Modelling Past and Future European Tourism Arrivals to Mauritius
Paper by Karim Jaufeerally, May 2002
Summary
This paper attempts to model tourism arrivals to Mauritius from a number of European countries (Austria, Belgium, France, Germany, Italy, Netherlands, Spain, Switzerland, Sweden and the U.K). A model, called model I, has been developed that establishes relationships between tourism arrivals and Gross Domestic Product in real terms for these European Countries. In the model, it is found that there exist very high correlates between arrivals and Gross Domestic Product of these European countries. Equations can be fitted to the data in order to model arrivals from 1990 to 1997. The high correlates found between the above variables tend to show that growth in GDP (Gross Domestic Product) is the driving force fueling increases in arrivals.
These equations can then be used to extrapolate arrivals to Mauritius from 2000 to 2010 when assuming a 2% yearly real increase in GDP and using published demographic figures for the above European countries. It is found that for a number of countries such as Germany, France, Belgium, Spain, Switzerland and Austria, arrivals can be expected to either level off soon or increase very slowly henceforth. Whereas for countries like the U.K., Italy, the Netherlands and Sweden significant increases in arrivals can be expected now. Comparison between projected figures from the model and actual arrivals for the years 1998 to 2000 reveals that for certain countries like France and Spain, the model underestimates arrivals. Whilst for the U.K. and Germany the model is not too far off.
Extrapolations have been carried out till 2010 only in the two models, because it is felt that with such straight forward models it would be unwise to extrapolate any further. Analysis of arrivals from South Africa, Reunion island and from the rest of the world will be dealt with in another paper.
Introduction
Since 1979 the number of tourists visiting Mauritius has increased dramatically. Arrivals have increased from 128,000 in 1979 to 656,453 in 2000 and in the meanwhile tourism has become a major foreign currency earner for Mauritius and is referred to as the third pillar of the Mauritian economy. According to a Government report, Vision 2020 (1995), somewhere between 1.2 million to 1.5 million tourists could be expected yearly by 2020. These very high figures imply a doubling of the present tourism arrivals. It is not publicly known whether Mauritius can welcome such numbers without undue consequences. Indeed, it is not even known whether the present stream of arrivals is sustainable or not.
It is important to try to establish what were the main factors that could have led to such an increase in arrivals. Once the main factors identified, then it becomes possible to make an educated assessment of the potential number of arrivals that can be expected in the coming years. The purpose of this paper is to describe two different approaches that have been used to model tourist arrivals in the past. Subsequently these models are extrapolated to make an estimate of future arrivals.
Model I examines the relation there is between arrivals from a number of European countries, its population and its Gross Domestic Product per capita.
Methods and Assumptions
In any modeling exercise, it is inevitable that certain assumptions are made. These must be made explicit at the onset. For the purpose of this model the assumptions are:
Model I
In Model I, we have made use of tourism arrivals statistics that detail the country of origin. For ten European countries individual arrivals statistics are available. These countries are Austria, Belgium, Italy, Germany, France, Netherlands, Spain, Switzerland, Sweden and the United Kingdom. Arrivals from remaining European countries are grouped under the term "Other European".
The Ten European Countries
Intuitively, the wealthier a country is, the more its citizens can be expected of travelling abroad. Hence, it is reasonable to think that the wealthier European citizens become, the more likely they are of coming to Mauritius.
Model I
In model I, for each of the ten European countries mentioned above, a graph was plotted of the Gross Domestic Product per capita of that European country (in 1997 US Dollars) against the ratio of tourists visiting Mauritius to the population of that European country for the years 1990 to 1997. The ratio of Tourist to Population (TP) is expressed as the number of tourists visiting Mauritius per 100,000 inhabitants of that European country. The ratio TP is in effect the proportion of the population of a given country that visited Mauritius in a given year.
A cursory examination of each of the ten graphs (see figures 1 to 10) shows that there is a strong link between the ratio of tourists per 100000 inhabitants (TP) and the Gross Domestic Product (GDP) for the years 1990 to 1997. Coefficients of Variation (R2) can be calculated for these countries according to the different types of curves fitted to the data. The one with the highest coefficient of variation R2 is the curve that matches most closely to the data. Three general types of equations have been used to find the best match possible and these are:
Linear Regression, Quadratics and Logistic Equations.
At this point it is inevitable that we indulge in a little mathematics. Linear Regression lines are of the form y = ax + b, Quadratics, or second degree polynomials are of the form: y = ax^{2} + bx + c. Mathematical techniques exist to fit straight lines or polynomials to data.
Logistic equations have also been used. It is in order, at this point, to explain what this equation is all about. It is an equation that is extensively used in population dynamics and ecology. It is used to describe the increase or decrease in the number of individuals in a given population with time. The equation has been modified a bit so that the time variable is replaced by real GDP and the number of individuals variable is replaced by the ratio of tourists to population (TP).
The choice of that equation is suggested by the general form the data takes for a number of countries when displayed graphically and by certain features of the logistic equation that are thought desirable for the model. These features are as follows:
Intuitively, this approach looks promising because the rapid initial growth is characteristic of emerging markets which after some time experience a slow down in growth as the full potential is being realised. Then follows the inevitable plateau characteristic of a mature and stable system.
Moreover it is clear that due to constraints, the number of tourists is bound sooner or later to reach a maximum beyond which no increase is possible or even desirable. Therefore an upper figure must exist. The fact that the growth rate as depicted by the equation eventually becomes zero does mean that a maximum will be reached at some point in the future, hence the interesting aspect of the logistic equation.
A note of warning
It is vitally important that the reader understands that whatever maximum figure the model comes up with, this is not indicative of the tourist carrying capacity of Mauritius. The model merely extrapolates in the future existing trends irrespective of what the tourist carrying capacity of the island may be. The tourist carrying capacity figure may be higher or lower than the maximum figure as calculated by the model. Yet the model is bound to be useful for when and if a maximum tourist carrying capacity is calculated, the model can be used to determine if arrivals to Mauritius are likely to exceed this carrying capacity or not. In either case, corrective action can then be taken.
The ten European Countries sources of tourists to Mauritius will now be discussed in turn
Results
Austria
Austria is a smallish but significant market for Mauritius as arrivals have shot up from 1490 in 1990 to reach 8317 in 1997, a more than fivefold increase. The relationship between GDP and TP is immediately clear from Figure 1. The following table shows which types of equations were fitted to the data, the respective forms of the equations and the degree of fit to the data.
Table
Type of Curve 
Equation 
R2 
Linear Regression Line 
TP = 0.02949188 x GDP  650.2151 
0.8871 
Quadratic Fit 
TP = 0.0000004637 x GDP^2  0.1957064 x GDP + 2003.1056 
0.9089 
Logistic Fit 
See appendix for exact form of equation 
0.9560 
It is seen that it is the logistic equation that gives a better fit because of the greatest R2.
Belgium
This market has also increased manyfold over the past years. In 1990, arrivals were 1920, in 1997 it reached 8162, a fourfold increase. There also exists a strong relationship between GDP per capita and Tourists per 100,000 inhabitants (Figure 2). The three types of equation fitted to the data are shown below.
Table
Type of Curve 
Equation 
R2 
Linear Regression Line 
TP = 0.0300 x GDP  627.211 
0.8940 
Quadratic 
TP = 0.00000177 x GDP^2 +0.11024 x GDP  1533.211 
0.8955 
Logistic 
See appendix for Eq. 
0.9198 
It can be seen that the linear regression line and the quadratic equation give very similar quality of fit to the data. However the logistic equation gives a slightly better fit.
France
France ranks first in terms of arrivals to Mauritius, hence this market is of prime importance to the local tourism industry (arrivals from Reunion are excluded). GDP per capita is plotted against TP. A linear Regression line, a quadratic equation and a logistic equation are fitted to the data (Figure 3). Very good fits are obtained in all cases as shown by the respective values of R2
Table
Type of Curve 
Equation 
R2 
Linear Regression Line 
TP = 0.069721 x GDP  1400.22022 
0.9066 
Quadratic Curve 
TP = 0.0000173792 x GDP^2 + 0.857802 x GDP  10324.50958 
0.9249 
Logistic Curve 
See appendix for Eq. 
0.9238 
Germany
Figure 4 shows the data and the three equations fitted accordingly. The degree of fits is good overall though significantly lower than in the previous cases.
Type of Curve 
Equation 
R2 
Linear Regression Line 
TP = 0.009798 x GDP  192.3386 
0.783 
Quadratic 
TP = 0.0000013592 x GDP^2 0.0749 x GDP  970.55 
0.8020 
Logistic 
See appendix for Eq. 
0.8097 
Italy
Figure 5 displays the data for Italy. It is the quadratic equation that gives the highest R2, though the logistic fit is quite good too.
Table
Type of Curve 
Equation 
R2 
Linear Regression Line 
TP = 0.01895 x GDP 327.7537 
0.700 
Quadratic 
TP = 0.000027541 x GDP^2 1.0361 x GDP + 9769.317 
0.8745 
Logistic 
See appendix for Eq. 
0.780 
Netherlands
Arrivals from this country are very much on the increase. Amazingly enough the coefficient of variation are very high especially for the quadratic and logistic equations and inspection of the graph (Figure 6) reveals a very close match indeed with the data points.
Table
Type of Curve 
Equation 
R2 
Linear Regression Line 
TP = 0.0045 x GDP  79.1835 
0.9028 
Quadratic 
TP = 0.0000013911 x GDP^2  0.050297 x GDP + 458.4598 
0.9835 
Logistic 
See appendix for equation 
0.9924 
Spain
Figure 7 shows the data and the fit for Spain. In all three cases the match obtained is very good as an inspection of figure 7 shows.
Table
Type of Curve 
Equation 
R2 
Linear Regression Line 
TP = 0.003926 x GDP  42.927 
0.889 
Quadratic 
TP = 0.0000004123 x GDP^2 + 0.01443 x GDP  109.71 
0.891 
Logistic 
See appendix 
0.900 
Sweden
Figure 8 reveals the data for Sweden. A quadratic offers a much better fit than a linear regression line as shown by inspection of Figure 8.
Table
Type of Curve 
Equation 
R2 
Linear Regression Line 
TP = 0.0152 x GDP  349.6045 
0.7516 
Quadratic 
TP = 0.00001015 x GDP^2 + 0.4825 x GDP + 5748.6479 
0.933 
Logistic 
See appendix for equation 

Switzerland
Figure 9 displays the data points for Switzerland and the best fit curves. What is immediately clear is that the relationship between GDP and TP is not readily apparent. The points are scattered all about the graphical plane. The bestfit curves obtained reveal this lack of direct relationship between the two variables by relatively low values of R2 compared to the previous countries considered.
Table
Type of Curve 
Equation 
R2 
Linear Regression Line 
TP = 0.09918 x GDP 3351.813 
0.5022 
Quadratic 
TP = 0.0000666799 x GDP^2 4.6495 x GDP +81099.100 
0.5167 
Logistic 
Not Applicable 

United Kingdom
Figure 10 shows the data points for the United Kingdom and the best fit curves for the three types of curves chosen. In all three cases, the fit obtained is very good and high values of R2 are obtained.
Table
Type of Curve 
Equation 
R2 
Linear Regression Line 
TP = 0.0116 x GDP  180.35 
0.8221 
Quadratic 
TP = 0.0000022996 x GDP^2 0.081665 x GDP +762.847 
0.8415 
Logistic 
See appendix for Eq. 
0.8369 
Discussion
The first striking feature of the above results for European countries is the strong link between Tourists per 100,000 population (TP) and GDP as expressed by the coefficient of variation R2. Indeed for most European countries, R2 varies from 0.70 to 0.99, except in the case of Switzerland with an R2 of the order of 0.50. Basically this means that, Switzerland excepted, between 70% to 99% of the variation in arrivals can be explained by a link between TP and GDP. From a theoretical perspective, this does not prove a link of causality between the two variables. However, given the nature of the GDP variable, which after all is a measure of wealth, it is safe to assume there is a causality relationship between GDP and TP.
A careful examination of Figure 1 to Figure 10 also reveals that although there was a recession in Europe in 1992 and 1993, when GDP fell for a number of European countries, the ratio TP did not fall for all countries but in fact continued to increase. Of course such a counter intuitive behaviour cannot be expected to recur in the future should there be bouts of recession in Europe.
The essential lessons to be drawn from the above are:
We are now in a position to use our bestfit curves to make an attempt at extrapolations. There are two main driving variables in our model, one is GDP per capita and the second is population. We shall assume that GDP will grow at a yearly rate of 2% in real terms and that demographic data and extrapolations for the countries concerned are essentially correct. We shall use the linear, logistic and quadratic extrapolations accordingly.
Extrapolations from Model I
As in any extrapolation exercise figures should be interpreted with great care and caution. Extrapolations have been carried out only till the years 2010. Please refer to the appendix for the details referring to the following extrapolations. All figures have been rounded to the nearest hundreds.
Austria
Year 
Linear Extrapolation Arrivals 
Quadratic Extrapolation Arrivals 
Logistic Extrapolation Arrivals 
Actual Arrivals 
1998 
9600 
11000 
9500 
7757 
1999 
10900 
13200 
10100 
8095 
2000 
12100 
15700 
10500 
8874 
2005 
19000 
32400 
11000 

2010 
26500 
57900 
11000 

It can be seen that it is the logistic model that is closest to the actual situation, the other two models being off the mark. The logistic model predicts that this market is expected to reach a maximum very soon, after which very little increase can be expected. The overestimation in arrivals for 1998, 1999 and 2000 may point to the possibility that the Austrian market is going to reach its full potential sooner.
Belgium
Year 
Linear Extrapolation Arrivals 
Quadratic Extrapolation Arrivals 
Logistic Extrapolation Arrivals 
Actual Arrivals 
1998 
10300 
10200 
9100 
8365 
1999 
12000 
11300 
9400 
9586 
2000 
13300 
12400 
9500 
10998 
2005 
21200 
16700 
9500 

2010 
29900 
18500 
9400 

The linear extrapolation overestimates arrivals significantly whereas the quadratic model is closer to actual figures though on the high side. The logistic model tends to underestimate arrivals and predicts a levelling off now. It is possible that the Belgian market will oscillate between the quadratic and logistic models.
France
Year 
Linear Extrapolation Arrivals 
Quadratic Extrapolation Arrivals 
Logistic Extrapolation Arrivals 
Actual Arrivals 
1998 
171300 
151300 
149200 
162775 
1999 
191800 
153500 
152500 
175431 
2000 
212700 
150700 
154500 
198423 
2005 
322400 
49600 
156800 

2010 
444500 
N / a 
157500 

N/a: Not applicable
France is a very special market, for two reasons. Firstly, it is our most important market in terms of arrivals and secondly, the ratio TP is the highest of all European countries. Any change in this market is of great consequence for the industry. It can be seen from the above figures that the linear model is the closest to the actual figures. Whereas the quadratic and logistic model underestimate significantly this market. Rapidly the quadratic model diverges to improbably low figures and the logistic model reaches a plateau too quickly. The very high arrivals predicted by the linear model by 2005 and 2010 makes this model unrealistic beyond the reach of a couple of years.
It could well be that the data series is over a too short period of time to be really meaningful. Longer time series will be needed to make more accurate extrapolations.
Germany
Year 
Linear Extrapolation Arrivals 
Quadratic Extrapolation Arrivals 
Logistic Extrapolation Arrivals 
Actual Arrivals 
1998 
52000 
48000 
47900 
43826 
1999 
56300 
49400 
49200 
45206 
2000 
60600 
50200 
50000 
52869 
2005 
83300 
43800 
51200 

2010 
108400 
16000 
51000 

With the linear extrapolation, arrivals should steadily increase to reach 100,000 by 2010. The quadratic model is off course very rapidly, whereas the logistic model predicts a plateau of 51,000 by 2005 and thereafter. It is safe to argue that the German market could oscillate between 50,000 and 100,000 by 2010. A wide but nevertheless useful margin.
Italy
Year 
Linear Extrapolation Arrivals 
Quadratic Extrapolation Arrivals 
Logistic Extrapolation Arrivals 
Actual Arrivals 
1998 
32,500 
48,900 
36,200 
36,614 
1999 
36,800 
70,500 
43,400 
36,675 
2000 
41,200 
97,700 
51,200 
39,000 
2005 
64,000 
328,500 
87,100 

2010 
88,700 
748,500 
102,700 

All three models are presently overestimating this market, especially the quadratic extrapolation which can be safely discarded as highly improbable due to the very high figures it predicts. It is safer and more reasonable to assume that for the time being the logistic model gives an upper figure whilst the linear model a middle of the range figure. From those figures it appears that the Italian market is still on the expanding phase and potentially can become a very important source of tourists to Mauritius.
Netherlands
Year 
Linear Extrapolation Arrivals 
Quadratic Extrapolation Arrivals 
Logistic Extrapolation Arrivals 
Actual Arrivals 
1998 
3,000 
3,600 
3,600 
3,085 
1999 
3,300 
4,400 
4,300 
4,110 
2000 
3,600 
5,300 
5,200 
4,925 
2005 
5,400 
11,500 
10,300 

2010 
7,400 
21,300 
13,700 

For the years 1998 to 2000 the quadratic and logistic extrapolations are in good agreement with the actual arrivals whereas the linear curve underestimates arrivals significantly. By 2010, the model predicts arrivals of between 14,000 to 21,000 a fairly narrow range.
Spain
Year 
Linear Extrapolation Arrivals 
Quadratic Extrapolation Arrivals 
Logistic Extrapolation Arrivals 
Actual Arrivals 
1998 
4,400 
4,200 
4,000 
4,738 
1999 
4,800 
4,600 
4,200 
6,204 
2000 
5,200 
4,900 
4,300 
7,226 
2005 
7,500 
6,000 
4,500 

2010 
10,000 
6,500 
4,500 

Presently, all three extrapolations have underestimated significantly this market though the linear extrapolation is less off the mark. It is clear that a longer time series will be needed to get a better estimate of the future potential of that market. Right now it appears that it is the linear extrapolation that is the most realistic.
Sweden
Year 
Linear Extrapolation Arrivals 
Quadratic Extrapolation Arrivals 
Logistic Extrapolation Arrivals 
Actual Arrivals 
1998 
4,400 
6,600 
7,500 
4,022 
1999 
5,100 
9,300 
11,000 
4,552 
2000 
5,900 
12,500 
15,800 
5,694 
2005 
9,800 
38,400 
60,500 

2010 
14,300 
84,960 
86,500 

The quadratic and logistic models are already overestimating considerably the Swedish market. It is only the linear model that appears to be in line with the actual arrivals. It is therefore safer to give more weight to the linear model only. Nevertheless, the Swedish market appears to be an expanding one still and could very easily reach 15,000 arrivals yearly by 2010.
Switzerland
Year 
Linear Extrapolation Arrivals 
Quadratic Extrapolation Arrivals 
Actual Arrivals 
1998 
21,000 
26,600 
16,178 
1999 
26,200 
42,400 
16,281 
2000 
31,800 
64,100 
20,473 
2005 
37,400 
92,100 

2010 
43,200 
126,700 

In the Switzerland case, we have only two models, the linear and the quadratic models. Both models are overestimating arrivals from that country. The quadratic model can safely be discarded as it diverges to figures that are highly improbable. Most probably a longer time series will be required before making a better assessment of the trend from that market.
United Kingdom
Year 
Linear Extrapolation Arrivals 
Quadratic Extrapolation Arrivals 
Logistic Extrapolation Arrivals 
Actual Arrivals 
1998 
44,000 
49,800 
48,600 
52,299 
1999 
47,000 
55,700 
53,700 
58,683 
2000 
50,000 
62,200 
59,100 
74,488 
2005 
65,800 
106,200 
96,500 

2010 
83,400 
174,000 
155,100 

All three models tend to underestimate significantly arrivals from that country. However, all three models predict very significant increases in arrivals in the years to come. Based on the above only, it appears that the United Kingdom will become a very important source of tourists to Mauritius. The three models predict arrivals between 80,000 to 175,000 by 2010.
Other Europeans
All other arrivals from the remaining European countries are grouped under one item: Other European. It can be seen from figure 11 that over the last decade, this group has exploded in terms of arrivals. In 1990, only 2090 tourists made up this group whereas in 2000, 32,824 tourists originated from this group of countries. It is no longer a marginal source of tourists. In this paper no attempt has been made to correlate arrivals from this group with the combined GDP of the group. To make an assessment of the potential of this market, we are simply going to extrapolate from past arrivals along a linear and a quadratic curve as is shown in the table below.
Year 
Linear Extrapolation 
Quadratic Extrapolation 
2000 
22,400 
26,200 
2005 
35,000 
71,800 
2010 
47,700 
139,300 
The linear curve implies a doubling of arrivals whereas the quadratic curve implies a fifth fold increase. It is best to be cautious and opt for the linear curve till a better model is at hand. Nevertheless the increase is substantial and the figures far from being insignificant.
Total Number of European Tourists 20002010 Model I
We are now in a position to estimate the total number of European tourists that are supposed to come to Mauritius till 2010. For that purpose, for each country we shall select figures from the curve that best models arrivals.
Country 
Model Chosen 
Arrivals 2000 
Arrivals 2005 
Arrivals 2010 
Austria 
Logistic 
10,500 
11,000 
11,000 
Belgium 
Logistic 
9,500 
9,500 
9,400 
France 
Logistic 
154,500 
156,800 
157,500 
Germany 
Logistic 
50,000 
51,200 
51,000 
Italy 
Logistic 
51,200 
87,100 
102,700 
Netherlands 
Logistic 
5,200 
10,300 
13,700 
Spain 
Linear 
5,200 
7,500 
10,000 
Sweden 
Linear 
5,900 
9,800 
14,300 
Switzerland 
Linear 
31,800 
37,400 
43,200 
United Kingdom 
Logistic 
59,100 
96,500 
155,100 
Other Europeans 
Linear 
22,400 
35,000 
47,700 
Total 

405,300 
512,000 
615,600 
Conclusion
In 2000 Mauritius welcomed 439,989 European tourists, the combined model predicted 405,300, an error of less than 8%. This small error is encouraging and does indicate that the model reflects to some extent the actual situation. As time goes by, the latest GDP figures available from European countries will have to be integrated into the model to obtain better and more accurate forecasting results. If the model can be trusted, it appears that tourism arrivals from Europe can be expected to increase substantially in the years to come. It is becoming abundantly clear that the environmental and social impacts of an increase in tourism will have to be more thoroughly studied and accounted for as this industry develops. A lack of foresight on behalf of concerned authorities and developers could result in severe backlash if the impacts of tourism are not controlled or mitigated soon enough.
The Appendix contains all the details concerning the calculations carried out for this paper.