Visitors to the Old Library, Trinity College, Dublin: An Econometric Analysis

Each year increasingly large numbers flock to Ireland's biggest tourist attraction, the Book of Kells and the Old Library, Trinity College. The Book of Kells is a copy of the four gospels written by Irish monks in Kells around 800AD. The Old Library was opened in the year 1793. These exhibits are thus unique. There is no close substitute for either of these in Ireland or indeed world-wide. It is likely therefore that demand for entrance tickets will be inelastic with respect to price. In the last fifteen years the number of people visiting the book of Kells and the Old Library has more than doubled. In this paper I hope to determine what has caused this rise. Why have the numbers continued to rise despite increasing ticket prices? By how much has the rise in ticket prices dampened the rise due to other factors, and most especially due to increasing overseas visitors to Ireland?

Over the past fifteen years the service provided has changed greatly. In 1992 a new shop was built and along with the Book of Kells and the Old Library, annual exhibitions were also put on display that are included in the price. The Dublin Experience runs from May to August and is shown eight times a day. Combination tickets for the show and the Book of Kells are available. Walking tours of the college have been running throughout this period, and they also offer combination tickets. Thus, these three services run in conjunction with each other, making a visit to Trinity College, and subsequently to the Book of Kells and the Old Library, all the more worthwhile. Unfortunately the impact of these improvements in services on the number of visitors is unquantifiable. It is highly likely that they will have had some, if not considerable, influence on the number of visitors. They should therefore, be kept in mind as we continue with our econometric analysis.

I will begin by specifying my dependent and independent variables that are to be used in the analysis. I will then turn to estimation of the relationship between them, and finally I will evaluate my results. Since both are located in the same building, I will subsequently refer to the two exhibits as the Book of Kells.

In order to determine the rise in the number of visitors to the Book of Kells, I have chosen the following variables:

As my dependent variable, Y, variations in which I hope to explain, I have taken the annual number of visitors to the Book of Kells. Charges to this exhibit were only introduced in 1983, and it was only at this point that the record of the number of visitors began. Therefore, I have chosen the years 1983-1997 for my study. In the early years charges were only in place from April to October, and consequently visitor numbers were only recorded for these months. In order to standardise the annual figures I have only taken the figures from April to October for each year. In these years there has been a significant upward trend, which will be examined using the following independent variables.

My first independent variable, X₁, is ticket prices. Since 1983 there have been huge changes in ticket prices, all in an upward direction. The price of an adult ticket has risen to seven times its original level that is from £0.50 to £3.50. Ordinarily one would expect demand to fall as price increases, that is we expect a negative correlation between Y and X₁. However, demand has continued to rise. What I hope to determine is whether or not other factors have more than offset this one, and if this is the case, how much did the rise in ticket prices dampen the rise due to these other factors? In this analysis I have taken adult ticket prices as a proxy for overall ticket prices.

My second independent variable is the number of overseas visitors to Ireland. I have only taken annual totals for the months of April to October. I found this to average at 75% of the annual figures, although it may in fact be less with the rise in Winter business in recent years. The main category of visitor to the Book of Kells, particularly in the summer months is overseas tourists (this has been observed through the number of free foreign language leaflets that have been used in the period). We would therefore expect a positive correlation between Y and X₂. Indeed the Book of Kells has been referred to as the National Tourism barometer. Within this period the number of overseas visitors to Ireland has risen almost threefold. Unfortunately the 1997 figures are not yet available from Bord Fáilte.

Sunday is the busiest day of the week and growth in Sunday business could possibly have been included as an explanatory variable. However, I have decided to neglect this variable because of the difficulty of obtaining precise data. I also considered quantifying changes in the composition of visitor groups as a possible explanatory variable. Visitor records categorise visitors into adult, OAP/pensioner, group and family. Group numbers have risen rapidly and now account for a third of all visits. I have decided not to include this influence because of difficulties in data collection.

This method will yield a relationship between the variables by estimating the size and the sign of b ₀, b ₁ and b ₂. The term represents the error term, that is factors affecting Y that are unaccounted for by X₁ and X₂.

To carry out the regressions on my data I used the econometrics computer package, Microfit. The results were as follows: My line of best fit was found to be;

Y = 11030.4 + 9997.6X₁ + .094192X₂

The correlation between the variables was found to be very high as indicated by the correlation coefficient, R² of 90%.

The following table shows the associated parameter estimates and t-statistics.

I then regressed Y on X₁ and X₂ individually, to determine the influence of each of these variables on Y.

Regressing Y on X₁ yielded:

Y= 97294.5 + 75533 X₁ R² = .84966 t-statistic = 7.8846

Regressing Y on X2 yielded:

Y= 93.9963 + .1074 X₂ R² = .90103 t-statistic = 10.0074

Unfortunately it then became apparent that there was a high degree of multicollinearity between X₁ and X₂. Regressing X₁ on X₂ gave R² = 0.92414. Intercorrelation of the variables is not always a problem. But since this R² value is greater than our multiple-regression value of R², drawing on Klein (in Maddala 1992) we could conclude that it will make the Y regression results less accurate, if not altogether invalid.

In order to evaluate my regression results I will examine and compare them with the expected relationships. From the multiple regression it can be seen that the chosen independent variables have high explanatory power. Very little of the variations in Y remain unexplained. The significance of this may be undermined by the high degree of multicollinearity between X₁ and X₂ however. Looking at the simple regressions reveals a little more however. As was initially supposed, there was a high positive correlation between Y and X₂ . X₂ was able to explain 90% of the variations in Y. The Book of Kells may indeed be referred to as the National tourism barometer therefore, since variations in the two are so closely correlated. Examining factors that determine the rise and fall in overseas visitors to Ireland may be the key to gaining deeper insights into variations in Y. Contrary to what we believed, Y and X₁ were positively correlated, and quite highly at that. The rise in ticket prices has not dampened the influence of the rise in overseas tourists in the multiple-regression analysis. This positive correlation is possibly due to the inelastic demand for this good which I alluded to earlier. It may further suggest that individuals marginal benefit from visiting the Book of Kells, or their marginal willingness to pay is actually higher than we would have supposed. This however, only explains why there was not a negative relationship between the two variables. The fact that there was a high positive relationship would suggest that tickets to the Book of Kells are a snob, or a so called 'Giffen' good. Could this really be the case? It is highly unlikely. It is most probable that there are other independent variables, omitted from this model, which have caused Y to rise, regardless of the price increases. Increases in demand for a good corresponding to increases in its price go against our economic theory. One final explanation for this positive correlation between Y and X₁ is that our dependent variable Y may be causing the variations in the independent factor X₁. Given the positive relationship, this would fit better with our theory. If the marginal willingness to pay meets the current price, ticket prices may not yet have begun to effect Y. The impact of the proposed price increase scheduled for 1998 will depend on the marginal willingness to pay. If it rises with the increase, the price increase will have little effect on demand. If it does not rise however, it may have a negligible negative impact on demand (this of course will also depend on inflationary changes).

The t-statistic, the ratio of the estimated parameter to its standard error, is used in the evaluation of a coefficients statistical significance. I will look first at the multiple regression case. X₂ is statistically significant at both the 5% and 10% levels, but X₁ is not statistically significant for either 5% or 10%. These results however, are due primarily to the problem of multicollinearity between X₁ and X₂. The computer is unable to read the area of Y that is determined by X₁ and X₂ together. Given that X₁ and X₂ are so closely correlated it is likely that all of the area explained by X1 is explained by X₂ also. Examination of the t-statistics for the simple regressions backs up this analysis. In this case both X₁ and X₂ are statistically significant for 5% and 10%.

In studying the rise in the number of visitors to the Book of Kells, my regression results were very encouraging. My model, which used ticket prices and national tourism figures as independent variables, explained 90% of the variation in the number of visitors to the Book of Kells. National tourism figures were positively correlated with the number of visitors to the Book of Kells as expected. Similarly, ticket prices were also positively correlated with the number of visitors, although this was unexpected. I found this result to be conflicting with economic theory - a sign that some important variable had possibly been omitted from my model. On subsequent study, a flaw was revealed in my regression analysis, namely the presence of high multicollinearity between my two independent variables. Consequently only one variable was statistically significant in the multiple-regression analysis. However, on observing the simple regression results , the two explanatory variables were statistically significant at both 5% and 10%.