5.1 Apply a chow-test for structural change on the returns to education and the gender wage gap comparing the years 2005 and 2015.
set more off
capt clear
version 14
use "_data/ex_mydf.dta", clear
. set more off
. capt clear
. version 14
.
. use "_data/ex_mydf.dta", clear
(PGEN: Feb 12, 2017 13:00:53-1 DBV32L)#### load dataset ####
# https://stackoverflow.com/questions/29012141/between-and-within-standard-deviation-of-panel-data-in-r
#### load dataset ####
ex_mydf <- readRDS(file = "_data/ex_mydf.rds")
asample <- ex_mydf %>%
filter(
# Working Hours
pgtatzeit >= 6,
# age
alter %>% dplyr::between(18, 65),
# Employment Status
pgemplst %in% c(1,2,4), # full-time(1), part-time(2), marg.-empl(4)
# population status
pop < 3 # only private households
) %>%
# filter unplausible cases
mutate(na = case_when(
pid %in% c(1380202, 1380202, 607602, 2555301) ~ 1,
pid == 8267202 & syear == 2007 ~ 1,
pid == 2633801 & syear == 2006 ~ 1,
pid == 2582901 & syear > 2006 ~ 1 )
) %>%
filter(is.na(na)) %>%
dplyr::select(syear, pgbilzeit, frau, ost, lnwage, erf)Apply a chow-test for structural change on the returns to education and the gender wage gap comparing the years 2005 and 2015.
use "_data/ex_mydf.dta", clear
*** Pooled OLS
* 2015
reg lnwage ost frau pgbilzeit c.erf##c.erf pgexpue i.pgallbet if asample==1 & syear==2015 [pw=phrf], cluster(hid)
estimates store m2015
* 2005
reg lnwage ost frau pgbilzeit c.erf##c.erf pgexpue i.pgallbet if asample==1 & syear==2005 [pw=phrf], cluster(hid)
estimates store m2005
gen per2015 = syear == 2015
reg lnwage ost frau pgbilzeit c.erf##c.erf pgexpue i.pgallbet per2015 if asample==1 & syear==2005 | syear==2015 [pw=phrf], cluster(pid)
estimates store pooled
esttab m2005 m2015 pooled , ar2 abs star(* .05 ** .01) replace nobase ///
nobase mtitle("2005" "2015" "pooled") nogaps
esttab m2005 m2015 pooled using table.rtf , ar2 abs star(* .05 ** .01) replace ///
nobase mtitle("2005" "2015" "pooled")
*** Test for structural change
reg lnwage i.per2015##i.ost i.per2015##i.frau i.per2015##c.pgbilzeit c.erf##c.erf pgexpue i.pgallbet per2015 if asample==1 & syear==2005 | syear==2015 [pw=phrf], cluster(pid)
reg lnwage ost frau pgbilzeit c.erf##c.erf pgexpue i.pgallbet if asample==1 & syear==2015 [iw=phrf],
estimates store m2015
reg lnwage ost frau pgbilzeit c.erf##c.erf pgexpue i.pgallbet if asample==1 & syear==2005 [iw=phrf],
estimates store m2005
suest m2005 m2015 , cluster(hid)
est table m2005 m2015, star
test [m2005_mean = m2015_mean]
test [m2005_mean]pgbilzeit=[m2015_mean]pgbilzeit
test [f1_mean]alter = [m1_mean]alter
test [f1_mean]_cons = [m1_mean]_cons
. use "_data/ex_mydf.dta", clear
(PGEN: Feb 12, 2017 13:00:53-1 DBV32L)
.
. *** Pooled OLS
. * 2015
. reg lnwage ost frau pgbilzeit c.erf##c.erf pgexpue i.pgallbet if asample==1 &
> syear==2015 [pw=phrf], cluster(hid)
(sum of wgt is 3.3458e+07)
Linear regression Number of obs = 14,034
F(10, 9953) = 330.48
Prob > F = 0.0000
R-squared = 0.3760
Root MSE = .45056
(Std. Err. adjusted for 9,954 clusters in hid)
------------------------------------------------------------------------------
| Robust
lnwage | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
ost | -.1987729 .0179708 -11.06 0.000 -.2339993 -.1635465
frau | -.1328419 .0130426 -10.19 0.000 -.1584081 -.1072758
pgbilzeit | .0746257 .0024972 29.88 0.000 .0697307 .0795208
erf | .0385242 .002168 17.77 0.000 .0342744 .042774
|
c.erf#c.erf | -.0006413 .0000501 -12.79 0.000 -.0007395 -.000543
|
pgexpue | -.0471266 .0047512 -9.92 0.000 -.05644 -.0378132
|
pgallbet |
[2] GE 20.. | .1147761 .0176681 6.50 0.000 .080143 .1494092
[3] GE 20.. | .2098906 .0203239 10.33 0.000 .1700517 .2497296
[4] GE 2000 | .312486 .0193109 16.18 0.000 .2746327 .3503392
[5] Selbs.. | -.0744961 .0496536 -1.50 0.134 -.1718271 .0228349
|
_cons | 1.291813 .0391646 32.98 0.000 1.215042 1.368583
------------------------------------------------------------------------------
. estimates store m2015
.
. * 2005
. reg lnwage ost frau pgbilzeit c.erf##c.erf pgexpue i.pgallbet if asample==1 &
> syear==2005 [pw=phrf], cluster(hid)
(sum of wgt is 2.8666e+07)
Linear regression Number of obs = 9,522
F(10, 6696) = 302.93
Prob > F = 0.0000
R-squared = 0.3550
Root MSE = .45353
(Std. Err. adjusted for 6,697 clusters in hid)
------------------------------------------------------------------------------
| Robust
lnwage | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
ost | -.3387678 .0176441 -19.20 0.000 -.3733558 -.3041797
frau | -.1809541 .0139264 -12.99 0.000 -.2082544 -.1536539
pgbilzeit | .0721785 .0031806 22.69 0.000 .0659435 .0784136
erf | .0384176 .0022836 16.82 0.000 .0339411 .0428942
|
c.erf#c.erf | -.0006552 .0000536 -12.22 0.000 -.0007603 -.0005501
|
pgexpue | -.0548967 .0070044 -7.84 0.000 -.0686275 -.0411658
|
pgallbet |
[2] GE 20.. | .1116015 .0186546 5.98 0.000 .0750326 .1481704
[3] GE 20.. | .2419907 .0175713 13.77 0.000 .2075453 .2764361
[4] GE 2000 | .2698741 .0207693 12.99 0.000 .2291597 .3105886
[5] Selbs.. | -.1874213 .0791409 -2.37 0.018 -.3425627 -.0322799
|
_cons | 1.417531 .0466424 30.39 0.000 1.326097 1.508965
------------------------------------------------------------------------------
. estimates store m2005
.
. gen per2015 = syear == 2015
. reg lnwage ost frau pgbilzeit c.erf##c.erf pgexpue i.pgallbet per2015 if asam
> ple==1 & syear==2005 | syear==2015 [pw=phrf], cluster(pid)
(sum of wgt is 6.4782e+07)
Linear regression Number of obs = 24,633
F(11, 21331) = 527.17
Prob > F = 0.0000
R-squared = 0.3652
Root MSE = .48016
(Std. Err. adjusted for 21,332 clusters in pid)
------------------------------------------------------------------------------
| Robust
lnwage | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
ost | -.2742035 .0134076 -20.45 0.000 -.3004833 -.2479237
frau | -.1418909 .0103735 -13.68 0.000 -.1622237 -.1215581
pgbilzeit | .0792116 .0021235 37.30 0.000 .0750493 .0833739
erf | .0447061 .0016721 26.74 0.000 .0414286 .0479836
|
c.erf#c.erf | -.0007516 .0000408 -18.42 0.000 -.0008316 -.0006716
|
pgexpue | -.0429604 .0038216 -11.24 0.000 -.050451 -.0354698
|
pgallbet |
[2] GE 20.. | .1030256 .0136136 7.57 0.000 .0763419 .1297094
[3] GE 20.. | .2173511 .0146506 14.84 0.000 .1886348 .2460674
[4] GE 2000 | .2873069 .0144674 19.86 0.000 .2589497 .3156641
[5] Selbs.. | -.0994286 .0420419 -2.36 0.018 -.1818339 -.0170233
|
per2015 | -.0569487 .0091188 -6.25 0.000 -.0748223 -.0390752
_cons | 1.228242 .0321654 38.19 0.000 1.165195 1.291289
------------------------------------------------------------------------------
. estimates store pooled
.
. esttab m2005 m2015 pooled , ar2 abs star(* .05 ** .01) replace nobase ///
> nobase mtitle("2005" "2015" "pooled") nogaps
---------------------------------------------------------
(1) (2) (3)
2005 2015 pooled
---------------------------------------------------------
ost -0.339** -0.199** -0.274**
(19.20) (11.06) (20.45)
frau -0.181** -0.133** -0.142**
(12.99) (10.19) (13.68)
pgbilzeit 0.0722** 0.0746** 0.0792**
(22.69) (29.88) (37.30)
erf 0.0384** 0.0385** 0.0447**
(16.82) (17.77) (26.74)
c.erf#c.erf -0.000655** -0.000641** -0.000752**
(12.22) (12.79) (18.42)
pgexpue -0.0549** -0.0471** -0.0430**
(7.84) (9.92) (11.24)
2.pgallbet 0.112** 0.115** 0.103**
(5.98) (6.50) (7.57)
3.pgallbet 0.242** 0.210** 0.217**
(13.77) (10.33) (14.84)
4.pgallbet 0.270** 0.312** 0.287**
(12.99) (16.18) (19.86)
5.pgallbet -0.187* -0.0745 -0.0994*
(2.37) (1.50) (2.36)
per2015 -0.0569**
(6.25)
_cons 1.418** 1.292** 1.228**
(30.39) (32.98) (38.19)
---------------------------------------------------------
N 9522 14034 24633
adj. R-sq 0.354 0.376 0.365
---------------------------------------------------------
Absolute t statistics in parentheses
* p<.05, ** p<.01
.
. esttab m2005 m2015 pooled using table.rtf , ar2 abs star(* .05 ** .01) repla
> ce ///
> nobase mtitle("2005" "2015" "pooled")
(note: file table.rtf not found)
(output written to table.rtf)
.
. *** Test for structural change
. reg lnwage i.per2015##i.ost i.per2015##i.frau i.per2015##c.pgbilzeit c.erf##
> c.erf pgexpue i.pgallbet per2015 if asample==1 & syear==2005 | syear==2015 [p
> w=phrf], cluster(pid)
(sum of wgt is 6.4782e+07)
note: per2015 omitted because of collinearity
Linear regression Number of obs = 24,633
F(14, 21331) = 425.08
Prob > F = 0.0000
R-squared = 0.3678
Root MSE = .47922
(Std. Err. adjusted for 21,332 clusters in pid)
------------------------------------------------------------------------------
| Robust
lnwage | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
1.per2015 | -.2139276 .0485717 -4.40 0.000 -.3091317 -.1187234
|
ost |
Ost | -.3496436 .0169352 -20.65 0.000 -.3828379 -.3164494
|
per2015#ost |
1#Ost | .1351972 .022936 5.89 0.000 .0902409 .1801536
|
frau |
weiblich | -.1687139 .0141056 -11.96 0.000 -.196362 -.1410657
|
per2015#frau |
1#weiblich | .0473041 .0181299 2.61 0.009 .0117682 .08284
|
pgbilzeit | .0739746 .0030055 24.61 0.000 .0680836 .0798656
|
per2015#|
c.pgbilzeit |
1 | .0090171 .0037316 2.42 0.016 .001703 .0163313
|
erf | .0445412 .0016719 26.64 0.000 .0412642 .0478182
|
c.erf#c.erf | -.0007475 .0000408 -18.32 0.000 -.0008275 -.0006676
|
pgexpue | -.0437749 .0038146 -11.48 0.000 -.0512517 -.0362981
|
pgallbet |
[2] GE 20.. | .1016492 .0135954 7.48 0.000 .0750011 .1282973
[3] GE 20.. | .2143009 .0146149 14.66 0.000 .1856546 .2429473
[4] GE 2000 | .2855804 .0144287 19.79 0.000 .2572989 .3138618
[5] Selbs.. | -.1000737 .0420785 -2.38 0.017 -.1825507 -.0175966
|
per2015 | 0 (omitted)
_cons | 1.320129 .0416619 31.69 0.000 1.238468 1.401789
------------------------------------------------------------------------------
.
. reg lnwage ost frau pgbilzeit c.erf##c.erf pgexpue i.pgallbet if asample==1 &
> syear==2015 [iw=phrf],
Source | SS df MS Number of obs = 33458470
-------------+---------------------------------- F(10, 33458459) > 99999.00
Model | 4089743.87 10 408974.387 Prob > F = 0.0000
Residual | 6786878.59 33458459 .202844925 R-squared = 0.3760
-------------+---------------------------------- Adj R-squared = 0.3760
Total | 10876622.5 33458469 .325078307 Root MSE = .45038
------------------------------------------------------------------------------
lnwage | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
ost | -.1987729 .0002097 -947.86 0.000 -.1991839 -.1983618
frau | -.1328419 .0001607 -826.85 0.000 -.1331568 -.132527
pgbilzeit | .0746257 .0000296 2523.19 0.000 .0745678 .0746837
erf | .0385242 .0000244 1581.12 0.000 .0384765 .038572
|
c.erf#c.erf | -.0006413 5.99e-07 -1069.73 0.000 -.0006424 -.0006401
|
pgexpue | -.0471266 .0000405 -1162.86 0.000 -.047206 -.0470472
|
pgallbet |
[2] GE 20.. | .1147761 .0002259 508.19 0.000 .1143334 .1152188
[3] GE 20.. | .2098906 .0002369 886.12 0.000 .2094264 .2103549
[4] GE 2000 | .312486 .0002238 1396.20 0.000 .3120473 .3129246
[5] Selbs.. | -.0744961 .0004086 -182.33 0.000 -.0752969 -.0736953
|
_cons | 1.291813 .0004696 2750.97 0.000 1.290892 1.292733
------------------------------------------------------------------------------
. estimates store m2015
. reg lnwage ost frau pgbilzeit c.erf##c.erf pgexpue i.pgallbet if asample==1 &
> syear==2005 [iw=phrf],
Source | SS df MS Number of obs = 28666228
-------------+---------------------------------- F(10, 28666217) > 99999.00
Model | 3240784.2 10 324078.42 Prob > F = 0.0000
Residual | 5889449.86 28666217 .205449148 R-squared = 0.3550
-------------+---------------------------------- Adj R-squared = 0.3550
Total | 9130234.05 28666227 .318501422 Root MSE = .45326
------------------------------------------------------------------------------
lnwage | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
ost | -.3387678 .0002323 -1458.61 0.000 -.339223 -.3383125
frau | -.1809541 .0001764 -1025.65 0.000 -.1812999 -.1806084
pgbilzeit | .0721785 .000034 2122.53 0.000 .0721119 .0722452
erf | .0384176 .0000287 1340.03 0.000 .0383615 .0384738
|
c.erf#c.erf | -.0006552 6.98e-07 -938.13 0.000 -.0006566 -.0006538
|
pgexpue | -.0548967 .0000627 -875.20 0.000 -.0550196 -.0547737
|
pgallbet |
[2] GE 20.. | .1116015 .0002286 488.16 0.000 .1111534 .1120496
[3] GE 20.. | .2419907 .0002503 966.98 0.000 .2415002 .2424812
[4] GE 2000 | .2698741 .0002497 1080.72 0.000 .2693847 .2703636
[5] Selbs.. | -.1874213 .0005092 -368.04 0.000 -.1884194 -.1864232
|
_cons | 1.417531 .0005342 2653.58 0.000 1.416484 1.418578
------------------------------------------------------------------------------
. estimates store m2005
.
. suest m2005 m2015 , cluster(hid)
Simultaneous results for m2005, m2015
Number of obs = 23,556
(Std. Err. adjusted for 14,186 clusters in hid)
------------------------------------------------------------------------------
| Robust
| Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
m2005_mean |
ost | -.3387678 .0176341 -19.21 0.000 -.37333 -.3042055
frau | -.1809541 .0139186 -13.00 0.000 -.208234 -.1536743
pgbilzeit | .0721785 .0031788 22.71 0.000 .0659482 .0784089
erf | .0384176 .0022823 16.83 0.000 .0339444 .0428909
|
c.erf#c.erf | -.0006552 .0000536 -12.23 0.000 -.0007602 -.0005502
|
pgexpue | -.0548967 .0070004 -7.84 0.000 -.0686173 -.0411761
|
pgallbet |
[2] GE 20.. | .1116015 .0186441 5.99 0.000 .0750598 .1481432
[3] GE 20.. | .2419907 .0175614 13.78 0.000 .207571 .2764104
[4] GE 2000 | .2698741 .0207576 13.00 0.000 .22919 .3105583
[5] Selbs.. | -.1874213 .0790962 -2.37 0.018 -.342447 -.0323955
|
_cons | 1.417531 .0466161 30.41 0.000 1.326165 1.508897
-------------+----------------------------------------------------------------
m2005_lnvar |
_cons | -1.582557 .0681554 -23.22 0.000 -1.716139 -1.448975
-------------+----------------------------------------------------------------
m2015_mean |
ost | -.1987729 .0179641 -11.06 0.000 -.2339819 -.1635638
frau | -.1328419 .0130378 -10.19 0.000 -.1583955 -.1072884
pgbilzeit | .0746257 .0024963 29.89 0.000 .0697331 .0795184
erf | .0385242 .0021672 17.78 0.000 .0342765 .0427719
|
c.erf#c.erf | -.0006413 .0000501 -12.80 0.000 -.0007395 -.000543
|
pgexpue | -.0471266 .0047495 -9.92 0.000 -.0564354 -.0378178
|
pgallbet |
[2] GE 20.. | .1147761 .0176616 6.50 0.000 .08016 .1493922
[3] GE 20.. | .2098906 .0203164 10.33 0.000 .1700713 .2497099
[4] GE 2000 | .312486 .0193037 16.19 0.000 .2746513 .3503206
[5] Selbs.. | -.0744961 .0496351 -1.50 0.133 -.1717792 .022787
|
_cons | 1.291813 .0391501 33.00 0.000 1.21508 1.368545
-------------+----------------------------------------------------------------
m2015_lnvar |
_cons | -1.595314 .0333955 -47.77 0.000 -1.660768 -1.52986
------------------------------------------------------------------------------
.
. est table m2005 m2015, star
----------------------------------------------
Variable | m2005 m2015
-------------+--------------------------------
ost | -.33876775*** -.19877286***
frau | -.18095415*** -.13284194***
pgbilzeit | .07217854*** .07462573***
erf | .03841764*** .03852422***
|
c.erf#c.erf | -.0006552*** -.00064125***
|
pgexpue | -.05489668*** -.0471266***
|
pgallbet |
[2] GE 20.. | .1116015*** .11477611***
[3] GE 20.. | .2419907*** .20989062***
[4] GE 2000 | .26987415*** .31248596***
[5] Selbs.. | -.18742128*** -.0744961***
|
_cons | 1.4175307*** 1.2918125***
----------------------------------------------
legend: * p<0.05; ** p<0.01; *** p<0.001
.
. test [m2005_mean = m2015_mean]
( 1) [m2005_mean]ost - [m2015_mean]ost = 0
( 2) [m2005_mean]frau - [m2015_mean]frau = 0
( 3) [m2005_mean]pgbilzeit - [m2015_mean]pgbilzeit = 0
( 4) [m2005_mean]erf - [m2015_mean]erf = 0
( 5) [m2005_mean]c.erf#c.erf - [m2015_mean]c.erf#c.erf = 0
( 6) [m2005_mean]pgexpue - [m2015_mean]pgexpue = 0
( 7) [m2005_mean]1b.pgallbet - [m2015_mean]1b.pgallbet = 0
( 8) [m2005_mean]2.pgallbet - [m2015_mean]2.pgallbet = 0
( 9) [m2005_mean]3.pgallbet - [m2015_mean]3.pgallbet = 0
(10) [m2005_mean]4.pgallbet - [m2015_mean]4.pgallbet = 0
(11) [m2005_mean]5.pgallbet - [m2015_mean]5.pgallbet = 0
Constraint 7 dropped
chi2( 10) = 60.97
Prob > chi2 = 0.0000
.
. test [m2005_mean]pgbilzeit=[m2015_mean]pgbilzeit
( 1) [m2005_mean]pgbilzeit - [m2015_mean]pgbilzeit = 0
chi2( 1) = 0.40
Prob > chi2 = 0.5262
.
.
. test [f1_mean]alter = [m1_mean]alter
equation [f1_mean] not found
r(303);
end of do-file
r(303);Chow Test
dv05 <- asample %>%
mutate(erf_q = erf^2) %>%
filter(syear == 2005) %>%
drop_na() %>%
pull(lnwage)
dv15 <- asample %>%
mutate(erf_q = erf^2) %>%
filter(syear == 2015) %>%
drop_na() %>%
pull(lnwage)
ivs05 <- asample %>%
mutate(erf_q = erf^2) %>%
filter(syear == 2005) %>%
drop_na() %>%
select(-lnwage) %>%
as.matrix()
ivs15 <- asample %>%
mutate(erf_q = erf^2) %>%
filter(syear == 2015) %>%
drop_na() %>%
select(-lnwage) %>%
as.matrix()
sctest(c(dv05, dv15) ~ rbind(ivs05, ivs15), type = "Chow", point = length(dv05), data = asample)##
## Chow test
##
## data: c(dv05, dv15) ~ rbind(ivs05, ivs15)
## F = 10, p-value <2e-16