[R] Restricted Least Squares

[Mike Lonergan]

     > -----Original Message-----
     > From: owner-r-help at stat.math.ethz.ch
     > [mailto:owner-r-help at stat.math.ethz.ch]On Behalf Of Philippe Grosjean
     > Sent: 09 April 2002 09:23
     > To: Ahmad Abu Hammour
     > Cc: R-help at stat.math.ethz.ch
     > Subject: RE: [R] Restricted Least Squares
     >
     >
     >  > Hi,
     >
     > > I need help regarding estimating a linear model where
     > restrictions are
     > imposed on the coefficients. An example is as follows:
     >
     > > Y_{t+2}=a1Y_{t+1} + a2 Y_t + b x_t + e_t
     >
     > > restriction
     > > a1+ a2 =1
     >
     > > Is there a function or a package that can estimate the
     > coefficient of a
     > model like this? I want to estimate the coefficients rather
     > than test them.
     >
     > > Thank you for your help
     >
     > > Ahmad Abu Hammour
     >
     > You don't need something special. Just consider that
     >
     > a2 = 1 - a1 and replace it in your equation, which gives:
     >
     > Y_{t+2}=a1Y_{t+1} + (1 - a1) Y_t + b x_t + e_t
     >
     > Best,
     >
     > Philippe Grosjean


& it becomes really nice when Y_{t+1} is subtracted from both sides:

Y_{t+2} - Y_{t+1} = a1Y_{t+1} - Y_{t+1} + (1 - a1) Y_t + b x_t + e_t

Substituting

Z_{t+1} = Y_{t+1} - Y_{t}


then gives:

Z_{t+1} = -a2Z_{t} + bx_t + e_t

Which is unconstrained and much easier, unless I've entirely missed the
point.

Cheers,

Mike.


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