Essential Statistics, Regression, and Econometrics, Second Edition

381 Pages·2012·6.996 MB·English

by  Smith, Gary

Essential Statistics,
Regression, and
Econometrics
Second Edition
Gary Smith
Pomona College
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Introduction
Econometricsiselegantandpowerful.Manydepartmentsofeconomics,politics,psychology,
andsociologyrequirestudentstotakeacourseinregressionanalysisoreconometrics.Sodo
many business, law, and medical schools. These courses are traditionally preceded by an
introductorystatisticscoursethatadherestothefirehosepedagogy:bombardstudentswith
informationandhopetheydonotdrown.Encyclopedicstatisticscoursesareamilewideand
aninchdeep,andmanystudentsrememberlittleafterthefinalexam.Thistextbookfocuses
on what students really need to know and remember.
EssentialStatistics,Regression,andEconometricsiswrittenforanintroductorystatistics
coursethathelpsstudentsdevelopthestatisticalreasoningtheyneedforregressionanalysis.
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.
Onereasonforthisbook’sfocusedapproachisthatthereisnotenoughtimeinaone-
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 what is essential.
This book does not cover the binomial distribution and related tests of a population
successprobability.Alsoomittedaredifference-in-meanstests,chi-squaretests,andANOVA
tests. Instructors who cover these topics can use the supplementary material at the book’s
website.
Theregressionchaptersattheendofthebooksetupthetransitiontoamoreadvanced
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 people mistakenly believe that statistics
courses are too abstract, mathematical, and tedious to be useful or interesting. To demon-
stratethepower,elegance,andevenbeautyofstatisticalreasoning,thisbookincludesalarge
number of compelling 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.
Thegoalistohelpstudentsdevelopthestatisticalreasoningtheyneedforlatercourses
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.
Mostofall,Iamindebtedtothethousandsofstudentswhohavetakenstatisticscourses
fromme—fortheirendlessgoodwill,contagiousenthusiasm,and,especially,forteachingme
how to be a better teacher.
ix
1
Data, Data, Data
CHAPTER OUTLINE
Measurements........................................................................................................................................2
FlyingBlindandClueless..................................................................................................................3
TestingModels.......................................................................................................................................4
ThePolitical BusinessCycle..............................................................................................................5
MakingPredictions................................................................................................................................5
Okun’sLaw.........................................................................................................................................5
NumericalandCategoricalData...........................................................................................................6
Cross-SectionalData..............................................................................................................................6
TheHamburgerStandard.................................................................................................................7
TimeSeriesData....................................................................................................................................8
SilencingBuzzSaws..........................................................................................................................8
Longitudinal(orPanel)Data...............................................................................................................10
IndexNumbers (Optional)...................................................................................................................10
TheConsumerPriceIndex..............................................................................................................11
TheDowJonesIndex......................................................................................................................12
DeflatedData.......................................................................................................................................12
NominalandRealMagnitudes......................................................................................................13
TheRealCostofMailingaLetter.................................................................................................15
RealPerCapita................................................................................................................................16
Exercises................................................................................................................................................16
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 your neighbor is unemployed; it
is a depression when you lose your job.” Herbert Hoover was president of the United
StateswhentheGreatDepressionbegan.Hewasverysmartandwell-intentioned,buthe
EssentialStatistics,Regression,andEconometrics.http://dx.doi.org/10.1016/B978-0-12-803459-0.00001-7 1
Copyright©2015GarySmith.PublishedbyElsevierInc.Allrightsreserved.
2 ESSENTIAL STATISTICS, REGRESSION, AND ECONOMETRICS
didnotknowthathewaspresidingoveraneconomicmeltdownbecausehisinformation
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.
In his December 3, 1929, State of the Union message, Hoover concluded that “The
problemswithwhichweareconfrontedaretheproblemsofgrowthandprogress”[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 60days 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 unem-
ployment data until 1940. Before then, the only unemployment data were collected in
the census, once every 10years. With hindsight, it is now estimated that between 1929
and 1933, national output fell by one-third, and the unemployment rate rose from
3percent to 25percent. The unemployment rate averaged 19percent during the 1930s
and never fell below 14percent. More than a third of the nation’s banks failed and
household wealth dropped by 30percent.
Behind these aggregate numbers were millions of private tragedies. One hundred
thousand businesses failed and 12million people lost their jobs, income, and self-
respect. Many lost their life savings in the stock market crash and the tidal wave of
bankfailures.Withoutincomeorsavings,peoplecouldnotbuyfood,clothing,orproper
medicalcare.Thosewhocouldnotpaytheirrentlosttheirshelter;thosewhocouldnot
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),sleptundernewspapers(Hooverblankets),andscavengedforfoodwhere
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.
Measurements
Today, we have a vast array ofstatistical 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 operations, estimate demand, and design marketing strategies.
Government statisticians measure corn production, air pollution, unemployment, and
inflation.
Theproblemtodayisnotascarcityofdata,butratherthesensibleinterpretationand
use of data. This is why statistics courses are taught in high schools, colleges, business
Chapter 1 • Data, Data, Data 3
schools, law schools, medical schools, and Ph.D. programs. Used correctly, statistical
reasoningcanhelpusdistinguishbetweeninformativedataanduselessnoise,andhelp
us make informed decisions.
Flying Blind and Clueless
US 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 imports to
record levels. Other countries retaliated by raising their taxes on goods imported from
the United States. Worldwide trade collapsed with US exports and imports falling by
more than 50percent.
In 1931, Treasury Secretary Andrew Mellon advised Hoover to “liquidate labor,
liquidatestocks,liquidatethefarmers,liquidaterealestate”[6].WhenFranklinRoosevelt
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 25percent. One of the most respected
financial leaders, Bernard Baruch, advised Roosevelt to “Stop spending money we
haven’t got. Sacrifice for frugality and revenue. Cut government spending—cut it as
rationsarecutinasiege.Tax–taxeverybodyforeverything”[8].Today—becausewehave
modelsanddata—weknowthatcuttingspendingandraisingtaxesareexactlythewrong
policies for fighting an economic recession. The Great Depression did not end until
World War II, when there was a massive increase in government spending and millions
of people enlisted in the military.
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
theGreatDepressionwaslargelyduetomonetaryforces,andtheysharplycriticizedthe
Fed’sperversepolicies.Ina2002speechhonoringMiltonFriedman’s90thbirthday,Ben
Bernanke,whobecameFedchairmanin2006,concludedhisspeech:“Iwouldliketosay
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,andFederalReservedidnotrepeattheerrorsofthe1930s.Facedwithacredit
crisis that threatened to pull the economy into a second Great Depression, the gov-
ernment did the right thing by pumping billions of dollars into a deflating economy.
Instead of destroying the economy, they saved it.
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.
4 ESSENTIAL STATISTICS, REGRESSION, AND ECONOMETRICS
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 rises and falls with in-
come. This “consumption function” was the lynchpin of his explanation of business
cycles. If people spend less, others will earn less and spend less, too. This fundamental
interrelationshipbetweenspendingandincomeexplainshowrecessionscanpersistand
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, farmers will buy new clothes,
and tailors will start going to the movies again. Not only do 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 to him
that households will spend more when their incomegoes up and spendless when their
income goes down. Eventually, a variety of data were assembled that confirmed his
intuition. Table 1.1 shows estimates of US aggregate disposable income (income after
taxes)andspendingfortheyears1929through1940.Whenincomefell,sodidspending;
and when income rose, so did spending.
Table1.2showsaverydifferent typeofdatabasedonahouseholdsurveyduringthe
years 1935–1936. Families with more income tended to spend more.
Today, economists agree that Keynes’ hypothesis is correct—that spending does
dependonincome—butthatotherfactorsalsoinfluencespending.Thesemorecomplex
models can be tested with data, and we do so in later chapters.
Table 1.1 US 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
Chapter 1 • Data, Data, Data 5
Table 1.2 Family Income and Spending, 1935–1936 [12]
IncomeRange($) AverageIncome($) AverageSpending($)
<500 292 493
500–999 730 802
1000–1499 1176 1196
1500–1999 1636 1598
2000–2999 2292 2124
3000–3999 3243 2814
4000–4999 4207 3467
5000–10,000 6598 4950
The Political Business Cycle
There seems to be a political business cycle in the United States, in that the unem-
ployment 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
unemploymentratewentup1.3percentagepoints)andGeorgeH.W.Bushin1992(the
unemployment rate rose 0.7 percentage points). In each case, the incumbent was soon
unemployed,too.Thethirdexceptionwasin2008,whenGeorgeW.Bushwaspresident;
the unemployment rate rose 1percent and the Republicans lost the White House. In
later chapters, we test the political business cycle model.
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
TheUSunemploymentratewas6.6percentwhenJohnF.Kennedybecamepresidentof
the United States in January 1961 and reached 7.1percent 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
higherifthesepeoplewereworking.Notonlywouldtheunemployedhavemoreincome
if they were working, but also they would create more food, clothing, and homes for
others to eat, wear, and live in.
6 ESSENTIAL STATISTICS, REGRESSION, AND ECONOMETRICS
One of Kennedy’s advisors, Arthur Okun, estimated the relationship between gross
domestic product (GDP) and the unemployment rate. His estimate, known as Okun’s
law, was that output would be about 3percent higher if the unemployment rate were 1
percentage point lower. Specifically, if the unemployment rate had been 6.1percent,
instead of 7.1percent, output would have been about 3percent higher.
This prediction helped sell the idea to Congress and the public that there are both
privateandpublicbenefitsfromreducingtheunemploymentrate.Laterinthisbook,we
estimate Okun’s law using more recent data.
Numerical and Categorical Data
Unemployment, inflation, and other data that have natural numerical values—5.1
percentunemployment,3.2percentinflation—arecallednumericalorquantitativedata.
The income and spending in Tables 1.1 and 1.2 are quantitative data.
Some data, for example, whether a person is male or female, do not have natural
numerical values (a person cannot be 5.1percent male). Such data are said to be cate-
goricalorqualitativedata.Withcategoricaldata,wecountthenumberofobservationsin
each category. The data can be described by frequencies (the number of observations)
or relative frequencies (the fraction of the total observations); for example, out of 1000
people surveyed, 510, or 51percent, were female.
The Dow Jones Industrial Average, the most widely reported stock market index, is
based on the stock prices of 30 of the most prominent US companies. If we record
whether the Dow went up or down each day, these would be categorical data. If we
record the percentage change in the Dow each day, these would be numerical data.
From 1901 through 2007, the Dow went up on 13,862days and went down on
12,727days. The relative frequency of up days is 52.1percent:
13;862
¼0:521
13;862þ12;727
For the numerical data on daily percentagechanges, wemight calculate asummary
statistic, such as the average percentage change (0.021percent), or we might separate
the percentage changes into categories, such as the number of days when the per-
centage change in the Dow was between 1 and 2percent, between 2 and 3percent,
and so on.
Cross-Sectional Data
Cross-sectionaldataareobservationsmadeatthesamepointintime.Thesecouldbeon
a single day, as in Table 1.3, which shows the price/earnings ratios for each of the Dow
Jones stocks on February 5, 2015. Cross-sectional data can also be for a single week,
month,oryear;forexample,thesurveydataonannualhouseholdincomeandspending
in Table 1.2 are cross-sectional data.
Chapter 1 • Data, Data, Data 7
Table 1.3 Price/Earnings Ratios for Dow Stocks, February 5, 2015
Company Price/EarningsRatio Company Price/EarningsRatio
Merck 32.3 CiscoSystems 18.4
Visa 30.4 Wal-MartStores 18.2
AT&T 29.0 Johnson&Johnson 18.0
Nike 27.8 UnitedTechnologies 17.6
Procter&Gamble 25.0 Microsoft 17.1
HomeDepot 24.7 GeneralElectric 16.2
WaltDisney 24.1 AmericanExpress 15.1
Pfizer 23.4 Intel 14.7
Coca-Cola 23.2 Caterpillar 14.2
3M 22.2 ExxonMobil 11.6
Boeing 20.1 GoldmanSachs 10.6
Verizon 19.8 Chevron 10.1
McDonald’s 19.6 IBM 10.1
EIduPontdeNemours 19.5 TravelersCompanies 10.0
UnitedHealthGroup 19.1 JPMorgan 9.9
The Hamburger Standard
The law of one price says that, in an efficient market, identical goods should have the
same price. Applied internationally, it implies that essentially identical goods should
cost about the same anywhere in the world, once we convert prices to the same cur-
rency. Suppose the exchange rate between US dollars and British pounds (£) is
1.50dollars/pound. If a sweater sells for £20 in Britain, essentially identical sweaters
shouldsellfor$30intheUnitedStates.IfthepriceoftheAmericansweatersweremore
than $30, Americans would import British sweaters instead of buying overpriced
Americansweaters.If thepricewerelessthan$30,the EnglishwouldimportAmerican
sweaters.
The law of one price works best for products (like wheat) that are relatively homo-
geneous and can be imported relatively inexpensively. The law of one price does not
work very well when consumers do not believe that products are similar (for example,
BMWs and Chevys) or when there are high transportation costs, taxes, and other trade
barriers. Wine can be relatively expensive in France if the French prohibit wine imports
or tax imports heavily. A haircut and round of golf in Japan can cost more than in the
UnitedStates,becauseitisimpracticalfortheJapanesetohavetheirhaircutinIowaand
play golf in Georgia.
Since 1986, The Economist, an influential British magazine, has surveyed the prices
of Big Mac hamburgers around the world. Table 1.4 shows cross-sectional data on the
prices of Big Mac hamburgers in 20 countries. The law of one price does not apply to
Big Macs, because Americans will not travel to Hong Kong to buy a hamburger for
lunch.