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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:

  1. 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.
  2. 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.
  3. What if the innovation-market-size curve is isoelastic, how would my answers to 1 and 2 change if at all?
  4. 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.

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