impossible trinity
Imagine a government with three things it would love to have at the same time: a stable, fixed exchange rate so trade is predictable; the freedom to set its own interest rates to manage its economy; and open borders that let money flow in and out freely. Each one is desirable. The catch, captured by the idea called the impossible trinity, is that no country can have all three at once. You can pick any two, but the third must be sacrificed.
Why? Suppose you want a fixed exchange rate and free capital flows. If you then try to set your own low interest rate while the world offers higher rates, money will flood out to chase better returns abroad, your currency will come under selling pressure, and to defend the peg you will have to raise rates back up — so you have lost control of your own interest rate. The three corners are: fixed exchange rate, independent monetary policy, and free capital movement. Real countries each pick a pair. The United States chooses independent policy plus free capital flows, and lets its exchange rate float. Hong Kong chooses a fixed rate plus free capital flows, and gives up independent monetary policy (its rates follow America's). China has historically chosen a managed rate plus independent policy, and kept capital controls.
The impossible trinity is one of the cleanest and most useful frameworks in international economics because it forces an honest choice and explains real policy. It tells you why a country with a peg cannot also slash rates to fight a recession, and why opening up to global capital means surrendering either exchange-rate stability or monetary independence. The caveat is that it is a simplification: the corners are not perfectly sharp, and countries often sit at messy in-between points, using partial capital controls or managed floats to bend the trilemma rather than fully obey it. But the core insight — that you cannot escape the trade-off entirely — has held up remarkably well.
Hong Kong keeps its dollar pegged to the US dollar and allows money to move freely in and out — so by the impossible trinity it must give up the third corner: it cannot set its own interest rates and instead must follow whatever the US Federal Reserve does, even when its own economy would prefer otherwise.
Pick any two of fixed rate, free capital, and independent policy — never all three.
The trilemma is a sharp simplification, not an iron law: countries often choose partial versions (limited capital controls, managed floats) that soften the trade-off, but they cannot escape it entirely.