【正文】 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* By [1], LN=LN*, PN=W/LN*。 P*=?PT*+(1?)PN* [5] Simple Derivations By [3] and [4], PT=W/LT and PT*=W*/LT* Since [2] holds, PT=W/LT。 PN*=W*/LN*。 PN=W/LN。 PN*LN*=WN*=W*。 PNLN=WN=W。 ?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 equivalent in either country’s sectors WT=WN=W。 ?Polarization or hollowing out of the middle. Obstfeld (1995), Eichengreen (1994) et. al. put forward the polar view argument. However, there are empirical researches against the view. See Figure 218 for a description of global exchange rate regimes evolutions and 219 for a skip of regime evolutions in emerging market economies from 19912020. ?Exchange Rate Regimes 47 Figure 218 Evolutions of Regimes (19902020) .1.2.3.4.5.6.790 91 92 93 94 95 96 97 98 99 00 01 02F I X E D I N T E R F L O A T I N GHollowing out 48 0102030405060708091 92 93 94 95 96 97 98 99 00 01 02 03F I X E D I N T E R F L O A T I N GFigure 219 Evolutions of Regimes in Emerging Markets (19912020) 49 ?Assignments ?Read the third section in the “Report on China’s Balance of Payment of 2020 and 2020” for a detailed survey of China’s foreign exchange market. ?Read Chapter 13 of the textbook. 50 ?Purchasing Power Parity ?Interestrate Parity ?Balance of Payment Approach ?Asset Market Approach ?Flexibleprice Moary Approach ?Stickyprice Moary Approach ?Portfolio Approach ?Summarization ?Assignments Contents 51 ?Purchasing Power Parity I. General Viewpoints The theory of purchasing 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 0