Re: st: biprobit postestimation (marginal effects)

[Austin Nichols <austinnichols@gmail.com>]

Fabian Guy <fabolous.vs@gmail.com>:

You have to write a program to predict the relevant probabilities and
calculate differences, then you can bootstrap the program to get SE
for your marginal effects. You should not assume "X is at the mean of
the sample" rather than simply predicting the relevant probability for
each sample case, then averaging across the sample, to get the mean
marginal effects rather than marginal effects at the mean; you would
not want a marginal effect for a sample case that is half female and
half male rather than the half the effect for males plus half the
effect for females.

On a more practical note, it is convenient to rename the variable for
which you want to impose a counterfactual value, then generate a new
variable with that name e.g. generate y2=0, predict, then drop the new
variable and rename back to your original data.

I can't tell how many marginal effects you really want to estimate in
your a,b,c below, given the 0 (1) notations, but perhaps you can
explain what the primary marginal effect of interest is.  For
instance, in item a, I would guess you want to know
dPr(y1==1|X,L.y1,y2,L.y2)/dL.y2 which means you average over the y2
and L.y1 and L.y2 possibilities, perhaps using observed lag values but
probabilities of y2 in your sample.

On Thu, Sep 19, 2013 at 6:10 AM, Fabian Guy <fabolous.vs@gmail.com> wrote:
> Dear Stata-Experts,
> I need your advice with a simple biprobit postestimation analysis. I
> think the problem that I have could be solved in a straightforward
> manner, but since I am not that familiar with Stata I would like to
> make sure that I do not mess things up.
>
> So, suppose I have a panel of i=1,...,I individuals and for each
> individual I have observation over time t=1,...,T.
> I estimate the following _pooled_ bivariate probit model:
> (y1 = L.y2 X)
> (y2 = L.y1 X)
> where X = common regressors in both equations (continuous, no binary
> variable included in this set). The estimation turns out that
> estimating a two equation probit is important, since the correlation
> parameter of the errors is significantly different from zero.
>
> I would like to compute the following marginal effects:
> a) Given X is at the mean of the sample, y2=0 (1), and L.y1=0 (1),
> what is the increase/decrease in the probability of y1=1 if L.y2
> increases from 0 to 1?
> b) Given X_subset is at the mean, y2=0 (1), and L.y1=0 (1), what is
> the increase/decrease in the probability of y1=1 if X_j increases by
> one unit?
> c) Given X is at the mean, L.y2 = 0 (1) y2=1 (0), and L.y1 = 0 (1),
> what is the Prob. of y1=1?
>
> For me it looks like that those marginal effects could be typically
> requested using biprobit. Do I have to use margins or predict for
> these calculations? Do I have to code this by my own or is there a
> Stata command with some options (like predict/margins) that could
> provide me a solution to those calculations?
>
> A possible variation would be to set L. variables as well to their
> average, however, I think it does not make much sense for dichotomous
> variables.
>
> I appreciate any advice very much.
>
> Best,
> Fabian
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