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st: Estimating Systems with Both Linear and Non linear Equations

From   Sinan Aral <[email protected]>
To   [email protected]
Subject   st: Estimating Systems with Both Linear and Non linear Equations
Date   Sun, 30 Sep 2007 15:37:38 -0400

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).



Sinan Aral
Assistant Professor, NYU Stern School of Business.
Research Affiliate, MIT Sloan School of Management.
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