I'm having trouble coming up with a way to estimate price elasticity for my ticket sales data. Tickets go on sale 15 days before the event, and demand increases as the event comes closer. Prices stay the same for the majority of this sales period, rising slightly in the last couple days. When sales are going particularly well, prices are pushed upwards, which is causing my issue. As demand is increasing, price is also increasing, making it difficult for me to come up with a realistic coefficient for price in any regression model.

I've looked into using instrumental variables, but I'm not sure if they apply in my situation. Because each event has a fixed capacity, ticket supply does not change, meaning there are no variables that influence supply. I've considered using the secondary ticket market as an approximation, but instrumental variables are difficult to find there as well. The supply of resold tickets and the amount of demanded tickets move almost perfectly together. Is there any way to isolate the influence of price in this situation? Let me know if data or further explanation would help.

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#### Best Answer

Well your problem, is the `Volume ~ Function(Price)`

and that Beta can give you the elasticity, but in your case `Volume`

is not only a function of `Price`

but also demand. I would solve the problem two ways:

`Volume ~ F(Price, Some Quantifier which is correlated to Demand that impacts demand irrespective of Price)`

For example Time, as time goes up Demand goes up- A log transformation on Y, i.e., demand, along with a log transformation on P, would give a price elasticity, as linear function of % change in demand with percent change in price. The Beta won't give the purest elasticity estimate, but will greatly reduce the noise, variability in Beta itself. Beta~N(u,sigma), sigma would be smaller.

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