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Re: st: RE: Treatreg with Bootstrap SEs - first stage


From   Guy Grossman <[email protected]>
To   [email protected]
Subject   Re: st: RE: Treatreg with Bootstrap SEs - first stage
Date   Wed, 9 Mar 2011 13:06:13 -0500

Thanks Jeff - this has been extremely useful.

First are the regression results without clustering nor bootstrap when
the reduced form is restricted. Then are regression results with
unrestricted reduced form and without clustering nor bootstrap

Guy

treatreg stranger npos_before agedc, treat(vrule =z)

Treatment-effects model -- MLE                    Number of obs   =         44
                                                  Wald chi2(3)    =       3.10
Log likelihood = -293.30954                       Prob > chi2     =     0.3766

------------------------------------------------------------------------------
             |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
stranger     |
 npos_before |  -4.003312   3.670015    -1.09   0.275    -11.19641    3.189785
       agedc |    19.2581   19.78198     0.97   0.330    -19.51387    58.03006
       vrule |  -36.13351   51.39635    -0.70   0.482    -136.8685    64.60148
       _cons |   233.3789   77.89184     3.00   0.003     80.71371    386.0441
-------------+----------------------------------------------------------------
vrule        |
           z |   2.478021   .5804117     4.27   0.000     1.340435    3.615607
       _cons |  -.9345324   .2744347    -3.41   0.001    -1.472415   -.3966503
-------------+----------------------------------------------------------------
     /athrho |  -.1668083   .2934679    -0.57   0.570    -.7419949    .4083783
    /lnsigma |   4.866947   .1075092    45.27   0.000     4.656233    5.077661
-------------+----------------------------------------------------------------
         rho |  -.1652782   .2854513                     -.6303489    .3870948
       sigma |   129.9237   13.96799                      105.2389    160.3985
      lambda |  -21.47355   37.48562                     -94.94401    51.99692
------------------------------------------------------------------------------
LR test of indep. eqns. (rho = 0):   chi2(1) =     0.32   Prob > chi2 = 0.5690
------------------------------------------------------------------------------


treatreg stranger npos_before agedc, treat(vrule =z npos_before agedc) first

Probit regression                                 Number of obs   =         44
                                                  LR chi2(3)      =      26.60
                                                  Prob > chi2     =     0.0000
Log likelihood = -16.787309                       Pseudo R2       =     0.4421

------------------------------------------------------------------------------
       vrule |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
           z |   2.504705   .5923703     4.23   0.000     1.343681     3.66573
 npos_before |   .0312567   .0485168     0.64   0.519    -.0638344    .1263479
       agedc |   .0488113   .2522365     0.19   0.847    -.4455631    .5431857
       _cons |  -1.402968   1.018711    -1.38   0.168    -3.399605    .5936681
------------------------------------------------------------------------------

Treatment-effects model -- MLE                    Number of obs   =         44
                                                  Wald chi2(3)    =       3.42
Log likelihood = -293.13633                       Prob > chi2     =     0.3319

------------------------------------------------------------------------------
             |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
stranger     |
 npos_before |  -4.209007   3.680126    -1.14   0.253    -11.42192    3.003907
       agedc |   19.04293   19.88008     0.96   0.338     -19.9213    58.00717
       vrule |  -39.05213    51.3033    -0.76   0.447    -139.6047    61.50049
       _cons |   237.2232   77.54155     3.06   0.002      85.2446    389.2019
-------------+----------------------------------------------------------------
vrule        |
           z |   2.519301   .5973311     4.22   0.000     1.348553    3.690048
 npos_before |   .0285118   .0492956     0.58   0.563    -.0681059    .1251294
       agedc |   .0302288   .2572896     0.12   0.906    -.4740496    .5345072
       _cons |  -1.311585   1.045363    -1.25   0.210    -3.360458     .737288
-------------+----------------------------------------------------------------
     /athrho |  -.1417195   .2938456    -0.48   0.630    -.7176462    .4342073
    /lnsigma |   4.866185    .107235    45.38   0.000     4.656008    5.076361
-------------+----------------------------------------------------------------
         rho |  -.1407782    .288022                     -.6154492    .4088314
       sigma |   129.8247   13.92175                      105.2152    160.1901
      lambda |  -18.27649   37.67748                     -92.12299    55.57002
------------------------------------------------------------------------------
LR test of indep. eqns. (rho = 0):   chi2(1) =     0.24   Prob > chi2 = 0.6277
------------------------------------------------------------------------------



On Wed, Mar 9, 2011 at 12:52 PM, Wooldridge, Jeffrey <[email protected]> wrote:
> I just noticed another problem which is probably not related to the standard error issue. You're only including z in the reduced form for vrule. While some find it acceptable, most do not. You are making restrictions on a reduced form by assuming npos_before and agedc have no partial effect on vrule
>
> What do the treatreg standard errors when you neither cluster nor use the bootstrap?
>
> By the way, there is nothing wrong with the usual 2SLS estimator in this context even though vrule is binary. I would use that, too, as it forces you to estimate an unrestricted reduced form.
>
> -----Original Message-----
> From: [email protected] [mailto:[email protected]] On Behalf Of Guy Grossman
> Sent: Wednesday, March 09, 2011 12:47 PM
> To: [email protected]
> Subject: Re: st: RE: Treatreg with Bootstrap SEs - first stage
>
> Thanks Jeff - see below results from the first stage.
>
>
> Probit regression                                 Number of obs   =         44
>                                                  LR chi2(1)      =      26.17
>                                                  Prob > chi2     =     0.0000
> Log likelihood = -17.005048                       Pseudo R2       =     0.4348
>
> ------------------------------------------------------------------------------
>       vrule |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
> -------------+----------------------------------------------------------------
>           z |   2.445756   .5688183     4.30   0.000     1.330892    3.560619
>       _cons |  -.9446696   .2747046    -3.44   0.001    -1.483081   -.4062585
> ------------------------------------------------------------------------------
>
>
> On Wed, Mar 9, 2011 at 12:17 PM, Wooldridge, Jeffrey <[email protected]> wrote:
>> A few observations.
>>
>> 1. I don't see how the bootstrapped standard errors are robust to clustering. Where have you specified that the bootstrap should be done by resampling the clusters?
>> 2. More importantly, I think you should not be trying to cluster with 44 observations and five clusters. Cluster-robust inference is not justified with such a small number of clusters. Heck, you have more observations per cluster than number of clusters! You really need lots of clusters that aren't very large. I believe you can get spurious rejections when you cluster with such a small number of clusters. From Stata's perspective, you have five observations when you cluster.
>> 3. N = 44 is small to be using any kind of IV procedure, especially a nonlinear one. But if you must, you should not be clustering.
>> 4. If you estimate the first-stage probit for vrule without clustering or bootstrapping, what is the t statistic on z?
>>
>> Jeff
>>
>>
>> -----Original Message-----
>> From: [email protected] [mailto:[email protected]] On Behalf Of Guy Grossman
>> Sent: Wednesday, March 09, 2011 11:53 AM
>> To: [email protected]
>> Subject: st: Treatreg with Bootstrap SEs - first stage
>>
>> 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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