国际金融(香港大学,WONG Ka Fu) pricee

21
If MHS is growing at a rate of
PH grows at a rate of because PH = MHs / L ( RH, YH ) I.e., expect H,t+1 = or , H,t+1 e = Hence, RH,t - RF,t = H,t+1e - F,t+1e = if F,t+1e = 0
Money supply level : MHs (t) Growth rate : (MHs (t+1) - MHs (t) ) / MHs (t) Define y(t) = ln( MHs (t) ) dy(t)/d(t) = d ln( MHs (t) )/dt = dy(t)/d MHs (t) d MHs (t) /dt = 1/ MHs (t) d MHs (t) /dt dt = t+1 - t = 1
22
If MHS is growing at a rate of
Log(MHS)
Slope =
t0 23
If MHS is growing at a rate of
RH
RH1
t0 24
If MHS is growing at a rate of
Log (PH)
Slope =
27
If the rate of MHS growth increases from to ( + )
Suppose RF,t fixed and F,t+1e = 0 because a stable monetary policy, for example.
RH,t increases by because H,t+1e is expected to increase by . Note that, however, MHS does not change at time t0 -only the future growth rate Hence, PH has to jump from
7
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
5
Absolute Purchasing Power Parity (Absolute PPP)
For a given reference commodity 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
Price levels and Exchange Rate in the Long Run
WONG Ka Fu 7th February 2001
1
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)
20
Fisher effect
Uncovered interest parity: RH,t = [EH/F,t+1e - EH/F,t ] / EH/F,t + RF,t let t+1 e = (Pt+1e - Pt ) / Pt and t+1 = (Pt+1 - Pt ) / Pt Relative PPP : (EH/F,t+1 - EH/F,t )/ EH/F,t = H,t+1 - F,t+1 (EH/F,t+1e - EH/F,t )/ EH/F,t = H,t+1e - F,t+1e RH,t - RF,t = H,t+1e - F,t+1e
PF
EH/F
because EH/F = PH / PF
17
Long-run exchange rate based on absolute PPP
EH/F = PH / PF PH = MHs / L ( RH, YH ) PF = MFs / L ( RF, YF )
EH/F = (MHs / MFs ) [L ( RF, YF ) /L ( RH, YH )]
9
Long-run exchange rate based on absolute PPP
EH/F = PH / PF PH = MHs / L ( RH, YH ) PF = MFs / L ( RF, YF )
Monetary policy = money supply
10
Effect of an increase in home money supply on LR EH/F
12
Effect of an increase in home interest rate on LR EH/F
RH
LH because L ( RH, YH ) because PH = MHs / L ( RH, YH )
PH
EH/F
because EH/F = PH / PF
13
Interest rate can change due to reasons other than monetary policy
2
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.
YH
LH because L ( RH, YH ) because PH = MHs / L ( RH, YH )
PH
EH/F
because EH/F = PH / PF
16
Effect of an increase in foreign output on LR EH/F
YF
LF because L ( RF, YF ) because PF = MFs / L ( RF, YF )
MHs PH
EH/F because PH = MHs / L ( RH, YH ) because EH/F = PH / PF
பைடு நூலகம்11
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
18
How is long-run exchange rate determined?
Anything that raises (lowers) LH lowers (raises) EH/F Anything that lowers (raises) LF lowers (raises) EH/F
t0 25
If MHS is growing at a rate of
Log(EH/F)
Slope =
t0 26
If MHS is growing at a rate of ( + )
PH grows at a rate of ( + ) because PH = MHs / L ( RH, YH ) I.e., expect H,t+1 = ( + ); or , H,t+1 e = ( + ) Hence, RH,t - RF,t = H,t+1e - F,t+1e = ( + ) if F,t+1e = 0
4
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
Factors that are not already explicit but implicit in the L(R,Y) function For example: technology advancement may improve the profitability of investment and hence the interest rate willing to pay to borrow money to invest.