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This question follows from the previous question on multiplicative BIAS in cross-price elasticity, but I think it deserves its own space.

I have scanner data from a small store branch belonging to a big drugstore retail chain (containing quantities purchased and prices only). I try to measure (among other things) the cross-price elasticity by very simple regression:

$$ln(x_i) = \beta_0 + \beta_i ln(P_i) + \sum_j^J \beta_j \cdot ln(P_j) + \epsilon$$

Where $\beta_j$ denotes the cross-price elasticity between product $i$ and product $j$.

Based on the basic intuition behind supply-demand models, I would expect that prices are, to some degree, endogenous due to simultaneity, when prices are a function of demand and demanded quantities are function of prices. However, when I compared my results with results from other methods, I found out as if I had no bias at all (at least the sign and relative magnitude of cross-price elasticity was ok). As 1muflon1 proves, though, this does not need to hold in general.

Therefore, the logical conclusion may be that the reason why I got the results I got come from the data themselves. If we consider the auxilary regression:

$$ln(P_j) = \gamma_0 + \gamma_1 ln(x_1) + \dots + \gamma_m ln(x_m) + u$$

In my case, I would expect $\gamma_1 = \gamma_2 = \dots = \gamma_m = 0$, as if the prices were, in fact, exogenous. The explanation I have in mind is that the store branch is small and thus cannot act as a price-setter, resulting in prices being independent of demand. However, the retail chain is relatively big (for my country), so I would expect the opposite to be true.

The question:

  • Are retail chains (drugstores), in general, just price-takers?
  • Is there a literature describing the insignificance of simultaneity bias in retail?
  • Can prices in a single store be independent of demand due to central policy of said retail chains and is there a literature for it? (i.e., if demand in a region with this store dramatically increases, the retail cannot locally increase its prices as it can do so just globally)
  • If so, how this would propagate into data? (i.e., they are biased on global level but not local level, what am I observing then)
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