7.1 Specify a random and a fixed effects model. Compare the results.
7.2 Execute the hausman test. Which model specification is more appropriate and why?
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 ####
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 <= 2, # only private households
# restrict number of years
syear > 2002) %>%
# 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))
# Prepare Panel Dataset
p.asample <- pdata.frame(asample, index = c("pid", "syear"))
# information if panel dataframe
pdim(p.asample)## Unbalanced Panel: n = 37989, T = 1-13, N = 167978# summary(p.asample)Specify a random and a fixed effects model. Compare the results.
use "_data/ex_mydf.dta", clear
xtset pid syear
* FE model
xtreg lnwage pgbilzeit c.erf##c.erf pgexpue ost frau i.pgallbet i.syear if asample==1 & syear>2002 , fe
est sto fixed
* RE model
xtreg lnwage pgbilzeit c.erf##c.erf pgexpue ost frau i.pgallbet i.syear if asample==1 & syear>2002 , re
est sto random
esttab fixed random
. use "_data/ex_mydf.dta", clear
(PGEN: Feb 12, 2017 13:00:53-1 DBV32L)
.
. xtset pid syear
panel variable: pid (unbalanced)
time variable: syear, 1984 to 2015, but with gaps
delta: 1 unit
. * FE model
. xtreg lnwage pgbilzeit c.erf##c.erf pgexpue ost frau i.pgallbet i.syear if as
> ample==1 & syear>2002 , fe
note: frau omitted because of collinearity
Fixed-effects (within) regression Number of obs = 156,029
Group variable: pid Number of groups = 33,894
R-sq: Obs per group:
within = 0.0401 min = 1
between = 0.3541 avg = 4.6
overall = 0.3156 max = 13
F(21,122114) = 242.73
corr(u_i, Xb) = 0.1227 Prob > F = 0.0000
------------------------------------------------------------------------------
lnwage | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
pgbilzeit | .0529867 .0023403 22.64 0.000 .0483998 .0575736
erf | .045247 .0015267 29.64 0.000 .0422547 .0482393
|
c.erf#c.erf | -.0006661 .0000183 -36.33 0.000 -.000702 -.0006301
|
pgexpue | -.0332011 .0032925 -10.08 0.000 -.0396543 -.0267478
ost | -.1209915 .0138824 -8.72 0.000 -.1482008 -.0937822
frau | 0 (omitted)
|
pgallbet |
[2] GE 20.. | .0495245 .0038447 12.88 0.000 .041989 .0570599
[3] GE 20.. | .0771106 .0044952 17.15 0.000 .0683001 .0859211
[4] GE 2000 | .0896249 .004655 19.25 0.000 .0805012 .0987486
[5] Selbs.. | -.0717673 .0070217 -10.22 0.000 -.0855298 -.0580048
|
syear |
2004 | -.0172732 .0041979 -4.11 0.000 -.0255011 -.0090453
2005 | -.0460263 .0046925 -9.81 0.000 -.0552235 -.0368291
2006 | -.0833928 .0052421 -15.91 0.000 -.0936673 -.0731183
2007 | -.1048617 .0058791 -17.84 0.000 -.1163846 -.0933387
2008 | -.1178463 .0066686 -17.67 0.000 -.1309167 -.1047759
2009 | -.109741 .0074812 -14.67 0.000 -.1244041 -.095078
2010 | -.1125573 .0082187 -13.70 0.000 -.1286657 -.0964488
2011 | -.1263725 .0090593 -13.95 0.000 -.1441287 -.1086164
2012 | -.1278882 .0099357 -12.87 0.000 -.1473619 -.1084144
2013 | -.1120904 .0106497 -10.53 0.000 -.1329637 -.0912171
2014 | -.0969339 .0114189 -8.49 0.000 -.1193146 -.0745531
2015 | -.0739467 .0123574 -5.98 0.000 -.098167 -.0497265
|
_cons | 1.564629 .0348093 44.95 0.000 1.496403 1.632854
-------------+----------------------------------------------------------------
sigma_u | .48874503
sigma_e | .28535324
rho | .74577917 (fraction of variance due to u_i)
------------------------------------------------------------------------------
F test that all u_i=0: F(33893, 122114) = 8.99 Prob > F = 0.0000
. est sto fixed
.
. * RE model
. xtreg lnwage pgbilzeit c.erf##c.erf pgexpue ost frau i.pgallbet i.syear if as
> ample==1 & syear>2002 , re
Random-effects GLS regression Number of obs = 156,029
Group variable: pid Number of groups = 33,894
R-sq: Obs per group:
within = 0.0369 min = 1
between = 0.4279 avg = 4.6
overall = 0.3879 max = 13
Wald chi2(23) = .
corr(u_i, X) = 0 (assumed) Prob > chi2 = .
------------------------------------------------------------------------------
lnwage | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
pgbilzeit | .0802379 .0008554 93.81 0.000 .0785614 .0819144
erf | .0396457 .000537 73.83 0.000 .0385932 .0406982
|
c.erf#c.erf | -.0006464 .0000129 -50.00 0.000 -.0006717 -.000621
|
pgexpue | -.05377 .0012146 -44.27 0.000 -.0561506 -.0513894
ost | -.2602876 .0057363 -45.38 0.000 -.2715306 -.2490446
frau | -.1655567 .0050538 -32.76 0.000 -.1754619 -.1556514
|
pgallbet |
[2] GE 20.. | .0832469 .0033899 24.56 0.000 .0766028 .0898909
[3] GE 20.. | .1399706 .0038861 36.02 0.000 .1323539 .1475873
[4] GE 2000 | .1697413 .0039608 42.85 0.000 .1619782 .1775044
[5] Selbs.. | -.0827156 .0063581 -13.01 0.000 -.0951774 -.0702539
|
syear |
1984 | 0 (empty)
1985 | 0 (empty)
1986 | 0 (empty)
1987 | 0 (empty)
1988 | 0 (empty)
1989 | 0 (empty)
1990 | 0 (empty)
1991 | 0 (empty)
1992 | 0 (empty)
1993 | 0 (empty)
1994 | 0 (empty)
1995 | 0 (empty)
1996 | 0 (empty)
1997 | 0 (empty)
1998 | 0 (empty)
1999 | 0 (empty)
2000 | 0 (empty)
2001 | 0 (empty)
2002 | 0 (empty)
2003 | 1.336591 .0125562 106.45 0.000 1.311981 1.361201
2004 | 1.321806 .0125879 105.01 0.000 1.297134 1.346478
2005 | 1.296002 .0126865 102.16 0.000 1.271137 1.320867
2006 | 1.261972 .0127316 99.12 0.000 1.237018 1.286925
2007 | 1.243458 .0127611 97.44 0.000 1.218447 1.268469
2008 | 1.23416 .0128557 96.00 0.000 1.208964 1.259357
2009 | 1.245013 .0129041 96.48 0.000 1.219722 1.270305
2010 | 1.243918 .0128664 96.68 0.000 1.218701 1.269136
2011 | 1.233039 .0128811 95.72 0.000 1.207793 1.258286
2012 | 1.231218 .0129403 95.15 0.000 1.205856 1.256581
2013 | 1.251511 .0128542 97.36 0.000 1.226317 1.276705
2014 | 1.264077 .0130704 96.71 0.000 1.23846 1.289695
2015 | 1.289241 .013119 98.27 0.000 1.263528 1.314953
|
_cons | 0 (omitted)
-------------+----------------------------------------------------------------
sigma_u | .41250016
sigma_e | .28535324
rho | .67634333 (fraction of variance due to u_i)
------------------------------------------------------------------------------
. est sto random
.
. esttab fixed random
--------------------------------------------
(1) (2)
lnwage lnwage
--------------------------------------------
pgbilzeit 0.0530*** 0.0802***
(22.64) (93.81)
erf 0.0452*** 0.0396***
(29.64) (73.83)
c.erf#c.erf -0.000666*** -0.000646***
(-36.33) (-50.00)
pgexpue -0.0332*** -0.0538***
(-10.08) (-44.27)
ost -0.121*** -0.260***
(-8.72) (-45.38)
frau 0 -0.166***
(.) (-32.76)
1.pgallbet 0 0
(.) (.)
2.pgallbet 0.0495*** 0.0832***
(12.88) (24.56)
3.pgallbet 0.0771*** 0.140***
(17.15) (36.02)
4.pgallbet 0.0896*** 0.170***
(19.25) (42.85)
5.pgallbet -0.0718*** -0.0827***
(-10.22) (-13.01)
2003.syear 0 1.337***
(.) (106.45)
2004.syear -0.0173*** 1.322***
(-4.11) (105.01)
2005.syear -0.0460*** 1.296***
(-9.81) (102.16)
2006.syear -0.0834*** 1.262***
(-15.91) (99.12)
2007.syear -0.105*** 1.243***
(-17.84) (97.44)
2008.syear -0.118*** 1.234***
(-17.67) (96.00)
2009.syear -0.110*** 1.245***
(-14.67) (96.48)
2010.syear -0.113*** 1.244***
(-13.70) (96.68)
2011.syear -0.126*** 1.233***
(-13.95) (95.72)
2012.syear -0.128*** 1.231***
(-12.87) (95.15)
2013.syear -0.112*** 1.252***
(-10.53) (97.36)
2014.syear -0.0969*** 1.264***
(-8.49) (96.71)
2015.syear -0.0739*** 1.289***
(-5.98) (98.27)
1984.syear 0
(.)
1985.syear 0
(.)
1986.syear 0
(.)
1987.syear 0
(.)
1988.syear 0
(.)
1989.syear 0
(.)
1990.syear 0
(.)
1991.syear 0
(.)
1992.syear 0
(.)
1993.syear 0
(.)
1994.syear 0
(.)
1995.syear 0
(.)
1996.syear 0
(.)
1997.syear 0
(.)
1998.syear 0
(.)
1999.syear 0
(.)
2000.syear 0
(.)
2001.syear 0
(.)
2002.syear 0
(.)
_cons 1.565*** 0
(44.95) (.)
--------------------------------------------
N 156029 156029
--------------------------------------------
t statistics in parentheses
* p<0.05, ** p<0.01, *** p<0.001Fixed Effects Model
# FE Model
fixed <- p.asample %>%
plm(lnwage ~ pgbilzeit + erf + I(erf^2) + pgexpue + ost + pgallbet + syear,
data = .,
model = "within"
# weights = phrf
)
tidy(fixed$coefficients[1:30])Random Model
# RE Model
random <- plm(lnwage ~ pgbilzeit + erf + I(erf^2) + pgexpue + ost + pgallbet + syear,
data = p.asample,
model = "random"
# weights = phrf
)
tidy(random)Execute the hausman test. Which model specification is more appropriate and why?
use "_data/ex_mydf.dta", clear
xtreg lnwage pgbilzeit c.erf##c.erf pgexpue ost frau i.pgallbet i.syear if asample==1 & syear>2002 , fe
estimates store fixed
xtreg lnwage pgbilzeit c.erf##c.erf pgexpue ost frau i.pgallbet i.syear if asample==1 & syear>2002 , re
estimates store random
hausman fixed random
. use "_data/ex_mydf.dta", clear
(PGEN: Feb 12, 2017 13:00:53-1 DBV32L)
.
. xtreg lnwage pgbilzeit c.erf##c.erf pgexpue ost frau i.pgallbet i.syear if as
> ample==1 & syear>2002 , fe
must specify panelvar; use xtset
r(459);
end of do-file
r(459);# Hausman Test
hausman <- phtest(fixed, random)
hausman##
## Hausman Test
##
## data: lnwage ~ pgbilzeit + erf + I(erf^2) + pgexpue + ost + pgallbet + ...
## chisq = 2000, df = 20, p-value <2e-16
## alternative hypothesis: one model is inconsistentother things
pvar(p.asample)## no time variation: psample sex gebjahr pid cid pgpbbilo pgbilztev frau na
## no individual variation: syear pgerljob pgbetr pgoeffd pgausb pgpartnr pgpsbil pgpbbil01 pgpbbil02 pgpbbil03 pgpsbila pgpbbila pgpsbilo pgpbbilo pgfamstd pgbilzeit pgerwzeit pgvebzeit pguebstd pgisco88 pgisei88 pgmps92 pgnace pgsiops88 pgegp88 pgkldb92 pgautono pgisced97 pgcasmin pgstib pgallbet pgexpft pgexppt pgexpue pgfield pgdegree pgtraina pgtrainb pgtrainc pgtraind pgfdt_f pgbilztch pgbilztev pgsndjob pgimpsnd pgjobend pgkldb10 pgisco08 pgisced11 cpi adj_fac2010 adj_fac2015 cpi_s lnwage erf erfq qualstand intern cpgbilzeit cerf na
## all NA in time dimension for at least one individual: pgerljob pgbetr pgoeffd pgausb pgpartz pgpartnr pgnation pgpsbil pgpbbil01 pgpbbil02 pgpbbil03 pgpsbila pgpbbila pgpsbilo pgpbbilo pgfamstd pgbilzeit pgerwzeit pgvebzeit pguebstd pgisco88 pgisei88 pgmps92 pgnace pgsiops88 pgegp88 pgkldb92 pgautono pgisced97 pgcasmin pgstib pgallbet pgexpft pgexppt pgexpue pgfield pgdegree pgtraina pgtrainb pgtrainc pgtraind pgfdt_f pgbilztch pgbilztev pgsndjob pgimpsnd pgjobend pgkldb10 pgisco08 pgisced11 lnwage erf erfq qualstand intern cpgbilzeit cerf na
## all NA in ind. dimension for at least one time period: pgerljob pgbetr pgoeffd pgausb pgpartz pgpartnr pgnation pgpsbil pgpbbil01 pgpbbil02 pgpbbil03 pgpsbila pgpbbila pgpsbilo pgpbbilo pgfamstd pgbilzeit pgerwzeit pgvebzeit pguebstd pgisco88 pgisei88 pgmps92 pgnace pgsiops88 pgegp88 pgkldb92 pgautono pgisced97 pgcasmin pgstib pgallbet pgexpft pgexppt pgexpue pgfield pgdegree pgtraina pgtrainb pgtrainc pgtraind pgfdt_f pgbilztch pgbilztev pgsndjob pgimpsnd pgjobend pgkldb10 pgisco08 pgisced11 lnwage erf erfq qualstand intern cpgbilzeit cerf na