FINAL MEETING

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FINAL MEETING OTHER METHODS

• Development
• Workshop

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General conclusions on causal analyses

• Magic tool of ceteris paribus
• Regression is ceteris paribus by definition
• But the data need not to be they are just a
  subsample of general populations and many other
  things confound
• Causal effects, i.e. cause and effect
• Propensity Score Matching
• Regression Discontinuity
• Fixed Effects
• Instrumental Variables

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If we cannot experiment..
Cross-sectional data
Panel data
IV
Propensity Score Matching DiD
Before After Estimators
Propensity Score Matching
Difference in Difference Estimators (DiD)
Regression Discontinuity Design
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Problems with causal inference
Confounding Influence (environment)
Treatment
Effect
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Instrumental Variables solution
Confounding Influence
Treatment
Outcome
Instrumental Variable(s)
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Fixed Effects Solution (DiD does pretty much the
same)
Fixed Influences
Confounding Influence
Treatment
Outcome
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Propensity Score Matching
Confounding Influence
Treatment
Treatment
Outcome
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Regression Discontinuity Design
Group that is key for this policy
Confounding Influence
Treatment
Effect
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A motivating story

• Today women in Poland have on average 1,7 kid
• About 50 years ago, women had 2,8 kids
• Todays women are 6 times more educated than 50
  years ago will a drop from 2.8 to 1.7 be an
  effect of this educational change?
• Natural experiment in 1960 schooling obligation
  was extended by one year (11 to 12 years).
• THE SAME women born just before 1953 went to
  primary and secondary schools a year shorter than
  born after 1953
• THE SAME ?
• RD allows to compare fertility (with individual
  characteristics) for women born around 1953

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Regression Discontinuity Design

• Idea
• Focus your analyses on a group for which treament
  was random (or rather independent)
• How to do it?
• Example weaker students have lower grades, but
  are also frequently delayed to repeat
  courses/years if we give them extra classes,
  better students will outperform them anyway, so
  how to test if extra classes help?
• RDD will compare the performance of students just
  above and just below threshold, so quite
  similar ones
• RDD will only work if people cannot prevent or
  encourage treatment by relocating themselves
  around threshold

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Regression Discontinuity Design

• Advantages
• Really marginal effect
• Causal, if RDD well applied
• Disadvantages
• Sample size largely limited
• Only local character of estimations
  (marginal?average)
• Problems
• How do we know how far away from threshold can we
  go (bandwidth)?
• How do we know if design is ok.?

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Regression Discontinuity Design

• Zastosowanie
• Trade off between narrow bandwidth (for
  independence assumption) and wide bandwidth to
  increase sample size
• One can try to find it empirically ( fuzzy RD
  design)
• Y is the effect, p is treatment probability.
• is effect of probability just above cut-off
• - is effect of probability just below cut-off

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Regression Discontinuity Design
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Regression Discontinuity Design
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Regression Discontinuity Design
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How to do this in STATA?

• First download package net instal rd
• Second define your model
• rd out, treatment, in if in weight ,
  options
• Third there are some options
• mbw(numlist) multiplication of bandwidth in
  percent (default "100 50 200" which means we
  always do 50, 100 and 200)
• z0(real) sets cutoff Z0 (treatment)
• ddens asks for extra estimation of
  discontinuities in Z density
• graph draws graphs weve seen automatically

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Sample results in STATA - data
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Output from STATA
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Output from STATA - graph
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Output from STATA fuzzy version
gen byte ranwincond(uniform()lt.1,1-win,win) rd
lne ranwin d, mbw(25(25)300) bdep ox
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One last thing ?

• Quintile regressions

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A motivating story
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Some basics doubts of an empirical economist

• Compare similar to similar
• Keep statistical properties
• Understand bezond average x
• Understand (and be independent of) outliers

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Robust estimators

• First flavour of robust regression with robust
  option
• Helps if problem is not systematic
• Does not help if problem is the nature of the
  process (e.g. heterogeneity)
• Second flavour of robust nonparametric
  estimators
• Complex from mathematical point of view
• Takes longer to compute
• But veeeery elastic
• gt Koenker (and his followers)

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How to do this in STATA?

• Estimate at median
• qreg y in
• Estimate at any other percentile
• qreg y in, quantile(q) where q is your
  percentile
• Estimate differences between different
  percentiles
• iqreg y in, quantile(.25 .75) reps(100)
  additionally may bootstrap

What is bootstrap for?
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Output from STATA
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Output from STATA
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Summarising all this crap
Confounding Influence (environment)
Treatment
???
Effect
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Problems

• Sample
• size
• heterogeneity
• Methods
• None is perfect
• Question important
• Nonparametric (kernel in PSM or QR) are robust,
  robust is not a synonim for miraculous