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Please help with a limit calculation

  1. Nov 9, 2013 #1
    Hi everyone! I have (I think a major) problem so I'm hoping you could give me some useful advice.
    I am working on my thesis where I am statistically estimating this type of equation:

    dlny=α+β1*dlnx+β2*dlnz+β3*dlnx*dlnz

    where dln stands for differencing a natural logarithm of the variable, eg

    dlnz=ln(zt)-ln(zt-1)

    so basically the approximation of the growth rate of x.

    After I estimate this equation, I get certain values for α and for the βs and I have this nice equation.

    My research question is:
    What will be the marginal effect of an increase in dlnx on dlny if z doesn't exist (ie it is zero).

    Obviously, the derivative of dlny with respect to dlnx is

    ∂lny/∂lnx=β13*dlnz

    and now I need to calculate how much that is when z (not dlnz) doesn't exist.

    Obviously, I have problem since dlnz in this case isn't defined:

    dlnz=ln(0)-ln(0)

    Is there any way I can manipulate mathematically my problem in order to get an answer to my question??

    Thank you very much in advance!
     
  2. jcsd
  3. Nov 9, 2013 #2
    * so basically the approximation of the growth rate of z
     
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