Under fixed exchange rates, a country's monetary policy is constrained by the need to maintain the peg; policy cannot be used for stabilization without abandoning the peg. Under floating rates, monetary policy is free to target inflation and employment. Intermediate regimes (bands, crawling pegs) offer flexibility at the cost of complexity. The choice of regime reflects a tradeoff between monetary autonomy and exchange rate stability.
From your study of interest rate parity, you know that capital markets impose a tight constraint: if a country's interest rate differs from the foreign rate, capital flows until that gap closes (adjusted for expected exchange rate changes). From monetary policy tools, you know that central banks set short-term interest rates to influence inflation and output. The exchange rate regime is the key mediating variable between these two forces — it determines whether the central bank is free to use interest rates for domestic stabilization, or whether rates must be devoted to defending the exchange rate.
Under a fixed exchange rate regime, the central bank commits to buying or selling its currency at a fixed price in terms of foreign currency. Maintaining this peg requires that the domestic interest rate closely track the foreign interest rate — specifically, uncovered interest parity says any gap creates capital flows that would break the peg. If a recession calls for lower interest rates, cutting them would trigger capital outflows as investors seek higher returns abroad. The resulting demand to sell domestic currency would push the exchange rate down, requiring intervention (selling foreign reserves to buy domestic currency). This can only continue until reserves are exhausted. The fundamental constraint is that you cannot simultaneously fix the exchange rate, maintain free capital flows, and use monetary policy independently — this is the impossible trinity (or Mundell-Fleming trilemma). A fixed-rate country with open capital markets sacrifices monetary independence.
Under a floating exchange rate regime, the exchange rate adjusts freely to clear the foreign exchange market. This liberates monetary policy: the central bank can cut rates to fight recession without worrying that the resulting capital outflows will create a defense burden — the exchange rate simply depreciates, which itself provides an additional stimulus channel by boosting export competitiveness. The cost is exchange rate volatility, which creates uncertainty for firms engaged in international trade and investment. Currency mismatches — where firms or governments borrow in foreign currency but earn in domestic currency — can turn a depreciation into a solvency crisis if the exchange rate moves sharply. This is why "fear of floating" is common in emerging markets even when they officially claim floating regimes.
Intermediate regimes — crawling pegs (the fixed rate is adjusted periodically according to a formula), currency bands (a range within which rates float freely), and managed floats (the central bank intervenes when moves become too large) — attempt to balance the two extremes. A crawling peg can accommodate inflation differentials without speculative crises, while a band provides some shock absorption while anchoring expectations. In practice, the choice of regime reflects a country's circumstances: trade openness (more open economies benefit more from exchange rate stability), inflation history (countries with poor monetary credibility use pegs as commitment devices), debt structure (countries with foreign-currency debt fear depreciation), and financial depth (more sophisticated financial markets can absorb volatility). The European Monetary Union represents the extreme fixed-rate case: a common currency completely eliminates exchange rate adjustment within the zone, requiring that fiscal transfers or labor mobility substitute for exchange rate flexibility as a shock absorber.