In correspondence with Dublin University Lawn Tennis Club (DULTC) in 1903 J.C. Parke declared 'with its[DULTC's] present prospects & energetic committee I can see nothing to prevent it becoming the foremost club in college.' The quality and quantity of membership in any athletic club are crucial in determining the club's success, just as 'the life's blood of [a country's] industrial engine is good old fashioned competition.' The purpose of this essay is neither to establish DULTC's ranking among Trinity College's athletic clubs nor to seek an explanation as to what motivates individuals to play tennis. My objective is to obtain an explanation, by application of microeconomic theoretical analysis, as to the considerable variation in student membership of DULTC from the academic years of 1978-79 to 1992-93. An explanation of this variation, (see chart below), in the quantity of members will be sought using econometric techniques, as significant variation in club membership determines club morale, the probability of competitive success, the financial status of the club and in essence the future existence of the club.
Chart 1
Explanatory Variables
Dublin University Central Athletics Committee (DUCAC) membership
DUCAC is a 'federal body composed of students, staff members, and graduates, established in 1919 by the Board of Trinity College to revive sport in the university after World War One.' To be officially recognised, a sports club must be affiliated to DUCAC. All affiliated clubs submit annual membership records and DUCAC have thus provided reasonably accurate records. The aggregated annual membership of affiliated clubs shall be the first explanatory variable, which shall henceforth be refered to as DUCAC membership (X1). A number of new clubs were affiliated during the investigated period. However, it is felt that their establishment did not lead to substitution away from DULTC, as DULTC's close substitutes, the badminton and squash clubs, were founded prior to 1978-79. Hence the year on year relationship between DULTC and DUCAC student membership is a priori expected to be positive.
Remembering R.H. Tawney's declaration that 'the most obvious facts are the most easily forgotten' it is evident that DULTC membership had some limiting influence. To represent this limiting force DUCAC membership was chosen as opposed to the student population of Trinity College. To postulate a positive relationship between DULTC membership and the College population, surely the only rational hypothesis, requires the assumption of a constant marginal propensity to join DULTC among all students. This assumption could possibly be analogous to the microeconomics assumption of a constant marginal utility of income, shown to be inconsistent with empirical evidence by P. Samuelson (1942). Empirical evidence from 1978-79 to 1992-93 shows that not only is the relationship not constant but that it is not even monotonic! i.e. given an increase in X1 it will always lead to an increase in the dependent Y variable (DULTC membership). Utilising DUCAC membership data merely requires the assumption that for students joining DUCAC their probability of joining DULTC is not negatively related to the number of students joining other athletic clubs.
The seven year period from 1983-84 to 1989-90 is of interest for two reasons. Firstly, during this period DULTC membership was extemely responsive to DUCAC membership, providing evidence of the strong positive relationship of the two. Secondly, it is a period of consistent decline in the number of students participating in sport during the 1980's, perhaps the converse to what one might have expected during the so called 'jogging decade'. One possible explanation is that, due to the high public profile of jogging, students associated sport with excessive commitment, personal effort, physical exhaustion and perhaps even pain, thus demand decreased.
Conformable Days
'Man whether civilised or savage is a child of nature, he is not the master of nature.'
The second explanatory variable taken is the number of conformable days per calendar year (X2). Where conformable days is the number of days per annum when snow, hail, and gales were not recorded at the meteorological station at Dublin Airport. One believes the number of conformable days provides a more realistic representation of students' incomplete knowledge of weather conditions than other measures would, such as mean values of rainfall, temperature or sunlight per annum. However the number of conformable days is still an idealised representation of students' evaluation of weather conditions.
The proposed relationship between DULTC membership and the number of conformable days is founded on the theoretical presumption that an economic agent's decision to consume a good or service is determined by the benefits, or utility, of consuming a particular good or service. This is somewhat unfortunate for the DULTC committee as this unpredictable variable could have a significant influence on DULTC membership since it determines the service the club can offer to College students. Weather conditions determine the quantity, as no service is available when the tennis courts are covered with snow or when gales prevail, and quality, a game of tennis on a hot and dry day is considerably different to a game on a cold and wet day, of service available to DULTC members. The higher the number of conformable days in any one year the higher the quantity and quality of service available to DULTC members. Members' utility, in an ordinal sense, or benefits received are thereby positively related to the number of conformable days and thus DULTC membership per academic year should be positively related to the number of conformable days per calendar year.
Excluded Explanatory Variables
Adam Smith noted that all economic behaviour may be understood as the rational pursuit of self interest as 'it is not from the benevolence of the butcher, the brewer, or the baker that we can expect our dinner but from their own regard to their own self interest.' Trinity College students, as consumers, seek to maximise their utility given their budget constraints and so when considering any consumption decision the price and associated costs are of paramount importance. So why have the DULTC annual membership fee and the playing costs been excluded from the model?
Membership Fee
Microeconomic theory postulates that the price of a commodity is by no means an arbitrary figure, as it is a representation of the markets valuation of a commodity. An increase in membership fee which exceeds the marginal willingness to pay of previous or potential (at old membership fee) members would, ceteris paribus, decrease club membership. However, this theoretical negative relationship is excluded from the model for two reasons. Firstly, over the fifteen year period the sample variance of membership fee is only 1.2499 hence there is clearly insufficient variation for it to be a regressor. Secondly, the cross price elasticity of demand, which could possess more explanatory power, cannot be calculated as DUCAC has incomplete information on membership fees charged by other clubs.
Playing Costs
The costs incurred by tennis players may be analysed in terms of fixed and variable costs. Fixed costs are the monetary expenditures incurred when purchasing a tennis racquet and tennis trainers. Fixed costs incurred by members are excluded from my model as, not surprisingly, DUCAC has no data on the above goods and constructing a mean price for racquets and trainers for each year is not satisfactory due to the considerable variation in price range and model for both goods each year. The cost of tennis balls used per game multiplied by the number of games played per year measures the variable cost that a member faces. There is no inclusion of this cost in the model as it is doubtful that any College student would attempt to forecast annual tennis ball expenditure!
The Model
In an attempt to estimate the significance of my explanatory variables the ordinary least squares technique shall be used, which will yield a line of best fit corresponding to the data. In this multiple regression the model will take the following form:
Y = B0 + B1X1 + B2X2+ Ui
Ui is the stochastic disturbance term, acknowledging the nonsystematic nature of the relationship. The investigation will arrive at an estimate of the sign, size and significance of the unknown parameters B0, B1, B2.
The Estimation
The estimation of the regression line was achieved using the SPSS econometric package, using 15 observations of annual data, from 1978-79 to 1992-93. The results of the multiple regression are as below. The Line of Best Fit has been estimated as:
Y = -670.530316 + 0.132062 X1 + 1.359159 X2
REGRESSION RESULTS
Y regressed on X1,X2
Variables in the Equation
Variable B SE B t Sig t or p-value
X1 .132062 .027176 4.859 .0004
X2 1.359159 .475173 2.860 .0143
Constant -670.5303 189.85828 -3.532 .0041
Y regressed on X1
Variables in the Equation
Variable B SE B t Sig t or p-value
X1 ..112041 .032718 3.424 .0045
Constant -.193.179 112.7950 -1.713 .1105
Y regressed on X2
Variables in the Equation
Variable B SE B t Sig t or p-value
X1 .764427 .759956 1.006 .3328
Constant -43.04551 230.375 -.187 ..8547
X1 regressed on X2
Variables in the Equation
Variable B SE B t Sig t or p-value
X2 -4.503418 4.685817 -.961 .3541
Constant 4751.4295 1420.471 3.345 .0053
R squared 0.47425
Evaluation
As expected the two X variables are positively related to Y and explain a significant degree of its variation, almost 69%. The author expected that, with the exception of the cricket club, few clubs would be as weather sensitive as the tennis club and there should consequently be little multicollinearity between the explanatory variables. A separate regression of X1 on X2 confirmed my expectations as an R2 of 0.066 was yielded. By regressing Y on X1 alone, an R2 of 0.474was yielded, showing that 47% of the variation of Y was explained by variation in X1.. However, by the same procedure on X2, an R2 of 0.07 was yielded, showing that only 7% of the variation in Y is explained by X2 This raises the question, whether these parameter estimates are statistically significant?
Statistical Evaluation
In order to address the above problem it is necessary to examine the t-statistics derived. The null hypothesis that there is no statistical relationship between the X and Y variables (H0: t =0) shall be considered. An estimate of a parameter is statistically significant if the t-statistic associated with it, at a particular significance level, causes one to reject the null hypothesis. For the multiple regression the estimates for 1 and 2 are statistically significant at both the 5% and 10% significant levels. Examining the regression of Y on X1, the t-statistic is 3.424, which shows a high degree of statistical significance. This is an indication of a causal relationship and confirms the strong relationship between X1 and Y. However, the estimate provided by regressing Y on X2 is statistically insignificant at both the 5% and 10% significant levels.
Conclusion
The objective of this essay was to obtain an explanation of the factors influencing the microeconomic phenomena of DULTC membership. By utilising microeconomic theory the author proposed some plausible explanatory variables and then sought their empirical determination. Despite the economic rationale behind the influence of weather conditions, its explanatory power was seen to be insignificant, thus demonstrating that theory and reality often diverge. However, the model is satisfactory as it enables prediction of DULTC membership, at 90% and 95% confidence intervals and thereby is crucial to DULTC's future policy. The effect which the proposed 1996-97 increase in membership fees will have on DULTC membership can now be measured, albeit by a second best approach, by comparison of the comparitive statics of 1996-97 membership and predicted membership.
Bibliography
Gujarati, D.N. (1995) Basic Econometrics (3nd ed.), Mc Graw-Hill, London
West. T.(1991) The Bold Collegians, Lilliput Press, Dublin
Dublin University Lawn Tennis, Gym & Racquets Club Minute Book,1903-1919.