Random Slopes [Coefficients] Model Static and Dynamic IV [next lecture] PANEL DATA MODELS.. reg lgdp llabor linvest pci, noheader.. adjusted for 58 clusters in province). reg lgdp llabor[r]
Trang 1PANEL DATA MODELS
Trang 2Panel data
data on MANY units and SEVERAL time periods
cross-sectional: MANY units and ONE time period
time-series: ONE unit and SEVERAL time periods
Trang 3 RINVEST: gross investment of provinces (mil VND)
PCI: 100-point scaled composite index measuring and ranking Vietnam’s provinces based on their overall economic governance quality
data for 50 provinces, 5 years (2008-2011)
Trang 5Why panel data?
more information
heterogeneity among units
allow to investigate the dynamics of change
Trang 6Manipulation of panel data
delta: 1 unit
time variable: year, 2007 to 2011
panel variable: province (strongly balanced) xtset province year
* Declare panel data (define i and t)
Trang 7Manipulation of panel data
(province*year uniquely identifies each observation)
Span(year) = 5 periods
Delta(year) = 1 unit
year: 2007, 2008, , 2011 T = 5province: 1, 2, , 58 n = 58 xtdescribe
* Describe panel data
Trang 8Manipulation of panel data
(province*year uniquely identifies each observation)
Span(year) = 5 periods
Delta(year) = 1 unit
year: 2007, 2008, , 2011 T = 5province: 1, 2, , 58 n = 58 xtdescribe
* Summarize panel data
Trang 9Manipulation of panel data
within 5.445562 41.77384 79.91406 T = 5 between 4.380076 49.67015 67.33098 n = 58pci overall 57.23728 6.969482 36.39006 77.19708 N = 290
within 1960123 -6043249 1.63e+07 T-bar = 4.7069 between 1.33e+07 1351629 8.79e+07 n = 58rinvest overall 8788711 1.37e+07 592714.3 9.53e+07 N = 273
within 4884013 -502939.8 5.25e+07 T-bar = 4.82759 between 2.89e+07 2651895 1.39e+08 n = 58rgdp overall 2.05e+07 2.96e+07 1485281 1.71e+08 N = 280 Variable Mean Std Dev Min Max Observations xtsum rgdp rinvest pci
* Summarize panel data
Trang 10Manipulation of panel data
(n = 58)
Total 290 100.00 103 177.59 56.31
1 155 53.45 54 93.10 57.41
0 135 46.55 49 84.48 55.10 pcidummy Freq Percent Freq Percent Percent Overall Between Within
xttab pcidummy
* Tabulate panel data
pcidumy: 1 = pci above average
53.45% on average have pci above average
93.1% ever have pci above average
57.41% ever have pci above average and always have pci above average
Trang 11Manipulation of panel data
xtline pci if province<=10, overlay
Trang 12Pooled OLS
Fixed Effects (FE) Model
Random Effects (RE) Model
Random Slopes [Coefficients] Model
Static and Dynamic IV [next lecture]
PANEL DATA MODELS
Trang 13Basic considerations
Pooled OLS
Unit-specific effects
Two-way effects model
Mixed model [or Random coefficients model]
Trang 15Pooled OLS
assumes identical intercept for all units and time
periods
_cons 2.726831 1.10059 2.48 0.016 5229367 4.930725 pci 0107977 .0063007 1.71 0.092 -.0018192 .0234146 linvest 6307949 .1446832 4.36 0.000 3410717 920518 llabor 4986047 .1981111 2.52 0.015 1018941 .8953153 lgdp Coef Std Err t P>|t| [95% Conf Interval] Robust
(Std Err adjusted for 58 clusters in province) reg lgdp llabor linvest pci, noheader vce(cluster province)
Trang 16Unit-specific effects model
rho .91156075 (fraction of variance due to u_i)
sigma_e .15132407
sigma_u .48582326
_cons 4.487843 1.062847 4.22 0.000 2.392626 6.583059 pci 0044829 .0017513 2.56 0.011 0010305 .0079352 linvest 258814 .0432882 5.98 0.000 1734788 .3441491 llabor 1.173004 .1696396 6.91 0.000 8385894 1.507419 lgdp Coef Std Err t P>|t| [95% Conf Interval]
corr(u_i, Xb) = -0.1768 Prob > F = 0.0000 F(3,210) = 53.67
overall = 0.6986 max = 5 between = 0.7075 avg = 4.7R-sq: within = 0.4340 Obs per group: min = 3
Group variable: province Number of groups = 58Fixed-effects (within) regression Number of obs = 271 xtreg lgdp llabor linvest pci, fe
Trang 17Two-way effects model
xtreg lgdp llabor linvest pci i.year, fe
rho .98652813 (fraction of variance due to u_i)
sigma_e .09500439
sigma_u .81298858
_cons 14.54723 .887371 16.39 0.000 12.79774 16.29672
pci 0009591 .0011657 0.82 0.412 -.0013392 .0032573 linvest 1053697 .028942 3.64 0.000 0483093 .1624302 llabor -.014794 .1268055 -0.12 0.907 -.2647969 .2352088 lgdp Coef Std Err t P>|t| [95% Conf Interval]
Trang 18Problems of FE models
FE models are equivalent to Pooled OLS with
unit-specific dummies, and/or
Trang 19Random effects model
rho .86012018 (fraction of variance due to u_i)
sigma_e .15132407
sigma_u .37524081
_cons 5.030108 .615074 8.18 0.000 3.824585 6.235631 pci 0042964 .0017863 2.41 0.016 0007954 .0077974 linvest 3487632 .0401863 8.68 0.000 2699996 .4275269 llabor 8752699 .0940686 9.30 0.000 6908988 1.059641 lgdp Coef Std Err z P>|z| [95% Conf Interval]
corr(u_i, X) = 0 (assumed) Prob > chi2 = 0.0000 Wald chi2(3) = 354.38
overall = 0.7433 max = 5 between = 0.7558 avg = 4.7R-sq: within = 0.4200 Obs per group: min = 3
Group variable: province Number of groups = 58Random-effects GLS regression Number of obs = 271 xtreg lgdp llabor linvest pci, re
Trang 20 FE: inefficient, but consistent
RE: efficient, but probably inconsistent
RE will be better if is consistent.
Trang 21Hausman test
Recall that RE will be better if is consistent
is unbiased if it is not systematically different from
Hausman test null hypothesis
if the null hypothesis is rejected: FE is better
if the null hypothesis is not rejected: RE is better
Trang 22Hausman test
xtreg lgdp llabor linvest pci, fe
estimate store fixed
xtreg lgdp llabor linvest pci, re
estimate store random
hausman fixed random
Trang 23Test: Ho: difference in coefficients not systematic
B = inconsistent under Ha, efficient under Ho; obtained from xtreg
b = consistent under Ho and Ha; obtained from xtreg pci 0044829 0042964 .0001865
linvest .258814 3487632 -.0899493 .0160913
llabor 1.173004 8752699 .2977342 141169
fixed random Difference S.E
(b) (B) (b-B) sqrt(diag(V_b-V_B)) Coefficients
hausman fixed random
Trang 24Random Coefficients Model
xtmixed lgdp llabor linvest pci || province: pci
LR test vs linear regression: chi2(2) = 341.52 Prob > chi2 = 0.0000 sd(Residual) 1501907 .0075356 1361241 .1657109 sd(_cons) 3422018 .0864983 2085088 .5616171 sd(pci) 0044457 .0017468 0020582 .0096027province: Independent
Random-effects Parameters Estimate Std Err [95% Conf Interval]
_cons 5.109057 .6147896 8.31 0.000 3.904092 6.314023 pci 0047026 .0018857 2.49 0.013 0010067 .0083985 linvest 3347195 .0395771 8.46 0.000 2571498 .4122891 llabor 8927864 .0958204 9.32 0.000 7049819 1.080591 lgdp Coef Std Err z P>|z| [95% Conf Interval]