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Many of you will be familiar with the use of the log log linear regression model to estimate elasticity. I am in this situation where I can get zero demand, the dependent variable, which obviously prevents the unbiased use of this model (ignoring the fact that this approach is probably biased in many ways in the first place).

There are various "hacks" one could apply. Simple ones include, for example, to ignoring 0 demand observations or adding a small constant to the dependent variable. There are also other more sophisticated methods.

I appreciate that this is a bit of an open ended question, but I would love to know what people do in practise in these situations please? Thanks and please do not close this question without giving me and others a chance (-:

PS:

Elasticity in my case is defined as the delta %change of nights sold relative to the delta %change in price per night - see also arc/midpoint formula:

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Here Q = nights sold.

My challenge is that I have many possible sales dates with no sales of nights but nights capacity. Thus night sold = 0

Maybe I can simply ignore them? Guess in the standard retail setting we also have supply/stock but may not have sales ...

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  • $\begingroup$ What is the variance structure of the model? Is the distribution of the response really covering the entire range of the cloglog functional? If it is just in a local domain, there are approximations one could consider. $\endgroup$ Commented Mar 4, 2024 at 20:26
  • $\begingroup$ I am not 100% sure I follow. Could you please provide more details/links/paper? Thanks? $\endgroup$ Commented Mar 4, 2024 at 20:38
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    $\begingroup$ You appear to be asking how to compute something that is undefined. Could you therefore provide a clear definition of "elasticity" that applies to your case? $\endgroup$ Commented Mar 4, 2024 at 20:55
  • $\begingroup$ This sounds like a matter of function not being defined at zero. I would model $P$ and $Q$ first using probabilistic programming and generate posterior samples. Then I would condition/filter on those posterior samples being defined for this elasticity function. Then I would compute the elasticity on the filtered sample to get the posterior estimates of the this elasticity function. Then I would have a cup of coffee and go for a walk. $\endgroup$ Commented Mar 4, 2024 at 21:15
  • $\begingroup$ Thanks Galen. Can you please point me to an example. On the other hand I started to use Double Machine Learning but I cannot really use log log as last step after debiasing and denoising ... $\endgroup$ Commented Mar 4, 2024 at 21:18

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