st: Testing for attrition bias using the BGLW test

[Julia Vaillant <vaillant@dial.prd.fr>]

Dear Statalist, 

I would like to run a BGLW test (Becketti, Gould, Lillard & Welch, 1988, « The Panel study of income dynamics after fourteen years, an evaluation", Journal ef Labor economics, 6:472-92) on my data but I can't figure out how exactly to do it. 

I have a sample of 1490 individuals in 1995 ("full panel"). 662 of these individuals remain in the panel ten years later ("stayers"). I want to test whether they have the same behavioural relationships at baseline, with income as a dependent variable and a set of covariates (age, sex, etc.) This can done using a BGLW test: running OLS regressions separately on the full panel and on the stayers. Then one can compare the coefficients for each variable and conclude whether the sub-sample of "stayers" is representative of the full sample in terms of the determinants of income. 

My problem: I don't know how to compare the coefficients. I can calculate the difference in each coefficient by hand, but that doesn't give me the standard error, so I can't test the significance. 
Using a set of interactions in a unique regression doesn't give exactly what I need, it gives the difference between the coefficient of the stayer and the non-stayer, instead of between  the stayer and the full sample.


I have run these regressions (simplified version with only 2 covariates) and put the results in the table below. I calculated the difference column by hand. 

VARIABLES  		full sample        stayers only      difference
-------------+----------------------------------------------------------------
            
age                   0.00506***     0.00488***     		-0.00018
                        (0.00125)        (0.00142)        	????
sex                   -0.0886**       -0.0944*       		  -0.0058
                        (0.0407)          (0.0511)          ???
Constant         		 5.997***       6.073***        	 0.076
                        (0.0387)          (0.0470)          ???
                                   
Observations    1342    660      
R-squared        0.016   0.022   


Note: standard-errors in parentheses.

How do I fill in the ????

Thank you for your help, 

Julia



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