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  • Income Elasticity with Logit Model

    Hi,

    This is my model:

    Code:
    logit smoker lninc
    Where lninc, is the log transformation of the income variable. I want to find the income elasticity of smoking participation.
    Is the following code sufficient to calculate this value:

    Code:
    margins, eyex(lninc)
    Or is it more appropriate to use:

    Code:
    margins, eydx(lninc)
    Seeing as the income variable has already been log transformed.

    Would the correct interpretation of this elasticity be the "average income elasticity of smoking participation"?

    Thank you for any help, anyone can provide.

  • #2
    For elasticity of income, it would be -margins, eydx(lninc)- given that lninc is already the log transform of income. That said, are you sure you really want elasticity when your outcome is already a probability? So you would be getting a relative change in the probability of smoker corresponding to a relative change in income. That's perfectly legal, but it strikes me as odd and difficult for people to wrap their minds around. Usually with probability outcomes it is simpler to look at the absolute change in probability. That would be a semi-elasiticity of income, and you would get it from -margins, dydx(lninc)-.

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    • #3
      Dear all,

      I have two questions, which extend Aaron James'

      I am interested in the percentage change in the probability of a positive outcome when the treatment variable is binary. Consider, for instance, the impact of being in a "Grade 2" job on the probability of being a smoker. Here is my model:

      Code:
      use http://www.stata-press.com/data/r15/smoking.dta, clear
      generate smoker = (cigs > 0) if !missing(cigs)
      logit smoker gradd2, nolog
      To compute the relative change in the probability of smoker, I type:


      Code:
      margins, eydx(gradd2)


      On average, individuals in gradd2 jobs are 33.4 percent more likely to be smokers.

      Question 1:

      Theoretically, this quantity should be arrived at by estimating the relative change in predicted probabilities: dP/P = [L(a*1 - cons) - L(a*0 - cons)] / L(a*smoker - cons), where a is the coefficient on smoker, cons is the constant term, and L denotes the logisitc function. However, this does not seem to be the case:


      Code:
      margins, expression((1/(1+exp(-1*_b[gradd2]-_b[_cons])) - 1/(1+exp(-0*_b[gradd2]-_b[_cons])))*(1+exp(-gradd2*_b[gradd2]-_b[_cons])))


      Now, it appears that individuals in gradd2 jobs are 34.4 percent more likely to be smokers.

      So, the queston is: what quantity exactly does "eydx" estimate after "logit"?


      Question 2:

      I know re-run the model, but I treat my gradd2 dummy explicitly as a factor variable:

      Code:
      logit smoker i.gradd2, nolog
      Now, the "margins" command returns a different value (30.7 percent more likely):


      Code:
      margins, eydx(gradd2)


      Why is this the case?

      Thanks a lot!

      Luca J. Uberti




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