Re: st: RE: pooled ols interpretation, thanks

[Constantine Daskalakis <C_Daskalakis@mail.jci.tju.edu>]

There are a bunch of things going on here. I'll take a shot.

*** (1) I assume that the outcome refers to annual family income.

> i have just run a regression which gives the following results, i have
> to do pooled regression. lfam stands for log of family income so that
> my coefficient will give me a percentage instead of dollars.
>
> lfam        coeff
>
> educ  (years of education)     0.12
> d91     (year 1991)    0.08
> d92     (year 1992)    0.96
> d93    (year 1993)    0.07
> exper   (work experience)   0.24

But I don't understand how you have only 3 years worth of data and 
still get these results for all 3 dummies (unless you are using a "no 
intercept" model?).

*** (2) The analyses are on the log scale. So, if we're talking 
natural log, then the effect estimate should be

exp(0.12) = 1.13.

Cross-sectional interpretation:

Everything else being equal, higher education by 1 year is associated 
with a 13% higher annual family income. More strictly, the 13% refers 
to a comparison of geometric means across two groups of people that 
are 1 year of education apart. This 13% holds for all years. It does 
not matter if we talk about 91, or 92, or whatever (because the model 
assumes no year-by-education interaction)..

*** (3) The original question was a bit subtle.

> if i have the above result, how do i interpet educ- 0.12
> normally, i would say a with an additonal year of education, there will
> be 12% increase in family income. However, since i have applied d91,
> d92, d93  to make the data pooled and cross sectional, does i mean 12%
> increase in family income for over the three years? or 12% increase
> family income for  which year?

It talked about the same person gaining a year of education, i.e., 
about a longitudinal interpretation.

Indeed, in this case, we might say that 1 more year of education 
would gain this person an additional 13% in annual family income. But 
that's if "everything else is the same." Obviously, you can't gain a 
year's worth of education instantaneously (in order to have calendar 
year remain the same). So, for something like this, you would have to 
take into account the effect of time/year.

If, between 1992 and 1993, you gain 1 year of education, then your 
annual family income would be expected to increase (statistically 
speaking, this would happen instantaneously, as soon as you gained 
that additional year) by a factor equal to

exp(0.96-0.08+0.12) = exp(0.96-0.08)*exp(0.12) = 2.41 * 1.13 = 2.72

or, about threefold!

Of that 272%, only about 13% would be due to the educational gain 
(the rest would have occurred anyway just by the passage of time). 
But note that the partitioning is multiplicative (because of the log 
scale), not additive.


At 03:03 PM 1/19/2007, Austin Nichols wrote:

> Justin--
> I agree with Michael that your answer is worded in such a way as to
> confuse someone into thinking that the marginal effect of another year
> of education is 20% in 1991 in the model described.  That said, any
> interpretation of the type "with an additonal year of education, there
> will be 12% increase in family income" (Joanne's wording) is clearly
> wrong, as it ascribes a causal interpretation to a simple association.
> A better interpretation is along the lines of  "families have a mean
> education of X and mean income of Y in this data; families with an
> additional year of education have 12% higher family income on average"
> with appropriate caveats about measurement of education and any
> secular trends (e.g. how "family" education is measured, and what's
> happening to that measure of education and income over the sample
> period).


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________________________________________________________________
Constantine Daskalakis, ScD
Assistant Professor,
Thomas Jefferson University, Division of Biostatistics
1015 Chestnut St., Suite M100, Philadelphia, PA 19107
   Tel: 215-955-5695
   Fax: 215-503-3804
   Email: c_daskalakis@mail.jci.tju.edu
   Webpage: http://www.jefferson.edu/clinpharm/biostatistics/


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