CLASSICAL THEORY OF EXCHANGE RATES =

QUANTITY THEORY OF MONEY PLUS

PURCHASING POWER PARITY THEORY

QUANTITY THEORY: MV = PY . It implies that price increases are caused by increases in M, for given Y and V:

 P = M V / Y (1)

 P^f = M^f V^f / Y^f (2)

Evidence: this is correct over long periods of time.

PPP (PURCHASING POWER PARITY): Prices of comparable goods should not be different in two locations when expressed in the same currency:

P = S P^f (3)

Price of home goods in $ = spot exchange rate ($ per foreign) x Price of foreign goods (in foreign currency).

(3) implies: S = P / P^f (3’)

i.e. the spot exchange rate depend on relative domestic and foreign prices.

(3) implies also: RER = S P^f / P = 1 (4)

i.e. the real exchange rate (RER) is constant.

(3’) expressed in growth rates implies that:

(S_t - S_t-1)/S_t-1 = (P_t - P_t-1)/P_t-1 - (P^f_t- P^f_t-1)/P^f_t-1 (5)

i.e. the rate of depreciation of the domestic currency is equal to the difference between home inflation and foreign inflation.

Putting PPP (3’) and the quantity theory (1 & 2) together, we get:

S = (M/M^f) (V/V^f)(Y^f/Y) (6)

The domestic currency depreciates (S rises) if we issue more money than the other country (M rises more than M^f).

Evidence on (6) in Figure 1.

Consider next the relation between depreciation and money growth; taking rates of growth of (6) we get:

(S_t - S_t-1 ) / S_t-1 = (M_t - M_t-1 ) / M_t-1 + (M^f_t - M^f_t-1 ) / M^f_t-1 (7)

(+ output growth differentials across countries @ 0)

Evidence in Figure 2: (7) is a works pretty well for long periods.

EXCHANGE RATES AND PPP IN THE SHORT RUN

The PPP works well for long periods of time but not so well for short term movements. According to the PPP, the RER should be constant over time but, in reality, it is not. See Figure 6 for some evidence on Germany, Japan and Mexico.

PPP is based on the idea of goods arbitrage.

Reasons for the failure of PPP in the short run:

1. The CPI of different countries are not comparable since they include very different goods.

2. The CPI includes many goods that are not traded (such as services); the PPP will not hold for these goods.

3. PPP (or the Law of One Price, LOP) holds better for homogenous commodities that are traded internationally (gold, oil, agricultural commodities, raw materials).

4. Even for homogenous goods, the PPP might hold very well. Example: The price of Big Macs (see the Economist’s Big Mac standard).

5. If firms can "price discriminate" between domestic and foreign markets, PPP/LOP will not hold for homogenous goods. The price of German (Japanese) cars is very different in the US relative to Germany (Japan). Price discrimination is feasible only under some conditions.

6. If goods are not homogenous (Japanese cars are not the same cars as US cars), the US price in dollars of Japanese cars does not have to be equal to the price in dollars of US cars. Moreover, changes in the nominal exchange rates will affect the relative price of Japanese versus US cars.

Some examples: GM and the Dollar in the 1980s; Japanese cars in the US in the 1990s.