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st: RE: Standard Errors of Regression Coefficients


From   "Millimet, Daniel" <millimet@post.cis.smu.edu>
To   <statalist@hsphsun2.harvard.edu>
Subject   st: RE: Standard Errors of Regression Coefficients
Date   Mon, 19 Aug 2002 15:43:04 -0500

since these are linear, you can use the -test bi* = 0- 
otherwise, in general, you can use the delta method to
obtain std errors of some parameter which is a function
of the estimated parameters.
 
dann

	-----Original Message----- 
	From: RonDorsey [mailto:ron@dorsey21.fsnet.co.uk] 
	Sent: Mon 8/19/2002 3:20 PM 
	To: statalist@hsphsun2.harvard.edu 
	Cc: 
	Subject: st: Standard Errors of Regression Coefficients
	
	

	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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