APPLIED ECONOMETRICS Lecture 1 - Identification

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APPLIED ECONOMETRICSLecture 1 - Identification
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Defining Identification
Experiments
Natural Experiments
Instrumental variables
Econometric Identification
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WHAT IS IDENTIFICATION?

• Graduate and professional economics mainly
  concerned with identification in empirical work
• Concept of understanding what is the causal
  relationship behind empirical results
• This is essential for learning from empirical
  research
• Time-series example Interest rates and GDP
• Cross-section example Management Productivity

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WHAT IS DRIVING THIS RELATIONSHIP?
Correlation 0.233
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REASONS FOR CORRELATION

• Imagine variables Yt and Xt are correlated
• There can be three reasons for this, which are
  not mutually exclusive
• Cause Changes in Xt drive changes in Yt
• Reverse Cause Changes in Yt drive changes in Xt
• Correlated variable Changes in Zt drives Xt and
  Yt

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WHAT IS DRIVING THIS RELATIONSHIP?
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SO HOW DO WE GET IDENTIFICATION

• Four broad approaches for identification
• Experiments you generate the variation
• Natural Experiments you know what generated the
  variation
• Instrumental variables you have a variable that
  can provide you variation
• Econometric Identification you rely on
  (testable) econometric assumptions for
  identification

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Defining Identification
Experiments
Natural Experiments
Instrumental variables
Econometric Identification
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EXPERIMENTS (1)

• Experiments are totally standard in Science
  Medicine
• For example
• Set up a treatment and control group for a new
  drug, making sure these are comparable (or
  randomly selected)
• Ensure the sample sizes are large enough to
  obtain statistical significance
• Ensure the experiment is unbiased i.e. the drug
  and the placebo are as similar as possible
• Run the experiment

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EXPERIMENTS (2)

• Economists like to use the language of Science
• For example the UK considered introducing an
  Education Maintenance Allowance, to pay kids to
  stay on at school. But want to test first to see
  if this would this work.
• Set up a treatment and control regions to match
  these in characteristics
• Select enough regions to get large sample sizes
• Observe agents actions to evaluate impact (rather
  than self reported outcomes)
• Run the experiment

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EXPERIMENTS (3)

• Experiments are rare in economics because they
  are expensive, although they becoming more
  popular
• Typical areas for running experiments include
• Development economics cheaper to run
  experiments in the third World (water supply or
  management practices)
• Consumer economics small stakes experiments
  that are easy to administer (credit cards)
• Individual business applications firms can
  finance these (retail store layout)
• But some fields will never have experiment for
  example macroeconomics

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Defining Identification
Experiments
Natural Experiments
Instrumental variables
Econometric Identification
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NATURAL EXPERIMENTS (1)

• Natural experiments are where fortunate
  situations create good underlying identification
• Typically several approaches
• Tax e.g. Response of RD to the cost of capital
  (Bloom, Griffith Van Reenen, 2002), (Chetty and
  Saez, 2003)
• Discontinuity (see over)
• Shock - financial crisis and Kibutzim
  (Abramitzky, 2007)
• Disasters - Ethiopian Jews airlift (Gould, Levy
  Passerman, 2004)

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NATURAL EXPERIMENTS (2)

• Natural experiments are almost the holly grail of
  modern applied economics
• In the absence of true experiments they provide
  the best way to provide simple identification
• Couple of standard way to use natural experiments
  in practice
• Discountinunity analysis and/or
• Difference in differences

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DISCONTINUITY ANALYSIS example 1
Imagine a 50 tax is levied on investment in the
rich coastal region A but not in the poor inland
region B. If you saw the graph below could you
say what the impact of the tax is on investment?
Estimated impact of the tax
Investment
Region A(no tax)
Region B(50 tax)
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DISCONTINUITY ANALYSIS example 2
Impact of telephones on price of fish in Kerala
(India)
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DIFFERNCES IN DIFFERENCES

• Identification comes from the differential change
  between the two groups pre and post-treatment
• difference out unobserved fixed effects
• difference out common time effects
• Key assumption of common time effects for the two
  groups

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POLICY EXAMPLE OF DIFF-IN-DIFF

• Small firms RD tax credit introduced in 2000 for
  firms with 250 or less employees
• So could look at firms before and after credit
• But other things also changing (2000 peak of
  dotcom boom etc)
• So need to set up a control group of companies
  look similar to firms getting the credit except
  dont get the credit
• Compare firms with 240 employees to those with
  260
• This is double-diff (or diff in diffs) to compare
  differences
• Between pre and post the credit (1999 versus
  2001)
• Between the treated (240 employees) and untreated
  firms (260 employees)

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Defining Identification
Experiments
Natural Experiments
Instrumental variables
Econometric Identification
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INSTRUMENTAL VARIABLES (1)

• Want to look at effect of schooling (Si) on
  earnings (Yi)
• Assume the true model is
• Yi a ß1 Si ß2 Ai
  vi
• where Ai is (unobserved) ability which is
  positively correlated with Si, and vi is random
  independent noise
• What would happen if we estimated the following
  instead?
• Yi a b1 Si ei
• where ei ß2 Ai vi

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INSTRUMENTAL VARIABLES (2)

• ------Background
• Assume estimating equation below in Ordinary
  Least Squares
• Y a ßX e
• The estimate of ß E(YX)/E(XX)
• E((ßX e )X)/E(XX)
• ß E(eX)/E(XX)
• ß only if e and X are independent
• But if e and X are correlated then the estimated
  is biased, and X is called endogenous
  (correlated with the error)
• ---------------------

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INSTRUMENTAL VARIABLES (3)

• Thus, estimation of the following would be
  biased
• Yi a b1 Si ei
• because Si and ei are correlated as ei is a
  function of ability
• Eb1 EYS/ESS
• E(ß1Siß2Aivi)S / ESS
• ß1 E(ß2Aivi)S / ESS
• ß1 ß2EAiS / ESS
• gt ß1
• So because ignore ability, which is correlated
  with schooling, we overestimate the impact of
  schooling on earnings

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INSTRUMENTAL VARIABLES (4)

• Imagine we had a variable called an instrument
  Z that was correlated with schooling but not
  ability.
• We could then use this to explain variation in
  schooling as it is not correlated with ability
• One example of this would be if the Government
  paid everyone born on even days to stay in school
• Then born on an even day would be an instrument
  for schooling correlated with schooling but not
  ability
• In practice instruments are often hard to find

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INSTRUMENTAL VARIABLES (5)

• Assume that Z is correlated with S but not A.
  Then the following instrumental variable
  estimator is consistent
• Eb1IV EYZ/ESZ
• E(ß1Siß2Aivi)Z / ESZ
• Eß1SiZ ß2AiZ viZ / ESZ
• ß1 (ß2EAiS EviZ) / ESZ
• ß1
• Stata will calculate this for you. All you need
  to find is a variable that only affects your
  dependent variable via the variable you are
  interested in

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INSTRUMENTAL VARIABLES

• Any questions on this?
• Imagine you wanted to evaluate the impact of crop
  yields on farmers behavior can anyone suggest a
  good instrument

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Defining Identification
Experiments
Natural Experiments
Instrumental variables
Econometric Identification
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ECONOMETRIC IDENTIFICATION

• Another way to obtain identification is try to
  model everything
• For example, we claim we know how ability is
  correlated with schooling and so model the whole
  system
• The problem with this is
• It is a lot more complicated
• It requires strong assumptions
• Thus, this is usually only undertaken when there
  is no obvious instrument or natural experiment

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SUMMARY

• Identification understanding the causality in a
  regression is essential for generating
  meaningful results
• There are a range of approaches but they all
  need some prior economic thought (i.e. is their a
  natural experiment?)