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st: RE: Treatreg with Bootstrap SEs - first stage
From
"Wooldridge, Jeffrey" <[email protected]>
To
<[email protected]>
Subject
st: RE: Treatreg with Bootstrap SEs - first stage
Date
Wed, 9 Mar 2011 12:17:21 -0500
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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