Impossible trinity

Why can no country fix its currency, open its borders to capital and set its own rates?

Three things a government might reasonably want. A stable exchange rate, so importers and exporters can plan. Open capital markets, so savings and investment can find each other across borders. And an interest rate set at home, so the central bank can cool a boom or soften a slump.

Each is defensible on its own. Any two can be had together, and real countries hold each of the three possible pairs today. But no country holds all three, and the claim is stronger than "it is difficult" — the combination is not available at any price. What makes it impossible rather than merely expensive?

Resist the urge to look for a cause. This is not a story about markets punishing bad policy; it is a constraint, and the way to see a constraint is to assume the forbidden combination and watch it contradict itself.

So suppose a country has all three. Capital moves freely, the exchange rate is fixed, and the central bank has just set its policy rate two points above the rate abroad.

What does an investor abroad see? A deposit at home pays two points more, and the fixed rate means converting in and out risks nothing — the government has promised the rate will not move. What is the right size of that trade? There is no natural limit: a better return with no offsetting risk, so the sensible position is as large as the investor can fund.

Money therefore floods in. Now look at the central bank's obligation. To hold the rate fixed it must buy the incoming foreign currency and hand over domestic currency in whatever quantity is offered — that is what defending a peg means. But handing over domestic currency is creating domestic money. The money supply expands, and it expands until the domestic interest rate is pushed back down to the foreign one.

Follow the logic once more in reverse. Suppose it sets the rate two points below. Money leaves, the bank must sell foreign reserves to hold the peg, the money supply contracts, and the domestic rate is dragged back up — until the reserves run out, at which point the peg goes instead.

Either way the third choice was never a choice. The central bank's rate ends up equal to the foreign rate, and the only thing it decided was how much of the adjustment happened through the money supply before the market did it for them. That is the whole proof: the peg plus open capital determines the interest rate, so there is no room left to set one.

Now the pairs make sense as the three ways of relaxing exactly one assumption. Give up the fixed rate — and the exchange rate absorbs the differential by moving, which is what a floating currency does. Give up open capital — and the arbitrage is blocked at the border, which is how a country can run its own rate behind a managed exchange rate. Give up the independent rate — and you accept whatever the anchor currency's central bank decides, which is what a currency board does, and what a member of a currency union does.

Each corner is occupied. Hong Kong has run a currency board since 1983, and its rates track the United States because that is the price of the peg. Euro area members gave up national policy rates entirely. Floaters like Canada set their own rates and accept a moving currency. Where a country has tried to hold all three, the resolution has been forced rather than chosen — Britain's exit from the exchange rate mechanism on 16 September 1992 followed an attempt to keep a peg and open capital while wanting rates its economy could bear.

One honest qualification. The trilemma is an argument about whether a policy rate can differ, not about how much good it does. Work in the past decade, most prominently by Hélène Rey, argues that a global financial cycle transmits through open capital markets so strongly that even a floating currency buys only partial autonomy — a dilemma rather than a trilemma. That debate is live, and this walk-through does not settle it.

The three corners are idealisations, not the actual menu. Real countries sit at intermediate points: managed floats, partial capital controls, heavy intervention. The constraint then binds proportionally — more capital mobility and more exchange-rate rigidity together leave less room for an independent rate. Reading it as three boxes rather than a continuous frontier is the most common misunderstanding.

Capital controls leak. The trilemma treats them as a switch, but in practice they are porous and erode as trade invoicing, mispricing and offshore markets find ways around them. The autonomy they buy is partial and decays — which is why controls usually accompany continuing intervention rather than replacing it.

Reserves postpone the contradiction, they do not remove it. A large reserve stock lets a country defend a peg for a long time. But each intervention is either sterilised — offset by an opposite domestic operation, which merely relocates the pressure — or it is not, in which case the money supply is doing exactly what the argument said.

The falsification test. If the constraint is real, a country with a hard peg and open capital should show its policy rate tracking the anchor's, regardless of its own domestic conditions. Hong Kong is the clean case: its rates follow United States policy even when its own cycle points the other way, which is the observation the trilemma predicts and no theory of independent policy can accommodate.

• Whether the global financial cycle really collapses the trilemma into a dilemma.
• What macroprudential tools can and cannot substitute for an independent policy rate.

Every term the collection defines is gathered in the glossary.