Macroeconomic Analysis
Econ 506 Fall 1998
C. Swanson
Dec. 1, 1998
Some mini-models that we have used without giving their due attention.
10. The Fisher Equation
Main features: (1) The nominal and real rates of interest are related by to each other by the inflation rate: i = r + p, where i is the nominal interest rate, r is the real interest rate and p is the rate of expected inflation. (2) This model/equation might be viewed as (a) a causal model: inflation expectations and the real interest rate, which are determined through different forces, together determine the nominal interest rate, or as (b) an identity: the real interest rate is the nominal interest rate (which is observable directly from bond prices) less the expected inflation rate (which can be obtained indirectly by surveying people).
11. Purchasing Power Parity
Main features: (1) The exchange rate is determined by the ratio of the price levels: e = Pdom/Pfor, where e is the exchange rate in domestic currency units per foreign currency unit, Pdom is the domestic price level, and Pfor is the foreign price level. Note that the units on both sides are (domestic currency units/foreign currency units). (2) The ratio is said to hold because goods should cost the same in different countries, once the exchange rate is accounted for. If a good was relatively more expensive in one country over a sustained period of time, a profit opportunity (but not an arbitrage opportunity) would arise for a merchant. (3) Because the equilibrating force is the possibility of trade, and since trade takes time, PPP is said to only hold in the long run, not in the short-run.
Problems. The dollar exchange rate is the value of the dollar in terms of a foreign currency unit. The price level is the value of the dollar in terms of domestic goods. (Really, the exchange rate and price level are measures of the reciprocals of respective values of the dollar.) It does not really make sense to say that the value of the dollar as measured by a foreign currency is determined by the value as determined by goods. The value of the dollar is determined simultaneously in both realms; whatever causes the dollar to gain value relative to domestic goods is likely to also cause it to gain value relative to the foreign currency and vice versa. We wouldn’t say that the price of carrots in San Francisco is determined by the price of carrots in New York City; we would say that the price of carrots is simultaneously determined in these two (and other) cities, although we would add that the price may differ in the two cities for a variety of reasons.
12. Pure exporters and the exchange rate
Main features: (1) Pure exporters always gain when the domestic currency depreciates and all else remains unchanged. Pure exporters always lose when the currency appreciates. Importers are affected in the opposite direction: pure importers lose when the dollar depreciates and gain when it appreciates. (2) The model has a profit function that is P(q) = ePfor(q)q – C(q), where P(q) is the profits (in dollars) for quantity q, e is the exchange rate (in dollars per foreign currency unit), Pfor(q) is the foreign demand function for the good, and C(q) is the cost function (in dollars) of producing at level q. Note that the units on both sides are dollars. When e increases, the optimizing q may change, but the entire profit function shifts upward. This proves that an increase in e (which is a devaluation of the dollar) raises the profits of an exporter.
Problems. The main problem with this model is whether it applies in any given circumstance. The internal logic is clear and imutable, but the assumptions are strong: (a) All revenues are from abroad and all costs are local, and (b) when the exchange rate changes, all else remains unchanged.
13. Money supply, asset demand and exchange rate changes
Main features: (1) Tight money in the U.S. raises the value of the dollar, and loose money lowers it. (2) The argument is that money tightening raises the interest rate on dollar denominated assets, making them more desirable. In order to obtain dollar denominated assets, dollars must be obtained in order to buy them. The demand for dollars therefore increases and the value of the dollar rises.
Problems. (a) The argument is a short-term story, not a long-term story. The value of a corporate stock share is determined largely by what is expected to happen to its value in the future. Slight delays in the issuance of new shares will reduce the current supply of shares temporarily, but are unlikely to have any short-run effects on the share price. Similarly, short-term variations in the quantity of dollars outstanding are unlikely to have any short-term effects on the value of the dollar, except in so far as they presage long-term changes in the quantity of outstanding dollars. (b) The argument is difficult to formalize.