Re: st: comparing coefficients accross models

 From Partha Deb <[email protected]> To [email protected] Subject Re: st: comparing coefficients accross models Date Thu, 11 Jan 2007 11:41:54 -0500

Traci,

Your substantive question got my attention when you first posted, and I'll admit I didn't read your post, nor subsequent helpful posts carefully, so with due apologies to those who've made suggestions, etc. I'll suggest that the -suest- type test you had in mind initially seemed perfectly appropriate to me.

You have 2 equations.

y1 = b0 + b1 * x + u1
y2 = a0 + a1 * x + u2

You can think of these as a SUR, but if your regressors are the same in both equations (as I've written it out), there is no advantage to using an SUR procedure. But, it's perfectly reasonable to test the hypothesis: H0: b1=a1 using a Wald test. That's what -suest- does. Perhaps newey2 doesn't e(b) and V(b) from each model, which is what you need for the test (and -suest-), but ivreg2 should.

Hope this helps.

Partha

Traci Schlesinger wrote:

thanks maarten! part of my issue is that the bureau of justice statistics says this is data on every person admitted to a state or federal prison in these years, but the realities of data collection seem to ensure that it is not, so i have been thinking of the data as a sample, even if a sample that included most of the population. also, because it is the dependent variable (black men's admission rate versus white men's admission rate) and not a response variable that changes across models, i don't think i can use interactions to answer this question. am i wrong?

i have a more precise question now. if i calculate a new dependent variable

gen disparity = black - white

by subtracting the white men's admission rate from the black men's admission rate, and run the same model on this variable, am i correct in thinking this can serve as a test?

for example, the results for the sentencing policy variable from the model on black admission rates are as follows:

| Robust
bmv_rate | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
mt_b | 25.63707 7.820457 3.28 0.002 9.929216 41.34492

for example, the results for the sentencing policy variable from the model on white men's admission rates are as follows:
| Robust
wmv_rate | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
mt_b | 2.133085 1.140938 1.87 0.067 -.1585574 4.424727

for example, the results for the sentencing policy variable from the model on white men's admission rates are as follows:

| Robust
bwmv_diff | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
mt_b | 23.50398 7.185369 3.27 0.002 9.071744 37.93622

since the sentencing variable in this last model has a coefficient that is the size of the sentencing coefficient from the first model minus sentencing coefficient from the second model, and is significant at .001, might I not argue that this is statistical evidence of disparate impact? I wouldn't use this is evidence that the sentencing policies "increased disparity" - the disparity measure would need to be a ratio not a difference -- but i think this is evidence of differential impact. does that seem accurate?

thanks for the help!

best
traci

Maarten buis wrote:
--- Traci Schlesinger <[email protected]> wrote:
By saying I should 'fudge it and compare them indirectly' do you
simply mean that i should compare them 'by eye' -- stating that not
only is the coefficient for mt_b larger in the model for blacks but
that the t-score is also higher? This is not so terrible for this
data, since according to the Bureau of Justice Statistics, this is
the full population of people admitted to prison (not a sample), but
I still think many people (esp. reviewers) would not be convinced
If you have the population, then "comparing them by eye" is all you can
do (or go Bayesian, but you probably don't want to go there).
Frequentist testing assumes that all uncertainty about a parameter is
the result of the fact that we only observed a random sample from the
population, not the actual population itself. Then it imagines what the
population would be like if the null hypothesis were true. Then it
looks at how likely it is to draw a random sample with the observed
test statistic or extremere, the p-value. If it is very unlikely to
draw such a sample "by accident" then we think that there must be
something wrong with the null hypothesis. Since you don't have a
sample, but the population concepts like the p-values loose their
meaning.

The idea behind testing is that what you find in a sample gives you
information about what happens in the population, but that information
is uncertain due to the fact that you are only looking at a sample.
Testing quantifies the uncertainty due to sampling. You have no
uncertainty on that account. You may have other sources of uncertainty:
is my model correct, are my variables measured without error, etc. But

-----------------------------------------
Maarten L. Buis
Department of Social Research Methodology
Vrije Universiteit Amsterdam
Boelelaan 1081
1081 HV Amsterdam
The Netherlands

Buitenveldertselaan 3 (Metropolitan), room Z434

+31 20 5986715

http://home.fsw.vu.nl/m.buis/
-----------------------------------------

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Partha Deb
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