I am reading the following paper: https://onlinelibrary.wiley.com/doi/full/10.1111/1756-2171.12113
The paper attempts to estimate the elasticity of pharmaceutical innovation (measured by # of new drugs introduced in a given time period) to expected future market size (measured by expected lifetime revenue). The authors use instrument variables Poisson regression in order to come up with a value of 0.23 for the elasticity.
My question is in the interpretation of this number (assuming that the authors have done their identification properly). Specifically:
- Assuming the price-innovation curve is not isoelastic (that is, it doesn't have a constant elasticity of 0.23 at all points), is it appropriate to use the elasticity when forecasting declines in market size of up to 30-40% (or any really big #)? In essence, if I ask: "if market size falls by 40%, would the number of new drugs fall by 40 * .23 = 9.2% as predicted by the elasticity? Or is the change in market size too large to use the one estimated elasticity as an estimate.
- Following up on 1, what would happen if I reduced market size by 100%? Intuitively, if I reduced a product's market size to 0 from its current value, the number of new drugs launched to that market of 0 size should be 0. But using the value of .23 would seem to indicate that the number of new drugs would only fall by 23%, which seems strange.
- What if the innovation-market-size curve is isoelastic, how would my answers to 1 and 2 change if at all?
- Using a regression approach to estimate elasticity, is it even possible to know whether the full curve is isoelastic or not?
Thanks so much in advance.