MACROECONOMICS: THE OPEN ECONOMY (II); PURCHASING POWER PARITY, DORNBUSCH OVERSHOOTING MODEL

ABSOLUTE PURCHASING POWER PARITY The Absolute Law of One Price (LOP) states that, for a

perfectly homogeneous good in a World without transaction costs or transport costs, the price of the good will be the same (when converted into a common currency) in all countries.

This is because of arbitrage: if there is a real price discrepancy, people will buy the good at a low price in one area and sell it for the higher price in the other.

Hence, the Absolute version of Purchasing Power Parity (PPP) can be derived: it states that:

EP*/P = 1 An example of trying to measure absolute PPP is The

economist’s ‘Big Mac Index’ Alternatively, one could try and use an index of prices to

get an idea – although a problem is that services can’t be traded (haircuts, for example).

The absolute PPP doesn’t tend to hold, as the assumptions are violated. However, one can relax the absolute LOP.

RELATIVE PURCHASING POWER PARITY The Relative LOP argues that, rather than there

being equal prices, there will be a constant deviation of prices from one time period to another – should there be any deviation in price.

The absolute LOP implies this, but this does not imply the absolute LOP, hence it is ‘weaker’.

It can be derived thusly: P = EP* (absolute PPP) [Taking natural Logs]: lnP = lnE + lnP* [Taking the time derivative]: ė = π – π* (Relative

PPP) Hence, the change in exchange rate over time is

equal to the inflation rate differential. Kassel used this method to decide what ex. Rate to

peg currencies at when the Gold Standard resumed post-WW1.

TESTING RELATIVE PPP Studies of relative PPP have to be conducted after 1972 (the

collapse of Bretton-Woods). Mark P. Taylor attempted to measure relative PPP by testing: q = ė + π* - π qt = βqt-1 + εt As qt-1 can be expressed as the stochastic error term for each

previous period, we observe that: qt = βεt + β2εt-1 + ... Thus β must be < 1, so that the shocks diminish over time and

the system is MEAN REVERTING. Studies have shown that β = 0.85, so while the system IS mean

reverting, there is a high degree of persistence. Indeed, what is often the case is that we observe that ė is

usually LARGER than π – π*, AND the fundamental determinants of inflation (Ms, G, y-ye).

I.e., there is EXCHANGE RATE OVERSHOOTING. Chartist analysts have attempted to look at the data and find

patterns which explain it, but it is an unconvincing approach. The Dornbusch overshooting model is more rigorous.

DORNBUSCH OVERSHOOTING MODEL Following model of the economy: IS: y = -ar + b[e+P*-P] + cg LM: M – P = dr + fy UIP: r = r* + ėe AS: Ṗ = φ(y - ȳ) Rational Expectations: ė = ėe

Through re-arranging the equations (YOU DON’T NEED TO DO THIS), we find:

ė = f (e [+], P [+], M [-], ... ) EQ: 1 Ṗ = h (e [+], P [-], M [+], ... ) EQ: 2

DORNBUSCH OVERSHOOTING MODEL We therefore have a system of two differential

equations in e and P. To obtain the loci of equilibrium points, we set the time derivatives equal to zero (YOU DON’T NEED TO DO THE WORKING OUT FOR THIS)

We find that: e = j(P [-], M [+], ... ) : EXCHANGE RATE LOCUS e = k(P [+], M [-], ... ) : PRICE LOCUS This means that the Ex. Rate locus will slope

downwards and shift UP/RIGHT after a monetary expansion + arrows of motion will point AWAY from the locus ( due to the sign of ‘e’ in EQ: 1).

It also means that the Price Level Locus will slope upwards and shift DOWN/RIGHT after a monetary expansion + arrows of motion will point TOWARD the locus (due to the sign of ‘P’ in EQ: 2).

Hence, there is a SADDLEPATH equilibrium: only ONE path will lead to equilibrium, all others will diverge.

DORNBUSCH OVERSHOOTING MODEL: ARROWS OF MOTION

45ė = 0

Ṗ = 0e = P

e

P

DORNBUSCH OVERSHOOTING MODEL: MONETARY EXPANSION (ONLY THING WE’LL BE EXAMINED ON)

45 ė = 0

Ṗ = 0

e = Pe

P

ė = 0

Ṗ = 0

Saddlepath Equilibrium

eA

eB

eC

PA PC

A

B

C

TIME LAG

DORNBUSCH OVERSHOOTING MODEL The diagram shows the effects of a monetary

expansion. Initially, the exchange rate locus (RED) shifts

upwards and rightwards, and the Price level locus (BLUE) shifts rightwards and downwards.

However, because we have assumed STICKY PRICES, we are initially stuck at PA.

The only exchange rate we can take, if we wish to converge on the equilibrium point (C), therefore is eB as it is on the SADDLEPATH. Any other exchange rate at that price will diverge from C.

Hence, as time passes, PA increases to PB. Thus, the exchange rate initially OVERSHOOTS it’s

long-run equilibrium value before returning to it. However, the ‘Random Walk’ model (a crude model

that states et = et-1 + μt ) is empirically BETTER.