Econ 7818: Mathematical statistics for econo-mistsEdward MoreyFall 2010 (August 24, 2010)Econ 7818 is the …rst course in the statistics/econometrics sequence for Ph.D.students in Economics. Statistics is the foundation of econometrics.Most of you are destined to become econometricans of one sort or another:di¤erent variations on the theme "applied econometrican."1 What is statistics?This will be the topic of our …rst lecture. Put simply: A course in statisticsstudies statistics. Every function of random variables is a statistic. (What’s arandom variable?) Econometricans develop statistics, then use these statistics,along with data, to estimate things about the world of interest to economists.Some quotes:To understand God’s thoughts we must study statistics, for theseare the measure of His purpose. (Florence Nightingale, famous deadnurse)Statistics are like a bikini. What they reveal is suggestive, butwhat they conceal is vital. (Aaron Levenstein)The …rst lesson that you must learn is, when I call for statisticsabout the rate of infant mortality, what I want is proof that fewerbabies died when I was Prime Minister than when anyone else wasPrime Minister. That is a political statistic. (Winston Churchill)There are three kinds of lies: lies, damned lies, and statistics.(Benjamin Disraeli, but sometimes attributed to Mark Twain)12 What is statistics? What is econometics? Somequotes.Quoting from the front of The Advanced Theory of Statistics, Vol. 2, by M.G.Kendall and A. Stuart. They attributed the exchange to the …ctitious K.A.C.Manderville, The Undoing of Lamia Gurdleneck.),"You haven’t told me yet," said Lady Nuttal, "what it is your…ancé does for a living.""He’s an s tatistican ." replied Lamia, with an annoying sense ofbeing on the defensive.Lady Nuttal was obviously taken aback. It had not occurred toher that statisticans entered into normal so cial relationships. Thespecies, she would have surmised, was perpetuated in some collateralmanner, like mules."But Aunt Sara, it’s a very interesting profession," said Lamiawarmly."I don’t doubt it," said her aunt, who obviously doubted it verymuch. "To express anything important in mere …gures is so plainlyimpossible that there must be endless scope for well-paid advice onhow to do it. But don’t you think that life with an statistican wouldbe rather, shall we say, humdrum?"Lamia was silent. She felt reluctant to discuss the surprisingdepth of emotional possibility which she had discovered below Edgar’snumerical veneer."It’s not the …gures themselves," she said …nally, "it’s what youdo with them that matter."2Some quotes from A Guide to Econometrics by Peter KennedyEconometrics is what econometricians do.Econometrics is the study of the application of statistical meth-ods to the analysis of economic phenomena.What distinguishes an econometrician from a statistician is theformer’s preo c cup ation with problems caused by violations of sta-tistician’s standard assumptions; owing to the nature of economicrelationships and the lack of controlled experimentation, these as-sumptions are seldom met.Econometricians are often accused of using sledgehammers tocrack open peanuts while turning a blind eye to data de…cienciesand the many questionable assumptions required for the successfulapplication of these many techniques.Econometric theory is like an exquisitely balance d French recipe,spelling out precisely with how many turns to mix the sauce, howmany carats of spice to add, and for how many milliseconds to bakethe mixture at exactly 474 degrees of temperature. But when thestatistical cook turns to raw materials, he …nds that hearts of cactusfruit are unavailable, so he substitutes chunks of cantaloupe; wherethe recipe calls for vermicelli he used shredded wheat; and he substi-tutes green garment die for curry, ping-pong balls for turtle’s eggs,and for Chalifougnac vintage 1883, a can of turpe ntine. (Valavanis)It is the preparation skill of the econometric chef that catches theprofessional eye, not the quality of the raw materials in the meal, orthe e¤ort that went into procuring them (Griliches)The art of the econometrician consists in …nding the set of as-sumptions which are both su¢ ciently speci…c and su¢ ciently real-istic to allow him to take the best p oss ible advantage of the dataavailable to him (Malinvaud)The applied econometrician: The applied econometrician, unlikethe theoretical econometrician, needs to worry as much about herdata as about the theory. The forecasts and predictions generatedby the econometric model are only as good as the data that producedthem.3A well-known econ ometrican recently mentioned to me that he was hiredby a group of wealthy gamblers to use his choice-mo deling skills to predict theoutcomes of horse races. It might be important that he get it right.43 Course Description:Econ 7818 is an introductory course in statistics for Ph.D. students in economics.Important components include probability theory, distribution theory, sta-tistics, estimators and estimates, properties of estimators, sampling, inference,estimators such maximum likelihood and OLS, and hypothesis testing. Exten-sive use will be made of the mathematical and statistical software, Mathematica.3.1 Web page:My web site is located at http:www.colorado.edu/economics/morey/index.html. From it you can link to the web page for Econ 7818, or you can go directly toweb page for the course at http:www.colorado.edu/economics/morey/7818/7818home.html.All assignments, review questions, readings, lecture notes, etc. will, hope-fully, be available there.53.2 Text and readings:The text for this course is Alexander Mood, Franklin Graybill, and Duane Boes,Introduction to the Theory of Statistics, McGraw Hill, 1974. ISBN 0-07-042864-6.While you want to acquire your own copy of the book and cherish it forever,I have put the chapters of the book on the course web page. The book is nolonger in print, but used copies are available from book sellers on the web.The text for 7828 is Green: Econometric Analysis, 6th edition. I recommendyou get it now rather than waiting.3.2.1 Another text that I might have chosen for this course isTakkeshi Amemiya, Introduction to statistics and econometrics, Harvard Uni-versity Press, 1994, ISSBN 0-674-46225-43.2.2 For those who are considering additional books, I recommend:Peter Kennedy, A Guide to Econometrics (4th edition), MIT Press, 1998. ISBN0-262- 61140-6. This is an