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METRICS TERM 2 > HANDOUT 6 > Flashcards

HANDOUT 6 Flashcards

1
Q

When we use OLS, what do we assume in order to get causal relations?

A

E(€i I X) = 0

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2
Q

What is the problem when we try to look at the effect of going to hospital on health?

A

SELECTION BIAS
E(€i I Di) ≠ 0
People who go to hospital are going to be naturally less healthy.

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3
Q

Health and hospital example: what do we observe?

A

E(Yi I Di=1) - E(Yi I Di = 0)

We compare the health outcomes of 2 different individuals, one is a hospital individual and the other isn’t.

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4
Q

Health and hospital example: what we observe is made up of…

A
  1. Average treatment effect on the treated

2. Selection bias

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5
Q

Health and hospital example: what is ATT?

A

ATT = E(Y1i I Di=1) - E(Y0i I Di=1)
Compare health of a hospital individual if they go to hospital, minus this same individual’s health would’ve been had they not gone to hospital.

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6
Q

Problem with ATT

A

‘What a hospital individual’s health would’ve been had they not gone to hospital’ = UNOBSERVED

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7
Q

Health and hospital example: what is selection bias?

A

E(Y0i I Di=1) - E(Y0i I Di=0)

Compare natural health of a hospital individual with a non-hospital individual (both for not going to hospital).

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8
Q

Sign of bias in Health and hospital example

A

Bias < 0
Natural health of hospital individuals worse than natural health of non-hospital individuals.
So sample of those going to hospital = not random.

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9
Q

3 solutions to OLS selection bias

A
  1. Randomly allocate people to go to hospital
  2. IV estimation: find instruments for Di
  3. DD estimator
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10
Q

Example of IV instrument for Health and hospital example

A

Need to find exogenous variation in Di. Some policy such as one day all ambulances strike, so the sample of those going to hospital depends on whether they are located near hospital = unrelated to health.

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11
Q

DD estimators are good for…

A

general pooled cross-sectional models

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12
Q

How do pooled cross-sectional models differ from Panel data>

A

Pooled cross-sectional = different individuals at points in time.
Panel data = we follow the same individuals.

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13
Q

General pooled cross-sectional model equation = explain dummies

A

Yit = alpha + dt + B1Xit + … + €it
dt = time dummy
NO Ai as no individual heterogeneity since different individuals.

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14
Q

treatment group =

A

set of observations affected by the new policy

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15
Q

Control group =

A

Set of observations NOT affected by the new policy

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16
Q

What is a “natural experiment”?

A

Change in government policy that is quasi-random. Leads to exogenous variation in X.

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17
Q

For DD estimator, big assumption =

A

COMMON TRENDS
we assume that in the absence of the policy, the treatment groups would’ve followed the same trends as the control group. Doesn’t necessarily mean same level.

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18
Q

When we collect data on treatment and control, what periods do we use?

A

Before and after policy change

We do NOT need exact same period for 2 groups - just before and after for both.

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19
Q

DD equation for min wage and employment in NJ vs PA.

A

Yist = alpha + gamma NJist + lambda dist +

delta (NJ ist x dist) + €ist

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20
Q

What coefficient is the DD estimator?

A

The coefficient on the interactive dummy term, which is = 1 for the treated group in the treated period.

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21
Q

What are our CLRM assumptions hold for DD?

A

Usual CLRM assumptions apply to €ist

Most importantly, E(€ist I interactive dummy) = 0 –> COMMON TRENDS ASSUMPTION.

22
Q

So, our DD estimator gives as causal effect IF…

A
  1. Our assumptions about €ist hold (especially common trends)
  2. The policy is exogenous
23
Q

Why is it difficult to test the common trends assumption?

A

Because we don’t actually know what would’ve happened to the treatment group in the absence of the policy.

24
Q

Method for testing common trends assumption

A

Look at pre-pre trends
Estimate the same model for 2 arbitrary points in history with no policy for either. If the coefficient on the interaction term = 0 –> common trends.

25
Q

Problem with testing common trends assumption using pre-pre trends

A

even if historical trends are parallel, there may be something else going on between pre&post treatment that affects the treatment group but not the control - so even in the absence of the policy of focus, trends would NOT have been parallel.

26
Q

Health scenario for State A and B to do DDD estimator. What’s the problem?

A

State A = introduces it’s own health policy that affects old, not young.
Problem is there’s a national policy affecting health of young relative to old at same time, so in absence of State policy old vs young NOT COMMON TRENDS.
State B = affect by national policy, but NO state policy.

27
Q

DDD estimator equation for old vs young, state A vs state B.

A

Yijt = do + d1 Oijt + d2 dijt + d3(Oijt x dijt) +

[p0 + p1 Oijt + p2 dijt + p3(Oijt x dijt)]Sijt + €ijt

28
Q

What coefficient gives us DDD estimator?

A

The coefficient on the TRIPLE INTERACTION TERM: Oijt x dijt x Sijt = treatment group in treated period in treatment state.

29
Q

In this DDD example, gamma 3 =

A

The state policy effect for old vs young in State A, minus the national policy effect for old vs young in state B.

30
Q

Assumption of common trends in DDD example

A

We assume that in the absence of the State policy, state A would’ve followed parallel trends to state B as would’ve been equally as affected by the national policy.

31
Q

Why can’t we just do a DD estimator for this example?

A

Because the coefficient on the interactive term = state policy effect + national policy effect - we need state B as a control to strip out the effect of the national policy, and isolate the effect of State A’s policy over and above anything else.

32
Q

What is RDD?

A

Regression Discontinuity design

Quasi-experimental designs for cross-sectional data.

33
Q

RDD example for maths test scores

A

We want to see the effect of achieving a merit in maths test during the year on final exam score. merit = mark >= 70. Compare those just above and just below the boundary.

34
Q

How can we ensure the variation in X is random for RDD for maths test scores?

A

If we take individuals just above and just below the boundary, they’re the same types of people, just subject to random shock.

35
Q

For RDD, how do we change X for the model?

A

X is continuous –> make in BINARY
D=1 treatment for X >=Xc
D=0 control for X

36
Q

What are we really interested in finding out for RDD?

A

Does receiving the treatment/prize lead to a jump in behaviour? Does exogenous variation in X –> premia in Y as a result of being just above Xc?

37
Q

Model equation for RDD

A 
Yi = alpha + delta Xi + B Di + €i
Di = 1 treatment 
Di = 0 control
38
Q

In RDD, X is called…

A

the assignment/running/forcing variable

39
Q

In RDD, Xc is…

A

The cut-off point along the assignment that determines the control and treatment groups.

40
Q

For RDD, we can reduce our sample down to…

A

Those just either side of the cut-off

41
Q

How does RDD compare to DD estimator?

A

RDD ≠ DD
WE compare different individuals for RDD. and rely on those just either side being very similar. We do NOT observe the treated and controlled individuals at the same X.

42
Q

OLS is fine for RDD as long as…

A

E(€i I Xi, Di)= 0

43
Q

Problem with X in RDD

A

It may NOT be linear - if it is actually non-linear, we could massively overestimate the discontinuity.

44
Q

How can we check to see if our functional form is OK for RDD?

A

Try changing the functional form and see if Beta is robust.

45
Q

How can we test that E(€i I Xi, Di) = 0 for RDD?

A

Impossible to test!!
But we can t-test for statistical difference in individual’s characteristics (gender, race, past performance) just above and just below boundary.

46
Q

RDD FAILS IF…

A

An individual can precisely manipulate their assignment variable i.e. an individual can precisely choose their maths test score by selecting a certain level of effort. In this case treatment and control group individuals are systematically different = variation in X is NOT exogenous.

47
Q

How do we estimate causal effects for cross-sectional?

A

IV

RDD

48
Q

How do we estimate causal effects for time-series?

A

IV (but worry about lags)

49
Q

How do we estimate causal effects for panel data?

A

IV, helped by FE

50
Q

How do we estimate causal effects for pooled cross-sectional?

A

DD / DDD estimators.

METRICS TERM 2 (6 decks)

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