Methods of Economic Investigation: Lent Term Radha Iyengar Office Hour: Monday Office: R425

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

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)

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

Econometrics is tool for useful thinking  We’re 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: don’t worry about what causes what

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

Regression Re-cap  In our standard OLS model we estimate something like  To estimate we need a condition like: E(X,ε) = 0  So generally, we’re interested in the relationship between our X of interest on y holding other stuff constant

OLS Estimation  If E(y|X)=Xβ, the OLS estimate is an unbiased estimate of β  Proof: Can write OLS estimator as:  If X is fixed we have that:

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?

Levitt (1997) American Economic Review Police Levels and Crime rates

Problems in Estimating Causal Effects  Reverse Causality  Omitted Variables  Measurement Error  Sample selection

Omitted Variables (should be familiar)  Suppose we want to estimate E(y │ X,W) assumed to be linear in (X,W), so that E(y │ X,W) =Xβ+Wγ or: y =Xβ+Wγ+ε  But you estimate y=Xβ+u  i.e. E(y │ X). Will have:

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

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: y=Xβ+ε  But also causal relationship in other direction: X=αy+u

Endogeneity (II)  Reduced form is: X=(u+αε)/(1-αβ)  X correlated with ε – 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.

Measurement Error  Most (all?) of our data are measured with error.  Suppose causal model is: y=X*β+ε  But only observe X which is X* plus some error: X=X*+u  Classical measurement error: E(u │ X*)=0

Implications of Measurement Error  Can write causal relationship as: Y=Xβ-u β +ε  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(y │ X*) but can only estimate E(y │ X)

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: y=Xβ +ε  But only observe if work, W=1, so estimate E(y|X,W=1) not E(y|X)  Sample selection bias if W correlated with ε – this is likely

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’

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”

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

Issues to keep in Mind -1 Internal 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

Issues to Keep in Mind –2 Where’s 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 exercise—if we’re wrong, can we use what we know and our estimates to get a sense of where the truth lies

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?