Pooled Cross Sections DifferenceinDifference for treatment effects How DiD can eliminate bias in crosssectional OLS Potential sources of bias after DiD Panel Data First Difference for two period panel data ID: 706247
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Slide1
Ch. 13. Pooled Cross Sections Across Time: Simple Panel Data.
Pooled Cross Sections
Difference-in-Difference for treatment effects
How
DiD
can eliminate bias in cross-sectional OLS.
Potential sources of bias after
DiD
Panel Data
First Difference for two period panel data.
Fixed effects for multi-period panel data.
How first differencing or fixed effects can eliminate bias in OLS
Potential issues with FD and FE modelsSlide2
Pooling Cross Sections across Time: Simple Panel Data Methods
Policy analysis with pooled cross sections
Two or more independently sampled cross sections can be used to evaluate the impact of a certain event or policy change
Effect of new garbage incinerator’s location on housing pricesExamine the effect of the location of a house on its price before and after the garbage incinerator was built:
After
incinerator was built
Before
incinerator was builtSlide3
Pooling Cross Sections across Time: Simple Panel Data Methods
Garbage incinerator and housing prices
Note: near incinerator had negative effect on housing prices before incinerator was built? Why?
Would be inappropriate to interpret negative effect of incinerator after it‘s built as a
causal effect. Some of effect is due to fact that incinerator was built near lower price homes.
More appropriate to look at difference-in-difference (DiD)
after incinerator was built: p near – p far = -30,688.27
before incinerator was built: = p near – p far =
-18,824.37
difference in differences (DiD) = -11,863.9
Slide4
Pooling Cross Sections across Time: Simple Panel Data Methods
Difference-in-differences in a regression framework
Show how
is the DiD estimator derived above
DiD regression allows for standard errors and t-stat of DiD effect.
If houses sold before and after the incinerator was built were systematically different, further explanatory variables should be included
Adding housing characteristics will also reduce the error variance and thus standard errors
Before/After comparisons in “natural experiments
”
DiD can be used to evaluate policy changes or other exogenous events
Difference in change of house price for those near vs not near incinerator (diff-in-diff)Slide5
Pooling Cross Sections across Time: Simple Panel Data Methods
Policy evaluation using difference-in-differences
Suppose that something happens in the treated group causing its growth to differ by
relative to the control group. DiD estimator will then include true effect of treatment
and the effect of the other factors causing growth to differ by
in the treated group.
Examples.
Minimum wage increase is the treatment. How is DiD estimate of employment effect biased if the state that passes the minimum wage has unusually high economic growth? Unusually low economic growth?Might use placebo test to be sure that DiD estimator isn‘t picking up effect of some other factor.
Minimum wage hike shouldn‘t affect employment growth of college graduates.
Compare
outcomes of the two groups before and after the policy
changeSlide6
Pooling Cross Sections across Time: Simple Panel Data Methods
Two-period panel data (Fixed Effect) analysis
Example: Effect of unemployment on city crime rate
Assume that no other explanatory variables are available. Will it be possible to estimate the causal effect of unemployment on crime?Yes, if cities are observed for at least two periods and other factors affecting crime stay approximately constant over those periods:
Unobserved
city specific time-invariant actors
(= fixed effect)Examples of time-constant variables that might affect city crime?
Other
unobserved
factors (=
idiosyncratic error)
Time
dummy for
the
second
periodSlide7
Pooling Cross Sections across Time: Simple Panel Data Methods
Effect of unemployment on city crime rate
Estimate differenced equation by OLS:
Secular increase in crime
across all cities.
+ 1
percentage
point
unemploy-ment
rate
leads
to
2.22
more
crimes
per 1,000
people
Fixed effect drops outSlide8
Pooling Cross Sections across Time: Simple Panel Data Methods
Discussion of first-differenced panel estimator
Further explanatory variables may be included in original equation
There may be arbitrary correlation between the unobserved time-invariant characteristics and the included explanatory variablesFor example, suppose cities with less educated workers (virtually a time-invariant characteristic) have higher crime and also higher unemployment – how would this bias OLS estimate of effect of unemployment?
First differences cause effect of any time-invariant variables to be differenced out of the regression. Eliminates bias from exclusion of important time-invariant variables that would emerge in OLS.
First-differenced estimates will be imprecise if explanatory variables vary little over time (no estimate possible if time-invariant)Slide9
Panel Data Methods with More than 2 Periods.
Fixed effects estimation
Estimate deviations from i-specific means using OLS
Estimates rely on time variation within cross-sectional units
(= within estimator)
xtset & xtreg in Stata.
Fixed effect, potentially
correlated with explanatory variables
Form time-averages for each individual
Because (the fixed effect is removed) Slide10
Example: Effect of training grants on firm scrap rate (number of defective items per 100 produced)
Fixed-effects estimation using the years 1987, 1988, and 1989:
Time-invariant
reasons
why
one
firm
is
more
productive
than
another
are
controlled
for
.
The important point is that these may be correlated with the other
explanatory
variables.
Stars denote
deviations from i-specific means
Training
grants
significantly
improve
productivity
(
with
a time lag)
Advanced Panel Data MethodsSlide11
Discussion of fixed effects estimator
Strict exogeneity in the original model has to be assumed
The R
2 of the demeaned equation is inappropriate measure of R2
The effect of time-invariant variables cannot be estimated
The effect of interactions with time-invariant variables can be estimated (e.g. the interaction of education with time dummies)If a full set of time dummies are included, the effect of variables whose change over time is constant cannot be estimated (e.g.
age)
Degrees of freedom have to be adjusted because the individual specific averages are estimated in addition to other coefficients (resulting degrees of freedom = NT-N-k)Advanced Panel Data MethodsSlide12
Applying panel data methods to other data structures
Panel data methods can be used in other contexts where constant unobserved effects have to be removed
Example: Wage equations for twins
Equation for twin 1 in family i
Equation for twin
2 in family i
Unobserved genetic and family characteristics that do not
vary across twins
Estimate differenced equation by OLS
Advanced Panel Data Methods (Ch.14)