I was recently made aware of data on the top grossing concert tours in America in the previous decade (hat tip to Mark J Perry).These data are easily read into statistical software where one can then generate an average price as revenue divided by tickets. Plot these and you get what might look like a demand curve.
To get something like an elasticity from this, one would typically take logarithms and regress one against the other. In this case, regressing ln(tickets) against ln(price) yields an elasticity estimate of about -0.5 but regressing ln(price) against ln(tickets) yields an elasticity estimate of about -2.0. If you were going to make pricing decisions based on these elasticity estimates, you might want a bit more precision than this. So what went wrong?
- Are these tours representative of other tours? Many applications of such an analysis would apply the estimate to another setting. For example, one might want this to inform pricing for bands outside of the to 50 or tours in other countries. It is probable that the demand for these mega-stars differs from the demand for up-and-coming bands or in for tours in different locations. But we don't really know how it differs.
- Does the demand curve differ across these tours? These data points may not be on the same demand curve. There could be differences in locations, production values, etc. that are also affecting the demand. It is likely that, were these factors included in the analysis, they would affect the elasticity estimates. Typically, one needs to collect data on these other factors affecting demand.
- Do important assumptions of regression analysis hold? This is subtle but it is key. Often, demand differs across observations in ways that we might recognize but are not able to measure. It is likely that some artists choose to tour less because there is so much demand that they get a big enough windfall from very few events. (For example, the point in the upper left is for Barbara Streisand who reportedly suffers stage fright.) Regression analysis assumes that the error terms are independent of the explanatory variables. But if artists with greater unobserved drawing power do not have to tour as much, this is violated. More generally, prices and quantities are affected by profit maximization which depends on unobserved variation in demand. In almost all cases, because the demand varies in ways that we do not observe, simple elasticity estimates will be biased. If managers do not know this, they might be lulled into false precision due to the apparent sophistication of regression analysis.
There are other empirical concerns as well and there are methods meant to address each one of them. However, they take more than a few weeks in a Managerial Economics class to learn. I have learned many of them only after a long career. (I joke with MBA students that they can hire me to do this. But because I am both slow and expensive, I am usually only hired for litigation where speed and cost do not seem to matter.)
Most of these estimation concerns are greatly alleviated by well-run experiments. These can yield quick, cheap and precise estimates of the important underlying parameters. And experiments in business are becoming so much more popular that they will largely replace regression analysis for these applications.