Coefficient Restrictions

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Amaziah
Posts: 18
Joined: Wed Apr 22, 2015 3:22 pm

Coefficient Restrictions

Postby Amaziah » Fri Apr 24, 2015 7:49 am

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.

startz
Non-normality and collinearity are NOT problems!
Posts: 3497
Joined: Wed Sep 17, 2008 2:25 pm

Re: Coefficient Restrictions

Postby startz » Fri Apr 24, 2015 7:54 am

Amaziah wrote: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.)

Amaziah
Posts: 18
Joined: Wed Apr 22, 2015 3:22 pm

Re: Coefficient Restrictions

Postby Amaziah » Fri Apr 24, 2015 8:34 am

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?

startz
Non-normality and collinearity are NOT problems!
Posts: 3497
Joined: Wed Sep 17, 2008 2:25 pm

Re: Coefficient Restrictions

Postby startz » Fri Apr 24, 2015 8:35 am

Code: Select all

ls (y-1*x1) c x2 x3.

Amaziah
Posts: 18
Joined: Wed Apr 22, 2015 3:22 pm

Re: Coefficient Restrictions

Postby Amaziah » Fri Apr 24, 2015 8:51 am

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.

startz
Non-normality and collinearity are NOT problems!
Posts: 3497
Joined: Wed Sep 17, 2008 2:25 pm

Re: Coefficient Restrictions

Postby startz » Fri Apr 24, 2015 8:56 am

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.

Amaziah
Posts: 18
Joined: Wed Apr 22, 2015 3:22 pm

Re: Coefficient Restrictions

Postby Amaziah » Fri Apr 24, 2015 9:04 am

Thank you very much. You have been extremely helpful.

Amaziah
Posts: 18
Joined: Wed Apr 22, 2015 3:22 pm

Re: Coefficient Restrictions

Postby Amaziah » Fri Apr 24, 2015 9:44 am

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?

startz
Non-normality and collinearity are NOT problems!
Posts: 3497
Joined: Wed Sep 17, 2008 2:25 pm

Re: Coefficient Restrictions

Postby startz » Fri Apr 24, 2015 9:52 am

Amaziah wrote: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

Code: Select all

(.5+.5*exp(c(2))/(1+exp(c(2))))=0

Amaziah
Posts: 18
Joined: Wed Apr 22, 2015 3:22 pm

Re: Coefficient Restrictions

Postby Amaziah » Fri Apr 24, 2015 10:13 am

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.

startz
Non-normality and collinearity are NOT problems!
Posts: 3497
Joined: Wed Sep 17, 2008 2:25 pm

Re: Coefficient Restrictions

Postby startz » Fri Apr 24, 2015 10:17 am

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.

Amaziah
Posts: 18
Joined: Wed Apr 22, 2015 3:22 pm

Re: Coefficient Restrictions

Postby Amaziah » Fri Apr 24, 2015 4:18 pm

Okay thanks. I'll look into that.


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