# Creating a model for prices including supply

I'm working on modeling secondary market ticket prices for sporting events, but the issue I'm running into is that the model (a linear regression) assumes that more season ticket holders and more tickets on places like StubHub mean that the game is more desirable, and thus the tickets should be worth more. The problem is that one year has a significantly higher number of both due to increased team performance, so it thinks prices should be going up when the increased supply of tickets on the secondary market is actually driving prices down. Is there anything I can do to address this problem?

• What's your regression equation? Are you just using OLS for this one team? – Andy Jun 16 '14 at 22:09
• My model currently includes games out of first place, the season tickets for the game, webpage visitors, the month, the high temperature, the number of stubhub tickets, and the average face value of the tickets listed on stubhub. And yes, it's OLS for one team. – user3704120 Jun 16 '14 at 22:15
• Hey, just to get some feedback: did you look into the links I provided together with the answer? Was this helpful to you? – Andy Jun 17 '14 at 20:43
• Yeah I did, and it sent me looking for a lot of other stuff that I didn't know about, so it was pretty helpful. I ended up figuring out my problem (which just involved messing with my factors some), but this was still informative. – user3704120 Jun 18 '14 at 15:50
• That's good to hear. If you were satisfied with the answer you might consider accepting it which you can do by clicking on the check mark underneath the up vote/down vote button. Thanks! – Andy Jun 18 '14 at 15:58

## 1 Answer

To account for this outlier year you could include a dummy variable which equals 1 for this particular year and 0 for all others, like $$p_t = \alpha + X'_t \beta + \gamma d_j + \delta q_t + \epsilon_t$$ where $d_j$ is the dummy for the outlier year $j$, $X_t$ include observable characteristics of the team and other explanatory variables, and $q_t$ is the supply of tickets.

If the effect of the team performance lasted longer than just this one year, for instance if the team moved into a better league, then the dummy $d_j$ should equal 1 for all the years after the team moved to the better league. It's best to plot the time series of the ticket prices to see whether you have a regime shift (i.e. ticket prices went up temporarily or permanently because of the league change) or just a change in the slope (i.e. a structural break).

As a side note: I'm sure you're already considering this but given that it wasn't mentioned in the question I quickly wanted to touch on it to make sure. Both prices and quantity supplied are outcomes of an equilibrium relationship between supply and demand. This means they are simultaneously determined. Therefore you could re-write the above regression equation as $$q_t = a + X'_t\pi + \rho d_j + \theta p_t + \nu_t$$ which results in what is called simultaneity bias (slide 8).