IV Estimation. Dr. Alexander Spermann. Summer Term 2012

Transcription

1 IV Estmaton Dr. Alexander Spermann Summer Term 2012

2 Evaluaton wth Non-Expermental Approaches Selecton on Unobservables Natural Experment (exogenous varaton n a Varable) DD Example: Card/Krueger (1994) Mnmum Wage IV Instrument z corellated wth endogenous x, but uncorrelated wth u Non-testable dentfyng assumpton =exluson restrcton (ntuton: excludes drect causal effect on outcome (van den Berg 2007)

3 Condtons for an Instrument 1) Cov (z,u) = 0 Exogenety condton cannot be tested Endogenety could be Cov (z,u) 0 mplcaton y z (Instrument) D because z u y Instrument unobserv. varables outcome

4 Condtons for an Instrument 2) Cov (z,x) 0 relevance condton can be tested mplcaton x negatve correlaton z postve

5 IV Estmator Cov( z, y) IV Cov( z, x) f z=x.e. x s exogenous Cov( x, y) Cov( x, y) IV OLS Cov( x, x) Var( x)

6 Example: Return to Educaton (Mncer equaton) log( wage) 0 1 educ 2 abl u f no proxy avalable 0 1 educ u educ s obvously endogenous and hdes abl n the error term u OLS would be based and nconstent because OVB.e. Cov(x,u) 0 endogenety problem OLS 11%

7 Instrumental Varables for Educaton Plausble arguments for the exogenety ambton to hold 1) Instrument IQ? Correlated wth y Correlated wth u (ablty) good proxy for ablty, but no nstrument for educ 2) Instrument mother s educaton? Correlated wth x But also correlated wth u va chld s ablty no nstrument 3) Instrument number of sblngs? Negatve correlaton wth x (some evdence on that) If no correlaton wth ablty nstrument IV 12.2% > 11% OLS underestmates true value OLS

8 Bnary IV Angrst/Krueger (1999) Census data for men 1980, born n the 30s Instrument: quarter of brth of educaton Q1 Q2 Q3 Q4 School starts Born n Q1- older than 6 years Younger than 6 years Later n school Than born n Q2-Q

9 Bnary IV Insttutonal detal n the U.S.: Start school at an older age+leave school wth 16 years (brthday) (compulsory schoolng laws) wth a legal leavng age End wth less educaton than others at the legal leavng age Born n Q1means less schoolng Correlaton 1. No correlaton wth ablty 2. Correlaton wth educ large data set 8% OLS IV 7.15% OLS overestmates Earn less Weak nstrument nstrument s correlated wth other unobserved factors (due to postve correlaton between educaton and quarter of brth,.e. the hgher Q the hgher educ)

10 Instrument: College Proxmty (Bnary Varable) Card 1995 log( wage) 0 1 educ 2 exp er... u Instrument Proxmty to college 1 f near college 0 f far from college

11 Instrument: College Proxmty (Bnary Varable) Correlaton 1. No correlaton wth u 2. Correlaton wth x (educ) check by regresson educ on nearc4 (s t negatve?) OLS 7.5% OLS underestmates true value due to negatve correlaton (the closer dstance the hgher educaton) IV 13.2% But large standard errors (18 x OLS s.e.) 95% confdence nterval Ths s the prce to pay for a consstent estmator

12 Instrument bnary varable: veteran Angrst 1990, AER log( earn) 0 1 veteran u bnary varable RSN= random sequence numbers randomly assgned to brthdays Correlated (self selecton) OLS based and nconsstent Vetnam draft lottery (1970) Natural experment Lottery numbers to young men (=nstrumen for veteran) randomly assgned drafted not drafted lottery numbers

13 Instrument Bnary Varable: Veteran Correlaton 1. Uncorrelated wth u due to random assgnment 2. Correlated wth x (veteran) because low numbers servce n Vetnam Result Veterans earn less ten years later Theory: penalty for lack of labor market experence

14 Dummy Varable Instrument (Calendo) Bnary nstrument z* wth {0,1} Source of exogenous varaton to approxmate randomsed trals E( y x, z* 1) E( y x, z* 0) IV P( D 1 x, z* 1) P( D 1 x, z* 0) Wald estmator

15 Problems of the Wald Estmator 1. Weak nstrument thngs could be worse neffcency nconsstency 2. Heterogenous treatment framework IV not applcable LATE s parameter of nterest

16 Heterogeneous Effects z {0,1} D=1 or D=0 populaton subgroups never takers always takers defer compler D=0 D=1 R=0 D=1 D=0 R=1 change behavour due to swtch n nstrument z=0 z=1 D=0 D=1 In perverse way change behavour n lne wth the nstrument before D=0 then z=0 z=1 after D=1 rule change monotoncty assumpton no coexstence of defers and complers

17 Applcaton JTPA Control group substtuton bas Treatment group dropout bas IV could control for that

18 LATE s defned for complers ~ ~ IV, LATE P( D E( J 1 X X,, z ~ z 1) 1) E( J P( D X, 1 z X, ~ z 0) 0) more detals: Angrst/Pschke 2009 Imbens/ Wooldrdge Präsentaton / Referentn / Fakultät oder Insttut 18