安慰劑檢驗介紹、操作及舉例

安慰劑檢驗介紹（Placebotest）安慰劑是一種附加實證檢驗的思路，并不存在一個具體的特定的操作方法。一般存在兩種尋找安慰劑變量的方法。比如，在已有的實證檢驗中，發(fā)現(xiàn)自變量Xi會影響自變量Zi與因變量Yi之間存在相關關系。在其后的實證檢驗中，采用其他主體（國家，省份，公司）的Xj變量作為安慰劑變量，檢驗Xj是否影響Zi與Yi之間的相關關系。如果不存在類似于Xi的影響，即可排除Xi的安慰劑效應，使得結果更為穩(wěn)健。另一種尋找安慰劑變量的方法。已知，Xi是虛擬變量，Xi=1，ift>T；Xi=0ift<T；Xi對Zi對Yi的影響的影響在T時前后有顯著差異（DID）。在其后的實證檢驗中，將Xi`設定為Xi`=1，ift>T+n；Xi`=0ift<T+n，其中n根據(jù)實際情況取值，可正可負。檢驗Xi`是否影響Zi與Yi之間的相關關系。如果不存在類似于Xi的影響，即可排除Xi的安慰劑效應，使得結果更為穩(wěn)健。舉例：以美國市場某種政策沖擊識別策略的因果關系考察，在最后部分選取英國同期的因變量，檢驗是否有類似的特征，就是安慰劑檢驗。以中國2007年所得稅改革作為減稅的政策沖擊以驗證減稅對企業(yè)創(chuàng)新的影響。亦可以通過把虛擬的政策實施時間往前往后推幾年，作為虛擬的政策時點，如果檢驗發(fā)現(xiàn)沒有類似的因果，文章的主要結論就更加可信了。以下是詳細的例題，安慰劑檢驗在最后。Thefollowingreplicationexercisecloselyfollowsthehomeworkassignment#2inECNS562.Thedataforthisexercisecanbefound

\o"eitc.dta"here.ThedataisabouttheexpansionoftheEarnedIncomeTaxCredit.Thisisalegislationaimedatprovidingataxbreakforlowincomeindividuals.

Forsomebackgroundonthesubject,seeEissa,Nada,andJeffreyB.Liebman.1996.LaborSupplyResponsestotheEarnedIncomeTaxCredit.QuarterlyJournalofEconomics.

111(2):605-637.Describeandsummarizedata.Calculatethesamplemeansofallvariablesfor(a)singlewomenwithnochildren,(b)singlewomenwith1child,and(c)singlewomenwith2+children.Createanewvariablewithearningsconditionalonworking(missingfornon-employed)andcalculatethemeansofthisbygroupaswell.Constructavariableforthe“treatment”calledANYKIDSandavariableforaftertheexpansion(calledPOST93—shouldbe1for1994andlater).Createagraphwhichplotsmeanannualemploymentratesbyyear(1991-1996)forsinglewomenwithchildren(treatment)andwithoutchildren(control).Calculatetheunconditionaldifference-in-differenceestimatesoftheeffectofthe1993EITCexpansiononemploymentofsinglewomen.Nowrunaregressiontoestimatetheconditionaldifference-in-differenceestimateoftheeffectoftheEITC.Useallwomenwithchildrenasthetreatmentgroup.Reestimatethismodelincludingdemographiccharacteristics.Addthestateunemploymentrateandallowitseffecttovarybythepresenceofchildren.Allowthetreatmenteffecttovarybythosewith1or2+children.

Estimatea“placebo”treatmentmodel.Takedatafromonlythepre-reformperiod.Usethesametreatmentandcontrolgroups.Introduceaplacebopolicythatbeginsin1992(so1992and1993bothhavethisfakepolicy).Recallthecodeforimportingyourdata:/*Lastmodified1/11/2011*/**************************************************************************Thefollowingblockofcommandsgoatthestartofnearlyalldofiles*/*Bracketcommentswith/**/orjustuseanasteriskatlinebeginningclear/*Clearsmemory*/setmem50m/*Adjustthisforyourparticulardataset*/cd"C:\DATA\Econ562\homework"/*Changethisforyourfilestructure*/logusingstata_assign2.log,replace/*Logfilerecordsallcommands&results*/display"$S_DATE$S_TIME"setmoreoffinsheetusingeitc.dta,clear*************************************************************************123456789101112131415#KevinGoulding#ECNS562-Assignment2

###########################################################################Loadtheforeignpackagerequire(foreign)

#Importdatafromwebsite#update:firstdownloadthefileeitc.dtafromthislink:#/open?id=0B0iAUHM7ljQ1cUZvRWxjUmpfVXM#Thenimportfromyourharddrive:eitc=read.dta("C:/link/to/my/download/folder/eitc.dta")</pre>NotethatanycommentscanbeembeddedintoRcode,simplybyputtinga<code>#</code>totheleftofyourcomments(e.g.anythingtotherightof<code>#</code>willbeignoredbyR).Alternately,youcandownloadthedatafile,andimportitfromyourharddrive:

eitc=read.dta("C:\DATA\Courses\Econ562\homework\eitc.dta")Recallfrompart1ofthisseries,thefollowingcodetodescribeandsummarizeyourdata:dessumInR,eachcolumnofyourdataisassignedaclasswhichwilldeterminehowyourdataistreatedinvariousfunctions.ToseewhatclassRhasinterpretedforallyourvariables,runthefollowingcode:1234sapply(eitc,class)summary(eitc)source('sumstats.r')sumstats(eitc)TooutputthesummarystatisticstabletoLaTeX,usethefollowingcode:12require(xtable)

#xtablepackagehelpscreateLaTeXcodefromR.xtable(sumstats(eitc))Note:Youwillneedtore-runthecodefor

sumstats()

whichyoucanfindinan

\o"SummaryStatisticsfunctioninR:

sumstats()"earlierpost.summarizeifchildren==0summarizeifchildren==1summarizeifchildren>=1summarizeifchildren>=1&year==1994meanworkifpost93==0&anykids==11234567891011121314#Thefollowingcodeutilizesthesumstatsfunction(youwillneedtore-runthiscode)sumstats(eitc[eitc$children==0,])sumstats(eitc[eitc$children==1,])sumstats(eitc[eitc$children>=1,])sumstats(eitc[eitc$children>=1&eitc$year==1994,])

#Alternately,youcanusethebuilt-insummaryfunctionsummary(eitc[eitc$children==0,])summary(eitc[eitc$children==1,])summary(eitc[eitc$children>=1,])summary(eitc[eitc$children>=1&eitc$year==1994,])

#Anotherexample:Summarizevariable'work'forwomenwithonechildfrom1993onwards.summary(subset(eitc,year>=1993&children==1,select=work))Thecodeaboveincludesallsummarystatistics–butsayyouareonlyinterestedinthemean.Youcouldthenbemorespecificinyourcoding,likethis:123mean(eitc[eitc$children==0,'work'])mean(eitc[eitc$children==1,'work'])mean(eitc[eitc$children>=1,'work'])Tryoutanyoftheotherheadingswithinthesummaryoutput,theyshouldalsowork:

min()

forminimumvalue,

max()

formaximumvalue,

stdev()

forstandarddeviation,andothers.Tocreateanewvariablecalled“c.earn”equaltoearningsconditionalonworking(if“work”=1),“NA”otherwise(“work”=0)–usethefollowingcode:gencearn=earnifwork==11234567eitc$c.earn=eitc$earn*eitc$workz=names(eitc)X=as.data.frame(eitc$c.earn)X[]=lapply(X,function(x){replace(x,x==0,NA)})eitc=cbind(eitc,X)eitc$c.earn=NULLnames(eitc)=zConstructavariableforthetreatmentcalled“anykids”=1fortreatedindividual(hasatleastonechild);andavariableforaftertheexpansioncalled“post93”=1for1994andlater.genanykids=(children>=1)genpost93=(year>=1994)12eitc$post93=as.numeric(eitc$year>=1994)eitc$anykids=as.numeric(eitc$children>0)Createagraphwhichplotsmeanannualemploymentratesbyyear(1991-1996)forsinglewomenwithchildren(treatment)andwithoutchildren(control).preservecollapsework,by(yearanykids)genwork0=workifanykids==0labelvarwork0"Singlewomen,nochildren"genwork1=workifanykids==1labelvarwork1"Singlewomen,children"twoway(linework0year,sort)(linework1year,sort),ytitle(LaborForceParticipationRates)graphsaveGraph"homework\eitc1.gph",replace123456789101112131415#Takeaveragevalueof'work'byyear,conditionalonanykidsminfo=aggregate(eitc$work,list(eitc$year,eitc$anykids==1),mean)

#renamecolumnheadings(variables)names(minfo)=c("YR","Treatment","LFPR")

#Attachanewcolumnwithlabelsminfo$Group[1:6]="Singlewomen,nochildren"minfo$Group[7:12]="Singlewomen,children"minfo

require(ggplot2)

#packageforcreatingniceplots

qplot(YR,LFPR,data=minfo,geom=c("point","line"),colour=Group,

xlab="Year",ylab="LaborForceParticipationRate")Theggplot2packageproducessomenicelookingcharts.Calculatetheunconditionaldifference-in-differenceestimatesoftheeffectofthe1993EITCexpansiononemploymentofsinglewomen.meanworkifpost93==0&anykids==0meanworkifpost93==0&anykids==1meanworkifpost93==1&anykids==0meanworkifpost93==1&anykids==112345a=colMeans(subset(eitc,post93==0&anykids==0,select=work))b=colMeans(subset(eitc,post93==0&anykids==1,select=work))c=colMeans(subset(eitc,post93==1&anykids==0,select=work))d=colMeans(subset(eitc,post93==1&anykids==1,select=work))(d-c)-(b-a)Nowwewillrunaregressiontoestimatetheconditionaldifference-in-differenceestimateoftheeffectoftheEarnedIncomeTaxCrediton“work”,usingallwomenwithchildrenasthetreatmentgroup.Theregressionequationisasfollows:Where

isthewhitenoiseerrorterm.geninteraction=post93*anykidsregworkpost93anykidsinteraction12reg1=lm(work~post93+anykids+post93*anykids,data=eitc)summary(reg1)Addingadditionalvariablesisamatterofincludingtheminyourcodedregressionequation,asfollows:genage2=age^2/*Createage-squaredvariable*/gennonlaborinc=finc-earn/*Non-laborincome*/regworkpost93anykidsinteractionnonwhiteageage2edfincnonlaborinc123reg2=lm(work~anykids+post93+post93*anykids+nonwhite

+age+I(age^2)+ed+finc+I(finc-earn),data=eitc)summary(reg2)Wewillcreatetwonewinteractionvariables:Thestateunemploymentrateinteractedwithnumberofchildren.Thetreatmentterminteractedwithindividualswithonechild,ormorethanonechild.geninteru=urate*anykidsgenonekid=(children==1)gentwokid=(children>=2)genpostXone=post93*onekidgenpostXtwo=post93*twokid123456789101112#Thestateunemploymentrateinteractedwithnumberofchildreneitc$=eitc$urate*eitc$anykids

###Creatinganewtreatmentterm:

#First,we'llcreateanewdummyvariabletodistinguishbetweenonechildand2+.eitc$manykids=as.numeric(eitc$children>=2)

#Next,we'llcreateanewvariablebyinteractingthenewdummy#variablewiththeoriginalinteractionterm.eitc$tr2=eitc$eraction*eitc$manykidsTestingaplacebomodeliswhenyouarbitrarilychooseatreatmenttimebeforeyouractualtreatmenttime,andtesttoseeifyougetasignificanttreatmenteffect.genplacebo=(year>=1992)genplaceboXany=anykids*placeboregworkanykidsplaceboplaceboXanyifyear<199