andechangerateinthelongrun國(guó)際金融香港(參考版)
2025-03-29 15:16本頁(yè)面
【正文】 1 Price levels and Exchange Rate in the Long Run WONG Ka Fu 7th February 2023 2 Basic math review X=A/B ? ln X = ln A ln B Y=Y(x) ? d ln Y / dx = d lnY / dY ? dY / dx = (1/Y) (dY/dx) 3 Basic math review P=P(t) ? d ln P / dt = d lnP / dP ? dP / dt =(1/P) (dP/dt) Take the change of t (dt) from s to s+1. ? d ln P / dt = [1/P(s)] [P(s+1) P(s) /1] = [P(s+1) P(s) ] / P(s) = percentage change in P at time s. 4 Law of one price ?In a petitive markets ?free of 1. transportation costs and 2. official barriers to trade (such as tariffs), ?identical goods sold in different countries must sell for the same price when their prices are expressed ?in terms of the same currency. 5 Law of one price implies exchange rate ? For any good i sold in both home and foreign countries PHi = (EH/F) ? (PFi) ?Hence, the implied exchange rate is EH/F = PHi / PFi 6 Absolute Purchasing Power Parity (Absolute PPP) ?For a given reference modity basket sold in both the home and the foreign countries PH = (EH/F) ? (PF) ?Hence, the implied exchange rate is EH/F = PH / PF ?The implied exchange rate from the Economist’s Big Mac index 7 Relative PPP ?Prices and exchange rates change such that the ratio of each currency’s domestic and foreign purchasing powers are preserved. ? Hence, (EH/F,t EH/F,t1 )/ EH/F,t1 = ?H,t ?F,t where ?t = (Pt Pt1 ) / Pt1 8 Relative PPP ?If absolute PPP does not hold because of frictions and other factors and we have EH/F = ? PH / PF where ? is a constant that measures the difference from absolute PPP. EH/F(t) = ? PH (t) / PF(t) ln EH/F (t)= ln ? + ln PH (t) ln PF(t) Taking derivative with respect to t: dln EH/F (t)/dt = dln ? /dt + dln PH (t)/dt dln PF(t)/dt 9 Relative PPP ?Hence, (EH/F,t EH/F,t1 )/ EH/F,t1 = ?H,t ?F,t where ?t = (Pt Pt1 ) / Pt1 percentage change in EH/F,t = percentage change in PH,t percentage change in PF,t 10 Longrun exchange rate based on absolute PPP ? EH/F = PH / PF ? PH = MHs / L ( RH, YH ) ? PF = MFs / L ( RF, YF ) ?Moary policy = money supply 11 Effect of an increase in home money supply on LR EH/F MHs PH EH/F because PH = MHs / L ( RH, YH ) because EH/F = PH / PF 12 Effect of an increase in foreign money supply on LR EH/F MFs PF EH/F because PF = MFs / L ( RF, YF ) because EH/F = PH / PF 13 Effect of an increase in home interest rate on LR EH/F RH PH EH/F because PH = MHs / L ( RH, YH ) because EH/F = PH / PF LH because L ( RH, YH ) 14 Interest rate can change due to reasons other than moary policy For example: technology advancement may improve the profitability of investment and hence the interest rate willing to pay to borrow money to invest. Factors that are not already explicit but implicit in the L(R,Y) function 15 Effect of an increase in foreign interest rate on LR EH/F RF PF EH
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