2SLS Interpretation

[Stefan Bradeanu]

Hello everyone,

I hope you are all well,

I have an analysis based on the convergence growth model and for testing the reverse causality in this model I ran a 2SLS regression with instrumental variables. However, when I ran the model I get insignificant results which would be normally interpreted as no causality between the variables (which I am sure is not the case since causality between income and education for example is running both ways) in my model even after carefully inspecting the data and using various instruments for my main variables.

Therefore, my question is, how I interpret these results? What are the possible interpretations for insignificant 2SLS results or I simply have to ignore it?

I should still mention the insignificant results of the 2SLS in my study or just ignore it.

Thank you very much to everyone.

. ivregress 2sls g_iwi_mean i_iwi_initial i_y_dep_initial i_o_dep_initial ln_density_initial
>  g_ln_pop_mean g_educ_mean i_urban_initial interval_v_initial c.i_y_dep_initial#c.inf_init
> ial Bangladesh India Pakistan Nepal Cambodia Indonesia Vietnam Philippines Thailand (g_wor
> king_age_mean = g_working_age_lag)
note: Thailand omitted because of collinearity

Instrumental variables (2SLS) regression          Number of obs   =        133
                                                  Wald chi2(18)   =     324.43
                                                  Prob > chi2     =     0.0000
                                                  R-squared       =     0.6535
                                                  Root MSE        =      2.953

------------------------------------------------------------------------------------
        g_iwi_mean |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------------+----------------------------------------------------------------
g_working_age_mean |   2.697712   6.523627     0.41   0.679    -10.08836    15.48379
     i_iwi_initial |  -.1795225   .1862335    -0.96   0.335    -.5445334    .1854885
   i_y_dep_initial |  -.2254004   .2376895    -0.95   0.343    -.6912632    .2404625
   i_o_dep_initial |  -.0476965   .4437751    -0.11   0.914    -.9174796    .8220867
ln_density_initial |  -.3872617   .2989893    -1.30   0.195    -.9732699    .1987465
     g_ln_pop_mean |   -2.95531   4.342148    -0.68   0.496    -11.46576    5.555143
       g_educ_mean |   1.012909   8.103293     0.12   0.901    -14.86925    16.89507
   i_urban_initial |   -.028095   .0291471    -0.96   0.335    -.0852223    .0290323
interval_v_initial |   -1.90502   5.477426    -0.35   0.728    -12.64058    8.830537
                   |
 c.i_y_dep_initial#|
     c.inf_initial |   .0007439   .0158664     0.05   0.963    -.0303536    .0318414
                   |
        Bangladesh |  -10.79152   18.13457    -0.60   0.552    -46.33462    24.75159
             India |   3.995187   6.616727     0.60   0.546    -8.973358    16.96373
          Pakistan |   3.770025   3.276182     1.15   0.250    -2.651173    10.19122
             Nepal |   2.650764   7.993771     0.33   0.740    -13.01674    18.31827
          Cambodia |   .2245071   9.617907     0.02   0.981    -18.62624    19.07526
         Indonesia |   -.312647   7.758975    -0.04   0.968    -15.51996    14.89466
           Vietnam |   -2.22392   16.88002    -0.13   0.895    -35.30815    30.86031
       Philippines |   1.166022   6.106007     0.19   0.849    -10.80153    13.13358
          Thailand |          0  (omitted)
             _cons |   36.85584    59.7841     0.62   0.538    -80.31885    154.0305
------------------------------------------------------------------------------------
Instrumented:  g_working_age_mean
Instruments:   i_iwi_initial i_y_dep_initial i_o_dep_initial ln_density_initial
               g_ln_pop_mean g_educ_mean i_urban_initial interval_v_initial
               c.i_y_dep_initial#c.inf_initial Bangladesh India Pakistan Nepal
               Cambodia Indonesia Vietnam Philippines g_working_age_lag

Best wishes,
Stefan Bradeanu

[Phil Bromiley]

Identifying why one get statistically insignificant results is quite difficult – it could be that the true results are that there's not a strong association or there could be any of a number of estimation issues.

The first thing I see in your estimate is that you have 19 parameters and only 133 observations. So, one interpretation would be simply that you're trying to estimate too many parameters with too few observations. This is not made easier when you instrument an endogenous variable which inherently creates a noisy measure of that variable. Your primary problem seems to be the large standard error on the parameter. Note also that I suspect the results only have asymptotic properties.

That said, there are a few standard things you could check. If you estimate the model with OLS, you can use the post estimation diagnostic tools to check for influential observations or outliers. You might use ivreg2 and look at the diagnostics provided. You might test for endogeneity.

[Stefan Bradeanu]

Dear Phil,

Thank you for your helpful response.