Dear all,
I am trying to understand why in this example when using the moulton correction developped by Angrist and Piscke (2009) I get some SE that are lower then when using the cluster option. I thought that the moulton correction will increase SE, but seems not to be the case for all coefficients. Can someone help me interpret what is going on?
use http://www.ats.ucla.edu/stat/stata/seminars/svy_stata_intro/srs, clear
regress api00 growth emer yr_rnd, robust
regress api00 growth emer yr_rnd, cl(dnum)
moulton api00 growth emer yr_rnd, cl(dnum)
moulton api00 growth emer yr_rnd, cl(dnum) moulton
loneway api00 dnum
results below:
thanks,
Gaby
use http://www.ats.ucla.edu/stat/stata/seminars/svy_stata_intro/srs, clear
. regress api00 growth emer yr_rnd, robust
Linear regression Number of obs = 309
F( 3, 305) = 33.15
Prob > F = 0.0000
R-squared = 0.2770
Root MSE = 111.54
------------------------------------------------------------------------------
| Robust
api00 | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
growth | -.1027121 .195606 -0.53 0.600 -.4876202 .2821961
emer | -5.444932 .5532104 -9.84 0.000 -6.533524 -4.35634
yr_rnd | -51.07569 20.28729 -2.52 0.012 -90.99645 -11.15493
_cons | 740.3981 12.13784 61.00 0.000 716.5136 764.2826
------------------------------------------------------------------------------
. regress api00 growth emer yr_rnd, cl(dnum)
Linear regression Number of obs = 309
F( 3, 185) = 19.72
Prob > F = 0.0000
R-squared = 0.2770
Root MSE = 111.54
(Std. Err. adjusted for 186 clusters in dnum)
------------------------------------------------------------------------------
| Robust
api00 | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
growth | -.1027121 .2291703 -0.45 0.655 -.5548352 .3494111
emer | -5.444932 .7293969 -7.46 0.000 -6.883938 -4.005927
yr_rnd | -51.07569 22.83615 -2.24 0.027 -96.12844 -6.022935
_cons | 740.3981 13.46076 55.00 0.000 713.8418 766.9544
------------------------------------------------------------------------------
. moulton api00 growth emer yr_rnd, cl(dnum)
OLS Regression: standard errors Number of obs = 309
adjusted for cluster effects using Moulton R-squared = 0.2770
Adj R-squared = 0.2698
Number of clusters (dnum) = 186 Root MSE = 111.541
------------------------------------------------------------------------------
api00 | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
growth | -.1027121 .2455165 -0.42 0.676 -.5858326 .3804084
emer | -5.444932 .7128514 -7.64 0.000 -6.847662 -4.042203
yr_rnd | -51.07569 20.57651 -2.48 0.014 -91.56558 -10.58579
_cons | 740.3981 17.78252 41.64 0.000 705.4061 775.39
------------------------------------------------------------------------------
Intraclass correlation in growth = 0.2567
Intraclass correlation in emer = 0.5444
Intraclass correlation in yr_rnd = 0.0494
Intraclass correlation in residual = 0.3775
. moulton api00 growth emer yr_rnd, cl(dnum) moulton
OLS Regression: standard errors Number of obs = 309
adjusted for cluster effects using Moulton R-squared = 0.2770
Adj R-squared = 0.2698
Number of clusters (dnum) = 186 Root MSE = 111.541
------------------------------------------------------------------------------
api00 | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
growth | -.1027121 .2203333 -0.47 0.641 -.5362779 .3308538
emer | -5.444932 .6285286 -8.66 0.000 -6.681734 -4.208131
yr_rnd | -51.07569 20.53625 -2.49 0.013 -91.48636 -10.66502
_cons | 740.3981 15.49653 47.78 0.000 709.9044 770.8917
------------------------------------------------------------------------------
Intraclass correlation in growth = 0.1107
Intraclass correlation in emer = 0.4466
Intraclass correlation in yr_rnd = 0.0794
Intraclass correlation in residual = 0.2204
. loneway api00 dnum
One-way Analysis of Variance for api00:
Number of obs = 310
R-squared = 0.7392
Source SS df MS F Prob > F
-------------------------------------------------------------------------
Between dnum 3879736.2 186 20858.797 1.87 0.0001
Within dnum 1369122.1 123 11131.074
-------------------------------------------------------------------------
Total 5248858.3 309 16986.596
Intraclass Asy.
correlation S.E. [95% Conf. Interval]
------------------------------------------------
0.34737 0.08516 0.18045 0.51428
Estimated SD of dnum effect 76.97107
Estimated SD within dnum 105.5039
Est. reliability of a dnum mean 0.46636
*
* For searches and help try:
* http://www.stata.com/help.cgi?search
* http://www.stata.com/support/statalist/faq
* http://www.ats.ucla.edu/stat/stata/
