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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 12:46:36 -0500
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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