Why the Exchange-Rate Regime Changes the Adjustment
A shift in demand for a country’s currency does not have the same immediate effect under every exchange-rate regime. With a floating rate, the exchange rate adjusts to clear the foreign-exchange market. With a fixed rate, the central bank intervenes to maintain the announced rate, so the shock instead changes official reserves and, unless the intervention is sterilized, the domestic monetary base.
The direction of the adjustment depends on how the exchange rate is quoted. This tutorial uses \(E\) to mean units of domestic currency per one unit of foreign currency. For example, if \(E=1.50\), one unit of foreign currency costs 1.50 units of domestic currency. A fall in \(E\) is an appreciation of the domestic currency; a rise is a depreciation.
The market relationships below assume that the price of foreign currency is \(E\), and quantities are measured in units of foreign currency. Demand for foreign currency slopes downward in \(E\), while its supply slopes upward. A positive domestic-currency demand shock shifts foreign-currency supply to the right. A negative shock shifts it to the left. These are short-run comparative-static results: they hold other factors affecting currency demand and supply constant.
Under a floating regime, the central bank does not defend a particular exchange rate. Under a fixed regime, it stands ready to buy or sell currencies at the announced rate. In discussing money-supply effects, let \(M\) denote the domestic monetary base. Assume intervention is unsterilized unless stated otherwise: no offsetting domestic asset transaction is made. This gives a one-for-one change in the monetary base, not necessarily in broader measures of money that depend on bank lending and other behavior.
Floating Rates: The Exchange Rate Absorbs the Shock
When the domestic currency becomes more desirable, foreign-exchange sellers offer more foreign currency to obtain it. With the central bank allowing the rate to float, the domestic currency appreciates: \(E\) falls. When demand for the domestic currency declines, less foreign currency is offered in exchange for it, and the domestic currency depreciates: \(E\) rises. In the basic floating-rate model, no intervention is needed, so this direct adjustment does not mechanically change official reserves or the monetary base.
Worked Example: A Positive Currency-Demand Shock Under a Float
In a hypothetical floating-rate economy, foreign-exchange demand and supply are measured in millions of foreign-currency units. Initially, demand is \(Q_D=180-40E\) and supply is \(Q_S=60+40E\). A positive shock to demand for the domestic currency shifts foreign-currency supply to \(Q'_S=84+40E\), while demand is unchanged. Find the initial and new exchange rates and quantities, and interpret the change.
Method and assumptions. Equate foreign-currency demand and supply at each equilibrium. The central bank does not intervene, and the schedules are linear over the relevant range.
Initial equilibrium. Set the original schedules equal:
Thus \(120=80E\), so \(E=1.50\). Substitution into either schedule gives \(Q_D=180-40(1.50)=180-60=120\) million foreign-currency units. Supply gives \(Q_S=60+40(1.50)=120\), a check on the equilibrium.
New equilibrium. Equate demand to the shifted supply:
Thus \(96=80E\), so \(E=1.20\). The quantity is \(Q_D=180-40(1.20)=180-48=132\) million. Shifted supply also gives \(Q'_S=84+40(1.20)=132\) million.
The quoted exchange rate falls from 1.50 to 1.20, a change of \((1.20-1.50)/1.50=-0.20\), or a 20% fall in the domestic-currency price of foreign currency. The domestic currency appreciates. Its reciprocal foreign-currency value rises from \(1/1.50=0.6667\) to \(1/1.20=0.8333\), a 25% increase. The two percentage changes differ because they use reciprocal quotes and different starting values. There is no intervention in this example, so official reserves and the monetary base do not change mechanically. The common mistake is to describe a fall in \(E\) as a domestic-currency depreciation; with this quote, it is an appreciation.
Fixed Rates: Intervention Replaces Exchange-Rate Adjustment
At a fixed rate, the central bank supplies or absorbs currency as needed to prevent the market exchange rate from moving away from the peg. If demand for domestic currency rises, the market would otherwise push \(E\) down. To resist that appreciation, the central bank buys foreign currency and pays by issuing domestic currency. Official foreign reserves rise, and an unsterilized purchase expands the monetary base.
If demand for domestic currency falls, the market would otherwise push \(E\) up. To resist depreciation, the central bank sells foreign currency from its reserves and receives domestic currency in payment. Reserves fall, and the domestic currency received is withdrawn from circulation, reducing the monetary base if the intervention is unsterilized.
The domestic-currency amount follows directly from the exchange-rate quote: one unit of foreign currency costs \(\bar E\) domestic units, so \(x\) foreign units cost \(\bar E x\) domestic units. The intervention also matches the market imbalance at the peg. For example, if buyers want 25 million more foreign-currency units than private sellers offer, the central bank must supply those 25 million units to maintain the rate.
Worked Example: Defending a Peg After Domestic-Currency Demand Falls
A hypothetical central bank maintains a peg of \(E=1.20\) domestic units per foreign unit. Before a shock, private demand and supply of foreign currency are both 100 million foreign units at the peg. A negative shock to demand for the domestic currency leaves private demand for foreign currency at 125 million, while private supply remains 100 million. Initial reserves are 600 million foreign units and the monetary base is 900 million domestic units. Find the intervention and the post-intervention balances, assuming no sterilization.
Method. Calculate the excess demand for foreign currency at the peg. The central bank must sell that amount of foreign currency, receiving domestic currency at the fixed rate.
At the peg, excess demand for foreign currency is \(125-100=25\) million units. The central bank sells 25 million foreign units from its reserves. The domestic-currency payment it receives is \(25(1.20)=30\) million domestic units.
Reserves after intervention are \(600-25=575\) million foreign units. The unsterilized sale withdraws 30 million domestic units, so the monetary base becomes \(900-30=870\) million domestic units.
The accounting check is consistent: private market participants receive the 25 million foreign units they demand in excess of private supply, while the central bank’s reserves fall by exactly 25 million. The monetary base falls by the domestic-currency value of the sale, 30 million. The common mistake is to add the payment to the monetary base: the central bank receives domestic currency and removes it from circulation, so the unsterilized base change is negative.
Sterilization: Offsetting the Monetary-Base Effect
The central bank can offset the monetary-base effect of foreign-exchange intervention through a domestic asset transaction. This is called sterilization. For example, after buying foreign currency and issuing domestic currency, the central bank can sell domestic securities and take domestic currency back out of the banking system. After selling foreign currency and receiving domestic currency, it can buy domestic securities and return domestic currency to the system.
Sterilization does not undo the foreign-exchange transaction. The central bank still changes its foreign reserves and intervenes at the peg. It offsets the change in domestic assets so the monetary base is unchanged in the simplified accounting model. By contrast, unsterilized intervention leaves the monetary-base change in place.
Worked Example: A Positive Currency-Demand Shock with Sterilization
At a hypothetical peg of \(E=2.00\) domestic units per foreign unit, a positive shock to demand for the domestic currency creates excess private supply of 40 million foreign units at the peg. The central bank buys this excess supply. Initial foreign reserves are 250 million foreign units and the monetary base is 1,000 million domestic units. It then sterilizes the intervention by selling domestic securities. Find the reserve change, the initial monetary-base effect, and the final monetary base.
Method. First account for the foreign-exchange purchase and its domestic-currency payment. Then apply the offsetting domestic-security sale.
The central bank buys 40 million foreign units. The domestic currency issued in payment is \(40(2.00)=80\) million. Before sterilization, reserves therefore rise by 40 million foreign units, from 250 to \(250+40=290\) million, and the monetary base rises from 1,000 to \(1,000+80=1,080\) million domestic units.
To sterilize, the central bank sells domestic securities and receives 80 million domestic units. This reduces the monetary base by 80 million, from 1,080 back to 1,000 million. Final reserves are 290 million foreign units; the final monetary base is 1,000 million domestic units.
The check is that the security sale offsets the full 80 million domestic-currency injection, but does not reverse the 40 million increase in foreign reserves. A common error is to report no reserve change after sterilization. Sterilization offsets the monetary-base effect, not the foreign-exchange intervention itself.
Deriving the Fixed-Rate Monetary Effect
The intervention accounting can be derived from the central bank’s transactions. Consider a central bank purchasing \(x\) foreign units at the peg \(\bar E\). The foreign asset side of its balance sheet increases by \(x\), and the payment creates domestic monetary liabilities of \(\bar E x\). If the purchase is unsterilized, there is no offsetting change in domestic assets. Thus the change in the monetary base is positive. Selling foreign currency reverses each transaction.
This derivation relies on payment being settled in domestic currency and on the intervention being unsterilized. If the central bank offsets the transaction with a domestic asset sale or purchase, the final monetary-base change is smaller or zero. Nor does the accounting identity by itself establish a particular change in bank lending, prices, or output; those outcomes require additional behavioral assumptions.
Compare the Regimes and Avoid Sign Errors
| Shock to demand for domestic currency | Floating regime | Fixed regime, unsterilized |
|---|---|---|
| Increase | Domestic currency appreciates; \(E\) falls. No required intervention. | Central bank buys foreign currency; reserves and monetary base rise. |
| Decrease | Domestic currency depreciates; \(E\) rises. No required intervention. | Central bank sells foreign currency; reserves and monetary base fall. |
A reliable way to solve these problems is to name the currency being demanded, translate the shock into a shift in the foreign-exchange market, and then apply the regime. At a peg, ask which currency the central bank must buy or sell to meet the imbalance. Finally, trace the payment separately from the reserve transaction. This prevents a market-quantity answer from being confused with a monetary-base answer.
With \(E\) in domestic currency per foreign unit, a rise in \(E\) is domestic-currency depreciation; a fall is appreciation.
More demand for domestic currency means more foreign currency is offered in exchange; less demand means less foreign currency is offered.
A float lets \(E\) adjust. A peg requires intervention to supply or absorb the excess foreign currency at the announced rate.
Purchasing foreign currency raises reserves and, without sterilization, the monetary base. Selling foreign currency lowers both.
The most frequent exam trap is to reason from “currency demand increased” directly to a rising exchange-rate number without checking the quote. Under the convention here, increased domestic-currency demand makes the domestic currency more valuable, so \(E\), the domestic-currency price of foreign currency, falls. Another trap is treating sterilization as if it reverses the reserve transaction. It offsets the monetary-base effect by changing domestic assets; the foreign-reserve change remains.
Check Your Understanding
For each problem, use the quote of domestic-currency units per foreign-currency unit. Assume unsterilized intervention unless the question says otherwise.
- Under a float, demand for the domestic currency rises and \(E\) moves from 3.00 to 2.70. What is the percentage change in \(E\), and what happens to the domestic currency? (Answer: \(E\) falls 10%; the domestic currency appreciates.)
- At a peg of \(E=0.80\), a negative domestic-currency demand shock creates excess demand for 12 million foreign units. By how much do reserves and the monetary base change under unsterilized intervention? (Answer: Reserves fall by 12 million foreign units; the monetary base falls by 9.6 million domestic units.)
- At a peg of \(E=1.25\), increased demand for the domestic currency creates excess supply of 24 million foreign units. The central bank buys the excess and does not sterilize. State the changes in reserves and the monetary base. (Answer: Reserves rise by 24 million foreign units; the monetary base rises by 30 million domestic units.)
- A central bank at a peg of \(E=4.00\) sells 15 million foreign units to resist depreciation, then sterilizes fully by buying domestic securities. What is the net change in reserves and the final change in the monetary base? (Answer: Reserves fall by 15 million foreign units; the final monetary-base change is zero.)
- In a floating-rate market, foreign-currency demand is \(Q_D=150-20E\), while initial supply is \(Q_S=30+20E\). A positive shock to domestic-currency demand shifts supply to \(Q'_S=50+20E\). Find the initial and new equilibrium exchange rates and the direction of the change. (Answer: Initially \(150-20E=30+20E\), so \(E=3.00\); after the shift, \(150-20E=50+20E\), so \(E=2.50\). The domestic currency appreciates.)