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Coefficient Restrictions
Posted: Fri Apr 24, 2015 7:49 am
by Amaziah
Is it possible to restrict a coefficient to be a specific value or between a range of values? For example:
Y=a+a1X1+a2X2+a3X3+e ,
where I want the parameter estimate, a1, to equal 1.
I know how to test for linear restrictions, but not how to impose them.
Re: Coefficient Restrictions
Posted: Fri Apr 24, 2015 7:54 am
by startz
Is it possible to restrict a coefficient to be a specific value or between a range of values? For example:
Y=a+a1X1+a2X2+a3X3+e ,
where I want the parameter estimate, a1, to equal 1.
I know how to test for linear restrictions, but not how to impose them.
Wherever you have "a1" in the formula, type in "1" instead. (A range of values isn't so easy.)
Re: Coefficient Restrictions
Posted: Fri Apr 24, 2015 8:34 am
by Amaziah
Thank you. I am used to typing the equation in the following manner:
ls y c x1 x2 x3.
Am I able to impose this restriction in this format?
Re: Coefficient Restrictions
Posted: Fri Apr 24, 2015 8:35 am
by startz
Re: Coefficient Restrictions
Posted: Fri Apr 24, 2015 8:51 am
by Amaziah
Thank you very much. Where could I learn to restrict x1 to a range a values? For example, I want x1 to fall between .5 and 1.
Re: Coefficient Restrictions
Posted: Fri Apr 24, 2015 8:56 am
by startz
There is no general procedure for doing this in EViews. Sometimes you can figure out a translation of the parameter that accomplishes what you want. For example, substitute for a1
a1=.5+.5*exp(b1)/(1+exp(b1))
If b1 = -infinity, this gives you .5. If b1 equals infinity, this gives you 1.0. So the unconstrained value of b1 maps into the constrained value of a1.
Re: Coefficient Restrictions
Posted: Fri Apr 24, 2015 9:04 am
by Amaziah
Thank you very much. You have been extremely helpful.
Re: Coefficient Restrictions
Posted: Fri Apr 24, 2015 9:44 am
by Amaziah
Would I estimate the model in the following manner:
ls (y-.5+.5*exp(b1)/(1+exp(b1))) c x2 x3
Is there any way to do this so the a1 (or the translation of a1) will be listed as a independent variable in the results?
Re: Coefficient Restrictions
Posted: Fri Apr 24, 2015 9:52 am
by startz
Would I estimate the model in the following manner:
ls (y-.5+.5*exp(b1)/(1+exp(b1))) c x2 x3
Is there any way to do this so the a1 (or the translation of a1) will be listed as a independent variable in the results?
Because you need to have explicit coefficients, the EViews syntax is probably something like
Code: Select all
ls y = c(1) + (.5+.5*exp(c(2))/(1+exp(c(2))))*x1 + c(3)*x2 + c(4)*x3
You can find out the value of "a1" in a kludgey way by doing a Wald test for
Re: Coefficient Restrictions
Posted: Fri Apr 24, 2015 10:13 am
by Amaziah
Okay. I should have been more specific from the beginning because I am proving not skilled enough to apply your solutions into my model.
I am trying to restrict a price variable based on the assumption that the own-price elasticity of demand is close to one, adjusted down for the proportion of net revenues from a specific product.
This is done because of a lack of remedies for endogeneity associated with the price variable (there are no acceptable instruments).
On the surface, I thought this would entail restricting the price coefficient to (-1+proportion of net revenues). I am unsure how to apply this formula in eviews.
I apologize for including this information earlier, but I didn't think it was necessary.
Re: Coefficient Restrictions
Posted: Fri Apr 24, 2015 10:17 am
by startz
You want to estimate a least squares problem subject to inequality constraints. I don't think EViews can do this. It can be done in a program like Matlab with a little work.
Re: Coefficient Restrictions
Posted: Fri Apr 24, 2015 4:18 pm
by Amaziah
Okay thanks. I'll look into that.