st: Treatreg with Bootstrap SEs - first stage

[Guy Grossman <guygrossman1@gmail.com>]

Dear friends,

I run the fit the following IV model, where stranger is a continuous
dependent variable, and vrule is an endogenous binary predictor,
instrumented by z (also binary). The associastion between the
instrument z and the endogenous predictor (vrule) is strong.

(1) stranger = npos_before + agedc + vrule + u
(2) vrule = z + e

I first fit a model with clustered SEs. I then  fit a second model
with bootstrapped SEs. What I find strange is the differences in the
SEs of the instrument in the bootstrap model. When standard errors
were clustered, the standard error of z is equal to .478 and is highly
significant, but in the bootstrap model the standard error of z is
equal to 6.58 (13 times larger).

My question is what can explain such difference in results, given that
I know the association between the binary endogenous predictor and the
instrument is strong.

Thanks!
Guy


eststo: treatreg stranger npos_before agedc, treat(vrule =z)
cluster(strata) nolog
Treatment-effects model -- MLE                    Number of obs   =         44
                                                  Wald chi2(0)    =          .
Log pseudolikelihood = -293.30954                 Prob > chi2     =          .
                                 (Std. Err. adjusted for 5 clusters in strata)
------------------------------------------------------------------------------
             |               Robust
             |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
stranger     |
 npos_before |  -4.003312   2.181331    -1.84   0.066    -8.278642    .2720188
       agedc |    19.2581   11.40533     1.69   0.091    -3.095944    41.61213
       vrule |  -36.13351   19.98177    -1.81   0.071    -75.29706    3.030042
       _cons |   233.3789     33.044     7.06   0.000     168.6139     298.144
-------------+----------------------------------------------------------------
vrule        |
           z |   2.478021   .4780614     5.18   0.000     1.541038    3.415005
       _cons |  -.9345324   .1497078    -6.24   0.000    -1.227954   -.6411105
-------------+----------------------------------------------------------------
     /athrho |  -.1668083   .3755606    -0.44   0.657    -.9028935     .569277
    /lnsigma |   4.866947   .1144261    42.53   0.000     4.642676    5.091218
-------------+----------------------------------------------------------------
         rho |  -.1652782   .3653015                     -.7177039    .5148281
       sigma |   129.9237   14.86666                      103.8218    162.5878
      lambda |  -21.47355   47.79572                     -115.1514    72.20435
------------------------------------------------------------------------------
Wald test of indep. eqns. (rho = 0): chi2(1) =     0.20   Prob > chi2 = 0.6569
------------------------------------------------------------------------------

eststo: treatreg stranger npos_before agedc, treat(vrule =z)
vce(bootstrap, reps(1000)) first
Treatment-effects model -- MLE                  Number of obs      =        44
                                                Replications       =       954
                                                Wald chi2(3)       =      3.76
Log likelihood = -293.30954                     Prob > chi2        =    0.2892
------------------------------------------------------------------------------
             |   Observed   Bootstrap                         Normal-based
             |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
stranger     |
 npos_before |  -4.003312   3.781918    -1.06   0.290    -11.41573    3.409111
       agedc |    19.2581   20.01746     0.96   0.336     -19.9754    58.49159
       vrule |  -36.13351   50.30376    -0.72   0.473    -134.7271    62.46005
       _cons |   233.3789   86.26582     2.71   0.007     64.30102    402.4568
-------------+----------------------------------------------------------------
vrule        |
           z |   2.478021   6.583954     0.38   0.707    -10.42629    15.38233
       _cons |  -.9345324   .2802209    -3.33   0.001    -1.483755   -.3853095
-------------+----------------------------------------------------------------
     /athrho |  -.1668083   .4793972    -0.35   0.728     -1.10641     .772793
    /lnsigma |   4.866947   .1126358    43.21   0.000     4.646185    5.087709
-------------+----------------------------------------------------------------
         rho |  -.1652782   .4663016                     -.8027896    .6485506
       sigma |   129.9237   14.63405                      104.1868    162.0183
      lambda |  -21.47355   60.81632                     -140.6713    97.72425
------------------------------------------------------------------------------

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