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I'm estimating demand and calculating price elasticity using logistic regression.

In logistic regression with level price, elasticity is $$ \alpha*price*(1-share)$$ while if one uses log of price, elasticity is $$ \alpha * (1-share) $$ I've noticed that if I estimate regression using level price, my elasticities vary highly within products. However, when I use log of price, elasticities for different products are very close to each other. I understand that it is because I have 22 products, and thus shares are very small and elasticities are mostly driven by $\alpha$.

Could someone please explain me on a high level why this happens. And should I use the regression with level price if I do not trust the elasticity estimates of the log price regression?

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  • $\begingroup$ I am not sure if your derivation is correct. See here for the log price case. The levels elasticity derivation is pretty similar. $\endgroup$ – Dimitriy V. Masterov Aug 6 '18 at 20:39
  • $\begingroup$ My derivation is correct, elasticity is dQ/dp * p/Q, not just dQ/dp. $\endgroup$ – Daria Aug 7 '18 at 21:20

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