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1、CornerSolutionResponseModelsPhDEconometricsWeiTanHanqingAdvancedInstituteofEconomicsandFinanceRenminUniversityofChinaWeiTan(RUC)CornerSolutionResponseModels1/63MotivationandExamplesWenowturntomodelsforlimiteddependentvariablesthathavefeaturesofbothcontinuousanddisc
2、reterandomvariables.Inparticular,theyarecontinuouslydistributedoverarangeofvalues,sometimesaverywiderange,buttheytakeononeortwofocalpointswithpositiveprobability.Suchvariablesariseofteninmodelingindividual,family,or…rmbehavior,andevenwhenstudyingoutcomesatamoreaggr
3、egatedlevel,suchastheclassroomorschoollevel.Themostcommoncaseiswhenthenonnegativeresponsevariable,y,hasa(roughly)continuousdistributionoverstrictlypositivevalues,butP(y=0)>0.Wecallsuchavariableacornersolutionresponseorcornersolutionoutcome,wherethecornerinthiscasei
4、satzero.WeiTan(RUC)CornerSolutionResponseModels2/63MotivationandExamplesForexample,considerthepopulationoffamiliesmakingcharitablecontributionsduringagivenyear.Ifyisthefractionofcharitablecontributionsmadetoreligiousorganizations,wearelikelytoseeawiderangeofvaluesb
5、etweenzeroandone,andthenpileupsatthetwoendpointsofzeroandone.Ifso,thecornersareatzeroandone,anditmakessensetotreatyashavingacontinuousdistributionovertheopeninterval(0;1).Cornersolutionresponsesareoftencalled“censoredresponses”,alabelthatcomesfromsituationswithactu
6、aldatacensoring.Consequently,theleadingmodelthatwecoverinthischapterissometimescalleda“censoredregressionmodel”.Instead,weusethesomewhatunconventionalnamecornersolutionmodelbecausewearetryingtocapturefeaturesofanobservedcornersolutionresponse.Theword“censored”impli
7、esthatwearenotobservingtheentirepossiblerangeoftheresponsevariable,butthatisnotthecaseforcornersolutionresponses.WeiTan(RUC)CornerSolutionResponseModels3/63MotivationandExamplesForexample,inamodelofcharitablecontributions,thevariableweareinterestedinexplaining,both
8、fortheoreticalreasonsandforthepurposesofpolicyanalysis,istheactualamountofcharitablecontributions.Thatthisoutcomemightbezeroforanontrivialfractio
