Methods of Economic Investigation: Lent Term

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Methods of Economic Investigation Lent Term

• Radha Iyengar
• Office Hour Monday 15.30-16.30
• Office R425

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Administrative Details

• 3 lectures per week for first 6 weeks all at
  10am
• Monday, 10-11
• Tuesday, 10-11
• Thursday, 10-11
• First Two Lectures each week Theory
• Thursday Lectures Empirical Application
• Recommended text Johnston and Dinardo not
  very technical and good explanation

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Course Outline

• How we do causal inference (2 Weeks)
• Data Structure
• Experimental vs. Non-experimental Methods
• Various Non-Experimental Methods (3 weeks)
• Difference-in-Differences
• Matching
• Instrumental variables
• Various Data Issues (1 week)
• Measurement Error
• Selection Bias
• Censoring
• Time series (4 weeks)

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Why Suffer through Econometrics?

• To predict the future (well, sort of)
• To answer hard questions on the effect of X on Y
• To understand what all those wacky economists are
  talking about

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Econometrics is tool for useful thinking

• Were going to use econometrics for 2 things
• Causal Effects
• Forecasting
• Causal effects are answers to what if
  questions
• What would happen to driving if we increased gas
  taxes were raised?
• Forecasting want best currently available
  predictors dont worry about what causes what

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Real-life Uses

• Class exercises will contain practical work with
  real data
• Number of purposes
• Makes concepts less abstract, easier to
  understand
• Gives real-world skills
• Gives insight into difficulty of of empirical
  work

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Regression Re-cap

• In our standard OLS model we estimate something
  like
• To estimate we need a condition like E(X,e) 0
• So generally, were interested in the
  relationship between our X of interest on y
  holding other stuff constant

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OLS Estimation

• If E(yX)Xß, the OLS estimate is an unbiased
  estimate of ß
• Proof Can write OLS estimator as
• If X is fixed we have that

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What do Regression Estimates tell us?

• Regressions tell us about correlations but
  correlation is not causation
• Example Regression of police on Crime
• As crime increases, police levels increase
• Do Police cause crime?

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Police Levels and Crime rates
Levitt (1997) American Economic Review
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Problems in Estimating Causal Effects

• Reverse Causality
• Omitted Variables
• Measurement Error
• Sample selection

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Omitted Variables (should be familiar)

• Suppose we want to estimate E(yX,W) assumed to
  be linear in (X,W), so that E(yX,W) XßW? or
• y XßW?e
• But you estimate
• yXßu
• i.e. E(yX). Will have

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Form of Omitted Variables Bias

• Where there is only one variable
• Extent of omitted variables bias related to
• size of correlation between X and W
• strength of relationship between y and W

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Reverse Causality/ Endogeneity

• Idea is that correlation between y and X may be
  because it is y that causes X not the other way
  round
• Interested in causal model
• yXße
• But also causal relationship in other direction
• Xayu

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Endogeneity (II)

• Reduced form is
• X(uae)/(1-aß)
• X correlated with e know this leads to bias in
  OLS estimates
• In hospital example being sick causes you to go
  to hospital not clear what good solution is.

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Measurement Error

• Most (all?) of our data are measured with error.
• Suppose causal model is
• yXße
• But only observe X which is X plus some error
• XXu
• Classical measurement error
• E(uX)0

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Implications of Measurement Error

• Can write causal relationship as
• YXß-u ß e
• Note that X correlated with composite error
• Should know this leads to bias/ inconsistency in
  OLS estimator
• Can make some useful predictions about nature of
  bias later on in course
• Want E(yX) but can only estimate E(yX)

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Sample Selection

• One explanation is sample selection
• Only have earnings data on women who work
• Women with small children who work tend to have
  high earnings (e.g. to pay for childcare)
• Employment rates of mothers with babies is 28,
  of those with 5-year olds is 50
• Causal model for everyone
• yXß e
• But only observe if work, W1, so estimate
  E(yX,W1) not E(yX)
• Sample selection bias if W correlated with e
  this is likely

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Common Features of Problems

• All problems have an expression in everyday
  language omitted variables, reverse causality
  etc
• All have an econometric form the same one
• A correlation of X with the error

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What can we do?

• More sophisticated econometric methods than OLS
  e.g. IV
• Better data Griliches
• since it is the badness of the data that
  provides us with our living, perhaps it is not at
  all surprising that we have shown little interest
  in improving it

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But Recent Trends

• Much more emphasis on good quality data and
  research design than statistical fixes the
  credibility revolution
• Field Experiments
• Natural Experiments
• Instrumental Variables
• Will illustrate this in course through
  wide-ranging examples

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Issues to keep in Mind -1Internal and External
Validity

• Estimates have internal validity if conclusions
  valid for population being studied
• Estimates have external validity if conclusions
  valid for other popoulations e.g. can generalise
  impact of class size reduction in Tennessee in
  late 1980s to class size reduction in UK in 2005
  nothing in data will help with this

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Issues to Keep in Mind 2Wheres the Bias

• No identification strategy is going to be
  perfect. We want to do the best we can and then
  build credibility
• What is the worst case scenario for this
  estimation?
• If our instrument/natural experiment is biased,
  what is generating that bias?
• What direction will our estimates be biased in?
• This of this as a bounding exerciseif were
  wrong, can we use what we know and our estimates
  to get a sense of where the truth lies

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Next Steps

• Start thinking about what we can do with data
• Next class Data structures
• How does our data affect what techniques can we
  use?
• What are the most common types of data for
  different types of questions?