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As a justification for estimating the regression, probit and the ordered logit models I consider an alternate specification. For all the previously estimated models I have assumed that each of the factors of the dual objective do not affect the other – in other words, the possibility of a

simultaneous system has not been accounted for. It could however be argued that the fans’ probability of attending the game is a function of the amount spent for the ticket and vice versa. To rule out this possibility I estimate a simultaneous system using a standard two-stage

estimation process. Because there is a binary and a continuous dependent variable, care must be taken in estimating the standard errors (Maddala 1983, pp 244-245). Fortunately, Keshk (2003) has recently developed a Stata program (CDSIMEQ procedure) that implements the two stage probit least squares (2SPLS) procedure and corrects the standard errors.

In the first stage, I regress the two dependent variables (‘net dollars’ and ‘attend game’) on a set of exogenous variables. In the second stage, the fitted variable for a given dependent variable is used as the exogenous variable for the other dependent variable. In particular, I use the first-stage regression to estimate net dollars*, the fitted value of the ‘net dollars’ variable. Then, in the second stage probit, it is analyzed whether net dollars* is significantly related to the ‘attend game’ variable. To identify the simultaneous system I include the “units bid on”

variable34. I estimated the simultaneous system with (a) the entire sample and (b) with individual

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Note that buying one forward as opposed to ten forwards (on a given team) influences the amount of money spent (and therefore the ‘net dollars’ variable) but does not increase the probability of attending the game.

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models for the team- and game-based fans. The results of the CDSIMEQ procedure indicate that the system is not simultaneous.

3.6 CONCLUSION

This chapter gives us a better understanding of the factors that affect fans’ decision- making in ticket markets. Accounting for fan heterogeneity, I allow fans to have different objectives in this market and consequently estimate different models to understand their behaviors.

An ordered logit model that parses out the effects of risk minimization and cost reduction is estimated for game-based fans; a regression model that identifies cost reduction strategies is estimated for team-based fans. The question of whether conventional wisdom on risk

management from financial markets can be applied to consumer markets is addressed. Some of the results from the finance literature do carry through. Consistent with the idea of diversifying one’s portfolio in financial markets, it is demonstrated that it is a good strategy for fans to buy forwards of many unique teams (to increase their chances of attending the game). Further, using a short-term indicator of performance (seeing if the team performs better at the week of purchase compared to its performance in the previous week) as a strategy to ‘pick’ the right teams does not pay off for game-based fans; it does seem like a good strategy for team-based fans who want to decrease their out-of-pocket expenses. More long-term performance measures should be used to guide buying decisions. Interestingly, heeding expert forecasts does not seem to be a good strategy for game-based fans.

The sports market setting used was for various reasons. Firstly, in this context the two forces at play (maximizing the probability of attending the game while minimizing the cost) can be clearly seen. Further, given that it is known which teams made it to the final game in the

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previous years I have the unique ability to classify fans’ transactions as being ‘good’ or ‘bad’. Consumers tend to have dual objectives (of maximizing their chance and minimizing their cost) in other environments with market-uncertainties as well. For instance, till recently, there was uncertainty regarding which format of DVD (HD or Blue ray) would emerge the winner. As of February 2008 Toshiba dropped out of the HD race leaving the market for Sony’s Blue ray partly because the fight between the two formats was keeping many consumers out of the market. According to a technology analyst “..consumers had held off investing in the latest recorders and players because they didn’t know which format would emerge dominant” (Kageyama 2008). In this market, before the uncertainty was resolved, consumers would have faced a similar dilemma - to pick the ‘right format’ to invest in while simultaneously seeking to minimize costs. Our methodology could be used to study the factors that would satisfy consumers’ dual objectives in such settings.

There are many interesting directions for future research even in the sports market context. For example, it would be interesting to study the value of having similar teams in a portfolio. Finance literature suggests a low correlation among portfolio holdings can help. The is because when one of the investments does not perform well the rest of the portfolio can remain balanced. In the context of sports teams, similarity could, arguably, be a function of which

conference the teams belong to. It is unclear that in a highly volatile market that operates for less than twenty-two weeks in a year, the recommendation of a dissimilar portfolio would continue to hold. Another issue of interest is to study what causes the difference in the amount paid by ‘successful’ fans (those who eventually attend the game). One could compare the effectiveness of strategies such as ‘buy and hold’ versus ‘buy and sell when team is not performing well’. While reselling a forward clearly helps the fan offset the total amount spent, given that there is a

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tradeoff in not holding the ‘right’ team until the end, it is unclear which strategy will be

preferred. Finally even though I used existing procedures to estimate the simultaneous models, a new procedure needs to be developed to be able to cluster standard errors in a system with a binary and a continuous dependent variable. Because clustering for standard errors cannot be properly accounted for in this setting it is recognized that the significance of some of the independent variables could be understated (Chaney et al 2007).

CHAPTER 4:

CONSUMER FORWARDS: THEORY AND EMPIRICAL APPLICATION