# RE: st: Ask Non linear equation

 From "Lachenbruch, Peter" <[email protected]> To <[email protected]> Subject RE: st: Ask Non linear equation Date Fri, 15 Feb 2008 09:32:11 -0800

```You may also wish to use the noconstant feature of regress.  Next, you
will want to estimate the variance of alpha2=gamma/alpha1  (I use gamma
to mean the product of alpha1 and alpha2).  This should be (using the
delta method)
var(gamma/alpha1)=var(gamma)/alpha1^2+var(alpha1)*gamma^2/alpha1^4-2cov(
alpha1,gamma)*gamma/alpha1^3

Don't trust my math here - I derived this a couple of times with
different answers...  At any rate, you will need to access the returned
matrices. Also, noconstant models have some tricky aspects that others
may be better able to discuss.

Tony

Peter A. Lachenbruch
Department of Public Health
Oregon State University
Corvallis, OR 97330
Phone: 541-737-3832
FAX: 541-737-4001

-----Original Message-----
From: [email protected]
[mailto:[email protected]] On Behalf Of David
Greenberg
Sent: Thursday, February 14, 2008 5:28 PM
To: [email protected]
Subject: Re: st: Ask Non linear equation

The logarithm of a product is the sum of the logs of the individual
factors. So you can rewrite this equation as
log(Y) = alpha1 {log(X) + log[exp(alpha2*Z)].  In the second term, the
log of the exponential is just alpha2*Z. So you can write this
as log(Y) = alpha1 log(X)  + alpha1*alpha2*Z.  Define Y' = log(Y),  X' =
log(X),  and you can estimate this as a linear equation.
You can then recover alpha2 by dividing the estimated coefficient of
Z by the estimated coefficient of X'.  Or you can impose a constraint on
the coefficients before doing the estimation.
- David Greenberg, Sociology Department, New York University.

----- Original Message -----
Date: Thursday, February 14, 2008 8:20 pm
Subject: st: Ask Non linear equation
To: [email protected]

> Dear al
>
> my research in new economic geographic has demand an
> calculation. I want to ask about how to do this wage
> equation :
>
> log (Y) = alpha1*log(X*exp(alpha2*Z))
>
> Y is the dependent variable / wage
> X and Z is the independent variable
> and I have to find the coofiecient of alpha1 and
> alpha2
>
> According to the text book, its a nonlinear equation.
> How can I program this equation in the non linear
> programming? how to do that? or can I use nl command
> that are already stored in STATA?
>
> I do really hope your help
>
> Thank you
>
> Regards
>
>
>
>
>
>
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```