APPLIED ECONOMETRICS Lecture 1 - Identification

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APPLIED ECONOMETRICS Lecture 1 - Identification. Defining Identification. Experiments. Natural Experiments. Instrumental variables. Econometric Identification. WHAT IS IDENTIFICATION?. Graduate and professional economics mainly concerned with identification in empirical work

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Defining Identification

Experiments

Natural Experiments

Instrumental variables

Econometric Identification

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
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
SO HOW DO WE GET 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
Defining Identification

Experiments

Natural Experiments

Instrumental variables

Econometric Identification

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 – i.e. the drug and the placebo are as similar as possible
• Run the experiment
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
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

Defining Identification

Experiments

Natural Experiments

Instrumental variables

Econometric Identification

NATURAL EXPERIMENTS (1)

Natural experiments are where fortunate situations create good underlying identification:

Typically several approaches:

• Tax e.g. 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)
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
DISCONTINUITY ANALYSIS – example 1

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?

Estimated impact of the tax

Investment

Region A(no tax)

Region B(50% tax)

DISCONTINUITY ANALYSIS – example 2

Impact of telephones on price of fish in Kerala (India)

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

DIFFERNCES IN DIFFERENCES
• 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
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)
Defining Identification

Experiments

Natural Experiments

Instrumental variables

Econometric Identification

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

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)

---------------------

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

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

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

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

Defining Identification

Experiments

Natural Experiments

Instrumental variables

Econometric Identification

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

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 (i.e. is their a natural experiment?)