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# st: moulton factor correction

 From Ana Gabriela Guerrero Serdan To stata listserve Subject st: moulton factor correction Date Wed, 24 Jun 2009 05:14:39 -0700 (PDT)

```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

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```

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