For a large university, you are asked to estimate the demand for tickets to women's basketball games. You can collect time series data over 10 seasons, for a total of about 150 observations. One possible model is
IATT ENDt = β0(l + β1JPRICE, + β2WINPERCt + β3RIVAL + β4WEEKENDt + β5t + ut,
where
PRICE, = the price of admission, probably measured in real terms-say, deflating by a regional consumer price index. WINPERCI = the team's current winning percentage.
RIVAL = a dummy variable indicating a game against a rival. WEEKEND, = a dummy variable indicating whether the game is on a weekend.
The / denotes natural logarithm, so that the demand function has a constant price elasticity.
(i) Why is it a good idea to have a time trend in the equation?
(ii) The supply of tickets is fixed by the stadium capacity; assume this has not changed over the 10 years. This means that quantity supplied does not vary with price. Does this mean that price is necessarily exogenous in the demand equation?
(iii) Suppose that the nominal price of admission changes slowly-say, at the beginning of each season. The athletic office chooses price based partly on last season's average attendance, as well as last season's team success. Under what assumptions is last season's winning percentage (SEASPERCt-1]) a valid instrumental variable for I PRICEt?
(iv) Does it seem reasonable to include the (log of the) real price of men's basketball games in the equation? Explain. What sign does economic theory predict for its coefficient? Can you think of another variable related to men's basketball that might belong in the women's attendance equation?
(v) If you are worried that some of the series, particularly IATTEND and IPRICE, have unit roots, how might you change the estimated equation?
(vi) If some games are sold out, what problems does this cause for estimating the demand function?