Panel Data Analysis
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Transcript Panel Data Analysis
Panel Data Analysis
INTRO
β’ Panel Data is where you observe behavior of
entities across time.
β’ Allows to control for unobservable variables
that change over time but not entity
β’ Allows to control for unobservable variables
across entities
β’ xtset entity time
xtline fatalityrate
, (ov)
Fixed Effect Models
πππ = π·π πΏππ + πΆπ + πΈπ + πππ (Eq 1)
πΌπ = πππ‘ππππππ‘ πππ πππβ πππ‘ππ‘π¦ π β¦ π
πΎπ‘ = πππ‘ππππππ‘ πππ πππβ π‘πππ ππππππ
πππ = π·π + π·π πΏπππ + β― + π·π πΏπππ + πΉπ π¬π + β― + πΉπ π¬π + πΈπ π»ππ + β― + πΈπ π»π + πππ
πΈπ = ππ’πππ¦ π£ππππππππ πππ πππβ πππ‘ππ‘π¦ (π β 1 ππ πππππ)
(Eq 2)
πΏπ = πππππππππππ‘ ππ πππ‘ππ‘π¦ π£πππππππ
ππ‘ = ππ’πππ¦ π£ππππππππ πππ πππβ π‘πππππππππ (π‘ β 1 ππ πππππ)
πΎπ‘ = πππππππππππ‘ ππ π‘πππ π£ππππππππ
fatalityrate sb_useage i.fips i.year
_Ifips_1-56
(naturally coded; _Ifips_1 omitted)
_Iyear_1983-1997
(naturally coded; _Iyear_1983 omitted)
MS
.012688284
.001351121
65
490
.000195204
2.7574e-06
Total
.014039406
555
.000025296
fatalityrate
Coef.
sb_useage
_Ifips_2
_Ifips_4
_Ifips_5
_Ifips_6
_Ifips_8
-.0037393
.0011998
.0010569
.0026309
-.005236
-.0046082
Std. Err.
.0011439
.0007563
.0007517
.0006915
.0006822
.0007407
t
-3.27
1.59
1.41
3.80
-7.68
-6.22
xi: reg fatalityrate sb_useage i.fips i.year
predict yhat
separate yhat, by(fips)
separate yhat, by(year)
twoway connected yhat1-yhat56
sb_useage|| lfit fatalityrate
sb_useage, clwidth(thick)
clcolor(black)
twoway connected yhat1983-yhat1997
sb_useage|| lfit fatalityrate
sb_useage, clwidth(thick)
clcolor(black)
P>|t|
=
=
=
=
=
=
556
70.79
0.0000
0.9038
0.8910
.00166
Eq 2
Dummy Variables
[95% Conf. Interval]
0.001
0.113
0.160
0.000
0.000
0.000
-.0059868
-.0002861
-.00042
.0012723
-.0065764
-.0060635
-.0014917
.0026858
.0025339
.0039896
-.0038956
-.0031528
.03
Model
Residual
Number of obs
F( 65,
490)
Prob > F
R-squared
Adj R-squared
Root MSE
.025
df
.02
SS
.015
Source
.01
. xi: reg
i.fips
i.year
0
.2
.4
sb_useage
.6
.8
Eq 1
n entity-specific intercepts
areg fatalityrate sb_useage, absorb(state)
areg fatalityrate sb_useage year2β¦year10, absorb(state)
. areg
fatalityrate sb_useage, absorb(state)
Linear regression, absorbing indicators
fatalityrate
Coef.
sb_useage
_cons
-.0170648
.0287933
state
Std. Err.
.0006547
.0003572
F(50, 504) =
Number of obs
F( 1,
504)
Prob > F
R-squared
Adj R-squared
Root MSE
t
=
=
=
=
=
=
556
679.47
0.0000
0.8460
0.8304
.00207
P>|t|
[95% Conf. Interval]
-26.07
80.61
0.000
0.000
-.018351
.0280915
44.747
0.000
-.0157786
.029495
(51 categories)
Eq 1
n entity-specific intercepts
xtset fips year
xtreg fatalityrate sb_useage, fe
. xtset fips year
panel variable:
time variable:
delta:
fips (strongly balanced)
year, 1983 to 1997
1 unit
. xtreg fatalityrate sb_useage, fe
Fixed-effects (within) regression
Group variable: fips
Number of obs
Number of groups
=
=
556
51
R-sq:
Obs per group: min =
avg =
max =
8
10.9
15
within = 0.5741
between = 0.0036
overall = 0.1622
corr(u_i, Xb)
F(1,504)
Prob > F
= -0.2067
fatalityrate
Coef.
sb_useage
_cons
-.0170648
.0287933
.0006547
.0003572
sigma_u
sigma_e
rho
.00444127
.00207142
.82133433
(fraction of variance due to u_i)
F test that all u_i=0:
Std. Err.
F(50, 504) =
t
=
=
-26.07
80.61
44.75
679.47
0.0000
P>|t|
[95% Conf. Interval]
0.000
0.000
-.018351
.0280915
-.0157786
.029495
Prob > F = 0.0000
xtreg options
fe: fixed effects
Explores relationship between estimations and outcomes within an
entity. Assumes each entity has own characteristics that may
influence yhat to control for.
re: random effects
Variation across entities is assumed to be random and uncorrelated
with the independent variables included in the model
be: between effects
pa: population-average