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st: Unit roots in non linear regression models


From   Johannes Muck <Johannes.Muck@dice.uni-duesseldorf.de>
To   statalist@hsphsun2.harvard.edu
Subject   st: Unit roots in non linear regression models
Date   Thu, 10 Feb 2011 12:15:42 +0100

Dear Stata listers,

I would like to estimate a nonlinear regression model of the form

y_it = a_i*(1 - exp(-b_i*t))

whereby 

a_i = exp(a1*x1 + a2*x1^2 + a3*x2 + a4*x3)

and

b_i = b0 + b1*z1 + b2*z2


The economic interpretation of the model is as follows: y_it denotes company
i?s market share in period t, a_i denotes company i?s long-term market
share, and b_it represents company i?s speed of convergence towards its
long-term market share.
y_it is observed for 129 companies for 63 periods on average. 

I tested whether each of the 129 time series exhibits a unit root using the
command 

?by company, sort: kpss y? 

the test strongly suggests that most of the 129 time series exhibit a unit
root.

I have two questions:

1) Can standard unit-root tests be applied although I am estimating a
nonlinear model?

2) Is there a possible remedy for the non-stationarity of y_it? From my
intuition I would say that using first-differencing will be no use in the
nonlinear case.

Thanks,

Johannes Muck
Düsseldorf Institute for Competition Economics (DICE)


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