Lecture 16 Fixed versus Floating Exchange Rates

Slides:



Advertisements
Similar presentations
International Financial System 4/2/2012 Unit 3: Exchange Rates.
Advertisements

INTERNATIONAL ECONOMICS. Chapter 12: International Monetary System.
Fixed Exchange Rates vs. Floating Exchange Rates.
Ch. 10: The Exchange Rate and the Balance of Payments.
Exchange rates Currencies are bought and sold in the foreign exchange market. The price at which one currency exchanges for another in the foreign exchange.
The International System
Chapter 15 International and Balance of Payments Issues.
Exchange-Rate Systems and Currency Crises
Economics 282 University of Alberta
The International Financial System
Exchange rates in a fixed exchange rate system
EXCHANGE RATES AND THE MARKET FOR FOREIGN EXCHANGE Lecture 05 /06.
Exchange Rate Regimes. Fixed Exchange Rates and the Adjustment of the Real Exchange Rate In the medium run, the economy reaches the same real exchange.
International Finance Lecture 3 EXCHANGE RATE AND BALANCE OF PAYMENTS.
© The McGraw-Hill Companies, 2012 Chapter 13: Essential macroeconomic tools The point is that you can’t have it all: A country must pick two out of three.
Copyright © 2006 Pearson Addison-Wesley. All rights reserved Introduction The Bretton Woods system collapsed in 1973 because central banks were unwilling.
Exchange Rate Regimes Lecture 2 IME LIUC 2010.
Forex Economics 285 Fall Exchange rates Current rate is ¥107 per US dollar –Depreciation of yen means more ¥ per $ At ¥107, an item costing ¥107,000.
1 Global Economics Eco 6367 Dr. Vera Adamchik Macroeconomic Policy in an Open Economy.
Exchange rates and exchange rate regimes International Finance
International Finance FINA 5331 Lecture 5 History of Monetary Institutions Read: Chapters 2 & 3 Aaron Smallwood Ph.D.
Chapter 20Copyright ©2010 by South-Western, a division of Cengage Learning. All rights reserved 1 ECON Designed by Amy McGuire, B-books, Ltd. McEachern.
Lecture 16 Fixed versus Floating Exchange Rates Econ 340.
International Economics
Fixed and Floating Exchange Rates
Distinguished Lecture on Economics in Government Exchange rate Regimes: is the Bipolar View Correct? Stanley Fischer Ahmad Bash P13-18.
Copyright  2006 McGraw-Hill Australia Pty Ltd. PPTs t/a International Trade and Investment: An Asia-Pacific Perspective 2e by Gionea. Slides prepared.
1 International Finance Chapter 19 The International Monetary System Under Fixed Exchange rates.
International Finance FINA 5331 Lecture 6: Exchange rate regimes Read: Chapters 2 Aaron Smallwood Ph.D.
Econ 141 Fall 2015 Slide Set 2 Introduction to exchange rates and exchange rate regimes.
The International Monetary System: Order or Disorder? 19.
1 International Macroeconomics Chapter 8 International Monetary System Fixed vs. Floating.
© 2012 Pearson Education, Inc. All rights reserved Alternative Exchange Rate Arrangements and Currency Risk Exchange rate systems around the world.
Chapter 19 The International Financial System. © 2013 Pearson Education, Inc. All rights reserved.19-2 Intervention in the Foreign Exchange Market A central.
Exchange Rates, Business Cycles, and Macroeconomic Policy in the Open Economy: Fixed Exchange Rates Prof Mike Kennedy.
Unit 3: Monetary Policy International Financial System 4/12/2011.
With floating exchange rates, changes in market demand and market supply of a currency cause a change in value. In the diagram below we see the effects.
MLI28C060 - Corporate Finance Seminar 1. Question 1. What are the eight contemporary currency regimes as defined by the IMF? Provide examples where possible.
International Monetary System Chapter Objectives Explain how exchange rates influence the activities of domestic and international companies.
The Balance of Payments & Exchange Rates. Balance of Payments The total of all economic transactions between a nation and the rest of the world Credits-
Government Influence On Exchange Rates
Starter: Recap… Macro effects of a currency depreciation
Currency crises and exchange rate policy
International Economics By Robert J. Carbaugh 8th Edition
International Economics By Robert J. Carbaugh 7th Edition
Exchange Rate Theories
International Economics By Robert J. Carbaugh 9th Edition
The International Financial System
International Monetary System.
Exchange rate regimes: Is the Bipolar view correct
Exchange Rates and The Open Economy
Introduction The Bretton Woods system collapsed in 1973 because central banks were unwilling to continue to buy over-valued dollar assets and to sell.
Starter: Recap… Macro effects of a currency depreciation
The International Financial System
Chapter 13: Essential macroeconomic tools The point is that you can’t have it all: A country must pick two out of three. Paul Krugman (1999)
Lecture 15 International Macroeconomics
M42: The Foreign Exchange Market
Exchange Rate Policies
Module Exchange Rate Policy
Exchange Rates and Macroeconomic Policy
Chapter 10 International
NS3040 Summer Term 2018 Issues With Bretton Woods II
Chapter 10.
Exchange Rate Policy 02/28/17 AP Macro Mr. Warner.
Module Exchange Rate Policy
Exchange Rate Policies
Exchange Rate Arrangements: Various Options
Presentation transcript:

Lecture 16 Fixed versus Floating Exchange Rates Econ 340 Lecture 16 Fixed versus Floating Exchange Rates

Outline: Fixed versus Floating Exchange Rates Both Systems Are Used What the “Experts” Recommend Pros and Cons of Floating Disruption When Rates Move Automatic Adjustment Pros and Cons of Pegging Stability Instability Alternatives Crawling Peg Monetary Unification The Problem of Undervalued Currencies Econ 340, Deardorff, Lecture 16: Fixed/Float

Who Uses Fixed and Float Lessons from the list of exchange arrangements (below) Floating rates are used by many countries Rich & poor Large & small All over the world Pegged rates are used today mostly by small countries Many countries are between fixed and floating (Source of table below: IMF, “Annual Report on Exchange Arrangements and Exchange Restrictions 2016”. Report for 2017 not yet available.) Econ 340, Deardorff, Lecture 16: Fixed/Float

Exchange Arrangements of Sample Countries, as of 2016 Freely Floating Exchange Rates 52 countries + euro 19 Australia Mexico Canada Sweden India United Kingdom Japan United States Pegged Exchange Rates 44 countries Belize (to $) Morocco (to basket) Denmark (to €) Nepal (to ₹ (rupee)) Jordan (to $) Saudi Arabia (to $) ANNUAL REPORT ON EXCHANGE ARRANGEMENTS AND EXCHANGE RESTRICTIONS 2015 (IMF, through library electronic resources). But can’t find for 2017. Econ 340, Deardorff, Lecture 16: Fixed/Float

Exchange Arrangements of Sample Countries, as of 2016 Between Floating and Pegged: Stabilized Arrangement 18 countries Bolivia Singapore Lebanon Vietnam Crawling Peg or Crawl-like Arrangement 13 countries Nicaragua (to $) Croatia (to €) Other Managed Arrangement 20 countries Liberia China Malaysia Pakistan Econ 340, Deardorff, Lecture 16: Fixed/Float

Exchange Arrangements of Sample Countries, as of 2016 More Fixed than Pegged: Currency Board 11 countries Hong Kong (to $) Bulgaria (tp €) No Separate Legal Tender 14 countries Ecuador ($) Montenegro (€) Currency Board Peg to another currency Vary money supply automatically with changes in international reserves (= forced non-sterilization) Econ 340, Deardorff, Lecture 16: Fixed/Float

Distribution of Currency Arrangements, 2016 “Hard Peg” “Soft Peg” Floating More Flexible More Fixed Econ 340, Deardorff, Lecture 16: Fixed/Float

Econ 340, Deardorff, Lecture 16: Fixed/Float

Who Uses Fixed and Float More lessons from the IMF report of exchange arrangements Relatively few use a “hard peg” (exchange rate that never changes, due either to no local currency or currency board) “Soft peg” and floating are both common. Soft peg is peg that is open to change, including a standard pegged exchange rate and variation like crawling peg After currency crisis of 2008-9, some have moved from floating to a soft peg Recently a few more have switched back to floating http://www.imf.org/external/pubs/nft/2014/areaers/ar2014.pdf Econ 340, Deardorff, Lecture 16: Fixed/Float

Outline: Fixed versus Floating Exchange Rates Both Systems Are Used What the “Experts” Recommend Pros and Cons of Floating Disruption When Rates Move Automatic Adjustment Pros and Cons of Pegging Stability Instability Alternatives Crawling Peg Monetary Unification The Problem of Undervalued Currencies Econ 340, Deardorff, Lecture 16: Fixed/Float

What “Experts” Recommend Some favor freely floating rates Let exchange rate adjust to fix imbalances “Let the market work” Others favor perfectly fixed rates Define currency rigidly in terms of something you can’t control Gold Foreign currency (“Currency Board”) AND give up control of the money supply Let flows of money fix imbalances i.e., do not sterilize! Econ 340, Deardorff, Lecture 16: Fixed/Float

What “Experts” Recommend Advocates of floating rates Milton Friedman (Nobel Prize 1976): “A country that enters into a hard-fixed rate bears an economic cost. The cost is discarding a means—a flexible exchange rate—of adjusting to external forces that impinge on it differently than on the other country or countries whose currency it shares.” Quote from ONE WORLD, ONE MONEY?, OPTIONS POLITIQUES, MAI 2001, http://www.irpp.org/po/archive/may01/friedman.pdf Econ 340, Deardorff, Lecture 16: Fixed/Float

What “Experts” Recommend Advocates of floating rates Jeffrey Sachs: “Once reserves are gone, investors panic. The worst mistake is for countries to wait too long to float their currencies.” Econ 340, Deardorff, Lecture 16: Fixed/Float

What “Experts” Recommend Advocates of fixed rates Robert Mundell (Nobel Prize 1999): “A world currency of some sort has existed for most of the past 2,500 years. Two thousand years ago, in the age of Caesar Augustus, it was the Roman aureus... A hundred years ago it was the gold sovereign. Less than thirty years ago it was the 1944 gold dollar. The world has been without a universal currency for only a tiny fraction of its history.” Quote from ONE WORLD, ONE MONEY?, OPTIONS POLITIQUES, MAI 2001, http://www.irpp.org/po/archive/may01/friedman.pdf Econ 340, Deardorff, Lecture 16: Fixed/Float

What “Experts” Recommend Milton Friedman: “If [over the last 30 years] the Canadian dollar had been rigidly tied to the US dollar, those differences would have required Canada to deflate relative to the United States, with unfortunate consequences for Canada that would have strained, to put it mildly, the trade relations between the two countries, and have put strong pressure on Canada to devalue or float.” Quote from ONE WORLD, ONE MONEY?, OPTIONS POLITIQUES, MAI 2001, http://www.irpp.org/po/archive/may01/friedman.pdf Econ 340, Deardorff, Lecture 16: Fixed/Float

What “Experts” Recommend Robert Mundell: “Exchange rate uncertainty imposes a cost of trade much like a tariff ... If Canada and the United States shared a stable common currency or an irrevocably fixed exchange rate, Canada’s real income would soar, closing a large part of the gap between the two countries’ GDP per capita.” Quote from ONE WORLD, ONE MONEY?, OPTIONS POLITIQUES, MAI 2001, http://www.irpp.org/po/archive/may01/friedman.pdf Econ 340, Deardorff, Lecture 16: Fixed/Float

What “Experts” Recommend “Bradford DeLong, an economic historian at the University of California at Berkeley, explains the debate to his students this way: ” (WSJ) To Mr. Friedman, an exchange rate is a price; therefore, it is an infringement on human freedom to peg it. To Mr. Mundell, an exchange rate is a promise; to change it is to default on a commitment. Econ 340, Deardorff, Lecture 16: Fixed/Float

What “Experts” Recommend Allan Meltzer (Carnegie-Mellon): “The best you can say of what economic research has produced is: You can make a case for freely floating exchange rates if you’re willing to live with the consequences. You can make a case for fixed exchange rates if you’re willing to live with the consequences. You can’t make much of a case for anything in between.” (WSJ) Econ 340, Deardorff, Lecture 16: Fixed/Float

What “Experts” Recommend Where they agree: An “adjustable peg” is worse than both fixed and floating rates Friedman: “The reasons why a pegged exchange rate is a ticking bomb are well known.” Mundell: “I have never nor ever would advocate a general system of “pegged” rates. Pegged rate systems always break down.” Adjustable peg is what the IMF (above) called a “soft peg” Quotes from ONE WORLD, ONE MONEY?, OPTIONS POLITIQUES, MAI 2001, http://www.irpp.org/po/archive/may01/friedman.pdf Econ 340, Deardorff, Lecture 16: Fixed/Float

Outline: Fixed versus Floating Exchange Rates Both Systems Are Used What the “Experts” Recommend Pros and Cons of Floating Disruption When Rates Move Automatic Adjustment Pros and Cons of Pegging Stability Instability Alternatives Crawling Peg Monetary Unification The Problem of Undervalued Currencies Econ 340, Deardorff, Lecture 16: Fixed/Float

Pros and Cons of Floating Con: Exchange rates DO MOVE; And when they do, they cause Macro effects (as we saw last time) Depreciation Stimulates aggregate demand, but not necessarily when needed: may just cause inflation Changes values of assets and liabilities Appreciation Reduces aggregate demand, may cause recession or deflaton Econ 340, Deardorff, Lecture 16: Fixed/Float

Pros and Cons of Floating Con: Exchange rates DO MOVE; when they do, they cause Micro effects: exports and imports subject to Uncertainty Instability Costly for traders Like trade barrier Reduces trade Econ 340, Deardorff, Lecture 16: Fixed/Float

Pros and Cons of Floating Example: The US dollar rose 50% during 1980-1985 Caused US auto and other industries to contract Major dislocation in middle US Ended in 1985 when, in “Plaza Accord,” major central banks agreed to intervene Econ 340, Deardorff, Lecture 16: Fixed/Float

Pros and Cons of Floating Pro: Exchange rate provides efficient and automatic across-the-board adjustment Suppose that, due to inflation, our prices are too high, causing our imports to rise and exports to fall Exchange depreciation fixes this for all sectors With fixed rates, individual prices and wages would have to fall to become competitive: much more painful That’s what Greece and other weak countries in the EU have had to do for several years now. Called “internal devaluation” Floating Permits countries to have independent monetary policies to deal with macroeconomic shocks Econ 340, Deardorff, Lecture 16: Fixed/Float

Pros and Cons of Floating Experience with exchange rates in the 1930s (not really floating, but they moved a lot) made governments prefer fixed rates After WWII, IMF was created, based on Pegged Exchange Rates Most currencies pegged to US $ IMF helped countries manage this When in trouble, countries were permitted by IMF to devalue Econ 340, Deardorff, Lecture 16: Fixed/Float

Outline: Fixed versus Floating Exchange Rates Both Systems Are Used What the “Experts” Recommend Pros and Cons of Floating Disruption When Rates Move Automatic Adjustment Pros and Cons of Pegging Stability Instability Alternatives Crawling Peg Monetary Unification The Problem of Undervalued Currencies Econ 340, Deardorff, Lecture 16: Fixed/Float

Pros and Cons of Pegging Pro: If it succeeds, exchange rate is stable, avoiding disruptions Con: If it fails, devaluation causes instability, just like floating rates, only worse The Problem: Pegged Rates are Prone to Crisis Econ 340, Deardorff, Lecture 16: Fixed/Float

Pros and Cons of Pegging Why Crisis? Pegged rate does not respond to market changes Some currencies become undervalued, others overvalued Inevitable unless all countries have exactly the same rate of inflation Crisis eventually erupts for overvalued currencies Econ 340, Deardorff, Lecture 16: Fixed/Float

Pros and Cons of Pegging Why Crisis for Overvalued Currency? $/€ Central bank must sell foreign currency Since reserves are finite, they eventually run out Market knows that when they do… S€ E0 E* Fed sells € D€ Q€ Econ 340, Deardorff, Lecture 16: Fixed/Float

Pros and Cons of Pegging Why Crisis for Overvalued Currency $/€ Intervention will stop Currency will depreciate Knowing this, people don’t want to hold the overvalued currency, so… S€ E0 E* D€ Q€ Econ 340, Deardorff, Lecture 16: Fixed/Float

Pros and Cons of Pegging Why Crisis for Overvalued Currency $/€ Before reserves run out, capital outflow increases demand And reserves fall faster “Speculative Attack” S€ E0 E* D€1 Fed sells more € D€ Q€ Econ 340, Deardorff, Lecture 16: Fixed/Float

Pros and Cons of Pegging Pegged rates offer speculators a “one-way bet” Once they see that reserves are falling… … they bet on a devaluation by selling the country’s currency If they are right, they win If they are wrong, they break even (since the exchange rate doesn’t change) They can’t lose, so they bet a lot But their bets drain reserves keven faster, forcing crisis Econ 340, Deardorff, Lecture 16: Fixed/Float

Pros and Cons of Pegging Crisis even without Overvaluation Crisis only requires expectation of devaluation The expectation doesn’t have to be justified; it only has to be believed Can happen even to a currency that is not overvalued How? By “contagion”. If one country has a crisis, for whatever reason Other countries that are near it, or similar to it, may become suspect That’s part of what happened in the Asian Crisis that started in 1997 (more on that in a later lecture) Some countries have feared contagion in recent years Econ 340, Deardorff, Lecture 16: Fixed/Float

Pros and Cons of Pegging Result: “Pegged Rates” are not Fixed In a world of pegged exchange rates, over time Some currencies become undervalued Other currencies become overvalued Why? Many reasons (see Makin) Bretton Woods: US inflation caused dollar to become overvalued Europe in the 1990s: German tight money after reunification, caused others to become overvalued Econ 340, Deardorff, Lecture 16: Fixed/Float

Pros and Cons of Pegging Result: “Pegged Rates” are not Fixed Overvalued currencies are subject to speculative attacks When they do devalue, they do it Suddenly By large amounts This is just as disruptive as changes in a floating rate, perhaps more so Econ 340, Deardorff, Lecture 16: Fixed/Float

Pros and Cons of Pegging The choice is not between fixed and floating: E Time Econ 340, Deardorff, Lecture 16: Fixed/Float

Pros and Cons of Pegging The choice is between pegged and floating: E Which is more stable? Time Econ 340, Deardorff, Lecture 16: Fixed/Float

Outline: Fixed versus Floating Exchange Rates Both Systems Are Used What the “Experts” Recommend Pros and Cons of Floating Disruption When Rates Move Automatic Adjustment Pros and Cons of Pegging Stability Instability Alternatives Crawling Peg Monetary Unification The Problem of Undervalued Currencies Econ 340, Deardorff, Lecture 16: Fixed/Float

Econ 340, Deardorff, Lecture 16: Fixed/Float Alternatives Mixtures of pegged and floating rates Crawling peg Change the pegged rate slowly and predictably in response to a fall or rise in reserves Slow movement of the peg is supposed to stop the loss of reserves before crisis hits Still subject to speculative attack Econ 340, Deardorff, Lecture 16: Fixed/Float

Econ 340, Deardorff, Lecture 16: Fixed/Float Alternatives Mixtures of pegged and floating rates Wider band Let the rate move freely in a large band around the official pegged rate Less intervention should be needed Does not help if country has, say, higher inflation than others: crisis still inevitable Econ 340, Deardorff, Lecture 16: Fixed/Float

Econ 340, Deardorff, Lecture 16: Fixed/Float Alternatives Truly Fixed Exchange Rate Use another country’s currency Called “Dollarization,” even if not the US dollar Form a monetary union The Eurozone (we’ll look more at this next time) Econ 340, Deardorff, Lecture 16: Fixed/Float

Econ 340, Deardorff, Lecture 16: Fixed/Float Alternatives Truly Fixed Exchange Rate Currency Board Peg to another currency Replace central bank with “board” that automatically varies money supply one-for-one with international reserves If reserves fall, so does money supply, forcing adjustment This mimics the Gold Standard, where gold flowed among countries Econ 340, Deardorff, Lecture 16: Fixed/Float

Econ 340, Deardorff, Lecture 16: Fixed/Float Alternatives Truly Fixed Exchange Rate Currency Board How it’s supposed to work If exchange rate is over-valued (excess demand for foreign currency) Currency board sells reserves This reduces the domestic money supply 1-for-1 Falling money causes falling income and prices Imports fall, exports rise, and excess demand for foreign currency disappears If exchange rate is under-valued: Opposite Econ 340, Deardorff, Lecture 16: Fixed/Float

Econ 340, Deardorff, Lecture 16: Fixed/Float Alternatives Truly Fixed Exchange Rate Currency Board Didn’t work for Argentina, which had a crisis anyway Must not have followed the rules Hong Kong has had a currency board (pegged to US$) since 1983, and it has worked well Econ 340, Deardorff, Lecture 16: Fixed/Float

Econ 340, Deardorff, Lecture 16: Fixed/Float

Econ 340, Deardorff, Lecture 16: Fixed/Float

Econ 340, Deardorff, Lecture 16: Fixed/Float Alternatives Pegged Rate with Capital Controls Why did pegged rates work in the 1950s & 60s? Most countries had capital controls In spite of that, the system of pegged rates didn’t work perfectly: there were some crises Capital controls prevent inflow and outflow of capital, and thus limit speculation Today, most countries see capital controls as too costly But not all: China, Malaysia Econ 340, Deardorff, Lecture 16: Fixed/Float

Alternatives The Impossible Trinity Policy: Full Capital Controls See Frankel (This is the Missing Figure 3) Goal: Monetary Independence Increased Capital Mobility Goal: Exchange Rate Stability Goals Policy: Pure Float Policy: Monetary Union Goal: Full Financial Integration Econ 340, Deardorff, Lecture 16: Fixed/Float

Econ 340, Deardorff, Lecture 16: Fixed/Float Exchange Rates Since 1945 See reading by Buttonwood (column in The Economist) Bretton-Woods System, 1945-1971 Overseen by IMF Currencies were pegged, mostly to US $ Capital mobility was restricted, but gradually liberalized over time Frequent crises, as currencies became overvalued due to inflation Econ 340, Deardorff, Lecture 16: Fixed/Float

Econ 340, Deardorff, Lecture 16: Fixed/Float Exchange Rates Since 1945 August 15, 1971: Nixon cut the link of US $ to gold, signaling the end of pegged rates Countries stopped pegging, then restarted at different rates, but by 1973 they had given up Econ 340, Deardorff, Lecture 16: Fixed/Float

Econ 340, Deardorff, Lecture 16: Fixed/Float Exchange Rates Since 1945 Since 1973, major currencies have floated Exchange rates moved more than expected Crises did not disappear Monetary policy became more free: “ ‘the Greenspan put’: the use of interest-rate cuts to rescue financial markets, in effect underwriting asset prices.” Econ 340, Deardorff, Lecture 16: Fixed/Float

Outline: Fixed versus Floating Exchange Rates Both Systems Are Used What the “Experts” Recommend Pros and Cons of Floating Disruption When Rates Move Automatic Adjustment Pros and Cons of Pegging Stability Instability Alternatives Crawling Peg Monetary Unification The Problem of Undervalued Currencies Econ 340, Deardorff, Lecture 16: Fixed/Float

The Problem of Undervalued Currencies Overvalued currencies lead to crisis In that sense they are self correcting, since countries are forced, eventually, to devalue or float Undervalued currencies Do not lead to crisis, but only to accumulation of reserves May be viewed as harmful to trading partners Econ 340, Deardorff, Lecture 16: Fixed/Float

The Problem of Undervalued Currencies Until recently, the Chinese yuan was considered undervalued US administration put pressure on China to appreciate US Congress threatened to restrict imports Threats continue, even though yuan is no longer undervalued, as we saw last week Econ 340, Deardorff, Lecture 16: Fixed/Float

China’s Exchange Rate, US$/Yuan, 2000-2016 The yuan reached its peak in 2013, and began to fall in 2015 China currency.xlsx From IMF, IFS Econ 340, Deardorff, Lecture 14: Pegging

From 2014, China’s reserves have been falling See China Currency.xlsx Econ 340, Deardorff, Lecture 14: Pegging

Krugman’s Argument Would he say the same today? I doubt it. (From NYT, Mar 15, 2010) China’s current account surplus in 2010 will be over $450 billion US should declare China a “currency manipulator” in next report, Apr 15 (US did not, and hasn’t since.) China does not have US “over a barrel.” We have China over a barrel. We should repeat what we did in 1971: Then Nixon used a 10% surcharge on imports, so as to prod Japan, Germany, and others to appreciate We should use (or threaten) a 25% surcharge on Chinese exports. Would he say the same today? I doubt it.

Econ 340, Deardorff, Lecture 16: Fixed/Float Next Time The Euro What is it? History of European monetary integration Pros and cons of currency unification Effects on US What happened? Econ 340, Deardorff, Lecture 16: Fixed/Float