IV Estimation for Interaction term

[Hui Shen Khor]

Hi,

My dependent variable is life satisfaction (lifesat). My main independent variable is immigrant's mobility (where immpar=1 if immigrant and 0 for non-immigrant, mobility=1 if downward mobility, 0 if unchanged, 2 if upward mobility). I would like to check for endogeneity in my main independent variable (i.mobility##i.immpar ) using the IV estimation method. I suspect endogeneity in the mobility variable but not the immpar variable. The following is my regression model.

reg lifesat i.mobility##i.immpar i.mumethnic i.dadethnic i.dmsex i.hhincome1980 ib3.marital lnhhincome i.sc2000 household householdsq i.sc1980


Before running ivregress 2sls with my instruments. I would need to check for instrument relevance. This was done by runing the equation above excluding my dependent variable (lifesat) and including my instruments (childdepress, aspiration, paraspiration). The instrument relevance equation is as below. My main problem is, in this equation, my dependent variable is an interaction term, so my model is not valid. Hence is there any other way to check for instrument relevance in this case?

reg i.mobility##i.immpar i.childdepress##i.immpar i.paraspiration##i.immpar i.change##i.immpar i.mumethnic i.dadethnic i.dmsex i.hhincome1980 ib3.marital lnhhincome i.sc2000 household householdsq i.sc1980
test 1.childdepress# 1.immpar 1.childdepress#0.immpar 1.paraspiration#1.immpar 1.paraspiration#0.immpar 1.change#1.immpar 1.change#0.immpar

[Phil Bromiley]

You'll increase your chances of a useful answer by following the FAQ on asking questions - provide Stata code in code delmiters, readable Stata output, and sample data using dataex. Also, try to keep your question as short as possible - just what is needed to demonstrate the problem.

If you use ivreg2, it will provide some test statistics on the first stage. Normally, when you have interactions with an endogenous variable, you calculate them before the ivreg and then enter them as endogenous.

[Hui Shen Khor]

Hi Phil,

Okay, thanks!

[Hui Shen Khor]

Hi Phil,

I tried using ivreg2 and regressed the following but I am not sure whether this is the right approach and I am not sure how do I identify whether the instrument is relevant and exogenous. (Sorry, my output is a bit messy, is there any way to make it neater?)

ivreg2 lifesat i.mumethnic i.dadethnic i.dmsex i.hhincome1980 ib3.marital lnhhincome i.sc2000 household householdsq i.sc1980 (mobility mobility#immpar = childdepress childdepress#immpar aspiration#immpar), robust

This is my output:

. ivreg2 lifesat i.mumethnic i.dadethnic i.dmsex i.hhincome1980 ib3.marital lnhhincome i.sc2000 household householdsq i.sc1980 (mobility mobility#immpar = childdepress childdepress#immpar aspiration#immpar), robust
Warning - endogenous variable(s) collinear with instruments
Vars now exogenous: 2.mobility#0b.immpar
Warning - collinearities detected
Vars dropped: 2.mobility#1.immpar 1.childdepress#1.immpar
1.aspiration#1.immpar 1.mobility#1.immpar

IV (2SLS) estimation
--------------------

Estimates efficient for homoskedasticity only
Statistics robust to heteroskedasticity

Number of obs = 2424
F( 29, 2394) = 1.28
Prob > F = 0.1477
Total (centered) SS = 6929.985149 Centered R2 = -4.7435
Total (uncentered) SS = 143190 Uncentered R2 = 0.7220
Residual SS = 39802.47715 Root MSE = 4.052

--------------------------------------------------------------------------------------------------
| Robust lifesat | Coef. Std. Err. z P>|z| [95% Conf. Interval]
---------------------------------+----------------------------------------------------------------
mobility | 1.421322 10.10332 0.14 0.888 -18.38081 21.22346
mobility#immpar |
Unchanged#Immigrant | 15.81265 64.38565 0.25 0.806 -110.3809 142.0062
Downward Mobility#Non-immigrant | -10.41122 15.08057 -0.69 0.490 -39.96859 19.14616
Downward Mobility#Immigrant | -14.24118 12.28152 -1.16 0.246 -38.31251 9.83015
Upward Mobility#Immigrant | 0 (omitted)
Upward Mobility#Non-immigrant | -2.365911 20.55986 -0.12 0.908 -42.6625 37.93068

mumethnic | 2.921614 6.287931 0.46 0.642 -9.402505 15.24573

dadethnic | 1.185108 2.231133 0.53 0.595 -3.187833 5.558049

dmsex | .3294461 .387265 0.85 0.395 -.4295794 1.088472

hhincome1980 |
>50 | 1.332205 1.187501 1.12 0.262 -.9952549 3.659665
>100 | 4.136968 3.368989 1.23 0.219 -2.466129 10.74006
>150 | 7.607325 6.174632 1.23 0.218 -4.49473 19.70938
>200 | 10.05226 8.219906 1.22 0.221 -6.058463 26.16298

marital |
Married | -.8410905 1.120309 -0.75 0.453 -3.036856 1.354675
Cohabiting | -1.14691 1.098057 -1.04 0.296 -3.299063 1.005243
Separated | -1.755877 3.061416 -0.57 0.566 -7.756142 4.244387
Divorced | -1.453244 2.069197 -0.70 0.482 -5.508796 2.602307

lnhhincome | -2.800261 2.714208 -1.03 0.302 -8.12001 2.519488

sc2000 |
2 | .0239444 .5260409 0.05 0.964 -1.007077 1.054966
3 | -.1319226 .4301305 -0.31 0.759 -.974963 .7111178
4 | .1389574 .5736966 0.24 0.809 -.9854673 1.263382
5 | .0475651 .6224078 0.08 0.939 -1.172332 1.267462
6 | -.8194098 .9415465 -0.87 0.384 -2.664807 1.025987
household | .0130625 .1636738 0.08 0.936 -.3077323 .3338572

householdsq | -.0010682 .0349123 -0.03 0.976 -.069495 .0673586

sc1980 |
2 | .0157699 .3621864 0.04 0.965 -.6941025 .7256422
3 | .2486629 1.002472 0.25 0.804 -1.716146 2.213471
4 | .1549085 .496502 0.31 0.755 -.8182176 1.128035
5 | .6548593 .7546391 0.87 0.386 -.8242061 2.133925
6 | .448501 1.478245 0.30 0.762 -2.448806 3.345808
|
_cons | 18.48735 17.62135 1.05 0.294 -16.04986 53.02455
--------------------------------------------------------------------------------------------------
Underidentification test (Kleibergen-Paap rk LM statistic): 0.295
Chi-sq(2) P-val = 0.8628
------------------------------------------------------------------------------
Weak identification test (Cragg-Donald Wald F statistic): 0.174
(Kleibergen-Paap rk Wald F statistic): 0.058
Stock-Yogo weak ID test critical values: <not available>
------------------------------------------------------------------------------
Hansen J statistic (overidentification test of all instruments): 0.533
Chi-sq(1) P-val = 0.4654
------------------------------------------------------------------------------
Instrumented: mobility 0b.mobility#1.immpar 1.mobility#0b.immpar
1.mobility#1.immpar
Included instruments: 2.mobility#0b.immpar 1.mumethnic 1.dadethnic 2.dmsex
2.hhincome1980 3.hhincome1980 4.hhincome1980
5.hhincome1980 1.marital 2.marital 4.marital 5.marital
lnhhincome 2.sc2000 3.sc2000 4.sc2000 5.sc2000 6.sc2000
household householdsq 2.sc1980 3.sc1980 4.sc1980 5.sc1980
6.sc1980
Excluded instruments: childdepress 0b.childdepress#1.immpar
1.childdepress#0b.immpar 0b.aspiration#1.immpar
1.aspiration#0b.immpar
Dropped collinear: 2.mobility#1.immpar 1.childdepress#1.immpar
1.aspiration#1.immpar 1.mobility#1.immpar
Reclassified as exog: 2.mobility#0b.immpar
------------------------------------------------------------------------------

* Example generated by -dataex-. To install: ssc install dataex
clear
input float(mobility immpar) byte(aspiration change paraspiration finnow)
0 0 . . . 3
2 0 1 1 1 2
1 0 . . . 2
2 0 . . . 2
. 1 . 1 . 2
2 0 1 2 . 3
1 0 1 . 1 2
2 0 . . . 2
0 0 . . . 2
0 0 . . . 2
2 0 . 2 . 1
0 0 1 1 1 4
2 0 . 0 . 2
2 0 1 2 1 1
0 0 1 1 1 3
1 1 . . . 2
. 0 0 2 1 2
. 0 . . . 5
0 0 . . . 2
. 0 1 2 1 1
2 0 1 2 1 3
0 0 . . . 3
0 0 1 1 1 1
1 0 1 0 1 1
0 0 . . . 3
2 0 1 2 1 1
2 1 1 1 1 1
0 0 . 1 . 1
. 0 1 1 1 1
1 0 1 . 1 1
. 1 . . . 2
1 0 1 . 1 1
2 0 0 0 1 2
2 0 . 0 . 2
2 0 1 1 1 5
0 0 1 1 1 2
. 0 . . . 4
. 0 1 0 0 1
0 1 . . . 1
. 0 . . . 1
2 0 1 0 1 1
1 0 . 2 . 1
1 0 . . . 2
1 1 1 2 1 1
1 0 . 0 . 2
. 0 1 1 1 2
. 0 . . . 2
1 0 0 0 1 2
1 0 1 0 1 1
0 0 . . . 3
0 0 1 . 1 2
1 0 1 1 1 3
1 0 . . . 4
. 0 . . . 3
0 0 . 1 . 1
1 0 1 2 1 2
1 0 . . . 1
1 0 1 0 1 3
2 0 . . . 1
2 0 . . . 2
2 0 . . . 3
2 0 1 2 1 2
2 0 1 0 1 1
0 0 1 1 1 1
1 0 . . . 1
. 0 1 1 1 4
1 0 . 2 . 3
1 0 . . . 2
2 0 . . . 2
. 0 . . . 2
. 0 . . . 3
0 0 . . . 3
2 0 1 1 1 1
. 0 1 0 1 4
0 0 1 . 1 1
0 0 . . . 1
. 0 . 0 . 2
1 0 . . . 1
0 0 . . . 2
. 0 . . . 1
0 0 . . . 1
2 0 1 0 1 1
1 0 1 0 1 3
2 0 . . . 3
0 0 . . . 2
2 0 1 1 1 2
0 0 1 0 . 2
. 0 . . . 2
1 0 . . . 2
2 0 1 2 1 1
0 0 1 1 1 2
1 0 1 1 1 2
1 0 1 . 1 3
2 0 . . . 1
0 0 1 2 . 1
0 0 1 0 1 1
. 0 . . . 1
2 0 . . . 2
. 0 . . . 1
. 0 1 0 1 1
end
label values mobility mobility
label def mobility 0 "Unchanged", modify
label def mobility 1 "Downward Mobility", modify
label def mobility 2 "Upward Mobility", modify
label values immpar immpar
label def immpar 0 "Non-immigrant", modify
label def immpar 1 "Immigrant", modify
label values aspiration aspiration
label def aspiration 0 "does not matter", modify
label def aspiration 1 "matters to have high earnings/wages", modify
label values change change
label def change 0 "No", modify
label def change 1 "Yes", modify
label def change 2 "Don't know", modify
label values paraspiration paraspiration
label def paraspiration 0 "No", modify
label def paraspiration 1 "Yes", modify
label values finnow finnow
label def finnow 1 "Living comfortably", modify
label def finnow 2 "Doing alright", modify
label def finnow 3 "Just about getting by", modify
label def finnow 4 "Finding it quite difficult", modify
label def finnow 5 "Or finding it very difficult", modify