View
223
Download
0
Category
Preview:
Citation preview
8/12/2019 L6-1Advanced Microeconometrics6
1/21
Advanced Microeconometrics
(lecture 6)The Economics and Econometrics of
Policy
Evaluations(1.introduction)
1M2R ETE 2011-2012 AdvancedEconometrics
8/12/2019 L6-1Advanced Microeconometrics6
2/21
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
2M2R ETE 2011-2012 AdvancedEconometrics
8/12/2019 L6-1Advanced Microeconometrics6
3/21
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
3M2R ETE 2011-2012 AdvancedEconometrics
8/12/2019 L6-1Advanced Microeconometrics6
4/21
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
4M2R ETE 2011-2012 AdvancedEconometrics
8/12/2019 L6-1Advanced Microeconometrics6
5/21
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
5M2R ETE 2011-2012 AdvancedEconometrics
8/12/2019 L6-1Advanced Microeconometrics6
6/21
8/12/2019 L6-1Advanced Microeconometrics6
7/21
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
7M2R ETE 2011-2012 AdvancedEconometrics
8/12/2019 L6-1Advanced Microeconometrics6
8/21
8M2R ETE 2011-2012 AdvancedEconometrics
8/12/2019 L6-1Advanced Microeconometrics6
9/21
Problems?
9M2R ETE 2011-2012 AdvancedEconometrics
8/12/2019 L6-1Advanced Microeconometrics6
10/21
An ideal context: randomized
experiments.
Individuals are randomly affected to
treatment and control group.
),( 10 iii YYT
10M2R ETE 2011-2012 AdvancedEconometrics
8/12/2019 L6-1Advanced Microeconometrics6
11/21
CIA: Conditional Independance
Assumption
Conditional to the observed caracteristics
there is no selection effect:
Estimation methods: OLS, Matching.
iiii XYYT /),( 10
11M2R ETE 2011-2012 AdvancedEconometrics
8/12/2019 L6-1Advanced Microeconometrics6
12/21
Other cases
The assignement depends upon the potential
outcomes: no general solution!
- Instrumental variables
- Differences in differences
- Regression discontinuity
12M2R ETE 2011-2012 AdvancedEconometrics
8/12/2019 L6-1Advanced Microeconometrics6
13/21
A general common assumption:
SUTVA
13M2R ETE 2011-2012 AdvancedEconometrics
8/12/2019 L6-1Advanced Microeconometrics6
14/21
The parameters of interest
14M2R ETE 2011-2012 AdvancedEconometrics
8/12/2019 L6-1Advanced Microeconometrics6
15/21
ATE and/or ATT
).(:programmein theeparticipatodecision tby the
accountintonot takenisbut thisityheterogeneoffactorsexistthereif-
ityheterogeneno:sindididualallforsametheistreatmenttheofeffecttheif-
:
)()1/()()1/(
01
0101
YYT
ATEATT
YYETYYEATEETEATEATT
15M2R ETE 2011-2012 AdvancedEconometrics
8/12/2019 L6-1Advanced Microeconometrics6
16/21
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
16M2R ETE 2011-2012 AdvancedEconometrics
8/12/2019 L6-1Advanced Microeconometrics6
17/21
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
17M2R ETE 2011-2012 AdvancedEconometrics
8/12/2019 L6-1Advanced Microeconometrics6
18/21
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
18M2R ETE 2011-2012 AdvancedEconometrics
8/12/2019 L6-1Advanced Microeconometrics6
19/21
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
19M2R ETE 2011-2012 AdvancedEconometrics
8/12/2019 L6-1Advanced Microeconometrics6
20/21
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
20M2R ETE 2011-2012 AdvancedEconometrics
8/12/2019 L6-1Advanced Microeconometrics6
21/21
Statistical tools?
Conditional hypothesis lead to
Matching/Regression discontinuity;
Modelling unobserved heterogeneity; remove
unobserved heterogeneity: IV technics and
developpements;
Beyond the mean: Quantile Regression!
21M2R ETE 2011-2012 AdvancedEconometrics
Recommended