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1、ApEc8212EconometricAnalysis---Lecture#1ConditionalExpectationsandRelatedConceptsstWebsitefortyposin(1editionof)Wooldridgebook:http://www.msu.edu/~ec/faculty/wooldridge/book2.htmI.IntroductoryRemarksTherearefourmainusesofeconometricsandstatistics:1.Tomeasureth
2、echaracteristicsofinterestingeconomicvariables(forexample,thedegreeofincomeinequality),andthecorrelationsbetweendifferentvariablesofinterest(forexample,thecorrelationinthereturnstotwoinvestments).2.Totestthevalidityofeconomictheories.3.Toquantifythemagnitudes
3、(anddirection)ofeconomicrelationshipsandparameters.4.Toforecast/predictfuturevaluesofvariables.ndrdthWorkonthe2and3(andmaybethe4)taskssoonleadstoattemptstomeasurecausalrelationships.Toavoidconfusion,researchersmustbeverycareful,andveryexplicit,whentheyanalyze
4、data.Youshouldstartsimpleandthengoontomorecomplicatedproblems.1InthisclasswewilluseWooldridge’stextbook,whichissomewhatmorerigorousthanGreene’stextbook.InhisChapter1,Wooldridgeexplainswhyhewantsassumptionstobemadeintermsofthepopulationfromwhichthedataweredraw
5、n,asopposedtomakingassumptionsaboutthedata.Greenedoesboth.AnexampleinwhichGreenemakesanassumptionaboutthedataishisassumptiononp.20thatE[εi
6、X]=0.BothεiandXrefertothedataathand,notthepopulationfromwhichthedataweredrawn.Greenestartsoutthiswaybecauseitiseasiertos
7、howsomeproofsofresults,butashistextbookcontinueshemovesmoreintothedirectionofmakingassumptionsaboutthepopulation.Forexample,allasymptoticresultsrelyonallowingthesamplesizetogotoinfinity,whichbasicallyexpandsthedatatoincludetheentirepopulationandthusamountstom
8、akingassumptionsaboutthepopulation.Consistentwiththisapproach,allofWooldridge’sdiscussionisasymptotic,whereasGreenestartswithfinitesamplepropertiesofestimationmethodsandthenlatercoversasymptoticresults.AfinalimplicationofWooldridge’sapproachisthatexplanatoryv
9、ariables(usuallydenotedby“x”)arealwaystreatedasvariables,neverasfixedconstants.2II.ConditionalExpectationsinEconometricsMosteconometricanalysisinvolvesestimatingaconditionalexpectation,th
