xtivreg re, weakiv and xtoverid

[David Jacobsz]

Dear all,

Currently, I am running into some trouble with xtivreg in combination with random effects.

I am researching the effect of bilateral tax treaties on FDI inflow, with several control variables and fixed effects for the source and resident country and year. As instruments I am using two dummies on common language and colonial relationship, a continuous variable on the number of treaties closed prior to the year of interest and the GDP of the source country. My regression is formulated as follows:

xtivreg ln_FDI (tt_d= comlang_off colony treaties_s ln_GDP_1) ln_Openness_1 ln_GDP_pc_1 ln_Telephone_1 PS_1 ln_Gov_exp_1 ln_GDP_Growth_1 ln_av_CPI_5 ln_M2_growth_1 i.Country_e i.cou_e i.year, re first

I want to test whether my instruments are weak or overidentified. However, the commands

weakivtest

and

xtoverid

do not appear to work in combination with re.


With regards to weakiv I get the following error:
error - unsupported xtivreg model g2sls
r(198);

Does anyone know how to circumvent this/knows of a different command that allows for testing weak iv for re models?


With regards to xtoverid, I have already tried to circumvent the issue of xtoverid being unable to deal with factor variables (my fixed effect variables) by coding the following:

fvrevar i.Country_e i.cou_e i.year
xi: xtivreg ln_FDI (tt_d= comlang_off colony treaties_s ln_GDP_1) ln_Openness_1 ln_GDP_pc_1 ln_Telephone_1 PS_1 ln_Gov_exp_1 ln_GDP_Growth_1 ln_av_CPI_5 ln_M2_growth_1 `r(varlist)', re first
xtoverid, cluster(country_pair_c)

However, I run into the problem that because of collinearity lot of factor variable dummies made by xi: are dropped in the second stage. This leads Stata to give the following error after xtoverid:
o. operator not allowed
r(101);

Does anyone know how to solve this?



I am using StataMP 17 (64-bit) on a Windows10 Enterprise OS.

My data looks as follows;

* Example generated by -dataex-. For more info, type help dataex
clear

input float(ln_FDI tt_d) double Openness_1 float(ln_GDP_pc_1 ln_Telephone_1) double PS_1 float(ln_Gov_exp_1 ln_GDP_Growth_1 ln_av_CPI_5 ln_M2_growth_1) double(Source WHTrates PE Other UN) byte(comlang_off colony) int treaties_s float ln_GDP_1
         0 0 . 6.931498    .317376 -2.671054 .  1.554339 2.1304839  2.970524 . . . . . 0 0 .  24.31324
         0 0 . 7.013929   .3144341 -2.571222 . 1.1674504 2.1967888 1.8431436 . . . . . 0 0 .  24.36789
         0 0 . 6.931498    .317376 -2.671054 .  1.554339 2.1304839  2.970524 . . . . . 0 0 .  24.31324
         0 0 . 6.940572   .3216475 -2.801084 . 1.7004848 1.7526053 2.1170902 . . . . . 0 0 .  24.34779
         0 0 . 7.152811  .28499976 -2.418561 . 3.2403915 3.0799816 2.8629184 . . . . . 0 0 .   24.4075
         0 0 . 7.129804  .29258543 -2.519349 .  2.423923  2.570989 2.9896774 . . . . . 0 0 .  24.41944
         0 0 . 7.113506    .300889 -2.411068 .  1.727542  2.480182  2.793149 . . . . . 0 0 . 24.436697
         0 0 . 7.013929   .3144341 -2.571222 . 1.1674504 2.1967888 1.8431436 . . . . . 0 0 .  24.36789
         0 0 . 6.931498    .317376 -2.671054 .  1.554339 2.1304839  2.970524 . . . . . 0 0 .  24.31324
         0 0 . 6.940572   .3216475 -2.801084 . 1.7004848 1.7526053 2.1170902 . . . . . 0 0 .  24.34779
         0 0 . 6.878675   .3373562 -2.763864 . 1.0090588 1.5797658 1.6744245 . . . . . 0 0 .  24.30974
         0 0 . 6.896047   .3469158 -2.655531 . 2.0730472 1.7911087  2.441974 . . . . . 0 0 .  24.35024
         0 0 .  6.04682          . -2.296179 . 1.1461606         .         . . . . . . 0 0 .  23.07021
   1.65107 0 . 6.182219          . -2.070934 .  3.113687         .         . . . . . . 0 0 . 23.242435
 -2.401703 0 .  6.26809          . -2.221302 . 2.3802252         .         . . . . . . 0 0 . 23.358213
 1.1734915 0 . 6.578401          . -2.410581 .  3.321026         . 4.4403205 . . . . . 0 0 .  23.69346
         0 0 . 6.592124          . -2.690477 .  2.076356         . 4.1396933 . . . . . 0 0 .  23.72987
         0 0 . 6.773696 .018065697 -2.712689 . 3.7566414   3.08054 4.1912484 . . . . . 0 0 .  23.93541
         0 0 . 6.990822  .05691534 -2.579152 . 3.3589735  3.109101  3.987368 . . . . . 0 0 . 24.180004
-3.0489736 0 . 7.075285  .04483942  -2.50206 .  .4143925   3.10329  3.752835 . . . . . 0 0 .   24.2959
  .7900314 0 . 7.152811  .28499976 -2.418561 . 3.2403915 3.0799816 2.8629184 . . . . . 0 0 .   24.4075
 -2.735222 0 . 7.129804  .29258543 -2.519349 .  2.423923  2.570989 2.9896774 . . . . . 0 0 .  24.41944
  .0842044 0 . 7.113506    .300889 -2.411068 .  1.727542  2.480182  2.793149 . . . . . 0 0 . 24.436697
 .03095823 0 . 7.013929   .3144341 -2.571222 . 1.1674504 2.1967888 1.8431436 . . . . . 0 0 .  24.36789
 1.1697117 0 . 6.931498    .317376 -2.671054 .  1.554339 2.1304839  2.970524 . . . . . 0 0 .  24.31324
 -.9001914 0 . 6.940572   .3216475 -2.801084 . 1.7004848 1.7526053 2.1170902 . . . . . 0 0 .  24.34779
  .3031813 0 . 6.878675   .3373562 -2.763864 . 1.0090588 1.5797658 1.6744245 . . . . . 0 0 .  24.30974
 -.7834536 0 . 6.896047   .3469158 -2.655531 . 2.0730472 1.7911087  2.441974 . . . . . 0 0 .  24.35024
         0 0 . 7.129804  .29258543 -2.519349 .  2.423923  2.570989 2.9896774 . . . . . 0 0 .  24.41944
-1.7108308 0 . 7.113506    .300889 -2.411068 .  1.727542  2.480182  2.793149 . . . . . 0 0 . 24.436697
-2.3509212 0 . 7.013929   .3144341 -2.571222 . 1.1674504 2.1967888 1.8431436 . . . . . 0 0 .  24.36789
         0 0 . 6.931498    .317376 -2.671054 .  1.554339 2.1304839  2.970524 . . . . . 0 0 .  24.31324
         0 0 . 6.940572   .3216475 -2.801084 . 1.7004848 1.7526053 2.1170902 . . . . . 0 0 .  24.34779
         0 0 . 6.878675   .3373562 -2.763864 . 1.0090588 1.5797658 1.6744245 . . . . . 0 0 .  24.30974
         0 0 . 6.896047   .3469158 -2.655531 . 2.0730472 1.7911087  2.441974 . . . . . 0 0 .  24.35024
         0 0 . 6.931498    .317376 -2.671054 .  1.554339 2.1304839  2.970524 . . . . . 0 0 .  24.31324
         0 0 .  6.04682          . -2.296179 . 1.1461606         .         . . . . . . 0 0 .  23.07021
         0 0 . 6.182219          . -2.070934 .  3.113687         .         . . . . . . 0 0 . 23.242435
         0 0 .  6.26809          . -2.221302 . 2.3802252         .         . . . . . . 0 0 . 23.358213
         0 0 . 6.592124          . -2.690477 .  2.076356         . 4.1396933 . . . . . 0 0 .  23.72987
         0 0 . 6.773696 .018065697 -2.712689 . 3.7566414   3.08054 4.1912484 . . . . . 0 0 .  23.93541
         0 0 . 6.990822  .05691534 -2.579152 . 3.3589735  3.109101  3.987368 . . . . . 0 0 . 24.180004
         0 0 . 7.075285  .04483942  -2.50206 .  .4143925   3.10329  3.752835 . . . . . 0 0 .   24.2959
         0 0 . 7.152811  .28499976 -2.418561 . 3.2403915 3.0799816 2.8629184 . . . . . 0 0 .   24.4075
         0 0 . 7.129804  .29258543 -2.519349 .  2.423923  2.570989 2.9896774 . . . . . 0 0 .  24.41944
         0 0 . 7.113506    .300889 -2.411068 .  1.727542  2.480182  2.793149 . . . . . 0 0 . 24.436697
         0 0 . 7.013929   .3144341 -2.571222 . 1.1674504 2.1967888 1.8431436 . . . . . 0 0 .  24.36789
         0 0 . 6.931498    .317376 -2.671054 .  1.554339 2.1304839  2.970524 . . . . . 0 0 .  24.31324
         0 0 . 6.940572   .3216475 -2.801084 . 1.7004848 1.7526053 2.1170902 . . . . . 0 0 .  24.34779
         0 0 . 6.878675   .3373562 -2.763864 . 1.0090588 1.5797658 1.6744245 . . . . . 0 0 .  24.30974
         0 0 . 6.896047   .3469158 -2.655531 . 2.0730472 1.7911087  2.441974 . . . . . 0 0 .  24.35024
         0 0 . 7.152811  .28499976 -2.418561 . 3.2403915 3.0799816 2.8629184 . . . . . 0 0 .   24.4075
         0 0 . 7.129804  .29258543 -2.519349 .  2.423923  2.570989 2.9896774 . . . . . 0 0 .  24.41944
         0 0 . 7.113506    .300889 -2.411068 .  1.727542  2.480182  2.793149 . . . . . 0 0 . 24.436697
         0 0 . 6.931498    .317376 -2.671054 .  1.554339 2.1304839  2.970524 . . . . . 0 0 .  24.31324
         0 0 . 6.940572   .3216475 -2.801084 . 1.7004848 1.7526053 2.1170902 . . . . . 0 0 .  24.34779
         0 0 . 6.878675   .3373562 -2.763864 . 1.0090588 1.5797658 1.6744245 . . . . . 0 0 .  24.30974
         0 0 . 6.896047   .3469158 -2.655531 . 2.0730472 1.7911087  2.441974 . . . . . 0 0 .  24.35024
         0 0 . 7.113506    .300889 -2.411068 .  1.727542  2.480182  2.793149 . . . . . 0 0 . 24.436697
         0 0 . 7.013929   .3144341 -2.571222 . 1.1674504 2.1967888 1.8431436 . . . . . 0 0 .  24.36789
-.56430537 0 . 6.896047   .3469158 -2.655531 . 2.0730472 1.7911087  2.441974 . . . . . 0 0 .  24.35024
         0 0 . 7.152811  .28499976 -2.418561 . 3.2403915 3.0799816 2.8629184 . . . . . 0 0 .   24.4075
         0 0 . 7.129804  .29258543 -2.519349 .  2.423923  2.570989 2.9896774 . . . . . 0 0 .  24.41944
         0 0 . 7.113506    .300889 -2.411068 .  1.727542  2.480182  2.793149 . . . . . 0 0 . 24.436697
         0 0 . 7.013929   .3144341 -2.571222 . 1.1674504 2.1967888 1.8431436 . . . . . 0 0 .  24.36789
         0 0 . 6.931498    .317376 -2.671054 .  1.554339 2.1304839  2.970524 . . . . . 0 0 .  24.31324
         0 0 . 6.940572   .3216475 -2.801084 . 1.7004848 1.7526053 2.1170902 . . . . . 0 0 .  24.34779
         0 0 . 6.878675   .3373562 -2.763864 . 1.0090588 1.5797658 1.6744245 . . . . . 0 0 .  24.30974
         0 0 . 6.896047   .3469158 -2.655531 . 2.0730472 1.7911087  2.441974 . . . . . 0 0 .  24.35024
         0 0 . 7.113506    .300889 -2.411068 .  1.727542  2.480182  2.793149 . . . . . 0 0 . 24.436697
         0 0 . 7.013929   .3144341 -2.571222 . 1.1674504 2.1967888 1.8431436 . . . . . 0 0 .  24.36789
         0 0 . 6.931498    .317376 -2.671054 .  1.554339 2.1304839  2.970524 . . . . . 0 0 .  24.31324
         0 0 . 6.940572   .3216475 -2.801084 . 1.7004848 1.7526053 2.1170902 . . . . . 0 0 .  24.34779
         0 0 . 6.878675   .3373562 -2.763864 . 1.0090588 1.5797658 1.6744245 . . . . . 0 0 .  24.30974
         0 0 . 6.896047   .3469158 -2.655531 . 2.0730472 1.7911087  2.441974 . . . . . 0 0 .  24.35024
         0 0 . 7.075285  .04483942  -2.50206 .  .4143925   3.10329  3.752835 . . . . . 0 0 .   24.2959
         0 0 . 7.152811  .28499976 -2.418561 . 3.2403915 3.0799816 2.8629184 . . . . . 0 0 .   24.4075
         0 0 . 7.129804  .29258543 -2.519349 .  2.423923  2.570989 2.9896774 . . . . . 0 0 .  24.41944
         0 0 . 7.113506    .300889 -2.411068 .  1.727542  2.480182  2.793149 . . . . . 0 0 . 24.436697
         0 0 . 7.013929   .3144341 -2.571222 . 1.1674504 2.1967888 1.8431436 . . . . . 0 0 .  24.36789
         0 0 . 6.931498    .317376 -2.671054 .  1.554339 2.1304839  2.970524 . . . . . 0 0 .  24.31324
         0 0 . 6.940572   .3216475 -2.801084 . 1.7004848 1.7526053 2.1170902 . . . . . 0 0 .  24.34779
         0 0 . 6.878675   .3373562 -2.763864 . 1.0090588 1.5797658 1.6744245 . . . . . 0 0 .  24.30974
         0 0 . 6.896047   .3469158 -2.655531 . 2.0730472 1.7911087  2.441974 . . . . . 0 0 .  24.35024
         0 0 . 7.152811  .28499976 -2.418561 . 3.2403915 3.0799816 2.8629184 . . . . . 0 0 .   24.4075
         0 0 . 7.129804  .29258543 -2.519349 .  2.423923  2.570989 2.9896774 . . . . . 0 0 .  24.41944
         0 0 . 7.113506    .300889 -2.411068 .  1.727542  2.480182  2.793149 . . . . . 0 0 . 24.436697
         0 0 . 7.013929   .3144341 -2.571222 . 1.1674504 2.1967888 1.8431436 . . . . . 0 0 .  24.36789
         0 0 . 6.931498    .317376 -2.671054 .  1.554339 2.1304839  2.970524 . . . . . 0 0 .  24.31324
         0 0 . 6.940572   .3216475 -2.801084 . 1.7004848 1.7526053 2.1170902 . . . . . 0 0 .  24.34779
         0 0 . 6.878675   .3373562 -2.763864 . 1.0090588 1.5797658 1.6744245 . . . . . 0 0 .  24.30974
         0 0 . 6.896047   .3469158 -2.655531 . 2.0730472 1.7911087  2.441974 . . . . . 0 0 .  24.35024
-2.7105775 0 . 7.152811  .28499976 -2.418561 . 3.2403915 3.0799816 2.8629184 . . . . . 0 0 .   24.4075
  .9476042 0 . 7.129804  .29258543 -2.519349 .  2.423923  2.570989 2.9896774 . . . . . 0 0 .  24.41944
  .3676981 0 . 7.113506    .300889 -2.411068 .  1.727542  2.480182  2.793149 . . . . . 0 0 . 24.436697
 -.3913492 0 . 7.013929   .3144341 -2.571222 . 1.1674504 2.1967888 1.8431436 . . . . . 0 0 .  24.36789
 .06083497 0 . 6.931498    .317376 -2.671054 .  1.554339 2.1304839  2.970524 . . . . . 0 0 .  24.31324
-.10954122 0 . 6.940572   .3216475 -2.801084 . 1.7004848 1.7526053 2.1170902 . . . . . 0 0 .  24.34779
 .06934997 0 . 6.878675   .3373562 -2.763864 . 1.0090588 1.5797658 1.6744245 . . . . . 0 0 .  24.30974
 .02848618 0 . 6.896047   .3469158 -2.655531 . 2.0730472 1.7911087  2.441974 . . . . . 0 0 .  24.35024
end

Thank you in advance!

Kind regards,

David

[Carlo Lazzaro]

David:
as far as the problem with the community-contributed module -xtoverid- is concerned, you should remove the omitted (o.) predictor(s) by hand, re-run the regression and finally invoke -xtoverid-.

[David Jacobsz]

Dear Carlo,

Thank you for your quick answer. The omitted predictors consist of dummies made for the different fixed effects, e.g., Zimbabwe or 2015 etc.
Do I understand it correctly that I then have to delete these individual predictors in order to resolve the issue? Would that not partially beat the point of controlling for these fixed effects and/or limit what one can say about the full model with regards to overidentification and the strength of the iv?

On an aside, the number of dummies (129) made for the fixed effects variables with

 fvrevar i.Country_e i.cou_e i.year xi: xtivreg ln_FDI (tt_d= comlang_off colony treaties_s ln_GDP_1) ln_Openness_1 ln_GDP_pc_1 ln_Telephone_1 PS_1 ln_Gov_exp_1 ln_GDP_Growth_1 ln_av_CPI_5 ln_M2_growth_1 `r(varlist)', re first

exceeds the total number of countries and years involved (198), should this be the case?

Best,

David

[Carlo Lazzaro]

David:
yes, you're correct. There's no way to move forward with the community-contributed module -xtoverid- without deleting the -o.- culprit manually.
The limitations you mention are the consequences of -xtoverid- being a glorious but a bit old-fashioned module (i sincerely hope that its Authors can find the time to update it, as it is a wonderful command).
As far as your last question is concerned, I do not think that the number of categorical predictors (that you should better reduce anyway) has any bearing on that, as you ca see from the following toy-example:

. use "https://www.stata-press.com/data/r17/nlswork.dta"
(National Longitudinal Survey of Young Women, 14-24 years old in 1968)

. g race2=race

. xi:xtreg ln_wage i.race i.race2 age, re
i.race            _Irace_1-3          (naturally coded; _Irace_1 omitted)
i.race2           _Irace2_1-3         (naturally coded; _Irace2_1 omitted)
note: _Irace2_2 omitted because of collinearity.
note: _Irace2_3 omitted because of collinearity.

Random-effects GLS regression                   Number of obs     =     28,510
Group variable: idcode                          Number of groups  =      4,710

R-squared:                                      Obs per group:
     Within  = 0.1026                                         min =          1
     Between = 0.1032                                         avg =        6.1
     Overall = 0.0945                                         max =         15

                                                Wald chi2(3)      =    3242.34
corr(u_i, X) = 0 (assumed)                      Prob > chi2       =     0.0000

------------------------------------------------------------------------------
     ln_wage | Coefficient  Std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
    _Irace_2 |  -.1209428   .0129079    -9.37   0.000    -.1462418   -.0956439
    _Irace_3 |   .0981941   .0538424     1.82   0.068    -.0073351    .2037233
   _Irace2_2 |          0  (omitted)
   _Irace2_3 |          0  (omitted)
         age |    .018534    .000331    55.99   0.000     .0178852    .0191828
       _cons |    1.15423   .0118069    97.76   0.000     1.131089    1.177371
-------------+----------------------------------------------------------------
     sigma_u |  .36581626
     sigma_e |  .30349389
         rho |  .59231394   (fraction of variance due to u_i)
------------------------------------------------------------------------------

. xtoverid
o. operator not allowed
r(101);

.

[David Jacobsz]

Dear Carlo,

Thank you for the response. The example is really helpful.

On the reduction of categorical predictors, those are all countries and years involved as I would like to address unobserved country and year between variation (I have to use re, as the within variation of the data is very low. It's not perfect but have not found a way around this issue but using re with these fixed effects). So therefore, it feels odd to reduce this. Is it then better to use a different fixed effects variable, e,g, categories indicating which income group, as defined by the World Bank, countries are in? Then the number of categorical would be limited to 4 different income groups and 15 years instead of 114 countries and 15 years.


Best,
David

[Carlo Lazzaro]

David:
yes, using World Bank categories instead of nations sounds helpful here.
The only issue that may creep up with this fix is that you panel switch from a N>T to T:>N dataset.
If this were the case, you should consider -xtgls- or -xtregar- instead on -xtreg-.

[David Jacobsz]

Dear Carlo,

If I understand the commands -xtgls- and -xtregar- correctly, they do not allow for IV estimations. However, based on literature, I am quite certain that the tax treaty dummy is endogenous and should be replaced with one or more instruments.
Therefore, I think these commands will be of no help.

Would it be an option to maintain N>T by setting

xtset country_pairs year

instead of setting it to

xtset income_level_pairs year

?

In total there are 3615 country pairs and 15 years, whereas there are only 4 World Bank income levels in total and 6 World Bank income level pairs in my dataset.
Or will it then be problematic to use the WB income level fixed effect?

Best,
David

[Carlo Lazzaro]

David:
you're right that T>N panel command do not have -iv- cousins.
That said, the first code can be the way to go, provided it is acceptable in your research field.

[David Jacobsz]

Dear Carlo,

Ok, thank you for helping out. Really appreciated!

Best,
David