l6-1advanced microeconometrics6

8/12/2019 L6-1Advanced Microeconometrics6

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Advanced Microeconometrics

(lecture 6)The Economics and Econometrics of

Policy

Evaluations(1.introduction)

1M2R ETE 2011-2012 AdvancedEconometrics


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The Evaluation Problem

Methods to identify the effect of policy, individual actions, investmenton one or more impacts of interest:

The effect of taxes on labour supply

The effect of education on wages

The effect of incarceration on recidivism

The effect of competition between schools on schooling quality

The effect of price cap regulation on consumer welfare

The effect of indirect taxes on demandThe effects of environmental regulation on incomes

The effects of labour market regulation and minimum wages on

wages and employment



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The treatment

The most basic form of the problem:

The effect of a discrete 0/1 treatment.

For an individual i, the treament status will bedenoted by a variable zero-one:

0/:groupControl

1/:groupTreatmentdnot treateisiif0

treatedisiif1

i

i

i

i

Ti

Ti

T

T



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Potential outcomes

For each individual there exists two potential

outcomes:

is the potential outcome without

treatment.

is the potential outcome with treatment.

Individuals could either participate in aprogramme or not participate, but not both!

10Y

1iY



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A classical example: benefit from a job

training

Two potential wages:

With training:

Without training:

Causal effect of the (treatment) training:

1iY

0i

Y

01 iii YY



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The fundamental problem of causal inference:

For one individual i, one cannot observe at the

same time his two potential outcomes.

If individual i participates, we observe but

not ; ex post is the counterfactual

If individual i does not participate, we observe

but not ; ex post is the counterfactual

1iY

1iY

1iY

0iY 0iY

0iY



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Problems?



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An ideal context: randomized

experiments.

Individuals are randomly affected to

treatment and control group.

),( 10 iii YYT



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CIA: Conditional Independance

Assumption

Conditional to the observed caracteristics

there is no selection effect:

Estimation methods: OLS, Matching.

iiii XYYT /),( 10



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Other cases

The assignement depends upon the potential

outcomes: no general solution!

- Instrumental variables

- Differences in differences

- Regression discontinuity



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A general common assumption:

SUTVA



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The parameters of interest



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ATE and/or ATT

).(:programmein theeparticipatodecision tby the

accountintonot takenisbut thisityheterogeneoffactorsexistthereif-

ityheterogeneno:sindididualallforsametheistreatmenttheofeffecttheif-

:

)()1/()()1/(

01

0101

YYT

ATEATT

YYETYYEATEETEATEATT



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A naive estimator

TYB

ATETYETYEBB

TYETYETYETYE

TYETYETYETYE

0

0010

011010

01

ifbiasnoisThere

),0/()1/(,

and

)0/()1/(),0/()1/(If

:)0/()0/(and)1/()1/(ofComparison



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A simple calculus leads to:

effect!treament

theofityheterogenethe:)0/()1/)())1(1(*2

effect,selectionthe:)0/()1/(*1

:biasofsourcestwoisThere

)0/()1/)())1(1(

)0/()1/(

0101

00

0101

00

TYYETYYETP

TYETYE

TYYETYYETP

TYETYEB



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Naive estimate and naive linear model

!unless,0)()/()/(ifbiasedisestimator

OLSthisand0)/(ifofestimatorunbiasedangivesOLSThe

means.observedthe

uponbasedestimatornaiveprevioustheisestimatorOLSThe

)(,,)1/()()(with

:)(

:modellinearsimpleatoleadsdefinitionthis

)1(

000

0010100

0

010

TYYETYETvE

TvE

YEETYYEYYTYEYv

vTvTYEY

TYTYTYY

iiiii

ii

iiiiiiiiiii

iiiiii

iiiiiiii



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Identification of ATT and ATE

).1/(and)0/(estimatemustone

)0/()0/())1(1()1/()1/()1(

)(b)

)1/(:estimatemustone

)1/()1/()1/(a)

01

0101

01

0

0101

TYETYE

TYETYETPTYETYETPATE

YYEATE

TYE

TYETYETYYEATT



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Control variates/conditional to

covariates

All what has been presented can be presented

in a conditional version: the CIA assumption

has already been presented in this form:

We can define: ATT(x), ATE(x),

iiii XYYT /),( 01

),1/()(

)/()()(

01

01

xXTYYExATT

xXYYExxATE

iiii

iii



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Statistical tools?

Conditional hypothesis lead to

Matching/Regression discontinuity;

Modelling unobserved heterogeneity; remove

unobserved heterogeneity: IV technics and

developpements;

Beyond the mean: Quantile Regression!


l6-1advanced microeconometrics6

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