This article presents an empirical study of Luenberger indicator in a portfolio selection context (Brandouy et al., 2010) that we use in Tourism. Over time, we gauge market segment efficiency of overnight stays growth by the shortage function in a mean–variance space. Luenberger productivity indicator is deduced and decomposed to efficiency and volume touristic changes. The first component reveals the portfolio strategy performance, and touristic volume change appraises global market growth. The empirical results based on a sample of French overnight stays volumes during 1998–2008 period show that there is a market decrease in 2008. However, we note that for some market segments a lower volume does not necessarily mean lower productivity. The France destination strategy drive until 2008, permits us to have a better and more stable growth than the previous period.
BarrosCPBottiLPeypochNRobinotESolonandrasanaBAssafA (2011) Performance of French Destinations: Tourism Attraction Perspectives. Tourism Management32(1): 141–146.
2.
BrandouyOKerstensKWoestyneV (2010) Portfolio Performance Gauging in Discrete Time Using a Luenberger Productivity Indicator. Journal of Banking and Finance34: 1899–1910.
3.
BriecW (1997) A graph type extension of farrell technical efficiency measure. Journal of Productivity Analysis8: 95–110.
4.
BriecWKerstensKLesourdJB (2004) Single Period Markowitz Portfolio Selection, Performance Gauging and Duality: A Variation on the Luenberger Shortage Function. Journal of Optimization Theory and Applications, 120(1): 1–27.
5.
BriecWLesourdJB (1999) Metric distance function and profit: Some duality result. Journal of Optimization Theory and Applications101: 15–33.
6.
ChambersRG (2002) Exact Non Radial Input, Output and Productivity Measurement. Economic Theory20: 751–765.
7.
ChambersRGPopeRD (1996) Aggregate productivity measures. American Journal of Agricultural Economics78: 1360–1365.
8.
ChambersRChungYFäreR (1998) Profit, directional distance function and nerlovian efficiency. Journal of Optimisation Theory and Applications98: 351–364.
9.
Crouch GI and Ritchie JRB (1994) Destination Competitiveness: Exploring Foundations for a Long-Term Research Program. Proceedings of the Administrative Sciences Association of Canada 1994 Annual Conference. June 25–28, Halifax, Nova Scotia, 79–88.
10.
DecropA (1999) Qualitative research methods for the study of tourist behaviour. In: PizamAMansfieldY (eds.) Behaviour in Travel and Tourism. 335–365. Consumer.
11.
FiaccoAVMcGormickGP1968Nonlinear Programming: Sequential Unconstrained Minimization Techniques. New York, NY: John Wiley.
12.
Hoerner J-M (2000). Pour la reconnaissance d’une science touristique. Revue Espaces, Tourisme & Loisirs no 173, Juillet-août.
13.
HoernerJ-MSicartC (2004) La science du tourisme – Précis franco-anglais de tourismologie, édition bilingue. Balzac, Collection: Homo touristicus.
14.
HoernerJ-M (2010) Le tourisme dans la mondialisation. L’Harmattan, Paris.
KennedyV (1998) Risk management in the Irish tourism industry: the contribution of a portfolio investment approach. Tourism Management19(2): 119–126.
17.
LuenbergerD (1984) Linear and Nonlinear Programming, 2nd edn. Reading, MA: Addison Wesley.
18.
LuenbergerDG (1992) Benefit functions and duality. Journal of Mathematical Economics21: 461–481.
19.
LuenbergerDG (1995) Microeconomic Theory, New York, NY: McGraw Hill.
20.
LuenbergerDG (1998) Investment Science, New York, NY: Oxford University Press.
21.
MarkowitzH (1952) Portfolio selection. Journal of Finance7: 77–91.
22.
MarkowitzH (1959) Portfolio Selection: Efficient Diversification of Investments, New York, NY: John Wiley.
23.
MoreyMRMoreyRC (1999) Mutual fund performance appraisals: A multi-horizon perspective with endogenous benchmarking. Omega27: 241–258.
24.
Randriamboarison R (2003) Modélisation et estimation de la demande touristique: un essai pour l’explication du paradoxe du secteur touristique français. Phd Thesis, GEREM, University of Perpignan.
25.
SenguptaJK (1989) Nonparametric tests of efficiency of portfolio investment. Journal of Economics50: 1–15.
26.
SharpeW (1963) A simplified model for portfolio analysis. Management Science9: 277–293.
27.
VarianH (1982) The nonparametric approach to demand analysis. Econometrica50: 945–973.
28.
VarianH (1983) Nonparametric tests of models of investment behavior. Journal of Financial and Quantitative Analysis18: 269–278.
29.
WalleAH (1997) Quantitative versus qualitative tourism research. Annals of Tourism Research24: 524–536.
