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st: Standard Errors of Regression Coefficients


From   "RonDorsey" <ron@dorsey21.fsnet.co.uk>
To   <statalist@hsphsun2.harvard.edu>
Subject   st: Standard Errors of Regression Coefficients
Date   Mon, 19 Aug 2002 21:20:09 +0100

Dear Statalisters

Once again I would value your advice.  I have run a fixed effects model and
am interested in the size and significance of the fixed effects for each
group.

I am aware that fixed effects is (essentially) the same as running OLS on
the model with group dummies (minus one group).  Since it is the fixed
effects I'm interested in, dummy coefficients only from OLS are reproduced
below:

Regression with robust standard errors Number of obs = 759
     F( 27,   731) = 3.86
     Prob > F = 0.0000
     R-squared = 0.1054
     Root MSE = 12.619


                                    Robust
diffpts     Coef.             Std. Err.         t         P>t

dum1     -5.032168     2.92946       -1.718     0.086
dum2     -9.752335     2.821768     -3.456     0.001
dum3     -7.194816     2.911494     -2.471     0.014
dum4     -3.296102     2.813756     -1.171     0.242
dum5     -2.073403     3.053997     -0.679     0.497
dum6     -2.028223     2.795275     -0.726     0.468
dum7     -2.925705     2.833143     -1.033     0.302
dum8     -1.564355     2.830483     -0.553     0.581
dum9     .3787652      2.563237      0.148     0.883
dum10   -6.388214     2.810872     -2.273     0.023
dum11   -4.371068     2.875142     -1.520     0.129
dum12   -8.458449     2.813401     -3.006     0.003
dum13   -2.659176     2.756806     -0.965     0.335
dum14    1.783952     2.830733      0.630     0.529
dum15   -5.033113     3.180156     -1.583     0.114
dum16   -3.483705     2.818563     -1.236     0.217
dum17   -3.617528     2.818313     -1.284     0.200
_cons     4.268866     2.278385      1.874     0.061

The t test here refers to whether diffpts in each group (team) differs
significantly from the excluded team (dum18).

My area of interest is whether or not each teams diffpts deviate from the
league average.  To measure this I have used the Suits(1984) technique
referred to in Greene (2000) p.562 to calculate the value of the dummy for
team 18 (and adjust the others accordingly)

i.e.    k = -(b1 + b2 + b3.......+ b17 + 0) / 18            where bi are the
dummy coefficients from OLS.

the 'new' dummy coefficients are bi* = bi + k

and the 'new' constant is c* = _cons - k

This gives:

Var                        bi*

_cons         0.61799696
dum1         -1.381299
dum2         -6.101466
dum3         -3.543947
dum4         0.35476704
dum5         1.57746604
dum6         1.62264604
dum7         0.72516404
dum8         2.08651404
dum9         4.02963424
dum10      -2.737345
dum11      -0.720199
dum12      -4.80758
dum13       0.99169304
dum14       5.43482104
dum15     -1.382244
dum16     0.16716404
dum17     0.03334104
dum18     3.65086904

Does anyone know how I calculate the standard errors for 'new' bi* and the
constant?

Given that the 'new' coefficients are a linear function of the original ones
I presume this is possible.  Having said that I'm sure it involves matrix
algebra (which I'm useless at!) and was hoping someone could devise a
routine to do the necessary calculations.

Many thanks for your time.

Best wishes

Ron Dorsey

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