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Essential Statistics, Regression, and Econometrics Essential Statistics, Regression, and Econometrics Gary Smith Pomona College AMSTERDAM(cid:129)BOSTON(cid:129)HEIDELBERG(cid:129)LONDON NEWYORK(cid:129)OXFORD(cid:129)PARIS(cid:129)SANDIEGO SANFRANCISCO(cid:129)SINGAPORE(cid:129)SYDNEY(cid:129)TOKYO AcademicPressisanimprintofElsevier AcademicPressisanimprintofElsevier 225WymanStreet,Waltham,MA02451,USA 525BStreet,Suite1800,SanDiego,California92101-4495,USA 84Theobald’sRoad,LondonWC1X8RR,UK ©2012GarySmith.PublishedbyElsevierInc.Allrightsreserved. Nopartofthispublicationmaybereproducedortransmittedinanyformorbyanymeans,electronicor mechanical,includingphotocopying,recording,oranyinformationstorageandretrievalsystem,without permissioninwritingfromthePublisher.Detailsonhowtoseekpermission,furtherinformationaboutthe Publisher’spermissionspolicies,andourarrangementswithorganizationssuchastheCopyrightClearance CenterandtheCopyrightLicensingAgencycanbefoundatourwebsite:www.elsevier.com/permissions ThisbookandtheindividualcontributionscontainedinitareprotectedundercopyrightbythePublisher(other thanasmaybenotedherein). Notices Knowledgeandbestpracticeinthisfieldareconstantlychanging.Asnewresearchandexperiencebroadenour understanding,changesinresearchmethods,professionalpractices,ormedicaltreatmentmaybecomenecessary. Practitionersandresearchersmustalwaysrelyontheirownexperienceandknowledgeinevaluatingandusing anyinformation,methods,compounds,orexperimentsdescribedherein.Inusingsuchinformationormethods theyshouldbemindfuloftheirownsafetyandthesafetyofothers,includingpartiesforwhomtheyhavea professionalresponsibility. Tothefullestextentofthelaw,neitherthePublishernortheauthors,contributors,oreditorsassumeany liabilityforanyinjuryand/ordamagetopersonsorpropertyasamatterofproductsliability,negligenceor otherwise,orfromanyuseoroperationofanymethods,products,instructions,orideascontainedinthe materialherein. LibraryofCongressCataloging-in-PublicationData Smith,Gary,1945- Essentialstatistics,regression,andeconometrics/GarySmith. p.cm. Includesbibliographicalreferencesandindex. ISBN978-0-12-382221-5(hardcover:alk.paper)1.Regressionanalysis–Textbooks. I.Title. QA278.2.S61272012 519.5–dc22 2011006233 BritishLibraryCataloguing-in-PublicationData AcataloguerecordforthisbookisavailablefromtheBritishLibrary. ISBN:978-0-12-382221-5 ForinformationonallAcademicPresspublications visitourwebsite:www.elsevierdirect.com PrintedintheUnitedStatesofAmerica 11 12 13 9 8 7 6 5 4 3 2 1 Introduction Econometrics is powerful, elegant, and widely used. Many departments of economics, politics, psychology, and sociology require students to take a course in regression analysis or econometrics. So do many business, law, and medical schools. These courses are traditionally preceded by an introductory statistics course that adheres to the fire hose pedagogy: bombard the students with information and hope they do not drown. Encyclopedic statistics courses are a mile wide and an inch deep, and many students remember little after the final exam. This textbook focuses on what students really need to know and remember. Essential Statistics, Regression, and Econometrics is written for an introductory statistics course that helps students develop the statistical reasoning they need for regression analysis. It can be used either for a statistics class that precedes a regression class or for a one-term course that encompasses statistics and regression analysis. One reason for this book’s focused approach is that there is not enough time in a one-term course to cover the material in more encyclopedic books. Another reason is that an unfocused course overwhelms students with so much nonessential material that they have trouble remembering the essentials. This book does not cover the binomial distribution and related tests of a population success probability. Also omitted are difference-in-means tests, chi-square tests, and ANOVA tests. These are not crucial for understanding and using regression analysis. Instructors who cover these topics can use the supplementary material at the book’s website. The regression chapters at the end of the book set up the transition to a more advanced regression or econometrics course and are also sufficient for students who take only one statistics class but need to know how to use and understand basic regression analysis. This textbook is intended to give students a deep understanding of the statistical reasoning they need for regression analysis. It is innovative in its focus on this preparation and in the extended emphasis on statistical reasoning, real data, pitfalls in data analysis, modeling issues, and word problems. Too many students mistakenly believe that statistics courses are too abstract, mathematical, and tedious to be useful or interesting. To demonstrate the power, elegance, and even beauty of statistical reasoning, this book includes a large number of xi Introduction interesting and relevant examples, and discusses not only the uses but also the abuses of statistics. These examples show how statistical reasoning can be used to answer important questions and also expose the errors—accidental or intentional—that people often make. The examples are drawn from many areas to show that statistical reasoning is an important part of everyday life. The goal is to help students develop the statistical reasoning they need for later courses and for life after college. I am indebted to the reviewers who helped make this a better book: Woody Studenmund, The Laurence de Rycke Distinguished Professor of Economics, Occidental College; Michael Murray, Bates College; Steffen Habermalz, Northwestern University; and Manfred Keil, Claremont Mckenna College. Most of all, I am indebted to the thousands of students who have taken statistics courses from me—for their endless goodwill, contagious enthusiasm, and, especially, for teaching me how to be a better teacher. ©2010byElsevierInc.Allrightsreserved. xii CHAPTER 1 Data, Data, Data Chapter Outline 1.1 Measurements 2 Flying Blindand Clueless 3 1.2 Testing Models 4 ThePolitical Business Cycle 5 1.3 Making Predictions 5 Okun’s Law 5 1.4 Numerical and Categorical Data 6 1.5 Cross-Sectional Data 6 TheHamburger Standard 7 1.6 Time Series Data 8 Silencing Buzz Saws 8 1.7 Longitudinal (or Panel) Data 10 1.8 Index Numbers (Optional) 10 TheConsumer Price Index 11 TheDow Jones Index 11 1.9 Deflated Data 12 Nominal andReal Magnitudes 13 TheReal CostofMailinga Letter 15 Real Per Capita 16 Exercises 17 You’re right, we did it. We’re very sorry. But thanks to you, we won’t do it again. —BenBernanke The Great Depression was a global economic crisis that lasted from 1929 to 1939. Millions of people lost their jobs, their homes, and their life savings. Yet, government officials knew too little about the extent of the suffering, because they had no data measuring output or unemployment. They instead had anecdotes: “It is a recession when our neighbor loses his job; it is a depression when you lose yours.” Herbert Hoover was president of the United States when the Great Depression began. He was very smart and well-intentioned, but he did not know that he was presiding over an economic meltdown because his information came from his equally clueless advisors—none of whom had yet lost their jobs. He had virtually no economic data and no models that predicted the future direction of the economy. EssentialStatistics,Regression,andEconometrics.DOI:10.1016/B978-0-12-382221-5.00001-5 ©2012GarySmith.PublishedbyElsevierInc.Allrightsreserved. 1 2 Chapter 1 In his December 3, 1929, State of the Union message, Hoover concluded that “The problems with which we are confronted are the problems of growth and progress” [1]. In March 1930, he predicted that business would be normal by May [2]. In early May, Hoover declared that “we have now passed the worst” [3]. In June, he told a group that had come to Washington to urge action, “Gentlemen, you have come 60 days too late. The depression is over” [4]. A private organization, the National Bureau of Economic Research (NBER), began estimating the nation’s output in the 1930s. There were no regular monthly unemployment data until 1940. Before then, the only unemployment data were collected in the census, once every ten years. With hindsight, it is now estimated that between 1929 and 1933, national output fell by one third, and the unemployment rate rose from 3 percent to 25 percent. The unemployment rate averaged 19 percent during the 1930s and never fell below 14 percent. More than a third of the nation’s banks failed and household wealth dropped by 30 percent. Behind these aggregate numbers were millions of private tragedies. One hundred thousand businesses failed and 12 million people lost their jobs, income, and self-respect. Many lost their life savings in the stock market crash and the tidal wave of bank failures. Without income or savings, people could not buy food, clothing, or proper medical care. Those who could not pay their rent lost their shelter; those who could not make mortgage payments lost their homes. Farm income fell by two-thirds and many farms were lost to foreclosure. Desperate people moved into shanty settlements (called Hoovervilles), slept under newspapers (Hoover blankets), and scavenged for food where they could. Edmund Wilson [5] reported that There is not a garbage-dump in Chicago which is not haunted by the hungry. Last summer in the hot weather when the smell was sickening and the flies were thick, there were a hundred people a day coming to one of the dumps. 1.1 Measurements Today, we have a vast array of statistical data that can help individuals, businesses, and governments make informed decisions. Statistics can help us decide which foods are healthy, which careers are lucrative, and which investments are risky. Businesses use statistics to monitor production, estimate demand, and design marketing strategies. Government statisticians measure corn production, air pollution, unemployment, and inflation. The problem today is not a scarcity of data, but rather the sensible interpretation and use of data. This is why statistics courses are taught in high schools, colleges, business schools, law schools, medical schools, and Ph.D. programs. Used correctly, statistical www.elsevierdirect.com Data, Data, Data 3 reasoning can help us distinguish between informative data and useless noise, and help us make informed decisions. Flying Blind and Clueless U.S. government officials had so little understanding of economics during the Great Depression that even when they finally realized the seriousness of the problem, their policies were often counterproductive. In 1930, Congress raised taxes on imported goods to record levels. Other countries retaliated by raising their taxes on goods imported from the United States. Worldwide trade collapsed with U.S. exports and imports falling by more than 50 percent. In 1931, Treasury Secretary Andrew Mellon advised Hoover to “liquidate labor, liquidate stocks, liquidate the farmers, liquidate real estate” [6]. When Franklin Roosevelt campaigned for president in 1932, he called Hoover’s federal budget “the most reckless and extravagant that I have been able to discover in the statistical record of any peacetime government anywhere, anytime” [7]. Roosevelt promised to balance the budget by reducing government spending by 25 percent. One of the most respected financial leaders, Bernard Baruch, advised Roosevelt to “Stop spending money we haven’t got. Sacrifice for frugality and revenue.Cutgovernmentspending—cutitasrationsarecutinasiege.Tax—taxeverybodyfor everything”[8].Today—becausewehavemodelsanddata—weknowthatcuttingspending andraisingtaxesareexactlythewrongpoliciesforfightinganeconomicrecession.TheGreat DepressiondidnotenduntilWorldWarIIcausedamassiveincreaseingovernmentspending andmillionsofpeopleenlistedinthemilitary. The Federal Reserve (the “Fed”) is the government agency in charge of monetary policy in the United States. During the Great Depression, a seemingly clueless Federal Reserve allowed the money supply to fall by a third. In their monumental work, A Monetary History of the United States, Milton Friedman and Anna Schwartz argued that the Great Depression was largely due to monetary forces, and they sharply criticized the Fed’s perverse policies. In a 2002 speech honoring Milton Friedman’s 90th birthday, Ben Bernanke, who became Fed chairman in 2006, concluded his speech: “I would like to say to Milton and Anna: Regarding the Great Depression. You’re right, we did it. We’re very sorry. But thanks to you, we won’t do it again” [9]. During the economic crisis that began in the United States in 2007, the president, Congress, and Federal Reserve did not repeat the errors of the 1930s. Faced with a credit crisis that threatened to pull the economy into a second Great Depression, the government did the right thing by pumping billions of dollars into a deflating economy. Why do we now know that cutting spending, raising taxes, and reducing the money supply are the wrong policies during economic recessions? Because we now have reasonable economic models that have been tested with data. www.elsevierdirect.com 4 Chapter 1 1.2 Testing Models The great British economist John Maynard Keynes observed that the master economist “must understand symbols and speak in words” [10]. We need words to explain our reasoning, but we also need models so that our theories can be tested with data. In the 1930s, Keynes hypothesized that household spending depends on income. This “consumption function” was the lynchpin of his explanation of business cycles. If people spend less, others will earn less and then spend less, too. This fundamental interrelationship between spending and income explains how recessions can persist and grow like a snowball rolling downhill. If, on the other hand, people buy more coal from a depressed coal-mining area, the owners and miners will then buy more and better food, the farmers will buy new clothes, and the tailors will start going to the movies again. Not only the coal miners gain; the region’s entire economy prospers. At the time, Keynes had no data to test his theory. It just seemed reasonable that households spend more when their income increases and spend less when their income falls. Eventually, a variety of data were assembled that confirmed his intuition. Table 1.1 shows estimates of U.S. aggregate disposable income (income after taxes) and spending for the years 1929 through 1940. When income fell, so did spending; and when income rose, so did spending. Table 1.2 shows a very different type of data based on a household survey during the years 1935–1936. As shown, families with more income tended to spend more. Today, economists agree that Keynes’ hypothesis is correct—that spending does depend on income—but that other factors also influence spending. These more complex models can be tested with data, and we do so in later chapters. Table 1.1: U.S. Disposable Personal Income and Consumer Spending, Billions of Dollars [11] Income Spending 1929 83.4 77.4 1930 74.7 70.1 1931 64.3 60.7 1932 49.2 48.7 1933 46.1 45.9 1934 52.8 51.5 1935 59.3 55.9 1936 67.4 62.2 1937 72.2 66.8 1938 66.6 64.3 1939 71.4 67.2 1940 76.8 71.3 www.elsevierdirect.com Data, Data, Data 5 Table 1.2: Family Income and Spending, 1935–1936 [12] Income Range($) Average Income ($) Average Spending($) <500 292 493 500–999 730 802 1,000–1,499 1,176 1,196 1,500–1,999 1,636 1,598 2,000–2,999 2,292 2,124 3,000–3,999 3,243 2,814 4,000–4,999 4,207 3,467 5,000–10,000 6,598 4,950 The Political Business Cycle There seems to be a political business cycle in the United States, in that the unemployment rate typically increases after a presidential election and falls before the next presidential election. The unemployment rate has increased in only three presidential election years since the Great Depression. This is no doubt due to the efforts of incumbent presidents to avoid the wrath of voters suffering through an economic recession. Two exceptions were the reelection bids of Jimmy Carter in 1980 (the unemployment rate went up 1.3 percentage points) and George H. W. Bush in 1992 (the unemployment rate rose 0.7 percentage points). In each case, the incumbent was soon unemployed, too. The third exception was in 2008, when George W. Bush was president; the unemployment rate rose 1 percent and the Republicans lost the White House. In later chapters, we test the political business cycle model. 1.3 Making Predictions Models help us understand the world and are often used to make predictions; for example, a consumption function can be used to predict household spending, and the political business cycle model can be used to predict the outcome of a presidential election. Here is another example. ’ Okun s Law The U.S. unemployment rate was 6.6 percent when John F. Kennedy became president of the United States in January 1961 and reached 7.1 percent in May 1961. Reducing the unemployment rate was a top priority because of the economic and psychological distress felt by the unemployed and because the nation’s aggregate output would be higher if these people were working. Not only would the unemployed have more income if they were working, but also they would create more food, clothing, and homes for others to eat, wear, and live in. www.elsevierdirect.com