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RD Flashcards

1
Q

NATE

A

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

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2
Q

ATT

A

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

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3
Q

ATC

A

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

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4
Q

ATE
ATE WITH DIFFERENT GROUP SIZES

A

E(Y1) - E(Y0)
π x ATT + (1- π) x ATC

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5
Q

BASELINE BIAS (BB)

A

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

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6
Q

DTEB

A

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

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7
Q

TOTAL BIAS

A

NATE - ATE
BB + DTEB

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8
Q

IPW

A

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)

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9
Q

INTERNAL VALIDITY

A

ABILITY TO IDENTIFY CAUSAL EFFECT IN STUDY SAMPLE

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10
Q

EXTERNAL VALIDITY

A

ABILITY TO GENERALIZE RESULTS TO OTHER CONTEXTS

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11
Q

ATE (EFFECT STANDARDIZATION)

A

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

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12
Q

CONFOUNDER

A

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

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13
Q

MEDIATOR

A

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

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14
Q

COLLIDER

A

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

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15
Q

DIRECT PATH

A

AN OPEN, DIRECT, CAUSAL PATH BETWEEN D AND Y

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16
Q

NON-CAUSAL OPEN PATH

A

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

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17
Q

CONDITIONING

A

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

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18
Q

HOW TO ESTIMATE COUNTERFACTUALS

A

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

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19
Q

INTENT TO TREAT (ITT)

A

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

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20
Q

P IN EQUATIONS

A

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

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21
Q

LOCAL AVARAGE TREATMENT EFFECT (LATE)

A

[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)

22
Q

METHOD OF BOUNDS

A

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

23
Q

ATE (ONE-ON-ONE MATCHING)

A

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

24
Q

CONDITIONAL INDEPENDENCE

A

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

25
Q

SIMPLE REGRESSION

A

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

26
Q

FIXED EFFECTS MODEL

A

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

27
Q

FIRST DIFFERENCE MODEL

A

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

28
Q

DIFFERENCE-IN-DIFFERENCE MODEL

A

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

29
Q

RDD (SHARP)

A

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

30
Q

LATEfrd

A

[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)]

31
Q

INSTRUMENTAL VARIABLES

A

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)]

32
Q

PATE

A

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)

33
Q

SUTVA

A

ASSUMPTION IN CAUSAL INFERENCE

  • NO SPILLOVER EFFECTS
34
Q

UNIT HOMOGENITY ASSUMPTION

A

Y1i = Y1j, Y0i = Y0j. FOR ANY i = j
NATE = ATE
ATE = ITE

D IS THE ONLY CAUSAL VARIABLE THAT AFFECTS Y

35
Q

INDEPENDENCE ASSUMPTION

A

TÄNK PÅ CONDITIONAL INDEPENDENCE

36
Q

EXCLUSION RESTRICTION

A

IN IV

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

37
Q

PROBLEMS WITH CAUSAL INFERENCE

A

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].

38
Q

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

A

BACKDOOR CRITERION

39
Q

D-SEPERATION

A

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

40
Q

Conditions needed for a perfect randomized expiriment

A

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

41
Q

Limits of randomized expiriments

A

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

42
Q

Conditional randomization

A

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

43
Q

Matching

A

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

44
Q

Under which assumptions are the IV equal to LATE?

A

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

45
Q

MMD

A

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

46
Q

POF

A

Potential outcomes framework

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

47
Q

In-time placebo

A

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”)

48
Q

In-space placebo

A

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)

49
Q

LATE assumptions

A
  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)
50
Q

ATE om inte vet atc eller ett

A

[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)

51
Q

Assumptions for POF

A

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

52
Q

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

A

[(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

tyska (4 decks)

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