Methods of Economic Investigation: Lent Term: First Six Weeks

1
Methods of Economic Investigation Lent Term
First Six Weeks

• Rajeev Dehejia
• Office Hour Monday 11.00-12.00
• Office R451

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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

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Lecture discipline

• Lectures are optional -- you dont have to come.
• But if you do choose to come
• Arrive on time.
• Pay attention in class.
• Things to do
• Ask questions!
• Things not to do
• Gossip about last night.
• Tell jokes (good or bad).
• Check e-mail, Facebook, news, the web.
• Text message (or talk on the phone!).
• Listen to music (good or bad).

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What is Econometrics For?

• To make life miserable for MSc students?
• To impress your mother with the magic of
  idempotent matrices?
• To provide credible answers to interesting
  questions?

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Econometrics is a means to an end not an end in
itself.

• Two different types of ends (may be others)
• Causal Effects
• Forecasting
• Causal effects are answers to what if
  questions
• What would happen to smoking if cigarette taxes
  were raised?
• Forecasting just want best currently available
  predictors dont worry about causality

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Emphasis on means to an end

• Recommended texts Wooldridge Intermediate
  Econometrics (not very technical),
  Cross-Sectional Econometrics (more advanced).
• 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 frustrations of empirical
  work
• Cute theory
• Fantastic econometric methodology
• Take it to the data and.

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How to Estimate Causal Effects?

• Want Effect of X on distribution of y, other
  relevant things being held constant
• Most common to be interested in effect on mean of
  y, i.e.

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Estimation of linear regression offers promising
approach

• Can interpret regression function (Xß) as
  estimate of E(yX)
• If conditional expectation linear in X then exact
• If conditional expectation non-linear then Xß
  linear approximation to true function
• This is same as

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Proposition 1.1 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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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

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General Problems in Estimating Causal Effects

• Omitted Variables
• Reverse Causality
• 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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In hospital example

• Prior health status an obvious omitted variable
• HEALTHPROB Coef. Std. Err. t
• --------------------------------------------
  
• PATIENT .1250091 .0078147 16.00
• HEALTHPROB1 .6282796 .0061896 101.51
  
• _cons .0554544 .0026937 20.59

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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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• 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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• 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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Selection Effects

• Following regression seems to show that women
  with young children earn more than those with
  older children
• LOGWAGE Coef. Std. Err. t
• ---------------------------------------
• AGEKID0 .0942016 .0083255 11.31
• AGEKID1 .1333421 .008284 16.10
• AGEKID2 .0833223 .0084401 9.87
• AGEKID3 .0526896 .0087102 6.05
• AGEKID4 .019879 .0087995 2.26
• _cons 1.808458 .0061696 293.12
• Is this sensible? probably not

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• 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

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Why is this? A brief exposition

• 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
• Heckman got Nobel prize for working out how to
  deal with this but not part of this course

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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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How To Surmount the Problems?

• 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
• Probably started in labour economics but now
  arriving in most fields
• Will illustrate this in course through
  wide-ranging examples

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Internal and External Validity

• Estimates have internal validity if conclusions
  valid for population being studied
• Estimates have external validity if conclusions
  valid for other populations 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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Choosing your data..

• Suppose interested in causal effect of X on y.
• Can choose the way in which X is determined in
  your sample
• may seem fanciful but field experiments becoming
  more common in economics
• Good reason to choose to do randomized controlled
  experiment