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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

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

-----Original Message-----
[] On Behalf Of Sinan Aral
Sent: Sonntag, 30. September 2007 21:38
Subject: st: Estimating Systems with Both Linear and Non linear

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 

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).



Sinan Aral
Assistant Professor, NYU Stern School of Business.
Research Affiliate, MIT Sloan School of Management.
Personal Webpage:
SSRN Page:

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