# Create model to be estimated by least squares regression

• November 22nd 2009, 02:28 PM
Billy Gordon
Create model to be estimated by least squares regression
I need to make a econometric model out of the following formula

It is the Cobb Douglas formula
Y= αK^β1L^β2

The question is, create a econometric model out of this formula, in such a method that it can be estimated by the concept of least squares regression.

I'm clueless atm (Crying)
• November 22nd 2009, 02:51 PM
matheagle
It looks like you need to take the logarithm to make this linear in the beta's.
Where is the error term and what is atm, a cash machine?
• November 23rd 2009, 01:32 AM
Billy Gordon
Quote:

Originally Posted by matheagle
It looks like you need to take the logarithm to make this linear in the beta's.
Where is the error term and what is atm, a cash machine?

I know what you mean with the error term, but that is not given. (atm is at the moment)

Just made a copy from the question

http://i48.tinypic.com/vsi64x.jpg

And what do you mean, take the logarithm to make this linear in the beta's?
The Formula has 2 variables, so it can't be linear right?

Uf, I wish I was a bit better in econometrics
• November 23rd 2009, 07:28 AM
matheagle
$\ln Y=\ln \alpha +\beta_1 \ln K +\beta_2 \ln L$

$Y^*=\ln Y$

$\epsilon=\ln \alpha$

$X_1=\ln K$

$X_2=\ln L$

THIS is LINEAR now.
• November 23rd 2009, 12:11 PM
Billy Gordon
I understand your pattern of thinking, thanks! LN and log are the same right?

And why does the formula have to be changed to a logarithm/or natural log in order to be estimated by the least squares method? Because basicly what I'm supposed to do, (i think), is just change the formulas in to Logarithms, and this way it can be estimated by the least squares regression, but why? is that? (Speechless)

thanks so far! I really want to be able to fully understand this.
• November 23rd 2009, 10:28 PM
matheagle
Quote:

Originally Posted by Billy Gordon
I understand your pattern of thinking, thanks! LN and log are the same right?

And why does the formula have to be changed to a logarithm/or natural log in order to be estimated by the least squares method? Because basicly what I'm supposed to do, (i think), is just change the formulas in to Logarithms, and this way it can be estimated by the least squares regression, but why? is that? (Speechless)

thanks so far! I really want to be able to fully understand this.

ln is log base e, but any base should work.
The idea is to make this LINEAR in the beta's