INSTRUMENTAL VARIABLES

INSTRUMENTAL VARIABLES Technical Track Sessin IV Sergi Urzua University f Maryland

Instrumental Variables and IE Tw main uses f IV in impact evaluatin: 1. Crrect fr difference between assignment f treatment and actual treatment E.g. Randmized Assignment with nn-cmpliers E.g. Fuzzy Regressin Discntinuity 2. Lk fr exgenus variatin (ex-pst) t evaluate the impact f a prgram in absence f a prspective design. Here: General Principles behind IV and an example with a fcus n use (1)

An example t start ff with Say we wish t evaluate a vluntary jb training prgram Any unemplyed persn is eligible (Universal eligibility) Sme peple chse t register (Participants) Other peple chse nt t register (Nn-participants) Sme simple ways t evaluate the prgram: Randm sample cntaining treatment status (P), exgenus cntrls (X) and utcme (Y). First alternative: T cmpare situatin f participants and nn-participants after the interventin. We already learned this estimatr wuld be biased!

Vluntary jb training prgram Say we decide t cmpare utcmes fr thse wh participate t the utcmes f thse wh d nt participate: A simple mdel t d this: y = α + β 1 P + β 2 x + ε P = 1 If persn participates in training 0 If persn des nt participate in training x = Cntrl variables (exgenus & bserved) Why wuld this nt be crrect? 2 prblems: Decisin t participate in training is endgenus (e.g. based n an unmeasurable characteristic). Variables that we mit (e.g. unmeasured) but that are imprtant P and ε are crrelated

What can we d t slve this prblem? We estimate: y = β 0 + β 1 x + β 2 P + ε S the prblem is the crrelatin between P and ε Intuitin f IV: Hw abut we replace P with smething else that is similar t P but is nt crrelated with ε

Back t the jb training prgram P = participatin ε = that part f utcmes that is nt explained by prgram participatin r by bserved characteristics Instrumental variable will be a variable Z that is: (1) Clsely related t participatin P. [i.e. Crr ( Z, P ) > 0] (2) but desn t directly affect peple s utcmes Y, except thrugh its effect n participatin. [i.e. Crr ( Z, ε ) = 0 ] Hard t cme up with such a variable ex-pst but if we anticipate this prblem, we can plan fr it

Generating an instrumental variable Encuragement design: - Say that a scial wrker visits persns t encurage them t participate. She nly visits 50% f persns n her rster, and She randmly chses whm she will visit If she is effective, many peple she visits will enrll. There will be a crrelatin between receiving a visit and enrlling. - But visit des nt have direct effect n utcmes (e.g. incme) except frm its effect thrugh enrllment in the training prgram. Randmized encuragement r prmtin visits can be a useful instrumental variable.

Characteristics f an instrumental variable Define a new variable Z Z = 1 If persn was randmly chsen t receive the encuragement visit frm the scial wrker 0 If persn was randmly chsen nt t receive the encuragement visit frm the scial wrker Crr ( Z, P ) > 0 Peple wh receive the encuragement visit are mre likely t participate than thse wh dn t Crr ( Z, ε ) = 0 N crrelatin between receiving a visit and benefit t the prgram apart frm the effect f the visit n participatin. Z therefre satisfies the cnditins fr being an instrumental variable

Tw-stage least squares (2SLS) Remember the riginal mdel with endgenus P: Step 1 y = β 0 + β 1 x + β 2 P + ε Regress the endgenus variable P n the instrumental variable(s) Z and ther exgenus variables P = δ 0 + δ 1 x + δ 2 Z + τ Calculate the predicted value f P fr each bservatin: P^ Since Z and x are nt crrelated with ε, neither will be Yu will need ne instrumental variable fr each ptentially endgenus regressr. P^

Tw-stage least squares (2SLS) Step 2 Regress y n the predicted variable P and the ther exgenus variables y = β 0 + β 1 x + β 2 + ε Nte: The standard errrs f the secnd stage OLS need t be crrected because P^ is a generated regressr. In Practice: Use STATA ivreg cmmand, which des the tw steps at nce and reprts crrect standard errrs. Intuitin: By using Z t predict P, we cleaned P f its crrelatin with η It can be shwn that (under certain cnditins) β 2,IV yields a cnsistent estimatr f γ 2 (large sample thery) P^

Example: Training & Earnings Cnsider the mdel: y = β 0 + β 2 P + ε Randm Sample f 10,000 bservatins Data cntains (y, P, Z ) 6,328 individuals with D=1 & 3,618 with D=0.

Example: Training & Earnings Cnsider the mdel: y = β 0 + β 2 P + ε First Strategy (Participants vs. Nn-participants) E(Y1 D=1) = -0.227 E(Y0 D=0) = 0.996 Thus, δ = E(Y1 D=1) - E(Y0 D=0) = -1.223*** Yu might cnclude then that the effect f the prgram is negative. Selectin bias?

Example: Training & Earnings Cnsider the mdel: y = β 0 + β 2 P + ε Let intrduce the instrument Z: Crr(Z,D)=0.37*** Pr(D=1 Z=1)=0.82 Pr(D=1 Z=0)= 0.45 Cv(y,Z) Cv(P,Z) E(Y Z 1) E(Y Z 0) E(P Z 1) E(P Z 0) 0.210

Example: Was it real? Cnsider the mdel: y = β 0 + β 2 P + ε I generated the data: Y1(u)=0.1 + 0.2 + ε1(u) Y0(u)=0.1 + + ε0(u) P = 1 if Z(u) Y0(u)>0, =0 therwise Y(u) = Y1(u) * P(u) + Y0(u) * (1-P(u)) THUS, I KNOW THE TRUE AVERAGE TREATMENT EFFECT

Example: Was it real? Cnsider the mdel: y = β 0 + β 2 P + ε In ur fake data, we bserve (D,Z,Y1,Y0,Y) Treatment Effect= E(Y1 D=1)-E(Y0 D=1) = 0.2 Selectin Bias = E(Y0 D=1)-E(Y0 D=0) =-1.423 δ = E(Y1 D=1)-E(Y0 D=0) = 0.2+(-1.423) = -1.22 IV gt it right (IV=0.21) This is nt rcket science!

Nn ecnmetric intuitin: Illustratin frm vluntary jb training prgram Ppulatin eligible fr jb training prgram Randm Sample Randmized assignment Standard Infrmatin nly Mnthly incme 1 year later = 700 Standard Infrmatin + Encuragement visit Mnthly incme 1 year later = 850 25% take-up 75% take-up Questin: what is the impact f the jb training prgram n the mnthly incme f participants?

Standard Infrmatin Package nly Mnthly incme 1 year later = 700 Standard + Additinal Infrmatin Package Mnthly incme 1 year later = 850 25% take-up 75% take-up Questin: what is the impact f the jb training prgram? Stage 1: Take-up difference between well infrmed and nt well infrmed :... Stage 2a: Incme difference between the well infrmed and nt well infrmed grup:.. Stage 2b: Impact f participatin: Incme difference scaled by take-up difference:

Reminder and a wrd f cautin crr (Z,ε) =0 If crr (Z, ε) 0, Bad instrument Finding a naturally gd instrument is hard! But yu can build ne yurself with a randmized encuragement design crr (Z,P) 0 If crr (Z, P) 0 Weak instruments : the crrelatin between Z and P needs t be sufficiently strng. If nt, the bias stays large even fr large sample sizes.

Reminder and a wrd f cautin: Hetergeneity It is pssible t shw that, in the cntext f hetergeneus effects, the IV apprach might NOT prvide meaningful results. Hwever, we can still evaluate using structural mdels. Example: Evaluating the impact f financial intermediatin

References Heckman, J., E. Vytlacil, S. Urzua (2006). Understanding instrumental Variables in Mdels with Essential Hetergeneity, Review f Ecnmics and Statistics, v88, n3. Heckman, J., S. Urzua(2010) Cmparing IV With Structural Mdels: What Simple IV Can and Cannt. Jurnal f Ecnmetrics, Vl. 156(1), 2010 Angrist, J. D. and A. Krueger (2001). Instrumental Variables and the Search fr Identificatin: Frm Supply and Demand t Natural Experiments, Jurnal f Ecnmic Perspectives, 15(4). Angrist, J. D., G. W. Imbens and D. B. Rubin (1996). Identificatin f Causal Effects Using Instrumental Variables, Jurnal f the American Statistical Assciatin, Vl. 91, 434. Angrist, J., Bettinger, E., Blm, E., King, E. and M. Kremer (2002). Vuchers fr Private Schling in Clmbia: Evidence frm a Randmized Natural Experiment, American Ecnmic Review, 92, 5. Imbens, G. W. and J. D. Angrist, (1994). Identificatin and Estimatin f Lcal Average Treatment Effects. Ecnmetrica, 62(2). Newman, J., M. Pradhan, L. B. Rawlings, G. Ridder, R. Ca, J. L. Evia, (2002). An Impact Evaluatin f Educatin, Health, and Water Supply Investments by the Blivian Scial Investment Fund., Wrld Bank Ecnmic Review, vl. 16(2).