Inclusion of Instrumental Variables in a fixed effects regression.

[Chumani Ward]

Hi.
I am currently looking into the influence of natural disasters on human capital outcomes, through a channel of time spent in school per day on average.

I was previously estimating the regression:

xtreg schooltime disaster worktime disaster*juntos foodsec i.headedu i.hhsize i.engrade i.male1317, fe vce(robust)

I have now realised this may be flawed due to the potential endogeneity of child labour.

How do I estimate an IV regression with the fixed effects (i.headedu i.hhsize i.engrade i.male1317)- when I attempt to use xtivreg these are all regarded as instruments.

Do ignore the fact I have used illness as an instrument for work time - I simply have not included the appropriate instrument in my dataset yet and was simply experimenting with the xtivreg function.

xtivreg schooltime disaster disjunt foodsec i.headedu i.hhsize i.engrade i.male1317 (worktime=illness), fe vce(robust)

Fixed-effects (within) IV regression Number of obs = 5,170
Group variable: panelid Number of groups = 1,797

R-sq: Obs per group:
within = 0.3322 min = 1
between = 0.2983 avg = 2.9
overall = 0.3055 max = 3


Wald chi2(46) = 72354.02
corr(u_i, Xb) = -0.0409 Prob > chi2 = 0.0000

(Std. Err. adjusted for 1,797 clusters in panelid)
---------------------------------------------------------------------------------------------------------------------------
| Robust
schooltime | Coef. Std. Err. z P>|z| [95% Conf. Interval]
----------------------------------------------------------+----------------------------------------------------------------
worktime | .1287912 .4123419 0.31 0.755 -.6793842 .9369665
disaster | -.0944764 .0821895 -1.15 0.250 -.2555649 .066612
disjunt | .0856131 .0669238 1.28 0.201 -.0455551 .2167813
foodsec | -.0278177 .0454041 -0.61 0.540 -.1168081 .0611726
|
headedu |
Grade 1 | .0126038 .4423399 0.03 0.977 -.8543665 .8795741
Grade 2 | .0768501 .3338125 0.23 0.818 -.5774105 .7311106
Grade 3 | .5601363 .3064648 1.83 0.068 -.0405236 1.160796
Grade 4 | .2633543 .4645616 0.57 0.571 -.6471697 1.173878
Grade 5 | -.0716441 .3552758 -0.20 0.840 -.7679718 .6246837
Grade 6 | -.0897396 .300384 -0.30 0.765 -.6784814 .4990023
Grade 7 | .2253852 .3912199 0.58 0.565 -.5413918 .9921621
Grade 8 | -.1489088 .4028726 -0.37 0.712 -.9385246 .6407071
Grade 9 | .0016159 .3557166 0.00 0.996 -.6955758 .6988076
Grade 10 | .00438 .3799709 0.01 0.991 -.7403493 .7491093
Grade 11 | -.2825485 .3089434 -0.91 0.360 -.8880664 .3229694
Technical, pedagogical, CETPRO (incomplete) | -.1182578 .3648522 -0.32 0.746 -.833355 .5968393
Technical, pedagogical, CETPRO (complete) | -.1425548 .32909 -0.43 0.665 -.7875594 .5024498
University (incomplete) | -.3287341 .3948545 -0.83 0.405 -1.102635 .4451666
University (complete) | -.2243074 .3914272 -0.57 0.567 -.9914906 .5428758
17 | 7.069925 .8942423 7.91 0.000 5.317242 8.822607
|
hhsize |
3 | -.378912 .2481087 -1.53 0.127 -.8651962 .1073722
4 | -.3047876 .2623209 -1.16 0.245 -.8189272 .2093519
5 | -.4060957 .2458137 -1.65 0.099 -.8878816 .0756903
6 | -.5009734 .2687139 -1.86 0.062 -1.027643 .0256962
7 | -.3873865 .2614733 -1.48 0.138 -.8998647 .1250917
8 | -.5171621 .2952392 -1.75 0.080 -1.09582 .0614961
9 | -.7016332 .3109017 -2.26 0.024 -1.310989 -.092277
10 | -.9152943 .3900462 -2.35 0.019 -1.679771 -.1508178
11 | -.4572916 .348474 -1.31 0.189 -1.140288 .2257049
12 | -.5672341 1.051112 -0.54 0.589 -2.627376 1.492908
13 | -.0910046 .951818 -0.10 0.924 -1.956534 1.774524
14 | -1.87063 .643668 -2.91 0.004 -3.132196 -.6090642
15 | .3921696 .7348378 0.53 0.594 -1.048086 1.832425
16 | -.7714237 .3806835 -2.03 0.043 -1.51755 -.0252977
18 | -3.006126 2.164402 -1.39 0.165 -7.248276 1.236024
|
engrade |
grade 1 (Primary, Grade 1) | 6.929719 1.650539 4.20 0.000 3.694722 10.16472
grade 2 (Primary, Grade 2) | 7.136609 1.612863 4.42 0.000 3.975455 10.29776
grade 3 (Primary, Grade 3) | 7.397258 1.61184 4.59 0.000 4.238109 10.55641
grade 4 (Primary, Grade 4) | 7.160685 1.368834 5.23 0.000 4.47782 9.84355
grade 5 (Primary, Grade 5) | 6.798999 1.311253 5.19 0.000 4.22899 9.369009
grade 6 (Primary, Grade 6) | 6.880128 1.316424 5.23 0.000 4.299984 9.460273
grade 7 (Secondary, Year 1) | 7.693101 1.338404 5.75 0.000 5.069877 10.31633
grade 8 (Secondary, Year 2) | 8.222997 1.359069 6.05 0.000 5.559271 10.88672
grade 9 (Secondary, Year 3) | 8.570332 1.39755 6.13 0.000 5.831186 11.30948
grade 10 (Secondary, Year 4) | 8.636233 1.34114 6.44 0.000 6.007647 11.26482
grade 11 (Secondary, Year 5) | 8.189262 1.246371 6.57 0.000 5.746419 10.6321
Incomplete Cent. Tecnico Productivo CETPRO/ Cent. Edu... | 5.797084 .7654099 7.57 0.000 4.296908 7.29726
|
male1317 |
1 | -.0236452 .0767005 -0.31 0.758 -.1739755 .126685
2 | -.043137 .2466737 -0.17 0.861 -.5266085 .4403344
3 | -.9392262 1.136624 -0.83 0.409 -3.166968 1.288516
|
_cons | 1.068231 2.062715 0.52 0.605 -2.974615 5.111078
----------------------------------------------------------+----------------------------------------------------------------
sigma_u | 1.0747064
sigma_e | 1.4006693
rho | .37056227 (fraction of variance due to u_i)
---------------------------------------------------------------------------------------------------------------------------
Instrumented: worktime
Instruments: disaster disjunt foodsec 1.headedu 2.headedu 3.headedu 4.headedu 5.headedu 6.headedu 7.headedu 8.headedu
9.headedu 10.headedu 11.headedu 13.headedu 14.headedu 15.headedu 16.headedu 17.headedu 3.hhsize 4.hhsize
5.hhsize 6.hhsize 7.hhsize 8.hhsize 9.hhsize 10.hhsize 11.hhsize 12.hhsize 13.hhsize 14.hhsize 15.hhsize
16.hhsize 18.hhsize 1.engrade 2.engrade 3.engrade 4.engrade 5.engrade 6.engrade 7.engrade 8.engrade
9.engrade 10.engrade 11.engrade 21.engrade 1.male1317 2.male1317 3.male1317 illness
---------------------------------------------------------------------------------------------------------------

[Phil Bromiley]

You didn't get a quick answer. You'll increase your chances of a useful answer by following the FAQ on asking questions - provide Stata code in code delimiters, readable Stata output (fixed fonts help), and sample data using dataex.

The instrument is is pretty clear. You need something exogenous associated (preferably highly associated) with the endogenous variable that does not belong in the primary equation. More instruments are often better. Stata includes all the included variables plus those variables identified in the endogeneity equation (worktime=illness) . My understanding is that it is important that all the exogenous variables in the main equation be included in the instrument set.

What meets these criteria in your sample is up to you. By the way, you might consider treating engrade, hsize, and headedu as continuous.