Conclusion
In this paper, the empirical literature on the demand for professional team sports has been discussed. Both the traditional short-run emphasis of demand studies and their main findings are outlined. Recent developments in demand estimates for the long run are then discussed. The main concern of the paper hinges on the appropriate interpretation of the diversity of findings in the literature. This paper argues that the more recent long-run studies should be emphasised because of their appropriate econometric methodology, but also because they reflect a changed emphasis from aggregating or averaging results across clubs over short-time periods. In this respect this paper argues that the determinants of demand are still not well understood, despite the many studies that have been conducted. In contrast a new research agenda is required that allows researchers to explore both the long-run and short run determinants of demand of both a sporting and economic nature simultaneously. Moreover, regressions should avoid averages over clubs. The cost of this approach is the time and expense of the researcher in constructing a data set. The benefit would be results that are more useful to the sporting commentator and regulator than is currently available.
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1 If we take the demand model A t=B1P tB2Y tB3 where A refers to attendance, P is price and Y is income, 't' is the index of observation, i.e. either time period or subject, and B i are coefficients then the demand model is non linear. This is because the coefficients are powers (this type of model is very common in empirical studies). This model cannot, therefore, be estimated by a linear regression. In contrast, we can estimate a linear regression model relating attendance to price and income if we use the logarithm of the values of the variables. Specifically, this implies that we have changed the model to LogA t=B 1+B 2LogP t+B 3LogY t. The coefficient estimates from this model will be elasticities. This is because changes in logarithms are proportionate changes. Moreover, the interaction between the variables is removed. Consequently, for example, B 2 would measure the slope of the logarithmic model Log A t/Log P t which will be the proportionate change in attendance resulting from the proportionate change in price - the price elasticity of demand. Note that the slope in the original non-linear model will not be ∂A t/∂P t=B 2 but a more complicated function based on the interaction of the variables i.e. ∂A t/∂P t =B 2B 1P tB2-1Y tB3.
2 Interestingly this is not the case with time-series econometrics. As DeMarchi and Gilbert’s (1989) volume on the development of identification in econometrics notes, concern over the issue of multicollinearity as a form of model specification versus a problem of data, that dates back to the origins of the discipline, has been discussed in the context of the development of cointegration analysis.
3 As discussed in the text, time-series econometrics has produced a meaningful classification system based on the data. Of course this is in terms of establishing the shortrun and long run effects of variables. Factor analysis could play a similar role in cross-section studies where the number of independent variables is much larger and getting increasingly so.
4 In their 1996 study, the authors included distance in their regressions in a quadratic manner. The results suggest a minima which implies that local derbies are important but that committed fans do not let distance put them off attending fixtures.
5 Another Association football example is Stoke City one of the author’s own city teams!
6 In probability terms uncertainty of outcome could be measured, for example, by pi(1-pi) for the ‘ith’ team’s fixture where p refers to the probability of a win. Uncertainty of outcome will be at a maximum where p=0.5.
7 A slope dummy variable is constructed by assigning, for example, a value of ‘1’ to the variable if it is felt that the result of the fixture is increasingly uncertain, and ‘0’ otherwise. The dummy variable is multiplied by the betting-odds variable and this composite variable included in the regression. This implies that a selection of observations on betting odds associated with increasing uncertainty of outcome are entered into the regression analysis again. If the coefficient on this variable is positive and significant then one has identified uncertainty of outcome.
8 Note that the regression is still linear in the parameters and, as such, ordinary least squares can still be employed. This approach can thus be thought of as trying to fit a line of best fit to the relationship between match results and squared betting odds. Intuitively plotting this graph would appear linear unlike the graph drawn between attendance and betting odds.
9 These features of teams and players are usually measured with dummy variables. For example, the presence of an international player in a match or team would be scored ‘1’ or ‘0’ otherwise.
10 For those unfamiliar with cricket as a sport, rainfall very often stops play. Accordingly one would expect a negative association between rainfall and attendances
11 This is not because the authors feel that female attendance is unimportant per se but simply that the data reflects the historical nature of the data which focussed on collecting male statistics. In this respect the number of members of the armed forces are also included as the study covers the period of the second-world war, the Korean war, and periods of national service.
12 In statistical terms this means that the equations were estimated simultaneously because some of the influences on the variables were seen to be common. Estimating the equations simultaneously increases the (statistical) efficiency of the estimates.
13 The reason lagged ‘level’ terms are involved is because a regression of this periods attendance cannot be done on this period’s attendance because this would produce perfect multicollinearity and the regression would fail.
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