Why Sterilization Matters
A central bank that buys or sells foreign currency changes the composition of its assets. Unless it takes a separate action to offset the payment, the transaction also changes the amount of domestic central-bank money in circulation. Sterilization is the separate domestic-asset operation used to offset that monetary-base effect. The distinction matters because two interventions of the same size can have different consequences for domestic liquidity, even though both change the central bank’s foreign-exchange holdings.
The earlier material on defending a peg establishes that a central bank can intervene by buying or selling foreign currency. Here the focus is the accounting: what happens to central-bank assets and liabilities, and what additional transaction changes an initially unsterilized intervention into a sterilized one? The balance-sheet calculations describe direct transactions. They do not, by themselves, establish how much the exchange rate will move.
A Simplified Central-Bank Balance Sheet
Use a simplified balance sheet with foreign-exchange reserves and domestic securities as assets, and the monetary base as a liability. The monetary base consists principally of currency held outside the central bank and commercial banks’ reserve balances at the central bank. In the examples, transaction values are stated in domestic currency, and any changes in the monetary base are changes in its liability to the public and banks.
Let \(q\) be the exchange-rate quotation in domestic-currency units per unit of foreign currency. If the central bank buys or sells \(F\) units of foreign currency, its transaction value in domestic currency is \(qF\). If it buys foreign currency, foreign assets rise by \(qF\); payment adds the same amount to domestic central-bank money. If it sells foreign currency, foreign assets and the monetary base fall by \(qF\), absent an offsetting operation.
Here \(B\) denotes the monetary base. These are the immediate transaction effects under the simplified assumptions that the central bank settles in domestic money, the foreign asset is recorded at the transaction’s domestic-currency value, and no other operation or valuation change occurs. They are not claims that every monetary aggregate or every market interest rate must change by exactly the same amount.
Worked Example: An Unsterilized Foreign-Currency Purchase
A central bank buys 20 million units of a foreign currency at an exchange rate of 1.25 domestic-currency units per foreign-currency unit. It makes no offsetting domestic-asset transaction. Find the change in the central bank’s foreign assets and monetary base, and show the balance-sheet effect.
Method and common mistake avoided. Convert the foreign-currency amount using the stated quote before recording the entries. The quote is domestic currency per foreign unit, so multiply by 1.25; dividing would reverse the quotation.
Step 1: Value the intervention. The domestic-currency value is \(20{,}000{,}000 \times 1.25 = 25{,}000{,}000\).
Step 2: Record the foreign-asset entry. The central bank acquires foreign assets worth $25,000,000 in domestic-currency terms, so foreign assets rise by $25,000,000.
Step 3: Record settlement. The central bank pays for the foreign currency by creating domestic central-bank money. The monetary-base liability rises by $25,000,000. Domestic securities do not change.
| Balance-sheet item | Change |
|---|---|
| Foreign assets | +$25,000,000 |
| Domestic securities | $0 |
| Monetary base liability | +$25,000,000 |
Check. Total assets increase by $25,000,000, and the monetary-base liability increases by the same amount. With no offsetting transaction, this purchase is unsterilized and the monetary base expands by $25,000,000.
How a Domestic-Asset Operation Sterilizes the Effect
To sterilize a foreign-currency purchase, the central bank can sell domestic securities. When a buyer pays for those securities, the payment reduces reserve balances at the central bank. The central bank’s domestic securities and monetary-base liabilities therefore fall together. If the sale is equal in domestic-currency value to the foreign-currency purchase, this second operation offsets the first operation’s monetary-base increase.
The direction reverses for a foreign-currency sale. Selling foreign reserves withdraws domestic money from circulation as payment reaches the central bank. To offset that contraction, the central bank can buy domestic securities. Its payment for those securities adds reserve balances back to the banking system. In either case, sterilization changes the composition of the central bank’s assets while neutralizing the direct change in the monetary base.
The identity is an accounting device, not a complete description of the central bank’s actual balance sheet. In practice, central banks may have other assets, liabilities, and capital, and foreign assets can change in domestic-currency value when exchange rates move. The transaction calculations below hold such valuation changes and other balance-sheet items constant so that the intervention and its offset can be isolated.
Worked Example: Fully Sterilizing a Foreign-Currency Purchase
A central bank buys 12 million units of a foreign currency at 0.80 domestic-currency units per foreign-currency unit. It then sells domestic securities worth exactly the transaction’s domestic-currency value. Find the monetary-base change and the changes in both asset categories.
Method and common mistake avoided. Calculate the foreign-currency purchase’s initial liquidity effect first, then record the domestic-security sale as a second transaction with the opposite effect on the monetary base. Do not treat the sale of securities as another injection of reserves.
Step 1: Value the foreign-exchange purchase. \(12{,}000{,}000 \times 0.80 = 9{,}600{,}000\) domestic-currency units.
Step 2: Record the purchase before sterilization. Foreign assets rise by $9,600,000, and payment increases the monetary base by $9,600,000.
Step 3: Record the domestic-security sale. The central bank sells securities worth $9,600,000. Domestic securities fall by $9,600,000, and the buyer’s payment reduces the monetary base by $9,600,000.
| Balance-sheet item | FX purchase | Security sale | Combined change |
|---|---|---|---|
| Foreign assets | +$9,600,000 | $0 | +$9,600,000 |
| Domestic securities | $0 | −$9,600,000 | −$9,600,000 |
| Monetary base liability | +$9,600,000 | −$9,600,000 | $0 |
Check. The combined change in assets is \(+$9{,}600{,}000-$9{,}600{,}000=0\), matching the zero change in the monetary base. The central bank ends with more foreign assets and fewer domestic securities, but the same monetary base.
Partial and Excessive Sterilization
The domestic-asset operation does not have to match the initial monetary-base effect. If its size is smaller, sterilization is partial and the monetary base still changes. If it is larger, the operation more than offsets the initial effect: the monetary base moves in the opposite direction from its initial change. The sign of each transaction matters as much as its size.
For a foreign-currency sale, the initial effect is a contraction. A domestic-security purchase offsets that contraction, but a smaller purchase leaves some contraction in place. For a foreign-currency purchase, the initial effect is an expansion. A domestic-security sale offsets that expansion; a sale larger than the purchase’s domestic-currency value produces a net contraction.
Worked Example: Measuring Partial Sterilization of a Reserve Sale
A central bank sells 6 million units of foreign currency at 1.30 domestic-currency units per foreign-currency unit. It uses part of the proceeds to buy domestic securities worth $5,850,000. Find the initial monetary-base effect, the final change, and the share of the initial effect offset.
Method and common mistake avoided. Treat the foreign-currency sale and domestic-security purchase as separate steps. A security purchase adds reserves; it does not add to the initial contraction caused by the reserve sale.
Step 1: Calculate the value of the foreign-currency sale. \(6{,}000{,}000 \times 1.30 = 7{,}800{,}000\) domestic-currency units.
Step 2: Find the initial monetary-base effect. The sale withdraws domestic money, so the initial change is \(-$7{,}800{,}000\).
Step 3: Add the domestic-security purchase. The central bank buys securities worth $5,850,000, increasing the monetary base by $5,850,000. The net change is \(-$7{,}800{,}000 + $5{,}850{,}000 = -$1{,}950{,}000\).
Step 4: Calculate the offset share. \($5{,}850{,}000 \div $7{,}800{,}000 = 0.75\), so 75% of the initial contraction is offset.
Check. Because the offset is positive but smaller than the original $7,800,000 contraction, the final change must remain negative. The result, a $1,950,000 contraction, has the correct sign. The intervention is partly sterilized, not fully sterilized.
What the Accounting Does—and Does Not—Show
The balance-sheet entries establish the direct change in the monetary base under the stated assumptions. They do not establish that broad money, domestic interest rates, or the exchange rate will remain unchanged under sterilization. Those outcomes depend on other economic conditions and on how financial-market participants respond. Similarly, an unsterilized intervention’s increase or decrease in the monetary base is not, by itself, a complete prediction of the exchange-rate outcome.
A central bank’s domestic-security operation may affect the supply of those securities held outside the central bank. Thus, even when the monetary base is held constant, the asset composition held by the public and the market’s response can differ from the unsterilized case. Keep the two questions separate: Was the monetary-base effect offset? is an accounting question; How did the exchange rate respond? requires further economic analysis.
For a clean calculation, use the following sequence:
Confirm whether the rate is domestic currency per foreign currency or the reverse before converting the intervention amount.
For a domestic-per-foreign quote, multiply the foreign-currency amount by the quoted rate.
A foreign-currency purchase expands the base; a sale contracts it, absent an offset.
A domestic-security sale contracts the base; a purchase expands it. Combine the signed changes.
Full sterilization gives zero net change; partial sterilization leaves a change in the original direction; an excessive offset reverses the net direction.
A frequent exam trap is to identify an intervention as sterilized merely because the central bank also trades domestic securities. The direction and size of that second trade determine whether it offsets the initial effect. For example, selling domestic securities after selling foreign reserves makes the monetary-base contraction larger, not smaller. To sterilize a foreign-reserve sale, the central bank must buy domestic securities.
These distinctions are aligned with the SOA VEE Economics (Validation by Educational Experience) syllabus. In a problem, state the exchange-rate quotation, show the domestic-currency conversion, record each balance-sheet transaction separately, and then calculate the net monetary-base change.
Check Your Understanding
For each problem, track the intervention and any domestic-asset operation separately. Assume transaction values are recorded at the stated exchange rate and ignore valuation changes.
- A central bank buys 4 million units of foreign currency at 1.50 domestic-currency units per foreign unit and does not sterilize. What is the monetary-base change? (Answer: an increase of $6,000,000.)
- A central bank buys 12 million units of foreign currency at 0.80 domestic-currency units per foreign unit, then sells domestic securities worth $7,200,000. What is the net monetary-base change, and what share of the initial effect is offset? (Answer: an increase of $2,400,000; 75% offset.)
- A central bank sells 3 million units of foreign currency at 1.20 domestic-currency units per foreign unit, then buys domestic securities worth $2,700,000. What is the net monetary-base change, and what share of the initial contraction is offset? (Answer: a decrease of $900,000; 75% offset.)
- A central bank buys 10 million units of foreign currency at 1.10 domestic-currency units per foreign unit, then sells domestic securities worth $12,100,000. What is the net monetary-base change, and is the intervention fully, partly, or excessively sterilized? (Answer: a decrease of $1,100,000; the operation is excessively sterilized.)
- A central bank begins with a monetary base of $90 million. It sells 5 million units of foreign currency at 1.40 domestic-currency units per foreign unit and then buys domestic securities worth $4.2 million. What is the ending monetary base and the percentage of the initial contraction offset? (Answer: $87.2 million; 60% offset.)