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st: marginal effects with quadratic terms

From   "Alan C. Marco" <[email protected]>
To   [email protected]
Subject   st: marginal effects with quadratic terms
Date   Fri, 17 Oct 2003 12:45:27 -0400

Dear statalist:

I'm using heckprob, and my model includes some quadratic terms. When displaying the marginal effects using mfx compute, Stata displays separate terms (obviously) for the linear and quadratic terms of the variable. That is it treats x1 and x2 as separate variables and does not understand that x2 = x1^2.

In displaying marginal effects of heckprob (or probit or logit or whatever) it seems one would be interested in the "total" marginal effect, not individual effects on the linear and quadratic terms.

Getting the total marginal effect is not so difficult, theoretically: the total marginal effect (Mt) for a variable x is:

Mt = M1 + 2*xbar*M2

where M1 is the marginal effect for the linear term, M2 is the marginal effect of the squared term, and xbar is the value of x at which mfx is evaluated.

However, how does one calculate the standard error for this estimate? I've looked all over and haven't found a straightforward approach. Second, since the "real" marginal effect of the variable in question is incorrect in the mfx output, doesn't this actually influence the calculations for *all* the marginal effects? [My understanding is that the calculations of the SEs for each marginal effect depend on values of the other marginal effects.] If so, then the output of mfx compute is suspect whenever one is using quadratic terms.

Many thanks in advance,


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