APPP Suppose the LOOP holds for any tradable goods, and the weights of each tradable goods in the basket both in home country and foreign country are the same when puting their price indices. Thus relation of the price indices between the two countries may take the following form. Where ?i stands for the weight of the ith tradable goods in the basket chosen by both countries. ?????niiiniii pSp1*1???Purchasing Power Parity 54 Obviously, the left hand is the general price index of home country, and the right hand also contains the part of foreign price index, namely, Finally, we have, S=P/P* This is the absolute form of PPP (APPP). Conclusion: The absolute form of PPP shows that the exchange rate is determined by both home and foreign price indices. ???niii pP1?and ???niii pP1** ??Purchasing Power Parity 55 IV. RPPP Transaction costs, different weights of tradable goods in the basket, as well as other considerations may lead to the failure of the absolute form of PPP. The relative form of PPP (RPPP) holds that there is a stable or constant deviation between home and foreign price indices. That is, S=?P/P* Where ? is a constant. This means real exchange rate (RER=SP*/P=?) should be constant or stable over times. ?Purchasing Power Parity 56 By taking natural logarithms both sides, Log(S)=log(?)+log(P)log(P*) Let s=log(S), p=log(P) and p*=log(P*), rewrite the equation and arrive at, s=log(?)+pp* Or, ?s=?p?p* =??* Conclusion: The RPPP states that the differentials between home and foreign inflation rates determine the percent change of the exchange rate. ?Purchasing Power Parity 57 V. Empirical Tests of PPP A large body of literature focuses on the empirical tests of PPP and unfortunately there has been still no consensus achieved. We simply test the theory by checking whether the real exchange rate is dependent of the nominal one or keeps stable over times. If yes, we conclude that PPP does hold and if no, it does not hold. For those who are interested in more sophisticated and advanced econometric methods on testing PPP, see Sarno and Taylor (2020), and MacDonald (2020) for a survey of the methodology employed. Figure 221 to 222 illustrate the simple test of PPP on a few countries’ exchange rates. ?Purchasing Power Parity 58 Figure 221 Simple Test of PPP on RMB Exchange Rate Source: BIS. 607080901 0 01 1 01 2 01 9 9 4 1 9 9 6 1 9 9 8 2 0 0 0 2 0 0 2 2 0 0 4 2 0 0 6 2 0 0 8R M B N E E R C H I N A R B C N?= 59 Figure 222 Simple Test of PPP on Australian Yen Source: BIS. 801 2 01 6 02 0 02 4 02 8 065 70 75 80 85 90 95 00 05A U S T R A L I A N E E R A U S T R A L I A R E E R?= 60 Figure 223 Simple Test of PPP on US$ Source: BIS. 7080901 0 01 1 01 2 01 3 01 4 065 70 75 80 85 90 95 00 05U S N E E R U S R E E R?= 61 Figure 224 Simple Test of PPP on UK Pound Source: BIS. 60801 0 01 2 01 4 01 6 01 8 02 0 065 70 75 80 85 90 95 00 05U K N E E R U K R E E R?= 62 Figure 225 Simple Test of PPP on Japanese Yen Source: BIS. 204060801 0 01 2 065 70 75 80 85 90 95 00 05J A P N E E R J A P R E E R?= 63 VI. What Is Wrong with PPP? Technical Problems ?The choice of price index ?Classifications of modities ?The choice of a base year Other Considerations ?Trade barriers and nontradables ?Departure from free petition ?HarrodBalassaSamuelson Effect ?Purchasing Power Parity 64 VII. A Short Comment ?The most influential theory ?A benchmark for the exchange rate determination ?An inplete theory of exchange rate determination ?Pioneering researches from the perspective of money quantity hypothesis ?Purchasing Power Parity 65 VIII. HarrodBalassaSamuelson Effect The theory was independently raised by Balassa and Samuelson in 1964. The theory proves that price index in richer countries or counties with higher percapita ine is higher than that in poorer counties or economies. Definitions ?LT and LN, productivity in the tradable and nontradable sectors。 PN=W/LN。 P*=?PT*+(1?)PN* And by [2] and [7], it is easily seen that, P=?PT+(1?)PN?SPT*+(1?)SPN*=SP* [8] Theorem3: PPP does not hold due to the productivity differentials between the two economies. ?Purchasing Power Parity 71 ?Interestrate Parity I. A Comparison with PPP Money Quantities Purchasing Power (Price of Goods) Exchange Rate Money Supply amp。 PN*=W*/LN*。 ?PT and PN, prices in the two sectors. And letters with a * stand for foreign variables. ?Purchasing Power Parity 66 Assumptions ?A twocountry, twosector (tradables and nontradables) model ?Wages are equi