Nick Bloom, Applied Econometrics, Winter 2010
APPLIED ECONOMETRICS
Lecture 1 - Identification
Nick Bloom, Applied Econometrics, Winter 2010
Defining Identification
Experiments
Natural Experiments
Instrumental variables
Econometric Identification
Nick Bloom, Applied Econometrics, Winter 2010
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
Nick Bloom, Applied Econometrics, Winter 2010
WHAT IS DRIVING THIS RELATIONSHIP?
Correlation =
Nick Bloom, Applied Econometrics, Winter 2010
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
Nick Bloom, Applied Econometrics, Winter 2010
WHAT IS DRIVING THIS RELATIONSHIP?
Nick Bloom, Applied Econometrics, Winter 2010
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
Nick Bloom, Applied Econometrics, Winter 2010
Defining Identification
Experiments
Natural Experiments
Instrumental variables
Econometric Identification
Nick Bloom, Applied Econometrics, Winter 2010
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 – . the drug and the
placebo are as similar as possible
• Run the experiment
Nick Bloom, Applied Econometrics, Winter 2010
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
Nick Bloom, Applied Econometrics, Winter 2010
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
Nick Bloom, Applied Econometrics, Winter 2010
Defining Identification
Experiments
Natural Experiments
Instrumental variables
Econometric Identification
Nick Bloom, Applied Econometrics, Winter 2010
NATURAL EXPERIMENTS (1)
Natural experiments are where fortunate situations create
good underlying identification:
Typically several approaches:
• Tax . Response of R&D 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)
Nick Bloom, Applied Econometrics, Winter 2010
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
Nick Bloom, Applied Econometrics, Winter 2010
DISCONTINUITY ANALYSIS – example 1
Region A
(no tax)
Region B
(50% tax)
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?
In
ve
st
m
en
t
Estimated impact
of the tax
Nick Bloom, Applied Econometrics, Winter 2010
DISCONTINUITY ANALYSIS – example 2
Impact of telephones on price of fish in Kerala (India)
Nick Bloom, Applied Econometrics, Winter 2010
DIFFERNCES IN DIFFERENCES
t0 denotes pre-treatment periods for which data are available
t1 denotes post-treatment periods for which data are available
Average change in outcome (pre and post-treatment) for treatment group
minus average change in outcome for control group
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
Nick Bloom, Applied Econometrics, Winter 2010
POLICY EXAMPLE OF “DIFF-IN-DIFF”
• Small firms R&D 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 don’t 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)
Nick Bloom, Applied Econometrics, Winter 2010
Defining Identification
Experiments
Natural Experiments
Instrumental variables
Econometric Identification
Nick Bloom, Applied Econometrics, Winter 2010
INSTRUMENTAL VARIABLES (1)
Want to look at effect of schooling (Si) on earnings (Yi)
Assume the true model is :
Yi = α + β1 Si + β2 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 = β2 Ai + vi
Nick Bloom, Applied Econometrics, Winter 2010
INSTRUMENTAL VARIABLES (2)
------Background
Assume estimating equation below in Ordinary Least Squares
Y = α + βX + e
The estimate of β = E(Y’X)/E(X’X)
= E((βX + e )’X)/E(X’X)
= β + E(e’X)/E(X’X)
= β 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)
---------------------
Nick Bloom, Applied Econometrics, Winter 2010
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
E[b1]=E[Y’S]/E[S’S]
=E[(β1Si+β2Ai+vi)’S] / E[S’S]
= β1 + E[(β2Ai+vi)’S] / E[S’S]
= β1 + β2E[Ai’S] / E[S’S]
> β1
So because ignore ability, which is correlated with schooling,
we overestimate the impact of schooling on earnings
Nick Bloom, Applied Econometrics, Winter 2010
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
Nick Bloom, Applied Econometrics, Winter 2010
INSTRUMENTAL VARIABLES (5)
Assume that Z is correlated with S but not A. Then the
following instrumental variable estimator is consistent
E[b1IV] =E[Y’Z]/E[S’Z]
=E[(β1Si+β2Ai+vi)’Z] / E[S’Z]
=E[β1Si’Z + β2Ai’Z +vi’Z] / E[S’Z]
= β1 + (β2E[Ai’S] + E[vi’Z]) / E[S’Z]
= β1
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
Nick Bloom, Applied Econometrics, Winter 2010
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
Nick Bloom, Applied Econometrics, Winter 2010
Defining Identification
Experiments
Natural Experiments
Instrumental variables
Econometric Identification
Nick Bloom, Applied Econometrics, Winter 2010
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
Nick Bloom, Applied Econometrics, Winter 2010
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 (. is their a natural experiment?)
