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Methods of Economic Investigation: Lent Term: First Six Weeks

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Title: 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

2
Administrative Details
  • 3 lectures per week for first 6 weeks all at
    10am
  • Monday, 10-11,
  • Tuesday,10-11
  • Thursday,10-11

3
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).

4
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?

5
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

6
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.

7
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.

8
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

9
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

10
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

11
General Problems in Estimating Causal Effects
  • Omitted Variables
  • Reverse Causality
  • Measurement Error
  • Sample selection

12
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

13
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

14
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

15
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

16
  • 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.

17
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

18
  • 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)

19
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

20
  • 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

21
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

22
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

23
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

24
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

25
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

26
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
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