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# st: RE: Estimating Systems with Both Linear and Non linear Equations

 From "Randy Akee " To Subject st: RE: Estimating Systems with Both Linear and Non linear Equations Date Mon, 1 Oct 2007 09:27:28 +0200

```Hi,
I found this faq posting helpful for me in solving non-linear equations,
using the nl command in stata:

http://www.stata.com/support/faqs/lang/nl.html

-----Original Message-----
From: owner-statalist@hsphsun2.harvard.edu
[mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Sinan Aral
Sent: Sonntag, 30. September 2007 21:38
To: statalist@hsphsun2.harvard.edu
Subject: st: Estimating Systems with Both Linear and Non linear
Equations

Hi All,

I am interested in estimating a system of equations in which one
equation is linear and one is non linear. I am trying to estimate a
traditional Cobb Douglas production function augmented with a binary
technology adoption variable. The goal is to estimate the output
elasticity of technology adoption controlling for traditional factors.
However, technology adoption is likely endogenous, so I would like to
estimate adoption and productivity simultaneously. One problem with this

is that the adoption equation is non linear with a binary dependent
variable and the production function is linear. I'm not sure whether
reg3 allows me to specify the functional form of the equations or not.
Can anyone make suggestions regarding how to implement such estimation
in STATA and also point me toward literature that has estimated a system

of equations describing the endogenous impact of technology adoption on
productivity?

Basic setup is as follows.

y = f(K, L, Tech. Adoption)
Adoption = f(Y,K,L)

Note the above is clearly basic. Several assumptions and restrictions
could be layered on top of this or more equations could be added. I am
really after advice on combining linear and non linear models in the
same system (or on stata commands that allow me to specify the
functional form of certain equations in a system using reg3).

Best

Sinan

--
Sinan Aral
Assistant Professor, NYU Stern School of Business.
Research Affiliate, MIT Sloan School of Management.
Personal Webpage: http://web.mit.edu/sinana/www
SSRN Page: http://ssrn.com/author=110270

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```

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