Abstract
In this article, we use both graphical and analytical methods to investigate the market structure of one of the world’s fastest growing industries. For the German and Italian datasets, we show that the size distribution of tourism industry is heavy-tailed and consistent with a power-law behavior in its upper tail. Such a behavior seems quite persistent over the time horizon covered by our study, provided that during the period 2004–2009, the shape parameter is always in the vicinity of 2.5 for Germany and 2.6 for Italy. Size of the tourism industry has been proxied by the lodging capacity of hotel establishments: hotels, boarding houses, inns, lodging houses, motels, apartment hotels, tourist villages, and tourist apartments. Data belonging to the EUROSTAT and ISTAT databases have been used for Germany and Italy, respectively. Our aim is not to provide the best fit to the data but simply to focus our attention on the right tail of the size distribution of tourism industry. Understanding the behavior of the upper tail is indeed fundamental to capture the structure of the market. This study adds a new evidence to the list of empirical phenomena for which power laws hold.
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Notes
The value of \(\alpha \) is always assumed greater than 1 since the constant \(C\) in (1) is given by the requirement that the distribution sums to 1, namely
$$\begin{aligned} 1=\int \limits _{x_\text {min}}^{\infty }{f(x)\mathrm{{d}}x}=C\int \limits _{x_\text {min}} ^{\infty }{x^{-\alpha }\mathrm{{d}}x}=\frac{C}{1-\alpha }\bigl [x^{-\alpha +1} \bigr ]^\infty _{x_\text {min}}. \end{aligned}$$This only makes sense if \(\alpha >1\), since otherwise the right-hand side of the normalization equation would diverge. If \(\alpha >1\), then \(C=(\alpha - 1)x^{\alpha -1}_\text {min}\), and the normalized expression for the power law is
$$\begin{aligned} f(x)=\frac{\alpha -1}{x_\text {min}} \Biggl (\frac{x}{x_\text {min}}\Biggr )^{-\alpha }. \end{aligned}$$(1) represents the probability density function of a continuous power-law distribution. For mathematical convenience, the continuous form is commonly used to also approximate a discrete power-law behavior, whose formula is not as simple, by rounding the continuous power-law value to the nearest integer. For more details, see Clauset et al. (2009)
The average error on the estimated scaling parameter that arises from using (3) decays as O\((x^{-2}_{\text {min}})\) and becomes smaller than 1 % of the value of \(\alpha \) as \(x_{\text {min}}\gtrsim \) 6.
“Hatted” symbols, such as \(\hat{x}_{\text {min}}\), are used to denote estimates derived from the data. “Hatless” symbols denote the true values, which are often unknown in practice.
For the upper tail of the distribution of tourism supply in Portugal, Provenzano (2012) has estimated the scaling parameter in the vicinity of \(2\).
See Clauset et al. (2009) for details.
References
Baggio R (2007) The web graph of a tourism system. Physica A 379(2):727–734
Blackwell C, Pan B, Li X, Smith W (2011) Power laws in tourist flows. http://www.panb.people.cofc.edu/pan/PowerLawsBlackwellPanLiUpdated.pdf. Accessed 27 Feb 2013
Choulakian V, Lockhart RA, Stephens MA (1994) Cramér-von Mises Statistics for Discrete Distributions. Can J Stat 22(1):125–137
Clauset A, Shalizi CR, Newman MEJ (2009) Power-law distributions in empirical data. SIAM Rev 51(4):661–703
Goldstein ML, Morris SA, Yen GG (2004) Problems with fitting to the power law distribution. Eur Phys J B 41(2):255–258
Guimerá R, Amaral LAN (2004) Modeling the world-wide airport network. Eur Phys J B 38(2):381–385
Kleiber C, Kotz S (2003) Statistical size distributions in economics and actuarial sciences. Wiley, New Jersey
Li W (2002) Zipf’s law everywhere. Glottometrics 5:14–21
Miguéns JIL, Mendes JFF (2008) Travel and tourism: into a complex network. Physica A 387(12):2963–2971
Provenzano D (2012) The ’power’ of tourism in Portugal. Tour Econ 18(3):635–648
Scott N, Cooper C, Baggio R (2008) Destination networks—theory and practice in four Australian cases. Ann Tour Res 35(1):169–188
Shih H-Y (2006) Network characteristics of drive tourism destinations: an application of network analysis in tourism. Tour Manag 27(5):1029–1039
Ulubasoglu MA, Hazari BR (2004) Zipf’s law strikes again: the case of tourism. J Econ Geogr 4(4):459–472
Acknowledgments
The authors wish to thank Marco Enea, Vito M.R. Muggeo, and Michele Tumminello for useful discussions and suggestions. The authors are also thankful to an anonimous referee for constructive criticisms and valuable comments.
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Provenzano, D. Power laws and the market structure of tourism industry. Empir Econ 47, 1055–1066 (2014). https://doi.org/10.1007/s00181-013-0769-3
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DOI: https://doi.org/10.1007/s00181-013-0769-3