The Impossible Trinity is a trilemma

Trilemma

A trilemma is a difficult choice from three options, each of which is unacceptable or unfavourable.There are two logically equivalent ways in which to express a trilemma: it can be expressed as a choice among three unfavourable options, one of which must be chosen, or as a choice among three...

 in international economics

International economics

International economics is concerned with the effects upon economic activity of international differences in productive resources and consumer preferences and the institutions that affect them...

 suggesting it is impossible to have all three of the following at the same time:

• A fixed exchange rate
  Fixed exchange rate
  A fixed exchange rate, sometimes called a pegged exchange rate, is a type of exchange rate regime wherein a currency's value is matched to the value of another single currency or to a basket of other currencies, or to another measure of value, such as gold.A fixed exchange rate is usually used to...
  
  .
• Free capital
  Capital (economics)
  In economics, capital, capital goods, or real capital refers to already-produced durable goods used in production of goods or services. The capital goods are not significantly consumed, though they may depreciate in the production process...
  
   movement (absence of capital control
  Capital control
  Capital controls are measures such as transaction taxes and other limits or outright prohibitions, which a nation's government can use to regulate the flows into and out of the country's capital account....
  
  s).
• An independent monetary policy
  Monetary policy
  Monetary policy is the process by which the monetary authority of a country controls the supply of money, often targeting a rate of interest for the purpose of promoting economic growth and stability. The official goals usually include relatively stable prices and low unemployment...
  
  .

It is both a hypothesis based on IS/LM model

IS/LM model

The IS/LM model is a macroeconomic tool that demonstrates the relationship between interest rates and real output in the goods and services market and the money market...

s that have been extended to include a balance of payments

Balance of payments

Balance of payments accounts are an accounting record of all monetary transactions between a country and the rest of the world.These transactions include payments for the country's exports and imports of goods, services, financial capital, and financial transfers...

 component, and a finding from empirical examples where governments which have tried to simultaneously pursue all three goals have always failed.

Theoretical derivation

The formal model for this hypothesis is the Mundell-Fleming model

Mundell-Fleming model

The Mundell–Fleming model, also known as the IS-LM-BP model, is an economic model first set forth by Robert Mundell and Marcus Fleming. The model is an extension of the IS-LM model...

 developed in the 1960s by Robert Mundell

Robert Mundell

Robert Mundell, CC is a Nobel Prize-winning Canadian economist. Currently, Mundell is a professor of economics at Columbia University and the Chinese University of Hong Kong....

 and Marcus Fleming

Marcus Fleming

John Marcus Fleming was Deputy Director of the research department of the International Monetary Fund for many years; he was already a member of this department during the period of Mundell's affiliation. At approximately the same time as Mundell, Fleming presented similar research on...

. The idea of the impossible trinity went from theoretical curiosity to becoming the foundation of open economy

Open economy

An open economy is an economy in which there are economic activities between domestic community and outside, e.g. people, including businesses, can trade in goods and services with other people and businesses in the international community, and flow of funds as investment across the border...

 macroeconomics in the 1980s, by which time capital control

Capital control

Capital controls are measures such as transaction taxes and other limits or outright prohibitions, which a nation's government can use to regulate the flows into and out of the country's capital account....

s had broken down in many countries, and conflicts were visible between pegged exchange rates and monetary policy autonomy. While one version of the impossible trinity is focused on the extreme case – with a perfectly fixed exchange rate and a perfectly open capital account

Capital account

The current and capital accounts make up a country's balance of payment . Together these three accounts tell a story about the state of an economy, its economic outlook and its strategies for achieving its desired goals...

, a country has absolutely no autonomous monetary policy – the real world has thrown up repeated examples where the capital controls are loosened, resulting in greater exchange rate rigidity and less monetary-policy autonomy.

Real world examples

In the modern world, given the growth of trade

International trade

International trade is the exchange of capital, goods, and services across international borders or territories. In most countries, such trade represents a significant share of gross domestic product...

 in goods and services

Goods and services

In economics, economic output is divided into physical goods and intangible services. Consumption of goods and services is assumed to produce utility. It is often used when referring to a Goods and Services Tax....

 and especially the fast pace of financial innovation, capital controls are often easily evaded. In addition, capital controls introduce numerous distortions. Hence, there are few important countries with an effective system of capital controls, though by early 2010 there has been a movement among economists, policy makers and the International Monetary Fund

International Monetary Fund

The International Monetary Fund is an organization of 187 countries, working to foster global monetary cooperation, secure financial stability, facilitate international trade, promote high employment and sustainable economic growth, and reduce poverty around the world...

 back in favour of limited use.
Lacking effective control on the free movement of capital, the Impossible Trinity asserts that a country has to choose between reducing currency volatility and running a stabilising monetary policy: it cannot do both. As stated by Paul Krugman

Paul Krugman

Paul Robin Krugman is an American economist, professor of Economics and International Affairs at the Woodrow Wilson School of Public and International Affairs at Princeton University, Centenary Professor at the London School of Economics, and an op-ed columnist for The New York Times...

:
Economists Michael C. Burda

Michael C. Burda

Michael Christopher Burda is an American macroeconomist and professor at the Humboldt University of Berlin.Since 1993 he has served as director of the Institute for Economic Theory II and since 2007 visiting professor at the European School of Management and Technology . He has also taught at...

 and Charles Wyplosz provide an illustration of what can happen if a nation tries to pursue all three goals at once. To start with they posit a nation with a fixed exchange rate at equilibrium with respect to capital flows as its monetary policy is aligned with the international market. However the nation then adopts an expansionary monetary policy to try to stimulate its domestic economy. This involves an increase of the monetary supply, and a fall of the domestically available interest rate. Because the internationally available interest rate adjusted for foreign exchange

Foreign exchange

Foreign exchange may refer to:Finance* Foreign exchange markets, where money in one currency is exchanged for another* Exchange rate, the price for which one currency is exchanged for another...

 differences has not changed, market participants are able to make a profit by borrowing in the country's currency and then lending abroad – a form of Carry trade. With no capital control market players will do this en masse. The trade will involve selling the borrowed currency on the foreign exchange market

Foreign exchange market

The foreign exchange market is a global, worldwide decentralized financial market for trading currencies. Financial centers around the world function as anchors of trading between a wide range of different types of buyers and sellers around the clock, with the exception of weekends...

in order to acquire foreign currency to lend abroad – this tends to cause the price of the nations currency to drop due to the sudden extra supply. Because the nation has a fixed exchange rate, it must defend its currency and will sell its reserves to buy its currency back. But unless the monetary policy is changed back, the international markets will invariably continue until the governments foreign exchange reserves are exhausted, causing the currency to devalue, thus breaking one of the three goals and also enriching market players at the expense of the government that tried to break the impossible trinity.

How Mundell Fleming is violated

1. The Mundell Fleming model assumes that the setting of interest rates via monetary policy is independent from the issuance of federal debt by the fiscal authority. In truth, the two are interlinked; there is no reason why the fiscal authority can't supersede the monetary authority in setting the interest rate that it pays on its own debt.
2. The Mundell Fleming model assumes that federal taxation and spending policy and its relation to the expansion / contraction of government debt have no effect on international capital flows when they in fact do. For instance, from the year 1996 to 2000, the outstanding US federal debt contracted in part because of the tax increases implemented during the end of President Bush I's presidency and in part because of the fall off in defense spending coinciding with the end of the cold war.
3. The Mundell Fleming model assumes that money supply and interest rates must move in tandem - meaning that when the federal reserve raises interest rates it is selling bonds into the market removing dollars from the federal reserve member banks. This pushes up interest rates and reduces dollars in circulation. The reverse is true when the federal reserve buys bonds back. However, the fiscal authority ultimately determines how many of those bonds are in circulation. The fiscal authority can reduce the bonds in circulation by running a budget surplus through some combination of higher tax revenues and reduced spending OR by selling nonguaranteed claims on future tax revenue.