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 -----
From: adiwan fahlan <[email protected]>
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
> advance
> 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
> Adiwan
>
>
>
>
>
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