Dynamic Panel Data Models - jose.fajardo · Dynamic Panel Data Models Prf. José Fajardo FGV/EBAPE....
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15/09/2014 1 Dynamic Panel Data Models Prf. José Fajardo FGV/EBAPE
Transcript of Dynamic Panel Data Models - jose.fajardo · Dynamic Panel Data Models Prf. José Fajardo FGV/EBAPE....
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Dynamic Panel Data Models
Prf. José FajardoFGV/EBAPE
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[(Steven) Nickell Bias]
i,t i i,t i i,t 1 i i,t i
2 T
i,t 1 i i,t i 2 2
y y ( ) + (y y ) ( )
(T 1) TCov[(y y ),( )]
T (1 )
Large when T is moderate or small.
Proportional bias for conventional T (5 - 15), is
on the order of 15% - 60%
−
ε−
− = − δ − + ε − ε
−σ − − δ + δ− ε − ε ≈− δ
x x 'β
.
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Cornwell and Trumball (1994) data on county level crime rates
Cornwell and Trumball (1994) data on county level crime rates
use cornwell.dta
xtset county year
reg lcrmrte l.lcrmrte if year ==87 | year==88
test l.lcrmrte
reg d.l.lcrmrte l2.lcrmrte l3.lcrmrte if year ==87 | year==88
test l2.lcrmrte l3.lcrmrte
ivreg d.lcrmrte (d.l.lcrmrte = l2.lcrmrte l3.lcrmrte) if year ==87 | year==88
Summary of Variables
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FE Estimation
Comparison OLS and FE
Xtivreg estimation
• xtivreg lcrmrte lprbconv lprbpris lavgsenldensity lwcon lwtuc lwtrd lwfir lwserlwmfg lwfed lwsta lwloc lpctymle lpctminwest central urban d82 d83 d84 d85 d86 d87 (lprbarr lpolpc= ltaxpc lmix), ec2sls
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A General DPD model
i,t i,t 1 i i,t
i,t i
2 2
i,t i i,t i,s i
i
y y c
E[ | ,c ] 0
E[ | ,c ] , E[ | ,c ] 0 if t s.
E[c | ] g( )
No correlation across individuals
−
ε
′= + δ + + ε
ε =
ε = σ ε ε = ≠
=
i,t
i
i i
i i
x β
X
X X
X X
OLS and GLS are inconsistent
i,t i,t 1 i i,t
i,t 1 i i,t
2
c i,t 2 i i,t
2
c
y y c
Cov[y ,(c )]
Cov[y ,(c )]
If T were large and -1< <1,
this would approach 1
−
−
−
′= + δ + + ε
+ ε =
σ + δ + ε
δσ− δ
i,tx β
Implication : Both OLS and GLS are
inconsistent.
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Anderson Hsiao IV Estimator
− − − − −− = − δ − + ε − ε
− = − δ − + ε − ε
− = − δ −
i,t i,t 1 i,t i,t 1 i,t 1 i,t 2 i,t i,t 1
i,3 i,2 i,3 i,2 i,2 i,1 i,3 i,2
i1
i,4 i,3 i,4 i,3 i,3 i
Base on first differences
y y ( ) + (y y ) ( )
Instrumental variables
y y ( ) + (y y ) ( )
Can use y
y y ( ) + (y y
x x 'β
x x 'β
x x 'β + ε − ε
−,2 i,4 i,3
i2 i,2 i,1
) ( )
Can use y or (y y )
And so on.
Levels or lagged differences?
Levels allow you to use more data
Asymptotic variance of the estimator is smaller with levels.
Arellano and Bond Estimator - 1
i,t i,t 1 i,t i,t 1 i,t 1 i,t 2 i,t i,t 1
i,3 i,2 i,3 i,2 i,2 i,1 i,3 i,2
i1
i,4 i,3 i,4 i,3 i,3 i
Base on first differences
y y ( ) + (y y ) ( )
Instrumental variables
y y ( ) + (y y ) ( )
Can use y
y y ( ) + (y y
− − − − −− = − δ − + ε − ε
− = − δ − + ε − ε
− = − δ −
x x 'β
x x 'β
x x 'β ,2 i,4 i,3
i,1 i2
i,5 i,4 i,5 i,4 i,4 i,3 i,5 i,4
i,1 i2 i,3
) ( )
Can use y and y
y y ( ) + (y y ) ( )
Can use y and y and y
+ ε − ε
− = − δ − + ε − εx x 'β
Arellano and Bond Estimator - 2
− = − δ − + ε − ε
− = − δ − + ε − ε
i,3 i,2 i,3 i,2 i,2 i,1 i,3 i,2
i1 i,1 i,2
i,4 i,3 i,4 i,3 i,3 i,2 i,4 i,3
i,1 i2 i,1 i,2
More instrumental variables - Predetermined
y y ( ) + (y y ) ( )
Can use y and ,
y y ( ) + (y y ) ( )
Can use y , y , ,
X
x x 'β
x x
x x 'β
x x
− = − δ − + ε − εi,3
i,5 i,4 i,5 i,4 i,4 i,3 i,5 i,4
i,1 i2 i,3 i,1 i,2 i,3 i,4
,
y y ( ) + (y y ) ( )
Can use y , y , y , , , ,
x
x x 'β
x x x x
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Arellano and Bond Estimator - 3
− = − δ − + ε − ε
− = − δ − + ε − ε
i,3 i,2 i,3 i,2 i,2 i,1 i,3 i,2
i1 i,1 i,2 i,T
i,4 i,3 i,4 i,3 i,3 i,2 i,4 i,
Even more instrumental variables - Strictly exogenous
y y ( ) + (y y ) ( )
Can use y and , ,..., (all periods)
y y ( ) + (y y ) (
X
x x 'β
x x x
x x 'β
− = − δ − + ε − ε
3
i,1 i2 i,1 i,2 i,T
i,5 i,4 i,5 i,4 i,4 i,3 i,5 i,4
i,1 i2 i,3 i,1 i,2 i, T
)
Can use y , y , , ,...,
y y ( ) + (y y ) ( )
Can use y , y , y , , ,...,
The number of potential instruments is huge.
These define the rows
x x x
x x 'β
x x x
of . These can be used for
simple instrumental variable estimation.
iZ
Instrumental Variables
− −
′ ′ ′ ′ ′ =
′ ′ ′
′
=
i,1 i,1 i,2
i,1 i,2 i,1 i,2 i,3
i,1 i,2 i,T 2 i,1 i,2 i,T 1
i,1
y , , 0 ... 0
0 y , y , , , ... 0 (T rows)
... ... ... ...
0 0 ... y , y ,..., y , , ,...
y ,
i
i
Predetermined variables
x x
x x xZ
x x x
Strictly Exogenous variables
Z
−
−
− −
′ ′ ′ ′ ′
′ ′ ′
i,1 i,2 i,T 1
i,1 i,2 i,1 i,2 i,T 1
i,1 i,2 i, T 2 i,1 i,2 i, T 1
, ,... 0 ... 0
0 y , y , , ,... ... 0 (T rows)
... ... ... ...
0 0 ... y , y ,..., y , , ,...
x x x
x x x
x x x
IV Variables and GMM Methods
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Cornwell and Trumball (1994)
use E:\paneldata\paneldata\EBAPE\aula6\cornwell.dtaxtset county yearDescribe
xtivreg lcrmrte lprbconv lprbpris lavgsen ldensity lwconlwtuc lwtrd lwfir lwser lwmfg lwfed lwsta lwloc lpctymlelpctmin west central urban d82 d83 d84 d85 d86 d87 (lprbarrlpolpc= ltaxpc lmix), ec2sls
xtabond lcrmrte lprbconv lprbpris lavgsen ldensity lwconlwtuc lwtrd lwfir lwser lwmfg lwfed lwsta lwloc lpctymlelpctmin west central urban d82 d83 d84 d85 d86 d87, twostep
xtabond lcrmrte lprbconv lprbpris lavgsen ldensity lwconlwtuc lwtrd lwfir lwser lwmfg lwfed lwsta lwloc lpctymle d82 d84 d85 d86 d87, twostep
estat abondestat sargan
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More Examples
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Crime
xtabond I
Where did all instruments come from?
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Specification tests
xtabond II: two step estimator
Two step estimator with robust s.e.
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Cornwell and Trumball (1994)
xtabond lcrmrte lprbconv lprbpris lavgsen ldensitylwcon lwtuc lwtrd lwfir lwser lwmfg lwfed lwstalwloc lpctymle d82 d84 d85 d86 d87, vce(robust)
xtabond lcrmrte lprbconv lprbpris lavgsen ldensitylwcon lwtuc lwtrd lwfir lwser lwmfg lwfed lwstalwloc lpctymle d82 d84 d85 d86 d87, twostep
xtabond lcrmrte lprbconv lprbpris lavgsen ldensitylwcon lwtuc lwtrd lwfir lwser lwmfg lwfed lwstalwloc lpctymle d82 d84 d85 d86 d87, twostepvce(robust)
xtabond III
xtabond III
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Predetermined Variables
xtabond IV
Arellano-Bover, Blundell-Bond Estimator
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Cornwell and Trumball (1994)
xtabond lcrmrte lprbarr lprbpris lprbconv ldensity lwconlwtuc lwtrd lwfir lwser lwmfg lwfed lwsta lwloc lpctymle d82 d84 d85 d86 d87, twostep endog(lavgsen) pre(lpolpc)
estat abond
estat sargan
xtdpdsys lcrmrte lprbarr lprbpris lprbconv ldensity lwconlwtuc lwtrd lwfir lwser lwmfg lwfed lwsta lwloc lpctymle d82 d84 d85 d86 d87, twostep endog(lavgsen) pre(lpolpc)
estat abond
estat sargan
xtdpdsys lcrmrte lavgsen ldensity lwcon lwtuc lwtrd lwfirlwser lwmfg lwfed lwsta lwloc lpctymle d82 d84 d85 d86 d87, twostep endog(lprbarr lprbpris lprbconv) pre(lpolpc)
xtdpd
xtdpd I
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Benefits of Flexibility
xtdpd III: Predetermined Variable: No dependentLagged Variable
Instruments for Models with MA(1) errors
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Instruments for Models with MA(1) errors
xtdpd IV
xtdpd V
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CR 1988
regress lwage L.lwage L2.lwage, vce(robust)estimates store OLSxtreg lwage L.lwage L2.lwage, fe vce(robust)estimates store FExtreg lwage L.lwage L2.lwage, re vce(robust)estimates store RExtabond lwage, lags(2) vce(robust)estimates store AB1xtabond lwage, lags(2) vce(robust) twostepestimates store AB2xtabond lwage, lags(2) maxldep(3) vce(robust) twostepestimates store AB3estimates table OLS FE RE AB1 AB2 AB3, b se t stats(sagan)
Example3.9-3.13.do
