Using time-invariant instruments to estimate IV models with panel data

[Bruno Hoepers]

Hi all. I have panel data containing information on whether localities in Brazil had a signal from a TV network in each year (globo_coverage_copy). I want to verify whether having access to the TV network had an impact on electoral turnout (turnout) in each locality for the elections of 1974, 1978, and 1982.

Because it is not possible to rule out the endogenous relationship between access to the network with turnout, I want to estimate an instrumental variable model.

The problem: my possible instruments, distance from state capital (dist_cap_est) and longitude (longitude) are time-invariant.

I decided to run IV-models using the "xtivreg" command. To my surprise, the model was estimated by Stata. The command line and output follow below.

Question: Is this model warranted? What can I do with time-invariant instruments in my case?

Any comments or suggestions would be greatly appreciated.

Thank you.

xtivreg turnout ln_i_r_pib_cap i_analf_15y_more_perc i_pop_rural_perc i_catholic i_child_alive i_wealth_noTV i_agesh1524 i_Doctors i_ipc_renta  ln_i_pop_tot i.year (globo_coverage_copy = dist_cap_est longitude) if turnout<0.99 & turnout>0.30, fe vce(robust)

Fixed-effects (within) IV regression Number of obs = 7,316
Group variable: amc_code_coded Number of groups = 2,623

R-squared: Obs per group:
Within = 0.0895 min = 1
Between = 0.0024 avg = 2.8
Overall = 0.0044 max = 3


Wald chi2(12) = 385.53
corr(u_i, Xb) = -0.7936 Prob > chi2 = 0.0000

(Std. err. adjusted for 2,623 clusters in amc_code_coded)
---------------------------------------------------------------------------------------
Robust
turnout | Coefficient std. err. z P>|z| [95% conf. interval]
----------------------+----------------------------------------------------------------
globo_coverage_copy | .092282 .0393212 2.35 0.019 .0152138 .1693502
ln_i_r_pib_cap. | .0383708 .0058274 6.58 0.000 .0269494 .0497922
i_analf_15y_more_perc | -.2276279 .0696617 -3.27 0.001 -.3641623 -.0910935
i_pop_rural_perc | .1414845 .0392187 3.61 0.000 .0646173 .2183516
i_catholic | -.2665283 .086608 -3.08 0.002 -.436277 -.0967797
i_child_alive | .0539361 .0130712 4.13 0.000 .028317 .0795552
i_wealth_noTV | .0005407 .0040325 0.13 0.893 -.0073628 .0084442
i_agesh1524 | .6324835 .1376984 4.59 0.000 .3625996 .9023673
i_Doctors | -.017186 .0055263 -3.11 0.002 -.0280173 -.0063548
i_ipc_renta | 0 (omitted)
ln_i_pop_tot | -.1037623 .0127742 -8.12 0.000 -.1287992 -.0787254
|
year |
1978 | .0143469 .0040212 3.57 0.000 .0064654 .0222284
1982 | .0070007 .0221405 0.32 0.752 -.0363939 .0503953
|
_cons | 1.094985 .140572 7.79 0.000 .8194689 1.370501
----------------------+----------------------------------------------------------------
sigma_u | .15485233
sigma_e | .05480401
rho | .88868879 (fraction of variance due to u_i)
---------------------------------------------------------------------------------------
Instrumented: globo_coverage_copy
Instruments: ln_i_r_pib_cap i_analf_15y_more_perc i_pop_rural_perc i_catholic
i_child_alive i_wealth_noTV i_agesh1524 i_Doctors i_ipc_renta
ln_i_pop_tot 1978.year 1982.year dist_cap_est longitude

[Sebastian Kripfganz]

Since your instruments are time-invariant, they are omitted when the within-groups transformation is applied. Consequently, your model is underidentified, which is reflected in the omitted coefficient of i_ipc_renta. While it might be confusing that Stata did not drop the coefficient of the endogenous regressor globo_coverage_copy instead, this is simply because Stata drops any of the coefficients at random if there are not enough instruments available.

You could use time-invariant variables as instruments for the untransformed level model, and combine them with a within-groups transformation for the other variables in a "system GMM" fashion. Here is an example with my own xtdpdgmm command:

xtdpdgmm turnout globo_coverage_copy ln_i_r_pib_cap i_analf_15y_more_perc i_pop_rural_perc i_catholic i_child_alive i_wealth_noTV i_agesh1524 i_Doctors i_ipc_renta  ln_i_pop_tot i.year if turnout<0.99 & turnout>0.30, model(mdev) iv(ln_i_r_pib_cap i_analf_15y_more_perc i_pop_rural_perc i_catholic i_child_alive i_wealth_noTV i_agesh1524 i_Doctors i_ipc_renta  ln_i_pop_tot i.year, norescale) iv(dist_cap_est longitude, model(level)) twostep vce(robust)

[Bruno Hoepers]

Thank you very much Sebastian.

Another issue just came out. My endogenous variable (globo_coverage_copy) is binary and my dependent variable is continuous. Do I have a "forbidden regression" problem here?

If so, what can I do to deal with this problem? Does your xtdpdgmm command solve that?

Thanks.

[Sebastian Kripfganz]

I don't see how this problem could be related to "forbidden regressions". More precisely: I don't see a problem.

[Bruno Hoepers]

Great to know Sebastian. Thanks a lot.

[Bruno Hoepers]

I ran the model you suggested, Sebastian. The output is not promising.


Generalized method of moments estimation

Step 1 f(b) = .00002646
Step 2 f(b) = .00003968

Group variable: amc_code_c~d Number of obs = 7316
Time variable: year Number of groups = 2623

Moment conditions: linear = 15 Obs per group: min = 1
nonlinear = 0 avg = 2.789173
total = 15 max = 3

(Std. err. adjusted for 2,623 clusters in amc_code_coded)
---------------------------------------------------------------------------------------
| WC-Robust
turnout | Coefficient std. err. z P>|z| [95% conf. interval]
----------------------+----------------------------------------------------------------
globo_coverage_copy | -2.588164 2.106394 -1.23 0.219 -6.71662 1.540293
ln_i_r_pib_cap | .2186754 .1568309 1.39 0.163 -.0887075 .5260584
i_analf_15y_more_perc | -1.534479 1.222464 -1.26 0.209 -3.930465 .8615063
i_pop_rural_perc. | 1.288622 1.168455 1.10 0.270 -1.001508 3.578753
i_catholic | -1.206615 1.517602 -0.80 0.427 -4.181061 1.767831
i_child_alive | -.5180913 .4670469 -1.11 0.267 -1.433486 .3973037
i_wealth_noTV | -.1857732 .1556404 -1.19 0.233 -.4908228 .1192764
i_agesh1524 | -4.663103 4.102109 -1.14 0.256 -12.70309 3.376882
i_Doctors | .1333259 .140901 0.95 0.344 -.142835 .4094868
i_ipc_renta | 128.5766 82.45916 1.56 0.119 -33.04037 290.1936
ln_i_pop_tot | .2030319 .2119065 0.96 0.338 -.2122973 .618361
_Iyear_1978 | .1660762 .1298005 1.28 0.201 -.0883281 .4204806
_Iyear_1982 | 1.493566 1.185464 1.26 0.208 -.8299012 3.817033
_cons | 1.469728 2.060726 0.71 0.476 -2.569221 5.508678
---------------------------------------------------------------------------------------