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Fiat money is money that derives its value from government regulation or law. The term fiat currency is used when a fiat money is used as the main currency of the country. The term derives from the Latin fiat ("let it be done", "it shall be").
Fiat money was first used in China about a thousand years ago. Fiat money has been used intermittently by various countries since, concurrently with currencies that were backed by metals, primarily silver or gold. After World War II, the Bretton Woods accord set up a world-wide system of currencies that was pegged to the US dollar, while the US dollar was itself pegged to gold. The Nixon Shock of 1971 ended the convertibility of the United States dollar to gold. Since then, all reserve currencies have been fiat currencies, including the U.S. dollar and the Euro.
A central bank typically introduces new money into circulation in the economy by purchasing financial assets or lending money to financial institutions. Commercial banks then multiply this base money by credit creation through fractional reserve banking, which expands the total supply of broad money (cash plus demand deposits). The amount of money in circulation is reduced by the opposite process. The value of fiat currencies is influenced by monetary policy.
Fiat money has been defined variously as:
While gold- or silver-backed representative money entails the legal requirement that the bank of issue redeem it in fixed weights of gold or silver, fiat money's value is unrelated to the value of any physical quantity. Even a coin containing valuable metal may be considered fiat currency if its face value is defined by law as different from its market value as metal.
In monetary economics, fiat money is an intrinsically useless product, used as a means of payment. In some micro-founded models of money, fiat money is created internally in a community making feasible trades that would not otherwise be possible, either because producers and consumers may not anonymously write IOUs, or because of physical constraints.
The Song Dynasty in China was the first to issue paper money, jiaozi, around the 10th century AD. Although the notes were valued at a certain exchange rate for gold, silver, or silk, conversion was never allowed in practice. The notes were initially to be redeemed after three years' service, to be replaced by new notes for a 3% service charge, but, as more of them were printed without notes being retired, inflation became evident. The government made several attempts to support the paper by demanding taxes partly in currency and making other laws, but the damage had been done, and the notes fell out of favor.
The successive Yuan Dynasty was the first dynasty in China to use paper currency as the predominant circulating medium. The founder of the Yuan Dynasty, Kublai Khan, issued paper money known as Chao in his reign. The original notes during the Yuan Dynasty were restricted in area and duration as in the Song Dynasty.
All these pieces of paper are, issued with as much solemnity and authority as if they were of pure gold or silver... and indeed everybody takes them readily, for wheresoever a person may go throughout the Great Kaan's dominions he shall find these pieces of paper current, and shall be able to transact all sales and purchases of goods by means of them just as well as if they were coins of pure gold.
Tally sticks were employed as fiat currency in medieval England when, due to gold shortage, Henry I initiated their use by the Exchequer in or around 1100; royal taxes had to be paid in tally sticks. In 1661, Johan Palmstruch issued the first regular paper money in the West (although Washington Irving records an earlier emergency use of it, by the Spanish in a siege during the Conquest of Granada), under royal charter from the Kingdom of Sweden, through a new institution, the Bank of Stockholm. While this private paper currency was largely a failure, the Swedish parliament eventually took over the issue of paper money in that country. By 1745, its paper money was inconvertible to specie, but acceptance was mandated by the government. This fiat currency depreciated so rapidly that by 1776 it returned to a silver standard. Fiat money also has other roots in 17th-century Europe, having been introduced by the Bank of Amsterdam in 1683.
In 17th century New France, now part of Canada, the universally accepted medium of exchange was the beaver pelt. As the colony expanded, coins from France came to be widely used, but there was usually a shortage of French coins. In 1685, the colonial authorities in New France found themselves seriously short of money. A military expedition against the Iroquois Indians had gone badly and tax revenues were down. Typically, when short of funds, the government simply delay paying merchants for purchases, but it was not safe to delay the payment of soldiers due to the risk of mutiny.
Jacques de Meulles, the Intendant of Finance, came up with an ingenious solution — the temporary issuance of paper money, printed on playing cards. This was purely a temporary expedient, and it was not until years later that its role as a medium of exchange was recognized. The first issue occurred in June 1685 and was redeemed three months later. However, the shortages of money reoccurred and more issues of card money were made in subsequent years. These cards were readily accepted by merchants and the public and circulated freely at face value. However, given their wide acceptance as money and the general shortage of coinage, many of the playing cards were not redeemed but remained in circulation. Eventually, the Governor of New France acknowledged their useful role as a circulating medium of exchange. 
As the finances of the French government deteriorated because of European wars, it reduced its financial support for its colonies, so the colonial authorities in Canada relied more and more on card money. By 1757, the government had discontinued payments in coin and all payments were made in paper. In an application of Gresham’s Law — bad money drives out good — people hoarded gold and silver, and used paper money instead. The costs of the war with the British led to rapid inflation in New France. Following the British conquest in 1760, the paper money became almost worthless, but business did not come to a halt because gold and silver that had been hoarded came back into circulation. Under the Treaty of Paris (1763), the French government agreed to convert the outstanding card money into debentures, but with the French government essentially bankrupt, these bonds fell into default and by 1771 they were worthless.
The Royal Canadian Mint still issues Playing Card Money in commemoration of its history, but now in 92.5% silver form with gold plate on the edge. It therefore has an intrinsic value which considerably exceeds its fiat value. 
An early form of fiat currency in the American Colonies were "bills of credit". Provincial governments produced notes which were fiat currency, with the promise to allow holders to pay taxes in those notes. The notes were issued to pay current obligations and could be called by levying taxes at a later time.
Since the notes were denominated in the local unit of account, they were circulated from person to person in non-tax transactions. These types of notes were issued particularly in Pennsylvania, Virginia and Massachusetts. Such money was sold at a discount of silver, which the government would then spend, and would expire at a fixed point in time later.
Bills of credit have generated some controversy from their inception. Those who have wanted to highlight the dangers of inflation have focused on the colonies where the bills of credit depreciated most dramatically – New England and the Carolinas. Those who have wanted to defend the use of bills of credit in the colonies have focused on the middle colonies, where inflation was practically nonexistent.
Colonial powers consciously introduced fiat currencies backed by taxes, e.g. hut taxes or poll taxes, to mobilise economic resources in their new possessions, at least as a transitional arrangement. The purpose of such taxes was later served by property tax. The repeated cycle of deflationary hard money, followed by inflationary paper money continued through much of the 18th and 19th centuries. Often nations would have dual currencies, with paper trading at some discount to specie backed money.
Examples include the “Continental” issued by the U.S. Congress before the Constitution; paper versus gold ducats in Napoleonic era Vienna, where paper often traded at 100:1 against gold; the South Sea Bubble, which produced bank notes not backed by sufficient reserves; and the Mississippi Company scheme of John Law.
During the American Civil War, the Federal Government issued United States Notes, a form of paper fiat currency popularly known as 'greenbacks'. Their issue was limited by Congress just slightly over $340 million. During the 1870s, withdrawal of the notes from circulation was opposed by the United States Greenback Party. The term 'fiat money' was used in the resolutions of an 1878 party convention.
After World War I, in theory, governments still promised to redeem notes in specie on demand. However, the costs of the war and the massive expansion afterward made governments suspend redemption in specie. Since there was no direct penalty for doing so, governments were not immediately responsible for the economic consequences of printing more money, which led to hyperinflation – for example the hyperinflation in the Weimar Republic.
From 1944 to 1971, the Bretton Woods agreement fixed the value of 35 United States dollars to one troy ounce of gold. Other currencies were pegged to the U.S. dollar at fixed rates. The U.S. promised to redeem dollars in gold to other central banks. Trade imbalances were corrected by gold reserve exchanges or by loans from the International Monetary Fund.
The Bretton Woods system collapsed in what became known as the Nixon Shock. This was a series of economic measures taken by United States President Richard Nixon in 1971, including unilaterally canceling the direct convertibility of the United States dollar to gold. Since then, a system of national fiat monies has been used globally, with freely floating exchange rates between the major currencies.
A central bank introduces new money into the economy by purchasing financial assets or lending money to financial institutions. Commercial banks then multiply this base money by credit creation through fractional reserve banking, which expands the total supply of broad money (cash plus demand deposits).
In modern economies, relatively little of the supply of broad money is in physical currency. For example, in December 2010 in the U.S., of the $8853.4 billion in broad money supply (M2), only $915.7 billion (about 10%) consisted of physical coins and paper money. The manufacturing of new physical money is usually the responsibility of the central bank, or sometimes, the government's treasury.
Monetary policy regulates a country's money supply, the amount of broad currency in circulation. Almost all modern nations have special institutions (such as the United States Federal Reserve System, the European Central Bank (ECB), and the People's Bank of China) for conducting monetary policy, often acting independently of the executive. In general, these institutions are called central banks and often have other responsibilities such as supervising the smooth operation of the financial system.
The primary tool of monetary policy is open market operations: the central bank buys and sells financial assets such as treasury bills, government bonds, or foreign currencies. Purchases of these assets result in currency entering market circulation, while sales of these assets remove currency. Usually, open market operations aim for a specific short term interest rate. In other instances, they might instead target a specific exchange rate relative to some foreign currency, the price of gold, or indices such as the Consumer Price Index. For example, the US Federal Reserve may target the federal funds rate, the rate at which member banks lend to one another overnight.
The adoption of fiat currency by many countries, from the 18th century onwards, made much larger variations in the supply of money possible. Since then, huge increases in the supply of paper money have taken place in a number of countries, producing hyperinflations – episodes of extreme inflation rates much higher than those observed in earlier periods of commodity money. The hyperinflation in the Weimar Republic of Germany is a notable example.
Economists generally believe that high rates of inflation and hyperinflation are caused by an excessive growth of the money supply. Today, most economists favor a low and steady rate of inflation. Low (as opposed to zero or negative) inflation reduces the severity of economic recessions by enabling the labor market to adjust more quickly in a downturn, and reduces the risk that a liquidity trap prevents monetary policy from stabilizing the economy. However, money supply growth does not necessarily cause inflation. Some economists maintain that under the conditions of a liquidity trap, large monetary injections are like "pushing on a string".
The task of keeping the rate of inflation low and stable is usually given to monetary authorities. Generally, these monetary authorities are the central banks that control monetary policy through the setting of interest rates, through open market operations, and through the setting of banking reserve requirements.
Modern Monetary Theory (MMT), also known as neochartalism, is a descriptive economic theory that details the procedures and consequences of using government-issued tokens as the unit of money, i.e., fiat money.
MMT aims to describe and analyze modern economies in which the national currency is fiat money, established and created exclusively by the government. In MMT, money enters circulation through government spending. Taxation and its Legal Tender power to discharge debt establish the fiat money as currency, giving it value by creating demand for it in the form of a private tax obligation that must be met using the government's currency. An ongoing tax obligation, in concert with private confidence and acceptance of the currency, maintains its value. Because the government can issue its own currency at will, MMT maintains that the level of taxation relative to government spending (the government's deficit spending or budget surplus) is in reality a policy tool that regulates inflation and unemployment, and not a means of funding the government's activities per se.
A fiat-money currency generally loses value once the issuing government or central bank either loses the ability to or refuses to further guarantee its value. But this need not necessarily occur, for example, the so-called Swiss dinar continued to retain value in Kurdish Iraq even after its legal tender status was withdrawn by the Iraqi central government which issued the notes.