A model explaining attendance

3.3A model explaining attendance

The survey on the impact of temperature, winning percentage and venue quality indicate that temperature matters, after all ice hockey is played indoors, and the relationship might not be equal to what has been found with outdoor sports events. To the contrary: when the temperature is high especially occasional spectators have other, substitute alternatives (outdoor activities) and that might diminish attendance. Winning percentage and brand equity are associated and they should have a positive impact on attendance. Since most spectators are male, venue quality should have less importance and it is not considered as an explanatory factor.

Based on the literature survey consider a consumer whose preferences are represented by utility function U, which has ice hockey games x, the subjective quality expected before the actual consumption decision s, and other goods consumption y as arguments. The subjective quality of each game for each consumer depends on previous personal consumption experiences and public information. This public information can be a prognosis about the temperature in evening and about weather conditions in general and about the earlier success of the home team.

(3-1) U = U(sx,y)

The wealth (labour and non-labour incomes) constraint is:

(3-2) px + y = W

where the other consumption prices are normalized to one and the price of the ice hockey game is p. The Lagrangian of the maximization of the consumer utility subject to the wealth constraint is

(3-3) L = U(sx,y) + λ(px + y - W)

The interior solution is then:

(3-4) U_x = λp

(3-5) U_y = λ

in addition to wealth constraint. The solution indicates that the ratio of the marginal utilities of ice hockey game consumption and other consumption is equal to price ratio.

Based on Bauer, Sauer and Schmitt (2004) and Coates and Harrison (2005), it is plausible to assume that interest (i.e. the expected utility) towards the game is higher when the home team has won the previous games. Both points per game from the beginning of the season and points from the last three games are suitable empirical measures for the winning ratio. Lévy-Garboua and Montmatquette (1996) model the expectations s are individual and based on past experience: s_it^t-1 = E_t-1(s_iτ) for the forthcoming period τ (τ=t, …T) conditional on the knowledge in t-1. Lévy-Garboua and Montmatquette also acknowledges that new consumption experience of the game x reveals a more accurate assessment of quality:

(3-6) s_it^t = s_it^t-1 + ε_it

irrespective of the fact whether the spectator has been looking at the game really or not since the public information sharpens also the assessment. After this knowledge the spectator revises his expectations in an adaptive manner depending on success in last and previous game with weight m_i and puts more weight on recent knowledge by forgetting at a constant rate δ_i > 0:

(3-7) s_i,t+1^t = (1- δ_i)[(1-m_i)s_it^t-1 + m_i s_it^t] = (1- δ_i)[s_it^t-1 + m_i ε_it]

(3-8) s_iτ^t-1=(1- δ_i)^τ-ts_it^t-1 τ =(t, …, T)

The subjective qualities depend on all previous experiences and public information but the recent knowledge has more weight. Thus the learning by consuming approach (Lévi-Garboua and Montmarguette 1996), current consumption does not have any direct impact on the utility coming from future consumption since experience only has a role of revealing the subjective preferences of the consumer. The rational addiction approach (Stigler and Becker 1977) is consistent with the forward-looking behavior since consumers are willing to sacrifice current utility to obtain larger utility in future due to larger cultural capital (S-B definition) accumulation. The learning by consuming approach is compatible with the heterogeneity of tastes and the independence of individual choises and it allows for differentiation of cultural goods (Seaman 2006, 444).
In the learing by consuming approach a general constant marginal utility for wealth demand functions can be derived from the solution of the optimization model:

(3-9) s_it^t-1x_it = F_i(p,y_i,λ,δ_i).

Since bigger wealth (incomes) allow a bigger consumption, it is reasonable to assume that also the ice hockey attendance increases by higher wealth. This is verified in several studies (Kahane and Shmanske 1997, Depken 2000, Coates and Harrison 2005, Coates and Humphreys 2007). However, a negative income elasticity has been found in several studies as outlined in the previous chapter. The literature on ice hockey game attendance has showed that the consumption varies according to team or game specific factors (GSF), time specific factors (TSF) which are connected to spectator expectations, s_iτ^t-1.

Another type of approach is to apply a perpetual inventory method. Expectations is current expectations and accumulated past expectations

(3-10)

where is accumulated expectations and is expectations in current period with depreciation rate Expectations stock is based on an estimate of the initial closing capital stock in the start of the ice hockey season. We assume a constant growth rate of success, , before the season starts. Back extrapolating yields:

(3-11)

with for capital formation of the current year. Given the general cumulative definition of the closing stock in (9) we can apply the following equation to calculate the initial stock:

(3-12) .

is the (constant) depreciation rate and is the growth rate of expectations in the years preceding the initial year, which can be positive or negative. Applying the sum formula for a geometric row leads to

(3-13) .

where is an estimate of the starting value . In theory, T should be infinite; for practical purposes it can be set to some positive number, like 100. The fixed effects approach that estimates the team specific constant term ά_i is suitable method for evaluating this perpetual inventory expectations model.
The solution to the general utility maximization model postulates that the demand for an ice hockey game and therefore attendance depends on the price of the event (p), wealth (W), forgetting related variable (δ) as well as game and time specific variables. Consider a model to be estimated to explain ice hockey games attendance (ATT):

(3-14)

H1a: Ice hockey game attendance should have a fairly low price supporting it being related to univore consumption pattern where the spectators do not consider other leisure activities substitutes.

H1b: The real cost related to the travel expenses are separately controlled. Since part of the travel expenses can be measured by the geographical distance between the home team and the visitor, the distance measure should be negative. This reduces the bias in the price elasticity.

H1c:. Wealth has an impact on demand for ice hockey game attendance and inclusion of this variable reduces the bias in the price elasticity.

H4a: Wealth measured by households’ annual incomes in the region has a negative impact on attendance.

H4b: Since the income variable is too rough, additional monthly variable for more detailed changes in household income changes or expectations is used to reduce the possible bias. The consumer confidence index (CCI) separately for men (CCIM) and for women (CCIM) is used also for robustness checks as well as the regional (Nuts-4 level) unemployment ratio is a proxy for business cycle that should have a negative impact on attendance.

H5: Weather conditions, measured as the temperature outside should have some impact on attendance.