# Should a Price Elasticity of Demand model exclude items that sold out or marked down from the original price

Consider a Price Elasticity of Demand model built with linear regression to estimate the Percent Change in Quantity Demanded given a Percent Change in Price specifically for specialty items which have a selling period of only a few weeks in all stores.

Data is aggregated based on shared item "Categories" (eg both winter coats and swim trunks are considered Clothing), each store's total sales units for the item's selling period is known rather than daily sales, items that sellout at a store will not be replenished, the demand curve is convex, and elasticity is constant along the curve.

$$Q=aP^{-b}\\ E=(dQ/dP)*P/Q\\ E=-abP^{(-b-1)}*(P/Q)\\ E=b\\$$ Because I'm using the log-log form of linear regression, the slope coefficient of the model is the estimated elasticity. If a store sells out of an item before the end of the item's selling period, I think it would result in a more positive slope coefficient and appear more inelastic than actual. If a store marks down the price of an item before the end of the item's selling period, I think it would result in a more negative slope coefficient and appear more elastic than actual.

If an item is sold out at one store or if its price is marked down during its shelf-life should the item be excluded from the data set for that particular store? If the data is removed, how would elasticity be affected?