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RE: st: RE: Treatreg with Bootstrap SEs - first stage
From
"Wooldridge, Jeffrey" <[email protected]>
To
<[email protected]>
Subject
RE: st: RE: Treatreg with Bootstrap SEs - first stage
Date
Wed, 9 Mar 2011 12:52:31 -0500
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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