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Math Help - Create model to be estimated by least squares regression

  1. #1
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    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
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  2. #2
    MHF Contributor matheagle's Avatar
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    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?
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  3. #3
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    Quote Originally Posted by matheagle View Post
    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



    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
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  4. #4
    MHF Contributor matheagle's Avatar
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    \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.
    Last edited by matheagle; November 23rd 2009 at 10:29 PM.
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  5. #5
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    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?

    thanks so far! I really want to be able to fully understand this.
    Last edited by Billy Gordon; November 23rd 2009 at 12:22 PM.
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  6. #6
    MHF Contributor matheagle's Avatar
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    Quote Originally Posted by Billy Gordon View Post
    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?

    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
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