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Say we have estimated a model: demand = a + b * price; where b represents the estimated point elasticity (assuming a log-log model).

Can we use this model to predict the demand in a new scenario where prices are 10% higher, then use these predictions to compute price elasticity for each data record based on the corresponding change in demand and price between the two scenarios?

M_M
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  • Price elasticity of what quantity? – eric_kernfeld Sep 07 '17 at 19:51
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    Assuming OP is asking about quantity demanded, the coefficient on price in a log-log model *is* the price elasticity of demand. The interpretation is that a 1% increase in price corresponds to a b% change in quantity demanded. To get the change in quantity demanded corresponding to a 10% increase in price, simply multiply b by 10 – Marquis de Carabas Sep 07 '17 at 20:01
  • Also see this post here: https://stats.stackexchange.com/questions/103201/how-to-interpret-log-log-regression-coefficients-for-other-than-1-or-10-percent – Marquis de Carabas Sep 07 '17 at 20:01
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    It's unlikely that this model actually estimates a demand curve without some strong additional assumptions. Any elasticity interpretation is contingent on price not being correlated with the error. You often get b>0 when you actually do this with market data. – dimitriy Sep 07 '17 at 20:16
  • Assuming that the model is well specified and the estimated elasticity is "correct". Does this approach appear reasonable (i.e. using the model to predict the demand, and then use this predicted demand to infer elasticity for each data record)? – M_M Sep 07 '17 at 20:27
  • This also depends on how you collected the data. If you do not have a dataset of consumers actually *observing* price changes, then you cannot infer a price elasticity as a causal effect. – Matthew Drury Sep 07 '17 at 20:28
  • This is true for a regression type model - not necessarily for a choice model (since consumers observe different prices for different products). For simplicity, let's assume that the data contain this info. – M_M Sep 07 '17 at 20:32
  • My question is concerned with the approach of obtaining elasticity based on the change in demand (prediction in the new scenario - base) wrt the change in price (new - base). Is this a reasonable approach given that these predictions are functions of the estimated point elasticity (b)? – M_M Sep 07 '17 at 20:37

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