Clustering SEs in Panel IVFE regression eliminates significance

[Moheb Malak]

Hello,

I am studying country structural transformation by regressing log(manufacturing value added per capita) on log(GDP per capita), its quadratic and cubic terms, population density, population and natural resources as share of GDP using a fixed effects country panel, as follows:

xtreg lmvapc lgdppc lgdppc2 lgdppc3 lpopdensity lpop dependency_ratio natural_resource_rent ,fe

However, due to suspected endogeneity of GDP per capita (since manufacturing is a component of GDP), I use the 2-year lagged GDP per capita as an instrument for GDP per capita, as follows:

ivregress 2sls lmvapc lpopdensity lpop dependency_ratio natural_resource_rent i.$id (lgdppc_weo lgdppc2_weo lgdppc3_weo = l2lgdp l2lgdp2 l2lgdp3)

When I use robust standard errors I get the below output:

Instrumental variables 2SLS regression            Number of obs   =      4,752
                                                  Wald chi2(181)  = 1531972.35
                                                  Prob > chi2     =     0.0000
                                                  R-squared       =     0.9861
                                                  Root MSE        =     .19314

---------------------------------------------------------------------------------------
                      |               Robust
               lmvapc | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
----------------------+----------------------------------------------------------------
           lgdppc_weo |    2.70563   1.304755     2.07   0.038     .1483583    5.262902
          lgdppc2_weo |  -.1551981   .1500386    -1.03   0.301    -.4492684    .1388722
          lgdppc3_weo |   .0041253   .0056705     0.73   0.467    -.0069887    .0152392
          lpopdensity |  -.0222306   .0199534    -1.11   0.265    -.0613386    .0168774
                 lpop |  -.1678059   .0371796    -4.51   0.000    -.2406766   -.0949351
     dependency_ratio |  -.0030668   .0009559    -3.21   0.001    -.0049402   -.0011933
natural_resource_rent |  -.0017048   .0009515    -1.79   0.073    -.0035697      .00016

However, when I try to cluster the errors (which is the default if I used xtivreg with vce robust), I would lose significance of all variables as follows:

Instrumental variables 2SLS regression            Number of obs   =      4,752
                                                  Wald chi2(181)  =     467.03
                                                  Prob > chi2     =     0.0000
                                                  R-squared       =     0.9861
                                                  Root MSE        =     .19314

                                     (Std. err. adjusted for 175 clusters in countryid)
---------------------------------------------------------------------------------------
                      |               Robust
               lmvapc | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
----------------------+----------------------------------------------------------------
           lgdppc_weo |    2.70563   3.188655     0.85   0.396    -3.544019    8.955279
          lgdppc2_weo |  -.1551981   .3662342    -0.42   0.672    -.8730039    .5626077
          lgdppc3_weo |   .0041253   .0139253     0.30   0.767    -.0231679    .0314184
          lpopdensity |  -.0222306   .0519262    -0.43   0.669    -.1240041    .0795429
                 lpop |  -.1678059   .1191995    -1.41   0.159    -.4014327    .0658209
     dependency_ratio |  -.0030668   .0027595    -1.11   0.266    -.0084753    .0023418
natural_resource_rent |  -.0017048   .0014137    -1.21   0.228    -.0044757     .001066

Is this a problem with the model or is clustering not appropriate in this case?

Thanks a lot in advance and best regards,
Moheb

[Fei Wang]

Moheb, clustering at the country level is appropriate in you case. But another two issues may need attention.

First, time fixed effects should be included to capture common shocks at a specific period.

Second, the validity of the IVs need to be examined carefully. At lease you may want to test whether the IVs are strong enough in the first stage. As you have non-iid errors, an unofficial command weakivtest will help do the test.

If the model is well specified and the IVs are convincing, then what you get is what you get even if estimates are insignificant -- BTW, in this case, you may check heterogenous effects of the regressors and it's possible that they are significant for part of the countries.