1 mar 2018 · Regression Discontinuity • Today we'll focus on difference-in-differences – Reminder on basic concepts/theory – Applications in Stata
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[PDF] Differences-in-Differences (using Stata)
(using Stata) (work in progress) Difference in differences (DID) Estimation step-by-step The coefficient for 'did' is the differences-in-differences estimator
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Difference-In-Differences (DID) estimators are widely used in economics to evaluate the impact of a policy The crucial assumption is referred to as the Parallel-
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1 mar 2018 · Regression Discontinuity • Today we'll focus on difference-in-differences – Reminder on basic concepts/theory – Applications in Stata
[PDF] Section 3 Difference-in-Difference Estimator
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5 fév 2019 · into the difference-in-differences estimation This flexible conditional DID approach ensures that varying treatment phases can be accounted for
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3/1/181Photo Credit Goes Here
IAPRI-MSU Technical Training
Difference-in-differences
1March2018IndabaAgriculturalPolicyResearchInstituteLusaka,ZambiaRecall from July/September trainings on introduction to impact evaluation (1)
3/1/182
Recall from July/September trainings on introduction to impact evaluation (2)• Wedidabriefoverviewofcommonmethodsofimpactevaluation(IE)• Randomizedevaluation• PropensityScoreMatching• Difference-in-Differences• InstrumentalVariables• RegressionDiscontinuity
• Todaywe'llfocusondifference-in-differences- Reminderonbasicconcepts/theory- ApplicationsinStata
Learning objectives
• Bytheendoftoday'ssession,youshouldbeableto:1. UnderstandthekeyassumptionofDIDmodels2. WritedowntheregressionequationforaDID
model3. Identifywhichparameterintheregression
4. EstimateaDIDmodelinStataandinterpretthe
results3/1/183
References
• Khandker,S.R.,Koolwal,G.B.andSamad,H.A.,2010.Othersuggestedreadingsandreferences-DIDsectionsin:• Angrist,J.D.,&Pischke,J.S.(2009).Mostlyharmless
• Angrist,J.D.,&Pischke,J.S.(2015).Mastering'metrics:The • Imbens,G.W.,&Wooldridge,J.(2007).What'snewin • Ravallion,M.(2008).Evaluatinganti-povertyprograms.REVIEW: With vs. Without • ThekeycomparisonwewanttomakeinIEisbetweenoutcomesWITHVS.WITHOUTtheintervention(project/program/policy)
• Impact="With"outcome-"without"outcome3/1/184
Impact=With-Without
Source:Khandkeretal.(2010)
Participants'incomeWITHtheprogram?• Y
4 Participants'incomeWITHOUTtheprogram(counterfactualincome)?• Y 2Programimpact?• Y
4 -Y 2Introducing Difference-in-Differences (DID)
• WhohasusedDIDbeforeandwhatwereyoustudying? • WhatistheDIDapproachtoconstructingacomparisongroup/ - "TheDIDestimatorreliesonacomparisonofparticipantsand - DIDImpact=(avg.ΔYparticipants)-(avg.ΔYnon-participants) • (avg.Y T after-avg.Y T before)-(avg.Y c after-avg.Y c before)• àwhyit'scalleddifference-in-differencesordoubledifference3/1/185
DID - visual representation
DIDimpact=(avg.Y
T after-avg.Y T before)-(avg.Y c after-avg.Y c before)Source:Khandkeretal.(2010)
Changeinparticipants'income?• Y
4 -Y 0Changeinnon-participants'(control)income?• Y
3 -Y 1DIDimpact?• (Y
4 -Y 0 )-(Y 3 -Y 1DID key assumption: parallel (common) trends
Paralleltrends="unobservedcharacteristicsaffectingprogramparticipationdonotvaryovertimewithtreatmentstatus"(Khandkeretal.2010,p.73)• I.e.,trendsintheoutcomevariablewouldbethesameinthetwogroupswithouttreatment(Angrist&Pischke2009);or• "...treatmentandcontroloutcomesmoveinparallelintheabsenceoftreatments"(Angrist&Pischke(2015,p.178)• Implies(Y
1 -Y 0 )=(Y 3 -Y 2Source:Khandkeretal.(2010)
Changeinparticipants'income(after-before)?• Y 4 -Y 0 Changeinnon-participants'(control)income(after-before)?• Y 3 -Y 1DIDimpact?• (Y
4 -Y 0 )-(Y 3 -Y 1 )• =Y 4 -Y 0 -Y 3 +Y 1 =Y 4 -Y 3 +Y 1 -Y 0Substitutein(Y
1 -Y 0 )=(Y 3 -Y 2 )(paralleltrendassumption):• =Y 4 -Y 3 +Y 3 -Y 2 =Y 4 -Y 2Sameaswithvs.without!
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What happens if trends are not parallel?
• DIDestimateisbiased • àSeenext2slidesandhandoutbasedonfiguresinRavallion(2008)forillustration
KeyassumptionforDID:Paralleltrends
Source: Ravallion (2008)
Selection bias Same
DID estimate = Treatment effect
Treatment effect
Parallel
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Selection bias
Source: Ravallion (2008)
Different
Non-paralleltrendscauseDIDtobebiased
Treatment effect
DID estimate
Treatment effect
(here DID estimate < Treatment effect )NOTparallel
Can partially test for parallel trends if have multiple pre-treatment waves of data• Use3wavesofdata:- 2wavespriortoimplementationofNAAIAP(2004&2007TAPRAsurveys)- 1waveafter(during)implementation(2010TAPRAsurvey)• Regresschangeinoutcomevariable(2007minus2004)ondummyforifHH
• Whilenoguaranteethattrendswouldhavebeenparallel2007to2010in3/1/188
DID simple numerical example
Source:Khandkeretal.(2010)
DIDimpact=(avg.Y
T after-avg.Y T before)-(avg.Y c after-avg.Y c before)DID data requirements
• Repeatedcross-sections - Separaterandomsamplesfromtherelevant OR• Paneldata- Randomsamplefromtherelevantpopulationand3/1/189
Regression DID - Basic Setup
Y it =α+γTreated i +λAfter t +δ(Treated i×After
t itWhere:• iindexesthecross-sectionalunitandtindexestime• Treated=1ifunitisultimatelytreated(exposedtoproject/program/policychange),
• After=1iftimeperiodisaftertheproject/program/policychange,• Treated×Afteristheinteractionofthesetwovariables• *Note:Notationaboveisforwhen"treatment"ortheproject/program/policychange
• Whichparameterrepresentsthecausaleffectofinterest(assumingthekey Regression DID - Basic Setup - with higher level project/program/policy change Y idt =α+γTreated d +λAfter t +δ(Treated d×After
t idt • Whichparameterrepresentsthecausaleffectofinterest(assumingthe keyassumptionshold)?• ThisisthemorecommoninstanceinwhichDIDisused• Wouldwanttoclusteryourstandarderrorsatthedistrictlevel
δ(theparameterontheTreatedXAfterterm)
3/1/1810
Regression DID - Basic Setup - with covariates
Canalsocontrolforadditionalcovariates:
Y idt =α+γTreated d +λAfter t +δ(Treated d×After
t )+X idt idt • Boldrepresentsvectors• Whichparameterrepresentsthecausaleffectofinterest(assumingthe keyassumptionshold)?δ(theparameterontheTreatedXAfterterm)
EX)2periods:
Y it =α+λAfter t +δTreated it +c i +u it • Firstdifferencetoremovec i (orestimateviaFE)ΔY i =λ+δΔTreated i +Δu i • Whichparameteristhecausaleffectofinterest (assumingthekeyassumptionshold)?Panel FE setup without control variables
3/1/1811
EX)2ormoreperiods
Y it =α+Year tλ+δTreated
it +X itβ+c
i +u it • WhereYearisavectorofyeardummies• EstimateviaFE • Whichparameteristhecausaleffectofinterest (assumingthekeyassumptionshold)?Panel FE setup with control variables
Examples & tweaking the variable names/notation to fit your particular situation (1)General:Y
it =α+γTreated i +λAfter t +δ(Treated i×After
t valuesinacityinMassachusetts• Newgarbageincineratorconstructionbeganin1981• Havehousingvaluedatafrom1978and1981plusinfoondistancefromhouse
• Let"nearinc"=1ifhouseisnear(within3miles/4.83km)incinerator,=0o.w. (farfromincinerator)• Let"y81"=1ifyearis1981,and=0o.w.(yearis1978)• HowwouldyouwritetheDIDregressionequationinthiscase?Whatisthekey
parameterofinterest?3/1/1812
Examples & tweaking the variable names/notation to fit your particular situation (1)General:Y
it =α+γTreated i +λAfter t +δ(Treated i×After
t valuesinacityinMassachusettsSpecific:rprice
it =α+γnearinc i +λy81 t +δ(nearinc i×y81
t it• Where- "rprice"isthehomevalueinrealUS$- "nearinc"=1ifhouseisnear(within3miles/4.83km)incinerator,=0o.w.
(farfromincinerator) - "y81"=1ifyearis1981,and=0o.w.(yearis1978) Examples & tweaking the variable names/notation to fit your particular situation (2)General:Y
it =α+γTreated i +λAfter t +δ(Treated i×After
t itExample:Angrist&Pischke(2009)-understandingcholeratransmissioninmid-1800s• Havedistrict-leveldatafromLondonondeathratesandwatercompanyin1849&
1852.Let:
- "deathr"bethedeathrateindistrictd- "Lambeth"=1ifdistrictdgetsitswaterfromtheLambethCompany(which- "y1852"=1ifyearis1852,and=0o.w.(yearis1849)• WritedowntheDIDequationforthisscenarioandusingthesevariablesSpecific:deathr
dt =α+γLambeth d +λy1852 t +δ(Lambeth d×y1852
t dt3/1/1813
Examples & tweaking the variable names/notation to fit your particular situation (3)General:Y
idt =α+γTreated d +λAfter t +δ(Treated d×After
t idtExample:Angrist&Pischke(2009)-effectofémin.wageonfastfoodemployment• Havedatafromneighboringstates(NJ&PA).Bothstateshave$4.25minimumwagein
- "employ"betheemploymentlevelofeachrestaurant- "NJ"=1ifstateisNJ,=0ifstateisPA- "Nov92"=1iftimeisNovember1992,and=0o.w.(timeisFebruary1992)• WritedowntheDIDequationforthisscenarioandusingthesevariables.Thinkcarefully
aboutwhichsubscriptstoputoneachvariable.Specific:employ
ist =α+γNJ s +λNov92 t +δ(NJ s×Nov92
t istDID good to consider if have natural experiment
• Bigpicturequestion:whydomanyHHsselllow,buyhigh(w.r.t.cropprices)?• Hypothesis:"short-termexpenditureneedsforcepoorhouseholdstosell
• Naturalexperiment:Malawichangedprimaryschoolcalendar- 2009:startinDecember.2010:startinSeptember.à HHshavetomakeschool-relatedexpendituresmuchearlierin2010than
3/1/1814
DID & natural experiment example (cont'd)
DIDregression:General:Y
it =α+γTreated i +λAfter t +δ(Treated i×After
t itSpecific:Cropsales
it =α+γChildren i +λy2010 t +δ(Children i×y2010
t itWhere• Cropsales=cumulativevalueofHHcropsalesthroughAugustofyeart• Children=#ofchildreninprimaryschool(0,1,2,3,etc.).Orcoulddo0/1• y2010=1ifyearis2010;=0ifyearis2009• EstimateseparatelyforHHsabovevs.belowthepovertyline
What other situations/examples appropriate for DID can you think of? • AndhowwouldyousetupyourDIDregressionequation? • General:Y=α+γTreated+λAfter+δ(Treated×After)+ε3/1/1815
DID vs. other methods
• KeydifferencebetweenPSMandDID:PSMassumesselectiononobservablesonly,DIDallowsselectiontobeafunctionoftime-constantunobservedfactors(a.k.a.timeinvariantunobservedheterogeneity)
- Wherehaveyouheardthistermbefore?- Whatifselectionisafunctionoftime-varyingunobservables? • Anotherkeydifference: - Randomizedevaluations&PSM-cross-sectionaldata - NeedrepeatedcrosssectionsorpaneldataforDID