Closed Economy Fixed Reserves (Floating Exchange)

Summary

Assumptions

  • With no intervention ΔR=0 thus ΔM=DCE
  • Four way equivalence theorem
    1. Purchasing power parity
      • In all three case the assumption is spot rate of excahnge at any date is underpinned by relative price levels in the two countries
    2. International Fisher Effect
      • Assumption of capital is mobile expected real rates of return should be equal

Model/Theory

Four way equivalence theorem

  1. Purchasing power parity -
    • explained by 
      1. aggregate price determination where you fix exchange rates to determine domestic money prices and fix reserves to predict exchange rate where equilibriums are both governed by PPP. where e=P/P*=(M/ky)/(M*/ky*)
      2.  Goods arbitrage but problems include 1. not all goods are traded 2. barriers to trade exist 3. not all commodities exhibit a high degree of substitutability. Further difficulty is why e rather than P adjusts.
      3. Demand for foreign exchange to buy imports (Z) = Supply from the resulting exports (X)
  2. International Fisher effect
    • Differences in nominal interest rates = differences in expected inflation.
  3. Interest rate parity
    • US exporter till receive £X at t=1
    • Could either do a forward foreign transaction f_0.X
    • Or borrow a loan, convert at spot and invest in US money market for X/(1+i_£).s_0(1+i_$)
    • These equate and simplify to the interest rate parity relationship.
  4. Expectations theory of exchange rates
    • Says that expected spot rate = unbiased predictor of the future spot rate. 
  5. Fisher open hypothesis

Predictions

Four way equivalence theorem

  1. Expected change in spot = Difference in expected inflation

Evidence

Only the covered interest rate parity holds all the time.

Evaluation

Two scenarios when a closed economy model is appropriate:

  1. Unified world economy employing a uniform currency or its close approximation fixed exchange rates pegs under the IMF from 1945 to 1971
  2. National currency to be linked to other currencies by a completely flexible exchange rates.

Four-way equivalence theorem - equilibrium but don't necessarily hold all the time. 

  • Purchasing power parity 
    • Problems include 1. not all goods are traded 2. barriers to trade exist 3. not all commodities exhibit a high degree of subsitutability 
    • Further difficulty is why e rather than P adjusts. 
  • Expectations
    • However, this assumes an absence of risk Thus the unbiased forward rate condition may not hold.