RD

Question 1

NATE

Answer 1

E(Y1 I D=1) - E(Y0 I D=0)

Question 2

ATT

Answer 2

E(Y1 I D=1) - E(Y0 I D=1)

Question 3

ATC

Answer 3

E(Y1 I D=0) - E(YO I D=0)

Question 4

ATE
ATE WITH DIFFERENT GROUP SIZES

Answer 4

E(Y1) - E(Y0)
π x ATT + (1- π) x ATC

Question 5

BASELINE BIAS (BB)

Answer 5

E(Y0 I D=1) - E(Y0 I D=0)

Question 6

DTEB

Answer 6

(1-π) x [[E(Y1 I D=1) - E(Y0 I D=1)] - [E(Y1 I D=0) - E(Y0 I D=0)]]

Question 7

TOTAL BIAS

Answer 7

NATE - ATE
BB + DTEB

Question 8

IPW

Answer 8

Dx1 / P(D=1, X=X) + (1-D)x1 / P(D=0, X=x)

MÅSTE RÄKNA UT IPW FÖR VARJE OUTCOME FÖRST, EX ANTAL (Y1 I D=1, X=1) = 4
TA HELA X=1 PO =6. IPW= 4/6
FÖR ATT FÅ RÄTT, VÄND PÅ DET, RÄKNA UT 6/4 ISTÄLLET

RÄKNA UT FÖR ALLA SEPARAT
(Y1 I D=1, X=1)
(Y1 I D=1, X=0)
(Y0 I D=0, X=1)
(Y0 I D=0, X=0)

SEDAN FÖR ATT FÅ E(Y1) = (ADDERA ALLA OBSERVATIONER FÖR (Y1 I D=1, X=1) x IPW FÖR (Y1 I D=1, X=1) + ALLA OBSERVATIONER FÖR (Y1 I D=1, X=0) x IPW FÖR Y1 I D=1, X=0)) / (ANTALET OBSERVATIONER FÖR (Y1 I D=1, X=1) x IPW FÖR Y1 I D=1, X=1 + ANTALET OBSERVATIONER FÖR (Y1 I D=1, X=0) x IPW FÖR (Y1 I D=1, X=0)

GÖR SAMMA MED IPW FÖR Y0, ATE ÄR DÅ RESULTATET VI FÅTT
E(Y1) - E(Y0)

Question 9

INTERNAL VALIDITY

Answer 9

ABILITY TO IDENTIFY CAUSAL EFFECT IN STUDY SAMPLE

Question 10

EXTERNAL VALIDITY

Answer 10

ABILITY TO GENERALIZE RESULTS TO OTHER CONTEXTS

Question 11

ATE (EFFECT STANDARDIZATION)

Answer 11

[E(Y1 I D=1, X=x) - E(Y0 I D=0, X=x)] x P(X=x)

Question 12

CONFOUNDER

Answer 12

WHEN BOTH OF (Z)s ARROWS POINT OUTWARD
AKA: Z AFFECTS OTHER VARIABLES

Question 13

MEDIATOR

Answer 13

WHEN A VARIABLE IS ON THE PATH BETWEEN D & Y
AKA: ONE ARROW POINTS IN TO (Z) AND ANOTHER OUT OF (Z)

Question 14

COLLIDER

Answer 14

WHEN ARROWS POINT IN TO (Z)
AKA: OTHER VARIABLES AFFECT Z
MEANS THE PATH IS CLOSED

Question 15

DIRECT PATH

Answer 15

AN OPEN, DIRECT, CAUSAL PATH BETWEEN D AND Y

Question 16

NON-CAUSAL OPEN PATH

Answer 16

WHEN THERE IS AN OPEN PATH BETWEEN D AND Y BUT IT’S NOT A CAUSAL PATH, AKA A BACKDOOR PATH

Question 17

CONDITIONING

Answer 17

INTRODUCE INFORMATION ABOUT A VARIABLE, CLOSES OR OPENS PATH (IF COLLIDER OR NOT)

Question 18

HOW TO ESTIMATE COUNTERFACTUALS

Answer 18

TAKE MEAN FROM OBSERVED RESULTS:
EX, (Y1 I D=1) MEAN IS 4, MEAN FOR (Y1 I D=0) IS 4 FOR ALL OBSERVATIONS

Question 19

INTENT TO TREAT (ITT)

Answer 19

E(Y I Z=1) - E(Y I Z=0)

Question 20

P IN EQUATIONS

Answer 20

THE SIZE OF THE GROUP
EX, WHOLE STUDY POP IS 10, 6 OF THEM ARE X=1. P= 6/10

Question 21

LOCAL AVARAGE TREATMENT EFFECT (LATE)

Answer 21

[E(Y I Z=1) - E(Y I Z=0)] / [E(D I Z=1) - E(D I Z=0)]

E(Y1 - Y0 I COMPLIER)
FÖR ATT RÄKNA UT ANTALET COMPLIERS, HUR MÅNGA SUBJECTS FICK TRETMENT I BÅDA GRUPPERNA, OM 90% AV DE I T-GROUP BLEV TREATED ÄR DE 90%, OM 40% AV DE I C-GROUP BLEV TREATED ÄR DE 40% (RÄKNA BARA TREATED, DISREGARD CONTROL)

EX, Y1=9, Y0=5,

LATE= (9-5) / (0,9 - 0,4)

Question 22

METHOD OF BOUNDS

Answer 22

RÄKNA UT ATE(MIN) OCH ATE(MAX) OM VI INTE VET VAD ALLA SUBJECTS GJORDE

ATE = (Y1 - Y0)

IN TREATMENT GROUP 60% Y=1 , 20% Y=0 AND 20% Y=?
I CONTROL: 20% Y=1, 60% Y=0 AND 20 Y=?

FÖR ATE(MIN) ASSUME THE Y=? VAR Y=0 OCH FÖR ATE(MAX) ASSUME THE Y=? VAR Y=1

ATE(MIN) = 0,6 - (0,2 + 0,2)
ATE(MAX) = (0,6 + 0,2) - 0,2

Question 23

ATE (ONE-ON-ONE MATCHING)

Answer 23

[E(Y I D=1, X=x) - E(Y I D=0, X=x)] x P(X=x)

Question 24

CONDITIONAL INDEPENDENCE

Answer 24

E(Y0 I D=0, X=x) = E(Y0 I D=1, X=x)
OCH
E(Y1 I D=1, X=x) = E(Y1 I D=0, X=x)

GER MATCHING ESTIMATOR:
[E(Y1 I D=1, X=x) - E(Y0 I D=1, X=x)] x P(X=x) = ATT

Question 25

SIMPLE REGRESSION

Answer 25

B0 + B1 x Di + ri B0 = (Y0 I D=0) B0 + B1 = E(Y1 I D=1) B1 = E(Y1 I D=1) - E(Y0 I D=0) = NATE

Question 26

FIXED EFFECTS MODEL

Answer 26

B0 + Bfe x (Dit + mean of Di) + B2 x (Xit + mean of Xi) + (Wit + mean of Wi) EX, FOR i=1 MEAN OF Y = 8. Y YEAR 1 = 8, Y YEAR 2 = 9, Y YEAR 3 = 7 Y(FE) = 8 - 8 = 0 FOR YEAR 1 Y(FE) = 9 - 8 = 1 FOR YEAR 2 Y(FE) = 7 - 8 = -1 FOR YEAR 4

Question 27

FIRST DIFFERENCE MODEL

Answer 27

B0 + Bfd x (Dit + D(it - 1)) + B2 x (Xit + X(it-1)) + (Wit + W(it-1)) EX, FOR i=1 MEAN OF Y = 8. Y YEAR 1 = 8, Y YEAR 2 = 9, Y YEAR 3 = 7 Y(FD) = - CANNOT COUNT THE FIRST YEAR Y(FD) = 9 - 8 = 1 FOR YEAR 2 Y(FD) = 7 - 9 = -2 FOR YEAR 4

Question 28

DIFFERENCE-IN-DIFFERENCE MODEL

Answer 28

Bdd = [E(Ypost I D*=1) - E (Yante I D*=1)] - [E(Ypost I D*=0) - E (Yante I D*=0)]

Question 29

RDD (SHARP)

Answer 29

ATEsrd = E(Y1 I D=1, X=C) - E(Y0 I D=0, X=C)

Question 30

LATEfrd

Answer 30

[E(Y I Z=1, X=c) - E(Y I Z=0, X=C)] / [E(DI Z=1, X=C) - E(D I Z=0, X=C)]

Question 31

INSTRUMENTAL VARIABLES

Answer 31

Z > D > Y CALCULATE % OF COMPLIERS, ALWAYSTAKERS AND NEVERTAKERS [Y(D=1, Z=1) / [Y(D=1, Z=1) - Y(D=0, Z=1)]] - [Y(D=1, Z=0) / [Y(D=1, Z=0) - Y(D=0, Z=0)]] Y(D=1, Z=1) = 865 Y(D=0, Z=1) = 1915 Y(D=1, Z=0) = 1372 Y(D=0, Z=0) = 5948 [865 / (865-1915)] - [1372 / (1372-5948)] = 0,331 - 0,188 = 0,123 COMPLIERS: 0,123 ALWAYSTAKERS: 0,188 [Y(D=1, Z=0) / [Y(D=1, Z=0) - Y(D=0, Z=0)] NEVERTAKERS: 1- (0,123 + 0,188) [I - (COMPLIERS + ALWAYSTAKERS)]

Question 32

PATE

Answer 32

E(Y I D=1, S=1,Z=z) - E(Y I D=0, S=1, Z=z) SAMPLE POPULATION EDUCATION (HI: 0,5, LOW: 0,5) TARGET POPULATION EDUCATION (HI: 0,2, LOW: 0,8) AVARAGE EFFECT RESULTS IN SAMPLE (HI: 2, LOW:6) PATE= (0,2 x 2) + (0,8 x 6)

Question 33

SUTVA

Answer 33

ASSUMPTION IN CAUSAL INFERENCE - NO SPILLOVER EFFECTS

Question 34

UNIT HOMOGENITY ASSUMPTION

Answer 34

Y1i = Y1j, Y0i = Y0j. FOR ANY i = j NATE = ATE ATE = ITE D IS THE ONLY CAUSAL VARIABLE THAT AFFECTS Y

Question 35

INDEPENDENCE ASSUMPTION

Answer 35

TÄNK PÅ CONDITIONAL INDEPENDENCE

Question 36

EXCLUSION RESTRICTION

Answer 36

IN IV Z DOES NOT HAVE A DIRECT EFFECT ON Y, ONLY ON D

Question 37

PROBLEMS WITH CAUSAL INFERENCE

Answer 37

We cannot observe both counterfactuals for the same person. We only observe one. Therefore, we can also not directly observe the ATE = E[Y1 − Y0].

Question 38

Which graphical criterion implies independence of D and Y1, Y 0

Answer 38

BACKDOOR CRITERION

Question 39

D-SEPERATION

Answer 39

ALL PATHS BETWEEN TWO VARIABLES ARE CLOSED We can deduce from a graph what correlations in the data are implied We can find testable implications of our assumptions

Question 40

Conditions needed for a perfect randomized expiriment

Answer 40

Random sample, randomization of treatment, large N, subjects need to comply, subjects should not drop out, perfect measurement

Question 41

Limits of randomized expiriments

Answer 41

Costs (of performing equivalent randomized experiments to test each treatment of interest may be prohibitive) Estimates based on results may be delayed for years Ethical concerns (Harmful treatments, deception) Realism and size of study population in field experiments (ethical concerns) Some variables cannot be manipulated Randomization is infeasible if we are interested in the effects of particular events in the past Random experiments break: noncompliance, attrition

Question 42

Conditional randomization

Answer 42

Conditional randomization means that we form groups of units with similar X and then actually randomize D within these groups.

Question 43

Matching

Answer 43

Matching is a data analysis algorithms that finds observations with same/similar X, but different treatment D.

Question 44

Under which assumptions are the IV equal to LATE?

Answer 44

Exclusion restriction (no direct effect on Y ), (as-if) random assignment (no back-door paths from Z to D or Y ), no defiers.

Question 45

MMD

Answer 45

Mills method of observed difference Looking for cause of effects. Look for cases with different outcomes and look for the cause of the difference.

Question 46

POF

Answer 46

Potential outcomes framework Looking for effects of causes. Look for cases with different D (causes) and look at the difference in outcome.

Question 47

In-time placebo

Answer 47

Apply method to dates when the intervention did not occur (e.g., change dataset so that Germany was unified in 1980 instead of 1991, and estimate the “effect”)

Question 48

In-space placebo

Answer 48

Re-assignment of the intervention to control units (e.g., change dataset so that Italy was unified in 1990, while Germany was not, and estimate “effect” on Italy)

Question 49

LATE assumptions

Answer 49

1. Relevance (Z creates variation in D) 2. Exogeneity (Z is randomly assigned) 3. Exclusion restriction (Z affects the outcome only through D) 4. Monotonicity (There are no defiers)

Question 50

ATE om inte vet atc eller ett

Answer 50

[E(Y1 I D=1) - E(Y0 I D=1)] - [E(Y1 I D=0) - E(Y0 I D=E)] x ANTALET OBSERVATIONER X/N BASICALLY DETTA E [E(Y I D=1, X=x) - E(Y I D=0, X=x)] x P(X=x)

Question 51

Assumptions for POF

Answer 51

Exchangability: of participants included in the study and members of the target population, possibly conditional on pre-treatment charasteristics of Z Positivity: treatment posibilites in sample population is greater than 0 within all strata of Z (does not have to be 1, or equal for all subjects) No interference: within the study and the target population

Question 52

ATE när vi saknar counterfactuals (och har ett x-värde)

Answer 52

[(E(Y1 I D=1, X=1) / E(Y0 I D=0, X=1)] x X/N )+ [E(Y1 I D=1, X=0) - E(Y0 I D=0, X=0)] x X/N