ENDOGENEITY - SIMULTANEITY

1
ENDOGENEITY - SIMULTANEITY

• Development
• Workshop

2
What is endogeneity and why we do not like it?
REPETITION

• Three causes
• X influences Y, but Y reinforces X too
• Z causes both X and Y fairly contemporaneusly
• X causes Y, but we cannot observe X and Z (which
  we observe) is influenced by X but also by Y
• Consequences
• No matter how many observations estimators
  biased (this is called inconsistent)
• Ergo whatever point estimates we find, we cant
  even tell if they are positive/negative/significan
  t, because we do not know the size of bias no
  way to estimate the size of bias

3
The magic of ceteris paribus

• Each regression is actually ceteris paribus
• Problem data may be at odds with ceteris paribus
• Examples?

4
Problems with Inferring Causal Effects from
Regressions

• Regressions tell us about correlations but
  correlation is not causation
• Example Regression of whether currently have
  health problem on whether have been in hospital
  in past year
•  HEALTHPROB       Coef.   Std. Err.      t   
  ---------------------------------------------
      PATIENT     .262982   .0095126   
  27.65          _cons     .153447    .003092   
  49.63  
• Do hospitals make you sick? a causal effect

5
The problem in causal inference in case of
simultaneity
Confounding Influence
Treatment
Outcome
6
Any solutions?
Confounding Influence
Treatment
Outcome
7
Instrumental Variables solution
Confounding Influence
Treatment
Outcome
Instrumental Variable(s)
8
Fixed Effects Solution (DiD does pretty much the
same)
Fixed Influences
Confounding Influence
Treatment
Outcome
9
Short motivating story ALMPs in Poland

• Basic statement 50 of unemployed have found
  employment because of ALMPs
• Facts
• 50 of whom? only those, who were treated (only
  those were monitored)
• only 90 of treated completed the programmes
• of those, who completed, indeed 50 work, but
  only 60 of these who work say it was because of
  the programme
• So how many actually employed because of the
  programme?

10
Short motivating story ALMPs in Poland
11
Basic problems in causal inference

• Compare somebody before and after
• If they were different already before, the
  differential will be wrongly attributed to
  treatment
• can we measure/capture this inherent difference?
• does it stay unchanged before and after?
• what if we only know after?
• If the difference stays the same gt DiD estimator
  gt assumption that cannot be tested for
• If the difference cannot be believed to stay the
  same?

12
Faked counterfactual or generating a paralel world

• MEDICINE takes control groups people as sick,
  who get a different treatment or a placebo gt
  experimenting
• What if experiment impossible?

13
What if experiment impossble?
Only cross-sectional data
Panel data
Instrumental variables
Propensity Score Matching DiD
Before After Estimators
Propensity Score Matching
Difference in Difference Estimators (DiD)
Regression Discontinuity Design
14
Propensity Score Matching
Confounding Influence
Treatment
Treatment
Outcome
15
Propensity score matching
Group Y1 Y0
Treated (D1) Observed counterfactual (does not exist)
Nontreated (D0) counterfactual (does not exist) observed

• Average treatment effect
• E(Y)E(Y1-Y0)E(Y1)-Y0
• Average treatment effect for the untreated
• E(Y1-Y0D0)E(Y1D0)-E(Y0D0)
• Average treatment effect for the treated (ATT)
• E(Y1-Y0D1)E(Y1D1)-E(Y0D1)

16
Propensity Score Matching

• Idea
• Compares outcomes of similar units where the only
  difference is treatment discards the rest
• Example
• Low ability students will have lower future
  achievement, and are also likely to be retained
  in class
• Naïve comparison of untreated/treated students
  creates bias, where the untreated do better in
  the post period
• Matching methods make the proper comparison
• Problems
• If similar units do not exist, cannot use this
  estimator

17
How to get PSM estimator?

• First stage run treatment on observable
  characteristics
• Second stage estimate the probability of
  treatment
• Third stage compare results of those treated
  and similar non-treated (statistical twinns)
• The less similar they are, the less likely they
  should be compared one with another

18
The obtained propensity score is irrelevant (as
long as consistent)

• NEAREST NEIGHBOR (NN)
• Pros gt tzw. 11
• Cons gt if 11 does not exist, completely
  senseless

19
The obtained propensity score is irrelevant (as
long as consistent)

• CALIPER/RADIUS MATCHING(NN)
• Pros gt more elastic than NN
• Cons gt who specifies the radius/caliper?

20
The obtained propensity score is irrelevant (as
long as consistent)

• Stratification and Interval
• Pros gt eliminates discretion in radius/caliper
  choice
• Cons gt within strata/interval, units dont have
  to be similar
• (some people say 10 strata is ql)

21
The obtained propensity score is irrelevant (as
long as consistent)

• KERNEL MATCHING (KM)
• Pros gt uses always all observations
• Cons gt need to remember about common support

Treatment Control





22
What is common support?

• Distributions of pscore may differ substantially
  across units
• Only sensible solutions!

23
Real world examples
24
Next week practical excercise

• Read the papers posted on the web
• I will post one that we will replicate soon