st: interpreting output from -xtivreg2-

["Paul Sicilian" <siciliap@gvsu.edu>]

I have both economic and statistical questions regarding output from the
user-written xtivreg2- command (available from ssc).  I will state my
questions up-front and then provide some background so that, hopefully,
the questions will make sense.

My questions are: 
1) Are we interpreting the endogeneity tests provided by xtivreg2-
correctly?
2) If yes to (1), do the combined results or our FE and IV/EGMM
regressions (regarding
children) make either economic or econometric sense to you?

Background
I am estimating ln(wage) regressions for married men on panel data. 
The r.h.s. variables of interest are wife's education, wife's work
experience within the marriage and marriage duration (and some
interactions among these variables). Some papers in this literature
argue that wife's work experience is endogenous in the husband's wage
equation and so use IV techniques with  (i) family nonearned income,
(ii) wife's age (and age squared) and (iii) various measures of the
number of children in the household as instruments.

I am dubious of using children as an instrument since children can
affect time use within the marriage, which could affect men's wages.  In
(non-IV) FE (within person) estimations, I find a statistically
significant (children) x (wife's work experience) interaction (and also
a positive (children) x (wife's education) interaction effect (F-stat
for the test of the joint significance of the children variables =3.05,
pvalue=0.0276 )). 

I also use xtivreg2- to deal with the potential endogeneity of wife's
work experience. Because of the FE results, I estimate some regressions
using only family non-earned income, wife's age and wife's age squared
as instruments. These instruments "pass" the endogeneity test using
Sargen's J Statistic (p-values around 0.6), but they "fail" the weak
instruments test (I am following the advice in Baum, Schaffer, and
Stillmans Stata Journal  (V. 7(4)) article and using the rule of thumb
that the K-P F-statistic should be greater than 10. I am getting F-stats
between 3 and 8, depending on sample and specification of the wage
equation).

However , if I include children (the actual variable is number of
children in the household), the F-statistic for the test of weak
instruments is about 67 and the J-test has a p-value still in the 0.6
range. Moreover, I use the -orthog- option to calculate the C-statistic
for just the children instrument and that has a p-value around 0.4. 

My understanding is that these results imply that children are a
legitimate instrument, seeming to contradict  the FE estimates that
suggest children affect mens wages.

Below is an example of an -xtivreg2- command I use (with children as an
instrument) and the(abbreviated) output from that command.

Thanks for your consideration.

-Paul

. xtivreg2 lwage sp_ed educ tenure tenure2 exper exper2 current
spedcurrent
urban south ncent west yr2-yr23 mine-ind_nr pro-occ_nr (sp_years =
V_total
sp_age sp_age2 childhh) if male==1 & white==1 & married==1 & wage2006>1
&
wage2006 < 400 & self!=1 & ag~=1 /// & farmer~=1 & farmlab~=1 & army!=1
&
current~=0 & sp_ed~=0 & yearmarried>1977, gmm2s robust fe
orthog(childhh)
.
.
FIXED EFFECTS ESTIMATION

Number of groups = 1498 Obs per group: min = 2
avg = 5.2
max = 13
2-Step GMM estimation

Estimates efficient for arbitrary heteroskedasticity
Statistics robust to heteroskedasticity
Number of obs = 7765
F( 43, 6224) = 94.65
Prob > F = 0.0000
Total (centered) SS = 769.5200468 Centered R2 = 0.3975
Total (uncentered) SS = 769.5200468 Uncentered R2 = 0.3975
Residual SS = 463.6217297 Root MSE = .272
.
. (output omitted)
.
Underidentification test (Kleibergen‐Paap rk LM statistic): 223.938
Chi-sq(4) P-val = 0.0000

Weak identification test (Kleibergen‐Paap rk Wald F statistic): 67.877
Stock-Yogo weak ID test critical values: 5% maximal IV relative bias
16.85
10% maximal IV relative bias 10.27
20% maximal IV relative bias 6.71
30% maximal IV relative bias 5.34
10% maximal IV size 24.58
15% maximal IV size 13.96
20% maximal IV size 10.26
25% maximal IV size 8.31
Source: Stock‐Yogo (2005). Reproduced by permission.
NB: Critical values are for Cragg‐Donald F statistic and i.i.d.
errors.

Hansen J statistic (overidentification test of all instruments): 1.617
Chi-sq(3) P‐val = 0.6554
-orthog- option:
Hansen J statistic (eqn. excluding suspect orthog. conditions): 1.066
Chi-sq(2) P-val = 0.5869
C statistic (exogeneity/orthogonality of suspect instruments): 0.552
Chi-sq(1) P-val = 0.4576
Instruments tested: childhh

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