Bài 11: Mô hình dữ liệu bảng Panel Data

Bạn đang xem bản rút gọn của tài liệu. Xem và tải ngay bản đầy đủ của tài liệu tại đây (680.2 KB, 24 trang )

PANEL DATA MODELS

</div>
<span class='text_page_counter'>(2)</span><div class='page_container' data-page=2>

Panel data



<b>data on MANY units and SEVERAL time periods</b>

</div>
<span class='text_page_counter'>(3)</span><div class='page_container' data-page=3>

Example

Viet Nam Provincial data on



GDP : provincial GDP (mil. VND)



LABFO: number of laborers of provinces (1000

persons)



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

</div>
<span class='text_page_counter'>(4)</span><div class='page_container' data-page=4>

Example

provcode province

year

rgdp

labfo

rinvest

pci

An Giang

1 2007 22000000

1221.3

5600000

66.4688

1 2008 25000000

1244.9

4600000

61.1247

1 2009 25000000

1227.3

4800000

58.177

1 2010 27000000

1255

4500000

61.9379

1 2011 29000000

1300.4

3900000

62.22 Bac Can

2 2007

1500000

177.2 592714

46.4687

2 2008

2000000

179.8 1100000

39.7762

2 2009

2400000

189.8 1100000

75.9563

2 2010

3400000

194 2600000

51.4864

2 2011

4200000

199.6 2900000

52.71

</div>
<span class='text_page_counter'>(5)</span><div class='page_container' data-page=5>

Why panel data?



more information



heterogeneity among units

</div>
<span class='text_page_counter'>(6)</span><div class='page_container' data-page=6>

Manipulation of panel data

delta: 1 unit

time variable: year, 2007 to 2011

panel variable: province (strongly balanced)

. xtset province year

</div>
<span class='text_page_counter'>(7)</span><div class='page_container' data-page=7>

Manipulation of panel data

58 100.00 XXXXX

58 100.00 100.00 11111

Freq. Percent Cum. Pattern

5 5 5 5 5 5 5
Distribution of T_i: min 5% 25% 50% 75% 95% max

(province*year uniquely identifies each observation)

Span(year) = 5 periods
Delta(year) = 1 unit

year: 2007, 2008, ..., 2011 T = 5
province: 1, 2, ..., 58 n = 58
. xtdescribe

</div>
<span class='text_page_counter'>(8)</span><div class='page_container' data-page=8>

Manipulation of panel data

58 100.00 XXXXX

58 100.00 100.00 11111

Freq. Percent Cum. Pattern

5 5 5 5 5 5 5
Distribution of T_i: min 5% 25% 50% 75% 95% max
(province*year uniquely identifies each observation)

Span(year) = 5 periods
Delta(year) = 1 unit

year: 2007, 2008, ..., 2011 T = 5
province: 1, 2, ..., 58 n = 58
. xtdescribe

</div>
<span class='text_page_counter'>(9)</span><div class='page_container' data-page=9>

Manipulation of panel data

within 5.445562 41.77384 79.91406 T = 5
between 4.380076 49.67015 67.33098 n = 58
pci 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 = 58
rinvest 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 = 58
rgdp overall 2.05e+07 2.96e+07 1485281 1.71e+08 N = 280

Variable Mean Std. Dev. Min Max Observations
. xtsum rgdp rinvest pci

</div>
<span class='text_page_counter'>(10)</span><div class='page_container' data-page=10>

Manipulation 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

</div>
<span class='text_page_counter'>(11)</span><div class='page_container' data-page=11>

Manipulation of panel data

xtline pci if province<=10, overlay

2007 2008 2009 2010 2011

YEAR

</div>
<span class='text_page_counter'>(12)</span><div class='page_container' data-page=12>

Pooled OLS

Fixed Effects (FE) Model

Random Effects (RE) Model

</div>
<span class='text_page_counter'>(13)</span><div class='page_container' data-page=13>

Basic considerations



Pooled OLS



Unit-specific effects



Two-way effects model



Mixed model [or Random coefficients model]

 



















 

 





</div>
<span class='text_page_counter'>(14)</span><div class='page_container' data-page=14>

Pooled OLS



assumes identical intercept for all units and time

periods



assumes errors are independent across all units i.

</div>
<span class='text_page_counter'>(15)</span><div class='page_container' data-page=15>

Pooled 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

</div>
<span class='text_page_counter'>(16)</span><div class='page_container' data-page=16>

Unit-specific effects model

rho .91156075 (fraction of variance due to u_i)

sigma_e .15132407
sigma_u .48582326

</div>
<span class='text_page_counter'>(17)</span><div class='page_container' data-page=17>

Two-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

2011 .4228365 .0253706 16.67 0.000 .3728171 .4728559

2010 .2969721 .0238665 12.44 0.000 .2499183 .3440259

2009 .1845611 .0219074 8.42 0.000 .1413696 .2277525

2008 .0979883 .0202528 4.84 0.000 .0580589 .1379177

year

</div>
<span class='text_page_counter'>(18)</span><div class='page_container' data-page=18>

Problems of FE models



FE models are equivalent to Pooled OLS with



unit-specific dummies, and/or



time-specific dummies

included.



Problem: so many dummy variables included in the

model, result in lower degree of freedom



Solution: Random Effects [RE] Model











</div>
<span class='text_page_counter'>(19)</span><div class='page_container' data-page=19>

Random effects model

rho .86012018 (fraction of variance due to u_i)

sigma_e .15132407
sigma_u .37524081

</div>
<span class='text_page_counter'>(20)</span><div class='page_container' data-page=20>

Problem of RE model



No dummy variables added, so efficient.



Assumption



If assumption is not satisfied, then

is

inconsistent.



In summary



FE: inefficient, but consistent



RE: efficient, but probably inconsistent



RE will be better if

is consistent.



2



,

uncorrelated with



 







</div>
<span class='text_page_counter'>(21)</span><div class='page_container' data-page=21>

Hausman 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







is not systematically different from

</div>
<span class='text_page_counter'>(22)</span><div class='page_container' data-page=22>

Hausman test

xtreg lgdp llabor linvest pci, fe

estimate store fixed

xtreg lgdp llabor linvest pci, re

estimate store random

</div>
<span class='text_page_counter'>(23)</span><div class='page_container' data-page=23>

Hausman test

(V_b-V_B is not positive definite)
Prob>chi2 = 0.0000

= 30.38

chi2(3) = (b-B)'[(V_b-V_B)^(-1)](b-B)
Test: 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

</div>
<span class='text_page_counter'>(24)</span><div class='page_container' data-page=24>

Random 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 .0096027
province: Independent

</div>