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Efficiency performance of the Algarve hotels using a revenue function
International Journal of Hospitality Management 35 (2013) 59–67
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International Journal of Hospitality Management journal homepage: www.elsevier.com/locate/ijhosman
Efficiency performance of the Algarve hotels using a revenue function Ricardo Oliveira, Maria Isabel Pedro ∗ , Rui Cunha Marques CEG-IST – Center for Management Studies, Av. Rovisco Pais, 1049 001 Lisbon, Portugal
a r t i c l e Keywords: SFA Revenue function Hotels Stars Location Golf
i n f o
a b s t r a c t The tourism industry, particularly the hotel sector, is becoming increasingly competitive and dynamic as a result of the pressures of globalized supply and demand in a context of uncertainty. The aim of this study is to discuss the efficiency of hotel companies in the Algarve (Portugal), a tourist destination of excellence in southwest Europe. In particular, we intend to assess the efficiency of the hotels in terms of star rating (four and five-star hotels), their location (Windward and Leeward), owning or not golf courses and owning just a single hotel or more than one. This analysis will be based on the parametric method of stochastic frontier approach using a revenue function. We found relevant levels of inefficiency. The results also point out the important role of the operational environment, particularly the hotel location and the existence of golf facilities. Star rating and owning multiples hotels do not seem to be so relevant. © 2013 Elsevier Ltd. All rights reserved.
1. Introduction The tourism industry, particularly the hotel sector, is becoming increasingly competitive and dynamic motivated by the pressures of globalized supply and demand (COM, 2010). However, it is also characterized by a context of uncertainty, despite the growth trend. This motivates the search for continuous and systematic improvement of processes and resources toward efficiency. Many authors have studied the efficiency, including Phillips (1999), Barros (2004) and Chen (2007), all pointing to the improvement of management practices. Differences in markets, tradable products, quality, location, differentiation and price, among other aspects, can generate the critical factors of success and survival of these organizations. Algarve is a tourist destination of worldwide excellence. It was considered two times the best worldwide golf destination in the last decade by the International Association of Golf Tour Operators (IAGTO, 2013). The Algarve golf courses were also distinguished by Rheingolf Magazine and by Golf Digest, putting San Lorenzo and Vilamoura Old Course between the 100 better golf courses of the world. Recently, in European Gala of World Travel Awards Europe (WTA, 2012), the Algarve was considered the best beach destination of Europe and Portugal was deemed the best golf destination. Also Hotel Quinta do Lago was considered the best hotel of the Mediterranean area, while Martinhal Beach was the best villa resort, the Dunas Douradas Beach Club, the best villas and apartments complex and Conrad Algarve Hotel (Hilton Group) the best new resort of the world. Graham Cooke, President of WTA,
∗ Corresponding author. Tel.: +351 912642544. E-mail addresses: [email protected] (R. Oliveira), [email protected] (M.I. Pedro), [email protected] (R.C. Marques). 0278-4319/$ – see front matter © 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ijhm.2013.05.005
underlined that the “Algarve is also one of the most beautiful coastline of the world”. The Algarve has an area of 5412 km2 with approximately 450 thousand inhabitants but receives an average of 7 million foreign tourists each year. Despite this, it is essential that hotel companies improve or, at least, maintain their performance levels, so that the Algarve will continue to be a desired place. This study aims to analyze the efficiency of hotel companies in the Algarve and simultaneously to assess the influence of certain exogenous variable on the efficiency of these companies. These variables are: location (Windward and Leeward), star rating (four and five-star hotels), owning golf courses or not and owning only one hotel or more than one. Taking into account the available data and the Algarve setting, we believe that these ‘explanatory’ factors might be the most determinant in the performance highlighted. On the one hand, there is no consensus if the existence of golf facilities, star-rating or the number of hotels of the same company influence positively the performance and, on the other hand, location is surprisingly very relevant with Windward and Leeward presenting significant differences and features. In this study, a revenue function was estimated through the stochastic frontier approach (SFA) methodology. As far as we know, it is the first study using a revenue function and also the first time that the hotel efficiency in the Algarve is analyzed using the SFA methodology, so this work is considered pioneer. The assessment and analysis of efficiency using the SFA methodology has been the target of a number of studies since the 80s to the more recent: Assaf et al. (2012), Assaf and Barros (2011) and Pérez-Calderón et al. (2011). A number of authors have been addressing this issue, but all of them estimate cost functions. The literature review carried out for this research, which will be presented in Appendix A, enabled us to find 20 studies worldwide, 10 in Asia, 7 in Europe, two in North America and one in Africa. From
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the 7 studies in Europe, 4 (57%) were made in Portugal and from the 10 in Asia 8 (80%) were applied in Taiwan. In this survey, the author with the largest number of publications was Barros, with 6 studies (2 individually), followed by Assaf with 3 papers. In this survey, the most used variables as inputs were the cost of labor (13), the number of employees (9), the capital (9), the number of rooms (7), the operating costs (6), the F&B costs (5) and the space of F&B (3). Regarding the outputs, the more used variables were the total revenue (7), the room revenue (4), the F&B revenue (4), the other revenue (4) and the sales (4). As referred to, no study was found in the hotel efficiency literature using the revenue function. Since the hotel sector is profit oriented, it makes sense to consider this specification and thus this paper can give a sound contribution to the literature. In addition, the case study is still little studied and it is important to investigate the influence of the explanatory factors on the performance. Following this introduction, the paper is organized as follows. Section two presents a literature review on hotel efficiency using the SFA methodology and a cost function, the third describes the methodology used, the fourth presents the case-study, the fifth shows the results and their discussion and, finally, the sixth draws the major conclusions and makes some considerations about future research.
2. Literature review According to the literature review, we found several studies related to hospitality and the SFA methodology to analyze efficiency. The specifications regarding the sample, methodology and the variables most commonly used in the studies are specified in Table 1. Several and different issues were investigated in the literature. For example, Assaf and Barros (2011) concluded that cost efficiency of the hotels of Luanda (Angola) is still low, although it increased over the period of study and reached an overall average of 67.11%. This study also presents market trends and mentions the need for investment and the management control and focuses on government policies to generate significant increases of cost efficiency. Assaf and Magnini (2012) studied the role of clients’ satisfaction on the efficiency of eight hotel chains in the United States of America. The conclusions suggest that including the variable “clients satisfaction” the average efficiency corresponds to 89.5%. Excluding that variable, it is just 80.2%. These authors say that “clients’ satisfaction” has an important influence on efficiency levels because it is associated with loyalty, thus allowing to reduce costs of future transactions and also price elasticity’s. Pérez-Calderón et al. (2011) studied the energy consumption of European hotels between 2004 and 2007. The hotels of higher dimensions presented high inefficiency, although better performances in 2007. They found no positive correlation between profitability of these hotels and efficiency. They concluded that hotels with higher scale have increased the sense of savings of energy and got better performances due to their higher level of resources. On the other hand, the investments made increased the level of efficiency in 2007, although with a negative impact on the economic and financial return. Yi-Hsing (2011) concluded that in contrast with previous studies, this study found no significant differences between average cost efficiency of metropolitan hotels of Taipe comparing them with non-metropolitans ones. However, the average cost efficiency of small-scale hotels is significantly higher than that of large-scale hotels. The average cost efficiency of domestic chain hotels is clearly higher than that of independent hotels, which is in turn higher than the average cost efficiency of international chain hotels. Khrueathai et al. (2011) studied the operational efficiency and technology gap
for hotels in Thailand. The findings suggest that the efficiency and the technological variation ratio is significantly different between hotels and within groups of hotels. The average operational efficiency of each hotel on the frontier, the group of hotels on the frontier and all groups are respectively 0.90, 0.83 and 0.53. The results suggest that to transfer technology and management technology on operations management of hotels with high efficiencies to the ones with low efficiency, requires organization. They concluded that the effectiveness of foreign hotel groups is higher than of domestic hotels and that hotels can get revenue from other sources of income, such as entertainment and F&B. Assaf et al. (2012) using a panel data sample of 78 Taiwanese hotels concluded that the hotel chains have significantly higher efficiencies than independent hotels. The average efficiency for chains and independent hotels is respectively 77.2% and 73.3%. They also concluded that the ratio of technology gap of independent hotels have achieved only 77.2% of its potential output, while the hotel chains have reached 87.5%. They also observed that large hotels have better returns than those of small size and in terms of average efficiency groups. Larger hotels have efficiencies levels of 73.2% and 70.1% while the small size ones have respectively 68.2% and 63.2%. In this study we investigate the efficiency of hotel companies in the Algarve (Portugal) using the parametric method of stochastic frontier with a revenue function. Particularly we observe the influence of the star rating (four and five-star hotels), the location (Windward and Leeward), the owning or not golf courses or just a single hotel or more than one hotel on efficiency. 3. Methodology 3.1. Overview The frontier methods have been increasingly used in the literature on the estimation of production or cost functions because they also enable us to estimate efficiencies of observations. These methods aim to find the best practice observations (that constitute the frontier) allowing then the estimation of the efficiencies of the other observations from this frontier. So, efficient decision units operate at the production or cost frontier with efficiencies equal to one, while inefficient ones operate below the production frontier or above the cost frontier and have efficiencies less than unity (Chen, 2007). The best known and widely used econometric methodology for estimating efficiency are the stochastic frontiers which had origin in the independent works of Aigner et al. (1977), Meeusen and Van den Broeck (1977) and Battese and Corra (1977). The major principle associated with the efficiency measurement derived from the work of Farrell (1957) on which it was proposed to measure the efficiency of a decision unit through the deviations from an isoquant curve – the idealized frontier. SFA is an econometric regression used to predict the behavior of a dependent variable from one or more independent variables, reporting on the margins of error of these forecasts. More specifically, concerning the efficiency estimation, the parametric methods aim to derive a relationship between the performance of an organization, the market conditions and the characteristics of the production processes. 3.2. Advantages and limitations According to Chen (2007), for example, the cost function of a company depend on the output vector (Y), the price of the input (w), the level of cost inefficiency (u) and a set of random factors (v). The cost function frontier is expressed by: C(y, w, u, v) = f (y, w) exp(u + v)
(1)
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Table 1 SFA studies in the hotel sector. Author
Methodology
Sample
Inputs
Outputs
Anderson et al. (1999)
SFA/Translog
48 hotels, USA
(1) Number of full-time equivalent employees; (2) Number of rooms; (3) Total gaming-related expenses; (4) Total food and beverage expenses; (5) Other expenses.
Total revenue.
Barros (2004)
SFA/Cobb-Douglas
42 hotels, Portugal
(1) Price of work; (2) Price of capital; (3) Price of food. Dummies: (1) Historical hotels; (0) Regional hotels.
(1) Sales; (2) Number of occupied nights.
Barros and Santos (2006)
SFA
15 hotels, Portugal
(1) Employees; (2) Physical capital. Input-prices: (1) Price of labor; (2) Price of capital.
(1) Sales; (2) Added value; (3) Earnings.
Barros (2006)
SFA/Translog
42 hotels, Portugal
(1) Labor; (2) Physical capital; (3) Nights slept; (4) Trend; (5) Historic; (6) Dimension.
Sales.
Chen (2007)
SFA/Cobb Douglas
55 hotels, Taiwan
(1) Cost of work; (2) Total costs of F&B; (3) Cost of materials.
Total revenue.
Rodríguez and Gonzalez (2007)
SFA, Cobb Douglas, Translog
44 hotels, Spain
(1) Annual operational expenses; (2) Ratio (Annual labor costs/number of full-time equivalent employees); (3) Ratio (annual assets depreciation/fix assets at current prices); (4) Ratio (annual financial expenses/debts).
(1) Annual operational revenue; (2) Exogenous specification for efficiency; (1) Time; (2) Work productivity.
Thang (2007)
SFA
474 hotels, Vietnam
(1) Number of employees; (2) Labor costs; (3) Net assets; (4) Total intermediary costs.
Total revenue.
Wang et al. (2007)
SFA/Malmquist
66 hotels, Taiwan
(1) Salaries; (2) Area of food and beverage; (3) Number of rooms; (4) Other operational costs.
(1) Number of occupied rooms; (2) Revenue of food and beverage; (3) Other revenues.
Shang et al. (2008)
SFA
57 hotels, Taiwan
(1) Rooms; (2) Capacity of F&B; (3) Employees; (4) Operational costs.
Rooms revenue.
Assaf et al. (2010)
SFA/Metafrontier
78 hotels, Taiwan
(1) Number of rooms; (2) Employees of rooms in full-time; (3) Drinks; (4) Other departments.
(1) Revenue of rooms, food & beverage and others; (2) Market share; (3) Number of guests for employee.
Bernini and Guizzardi (2010)
SFA/Translog
414 hotels, Italia
(1) Number of employees; (2) Book value of property; (3) Years of activity of the company; (4) Gross salaries of workers; (5) Ratio (total capital/material capital); Dummy: city by the sea; Dummy: art city.
Added value.
Chen et al. (2010)
SFA
57 hotels, Taiwan
(1) Number of guest rooms; (2) Number of employees; (3) Total space of catering division; Prices-inputs: (1) Average price of operational rooms; (2) Annual average price of salaries; (3) Mean price of F&B operations.
(1) Total F&B revenue; (2) Total revenue of rooms; (3) Other revenue; Operational ambience variables: (1) Number of guests by nationality; (2) Chain; (3) Distance to the airport; (4) Year.
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Table 1 (Continued) Author
Methodology
Sample
Inputs
Outputs
Hu et al. (2010)
SFA
66 international hotels, Taiwan
(1) Price of work; (2) Price of F&B; (3) Price of other operations.
(1) Rooms revenue; (2) F&B revenue; (3) Other operational revenues.
Pavlyuk (2010)
SFA
1606 beds hotels, Estónia, Letónia, Lituânia
(1) Infrastructures; (2) Employment; (3) Geographic position and natural attractions.
Factor of competitiveness.
Assaf and Barros (2011)
SFA/Bayesian
13 hotels, Angola
(1) Price of work; (2) Physical capital price.
(1) Revpar; (2) Occupation rate.
Assaf and Magnini (2012)
SFA/Bayesian e Distant Function
8 chain hotels, EUA
(1) Number of stores; (2) Number of full-time equivalent employees; (3) Other operational costs.
(1) Total revenue; (2) Occupation rate.
Khrueathai et al. (2011)
SFA/CobbDouglas/Metafrontier
1799 hotels, Tailand
(1) Number of rooms; (2) Room occupation rate by night; (3) Number of employees; (4) Operational expenses; (5) Assets.
Total revenue.
Pérez-Calderón et al. (2011)
SFA/Cluster Analysis
220 hotels, Europe
(1) Supply of materials; (2) Materials consumed; (3) Cost of employees.
Revenue.
Yi-Hsing (2011)
SFA/Meta-frontier
62 hotels, Taiwan
(1) Type of guests; (2) Dimension of the hotel; (3) Management network.
Sales revenue.
Assaf et al. (2012)
SFA/Metafrontier
78 hotels, Taiwan
(1) Number of rooms; (2) Number of full-time equivalent employees of room division; (3) Number of full-time equivalent employees of F&B division; (4) Number of full-time equivalent employees of other departments.
(1) Total room revenue; (2) Total F&B revenue; (3) Other revenue; (4) Market share of each hotel; (5) Performance of the employees.
or, on logarithmic form, as follows: ln C = f (y, w) + u + v
(2)
The SFA technique enables the decomposition of the error term (εi ) into two components: a component ui representing the inefficiency which is assumed to be a non-negative random variable, and a component vi that captures random shocks and the statistical noise influence to which the organizations are subject and which cannot be controlled (Coelli et al., 1998). It is assumed as having a normal distribution with mean zero and unknown variance. The two components reflect the idea that the efficiency depends first on a set of non-measurable variables, which has an unpredictable effect on efficiency, and a second set of measurable variables that allow for the specification of a statistical model of the efficiency expected value. The aggregate effect on the efficiency of non-measurable variables is assumed to be symmetrical around zero, while the dispersion of the individual efficiency around the expected value may have different expressions (probability distributions) (Battese and Coelli, 1995). The types of distributions for technical inefficiency that have been assumed are the half-normal, the exponential, the normal truncated and the gamma (Coelli et al., 1998; Kumbhakar and Lovell, 2000). The estimation of individual inefficiency can be obtained using the distribution of the inefficiency term conditioned to the estimation of the composite error term (Jondrow et al., 1982). The cost efficiency (CE) is defined by the ratio obtained by the division of the lowest possible cost for the observed cost, according to the following expression: CE =
c min c(y, w) exp(v) = c c(y, w) exp(u + v)
(3)
As CE takes values between 0 and 1, entities with CE = 1 are considered efficient and entities with CE < 1 are inefficient.
There are several advantages of the SFA methodology, particularly when compared with non-parametric benchmarking techniques, such as DEA (see Fried et al., 2008). The possibility of statistical inference analysis is the most noteworthy. These welldeveloped statistical tests allow for investigating the validity of the model specification (tests of statistical significance suggesting the inclusion or exclusion of factors) or the functional form. Another important advantage of the SFA methodology is that if an irrelevant variable is included, it will have a low or even zero weight in the calculation of efficiency indicators and their impact will be neglected (Barros, 2004). Furthermore, it copes easily with the operational environment and the extreme and outlier observations are less important and influent. On the other hand, the SFA methodology also has drawbacks. One of them is related to the large number of options that need to be defined a priori, namely the choice of type of function, the functional form used and the distribution to be followed by the error term ui . Lovell and Schmidt (1988) discuss several advantages and disadvantages of the SFA methodology in their works.
3.3. The revenue function While the (frontier) cost function is achieved for the minimum cost corresponding to a given level of outputs, the revenue function is associated with the revenue maximization for a given bundle of inputs. Two revenue functions can be distinguished depending on whether or not there is market power: the standard revenue function and the alternative revenue function. The revenue function was initially developed by McFadden (1978) and also by Diewert (1974) through a special case with a single input. The standard revenue function assumes that the inputs and outputs markets are perfectly competitive. Given the vectors input (p) and output-price
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(w) the hotel company maximizes revenue by adjusting the amount of inputs and outputs. The revenue function can be expressed as:
Jondrow et al. (1982) present the explicit results for the halfnormal model:
Ri (pi , wi , ui , vi ) = f (pi , wi ) exp(vi − ui )
E[uit |εit ] =
(4)
or on logarithm form: ln Ri = f (pi , wi ) + vi − ui
(5)
The revenue efficiency is defined as the ratio between the real revenue of the hotel company and the maximum that can be achieved by the most efficient hotel company, as shown in expression (6): RE =
R
(6)
Rmax
Assuming that (a) vi and ui are statistically independent of each other; and that (b) vi and ui are independent and identically distributed across observations, we are able to obtain the joint density of the components: fv,u (vi , ui ) = fv (vi )fu (ui )
(8)
which allows to obtain the marginal density of εi : ∞
fu (ui )fv (εi + ui ) dui
(9)
0
The estimation of the frontier is then performed by maximizing the log likelihood function, here the contribution of observation i to the log likelihood is: ln Li (a, b, u2 , v2 | ln Ri , pi , wi ) = ln fε (Ri − f (pi , wi )|u2 , v2 )
(10)
For the case of Normal–Half Normal Model, it is assumed: fv (vi ) = N[0, v2 ] = (1/v )(vi /v ), −∞ < vi < ∞ and ui = |Ui |, where fU (Ui ) = N[0, u2 ] = (1/u )(Ui /u ), −∞ < Ui < ∞ where (·) denotes the standard normal density. Resulting the log-likelihood function for the normal–half normal stochastic frontier model: ln L(˛, ˇ, , ) = −N ln − constant +
N i=1
ln ˚
−ε i
−
1 ε 2 i
2
(11)
where 2 = (u2 + v2 ); = u / v and ˚(·) the standard normal cumulative distribution function (CDF). 3.4. Exponential and gamma models On the estimation of technical inefficiency in stochastic frontiers, according to Greene (2005) are computed initially the error term (εi ) and then estimated uit . The standard estimator uit is performed from the estimation of the average of the function E[uit |εit ], formulating: f (uit |εi ) =
f (uit )f (εit |uit ) f (uit , εit ) = = f (εit ) f (εit )
∞ 0
fu (uit )fv (εit + uit ) fu (uit )fv (εit + uit ) duit (12)
It is used as estimator the conditional mean from the conditional distribution
∞ uit fu (uit )fv (εit + uit ) duit E(uit |εit ) = 0 ∞ 0
( ˜ it ) , ˚( ˜ it )
˜ it =
−εit
(14)
where (·) and ˚(·) are the density and the conditional distribution function of standardized normal distribution for the truncated nor˜ it by ˜ it + u2 / 2 mal model the result is obtained by replacing The corresponding expressions for the exponential and gamma models are, respectively: E[uit |εit ] = zit + v
(zit /v ) , ˚(zit /v )
zit = εit −
v2 u
(15)
and E[uit |εit ] =
q(P, εit ) q(P − 1, εit )
(16)
4. Case study 4.1. Sample
fe,u (ei , ui ) = fu (ui )fv (ei + ui )
1 + 2
˜ it +
(7)
and therefore, since εi = vi − ui :
fe (ei ) =
fu (uit )fv (εit + uit ) duit
(13)
The studied sample consists of observations (hotel companies) owning four and five-star hotels located in the Algarve that operated in 2005–2007 period. The sample is composed of 13 companies owning 20 five-star hotels and 15 companies owning 36 fourstar hotels, corresponding therefore to a sample with a total of 84 observations (28 observations per year). Table 2 summarizes the observations considered. The fourth column includes the total number of the four and five-star hotel existent in the Algarve. Table 3 describes the characteristics of the companies and the numbers of companies regarding the number of “stars”, “location”, “owner of golf” and “owner of more than one hotel”. All data used for this study relate to the years 2005, 2006 and 2007 and were collected from the database SABI (System for Library Automation) from the Bureau van Dijk Electronic Publishing and AHETA (Association of Hotels and Tourist Resorts of the Algarve). 4.2. Model specification Taking into account the literature review and the available data the model was defined. On the specification of the revenue function it was assumed as dependent variable the total revenue (TR), and as price of outputs the price of rooms (PR) and the price of F&B (PFB) As inputs, the number of rooms (NR), the number of employees (NE), the number of seats F&B (NFB), the other costs (OC) and the Capex (CAPEX) were adopted. To further characterize the revenue function it was also considered the following exogenous variables that reflect the surrounding operational environment: • Dummy “Star” to capture the effect of a hotel being rated five or four stars. The value 1 was assigned to five-star hotels and the value 0 to four-star hotels. • Dummy “Regions” aims to capture the effect of sub-regions “Windward” and “Leeward”, defining the Windward with value 1 and Leeward with a value zero. • Dummy “Golf” is intended to capture the effect of the companies with golf courses where value 1 refers to companies with golf and value 0 to companies without golf. • Dummy “Number” is intended to capture the effect of hotel companies owning two or more hotels or that only own one hotel, where 1 corresponds to the first case and 0 the second one. The specification of functional form chosen was the translog due to its flexibility, its ease of estimation and interpretation of
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Table 2 Sample and population of the Algarve hotel companies for the years 2005, 2006 and 2007. Stars
Companies (no.)
Hotels owned (no.)
Hotels at Algarve (no.)
Percentage of the total number of hotels (%)
Observations (no.)
5 4
13 15
20 36
28 141
71.33 25.53
39 45
Total
28
56
169
33.14
84
Table 3 Number of companies by criterion used. Variables
5 stars
5 stars 4 stars Windward Leeward With golf Without golf Only one hotel More than 1 hotel
13 – 7 6 3 10 7 6
4 stars – 15 13 2 4 11 6 9
Windward
Leeward
With golf
Without golf
– – 20 – 5 15 10 10
– – – 8 2 6 3 5
– – – – 7 – 5 2
– – – – – 21 8 13
results. Taking the revenue function, the following configuration is obtained: ln
RT = PFB
˛0 + ˇPR ln
Only 1 hotel – – – – – – 13 –
More than 1 hotel – – – – – – – 15
The results also suggest that regarding the Algarve criterion, which considers all hotel companies studied, the average revenue
PR + ˛LNR ln NR + ˛LNE ln NE + ˛LNFB ln NFB + ˛LOC ln OC PFB
+˛LCPX ln CAPEX 1 1 1 1 + ˛NR2 ln NR2 + ˛NE2 ln NE 2 + ˛NFB2 ln NFB2 + ˛OC2 ln OC 2 2 2 2 2 1 + ˛CPX2 ln CAPEX 2 2 +˛NRNE ln NR × ln NE + ˛NRNFB ln NR × ln NFB + ˛NROC ln NR × ln OC
(17)
+˛NRCPX ln NR × ln CAPEX +˛NENFB ln NE × ln NFB + ˛NEOC ln NE × ln OC + ˛NECPX ln NE × ln CAPEX +˛NFBOC ln NFB × ln OC + ˛NFBCPX ln NFB × ln CAPEX +˛OCCPX ln OC × ln CAPEX +DSTAR DSTAR + DREG DREG + DGOLF DGOLF + DNUM DNUM For the linear homogeneity in prices condition to be met the total revenue (dependent variable) and the price of rooms were divided by the price of F&B. Given the impossibility of estimating the translog function due to the wrong direction of the skewness of the ordinary least squares (OLS) residuals was considered a hybrid translog form.
can increase by 11.6% with the same level of costs, in both models. For other criteria, the ones suggesting greater potential for revenue growth are “owner of one hotel” and “four-star hotels”, the first one presenting a potential for growth between 15.9% and 13.8% and the second between 13.8%, and 14.5% respectively in the exponential and gamma models. The criterion “five-star” presents itself as the one with the least potential for revenue growth.
5. Results and discussion 5.1. Results Table 4 presents the estimates of average efficiency for various companies groups and for two cases where exponential and gamma probability distributions for technical inefficiency are assumed. Other distributions were considered, however, just for these two models reasonable results were found. The results obtained suggest that the magnitude of the average revenue efficiency, the dispersion, and the maximum and minimum values show no significant differences either by adopting an exponential or a gamma distribution to model the inefficiency. The variation of the average efficiencies in the exponential model compared to the gamma model concerning total revenue and the period 2005–2007, ranges between 0.064% in the Algarve criterion and 2.6% in the Leeward criterion.
Fig. 1. Average efficiencies SFA – exponential and gamma models.
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Table 4 Descriptive statistics of the exponential and gamma models. Variable
Algarve 4 stars 5 stars Windward Leeward With golf Without golf More than 1 hotel Only 1 hotel
Exponential
Gamma
Average
Maximum
Minimum
Standard error
Average
Maximum
Minimum
Standard error
0.884 0.862 0.909 0.869 0.920 0.900 0.878 0.921 0.841
0.996 0.996 0.994 0.996 0.996 0.996 0.995 0.996 0.994
0.206 0.522 0.206 0.522 0.206 0.681 0.206 0.522 0.206
0.149 0.155 0.139 0.143 0.158 0.110 0.160 0.105 0.179
0.884 0.855 0.918 0.880 0.894 0.923 0.871 0.903 0.862
1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000
0.163 0.472 0.163 0.472 0.163 0.653 0.163 0.472 0.163
0.160 0.165 0.149 0.152 0.182 0.089 0.176 0.132 0.187
As Fig. 1 shows the highest values of efficiency (0.923) occurred in companies with golf in the gamma model and companies with more than one hotel in the exponential model. The values of the lowest efficiency (0.841) occurred in companies with just one hotel in the exponential model and (0.855) in four-star hotels in the gamma model. From the results it is possible to take several conclusions. First, it can be concluded that the five-star hotels have higher efficiency than those of four-star. Several reasons can be pointed out for this result, such as the more and higher differentiated range of services and the more sophisticated and more purchasing power customer’s demand. A greater competitiveness of this kind of offer, in a much more globalized and international context, demands other management pattern. Second, the Leeward hotels have higher efficiency levels than the Windward ones. The higher concentration of fivestar hotels and golf courses and the brand image associated with golf product (e.g. Vilamoura and Quinta do Lago) along with the features of this region (e.g. the physical differences in the beaches and the proximity of the international airport) might justify this result. Third, the hotels with golf present higher efficiency than the hotels without golf. It seems logical since they involve customers with greater purchasing power and differentiation and added value created by the proximity between the golf course and the hotel. Finally, it can be concluded that companies with more than one hotel display higher efficiency than the ones with only one hotel, which can be justified by synergies gained with economies of scale and economies of scope and by the supply of several and differentiated products.
5.2. Estimation of results: exponential distribution Table 5 summarizes the results obtained in the model, which assumed an exponential distribution for technical inefficiency. The fact that most of the coefficients of the majority of the estimated function were statistically significant means that the selection is appropriate (Hu et al., 2010). The variables price and the number of rooms have positive coefficients suggesting that, on average, 1% increase in the price of room implies 0.82% on total revenue; 1% increase in the number of rooms will increase total revenue by 1.04%; 1% increase in “other costs” implies an increase of 0.18% in total revenue. The exogenous (environmental) variables (DREG and DGOLF) have a negative sign, meaning that companies located in the Windward and owners of golf courses influence negatively the revenue. The lambda value ( = u / v ) is very high (2006.49), meaning that the error term u has an important role in the composite error term, justifying the choice for the SFA methodology. The value = u2 /(u2 + v2 ) = 0.9984 close to 1 means that a significant proportion of the variance in the composite error is derived from the inefficiency effect, thereby justifying also the use of the SFA in this study.
5.3. Estimation of results: gamma distribution Table 6 presents the estimation of results for the gamma distribution. All variables are statistically significant at 1% level, including the operational environment (DSTAR, DREG, DGOLF and DNUM), so the model is considered appropriate. The variables number of employees and CAPEX have negative correlations with the total revenue. The negative correlation between total revenue and number of employees can be related to the excess of employees so that there is the possibility of increasing revenue without increasing the employees, meaning that the number of employees is too high given the level of revenue. Regarding CAPEX, the increases in revenue cannot influence this type of costs due to its nature. The lambda value ( = u / v ) has a high value (2.93), meaning that the error term u has an important role in the composite error term, also explaining the choice of the SFA methodology. The ϒ value equal to 1 also justifies the use of the SFA in this study.
Table 5 Results of translog estimations (exponential distribution). Variable
Coefficient
P[|Z| > z]
Constant PR ␣LNR ␣LNE ␣LNFB ␣LOC ␣LCPX ␣NR2 ␣NE2 ␣NFB2 ␣OC2 ␣CPX2 ␣NRNE ␣NRNFB ␣NROC ␣NRCPX ␣NENFB ␣NEOC ␣NECPX ␣NFBOC ␣NFBCPX ␣OCCPX ␥DSTAR ␥DREG ␥DGOLF ␥DNUM
−0.1091 0.8209 1.0441 −0.0559 0.1672 0.1825 −0.0245 0.2801 −0.5121 1.0684 0.0294 −0.1215 0.6464 −0.6824 −0.1914 0.0490 −0.8990 0.3170 0.0466 0.2821 −0.0492 −0.0089 0.1128 −0.1458 −0.2762 −0.0451
0.0003*** 0.0000*** 0.0000*** 0.2696 0.0270 0.0063* 0.4395 0.0796 0.0241 0.0000*** 0.7110 0.0410 0.0006*** 0.0002*** 0.0875 0.4599 0.0002*** 0.0064* 0.4087 0.0965 0.5831 0.8497 0.0290 0.0020** 0.0000*** 0.2619
Variance parameters for compound error: Theta 7.32769435 (0.0000***); Sigma v 0.00365257 (0.7415); Log likelihood function: 76.92515. Exponential frontier model; Sigma-squared (v) = 0.00001***; Sigma-squared (u) = 0.01862. * Statistical significance at 10%. ** Statistical significance at 5%. *** Statistical significance at 1%.
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Table 6 Results of translog estimations (gamma distribution). Variable
Coefficient
P[|Z| > z]
Constant PR ␣LNR ␣LNE ␣LNFB ␣LOC ␣LCPX ␣NR2 ␣NE2 ␣NFB2 ␣OC2 ␣CPX2 ␣NRNE ␣NRNFB ␣NROC ␣NRCPX ␣NENFB ␣NEOC ␣NECPX ␣NFBOC ␣NFBCPX ␣OCCPX ␥DSTAR ␥DREG ␥DGOLF ␥DNUM
−0.06821 0.8224 0.9908 −0.0870 0.2532 0.1542 −0.0133 0.1189 −0.1348 0.5542 0.0841 −0.1009 0.5173 −0.4622 −0.2808 0.0832 −0.9342 0.1061 0.0296 0.4216 −0.0100 0.0110 0.1158 −0.1458 −0.1621 −0.1209
0.0000*** 0.0000*** 0.0000*** 0.0000*** 0.0000*** 0.0000*** 0.0000*** 0.0000*** 0.0000*** 0.0000*** 0.0000*** 0.0000*** 0.0000*** 0.0000*** 0.0000*** 0.0000*** 0.0000*** 0.0000*** 0.0000*** 0.0000*** 0.1504 0.0000*** 0.0000*** 0.0000*** 0.0000*** 0.0000***
Variance parameters for compound error: Theta 2.49466868 (0.0000***); P 0.23732360 (0.0000***); Sigma v 0.851477 (0.9483); Log likelihood function 172.0464; Sigma-squared (v) = 0.00000***; Sigma-squared (u) = 0.03813. *** Statistical significance at 1%.
6. Concluding remarks This paper measures the revenue efficiency performance of hotel companies in the Algarve disaggregated into a set of criteria, including typology of hotels, location in the area of the Algarve, ownership of golf course as well as being owning one or more hotels. By applying SFA parametric method using a SFA revenue function with a translog specification interesting results were found. Extensive inefficiency was obtained in the Algarve hotels and most of the exogenous factors adopted were considered relevant. Best practices might be identified with this study as well as managerial considerations. Several models were tested but only exponential and gamma models were significant. The highest values of efficiency (0.923) took place in companies with golf in the gamma model and in companies with more than one hotel in the exponential model. The values of the lowest efficiency (0.841) occurred in companies with just one hotel in the exponential model and (0.855) in four-star hotels in the gamma model. Comparing both models by criteria, we found that, in general, higher efficiencies occurred more in five-star hotels than in fourstar hotels, in Leeward than in Windward, in companies with golf than without golf and in companies owning more than one hotel than in companies owning only one. The variation of efficiencies between the two distributions is low (between 0.064% and 2.6%) in the various criteria examined. In the two models there are three statistically significant variables: the price of rooms, the number of rooms and the other costs and all three variables have the expected sign (in this case a positive sign). With this result we can conclude that these variables are the main determinants of the revenue function. We can also conclude the important effect of the operational environment – dummies regions and golf, which are statistically significant and have a negative signal, meaning that total revenue is higher in companies located in the Leeward region and in companies without golf courses.
Summarizing, we can suggest the managers that if they intend to have higher levels of efficiency they must create synergies and develop economies of scope and scale that can be reached through alliances with other hotels (companies owning only one hotel) or through the exchange of services (hotels without golf can hire for their clients to use golf course of another hotel providing transport). Also important are the synergies developed through international communication and the promotion of the destination, as a whole and not individually, as it is done in the hotels of the Algarve. Focusing on the customer to identify clearly increase needs is also relevant. The implementation of the lean thinking in the hotels may reduce inefficient levels. Greater differentiation of services, especially the hotels located in the Windward (alternative forms of entertainment, food, leisure activities) and optimization of variables that contribute most to revenue (price and number of rooms and control the variable “other costs”) should also be considered. In these resilient times, managers must also be aware of the organizational culture to adjust it to the new contexts that require new attitudes and practices. Future research may consider other variables and other methodologies, allowing for comparisons of efficiency levels of national or international hotels. For example, it could be an interesting challenge to apply the same methodology to compare the results that were obtained with this study in hotels in cities located in other regions of Portugal or South Europe. The use of partial frontiers is another area that needs investment. Also the study of efficiency in functional areas and the chain value of hotels may prove important in understanding the causes of inefficiency. Studying I inefficiency in strategic implementation and organizational culture may be important challenges for managers. Investigating the correlation of the lean thinking and efficiency may also be interesting. Also inquiring the prospective customer about the company’s efficiency, particularly at the end of the tourist experience, may prove to be very useful in diagnosing inefficiencies which are not always observable by management. References Aigner, D., Lovell, K., Schmidt, P., 1977. Formulation and estimation of stochastic frontier production function models. Journal of Econometrics 6 (1), 21–37. Anderson, R., Fish, M., Xia, Y., Michello, F., 1999. Measuring efficiency in the hotel industry: a stochastic frontier approach. International Journal of Hospitality Management 18 (1), 45–57. Assaf, A., Barros, C., 2011. Bayesian cost efficiency of Luanda, Angola hotels. The Service Industries Journal 31 (9), 1549–1559. Assaf, A., Magnini, B., 2012. Accounting for consumer satisfaction in measuring hotel efficiency: evidence from the US Hotel industry. International Journal of Hospitality Management 31 (3), 642–647. Assaf, A., Barros, C., Josiassen, A., 2010. Hotel efficiency: a bootstrapped metafrontier approach. International Journal of Hospitality Management 29 (3), 468–475. Assaf, A., Barros, C., Josiassen, A., 2012. Hotel efficiency: a bootstrapped metafrontier approach. International Journal of Hospitality Management 31 (2), 621–629. Barros, C., Santos, C., 2006. The measurement of efficiency in Portuguese hotels with DEA. Journal of Hospitality and Tourism Research 30 (3), 378–400. Barros, C., 2004. A stochastic cost frontier in the Portuguese hotel industry. Tourism Economics 10 (2), 177–192. Barros, C., 2006. Analyzing the rate of technical change in the Portuguese hotel industry. Tourism Economics 12 (3), 325–346. Battese, G., Corra, G., 1977. Estimation of a production frontier model: with application to the pastoral zone of Eastern Australia. Australian Journal of Agricultural Economics 21 (3), 169–179. Battese, G., Coelli, T., 1995. A model for technical inefficiency effects in a stochastic frontier production function for panel data. Empirical Economics 20 (2), 325–332. Bernini, C., Guizzardi, A., 2010. Internal and locational factors affecting hotel industry efficiency: evidence from Italian business corporations. Tourism Economics 16 (4), 883–913. Chen, C., 2007. Applying stochastic frontier approach to measure hotel managerial efficiency in Taiwan. Tourism Management 28 (3), 696–702. Chen, C., Hu, J., Jern-Jou, L., 2010. Tourists’ nationalities and the cost efficiency of international tourist hotels in Taiwan. African Journal of Business Management 4 (16), 3440–3446. Coelli, T., Rao, P., Battese, G., 1998. An Introduction to Efficiency and Productivity Analysis. Kluwer Academic Publishers, Boston.
R. Oliveira et al. / International Journal of Hospitality Management 35 (2013) 59–67 COM, 2010. Europe, the World’s No. 1 Tourist Destination – A New Political Framework for Tourism in Europe. European Commission, Brussels, 30 June. Diewert, W., 1974. Functional forms for revenue and factor requirements functions. International Economic Review 15 (1), 119–130. Farrell, M., 1957. The measurement of productivity efficiency. Journal of the Royal Statistics Society 120 (3), 253–290. Fried, H., Lovell, K., Schmidt, S., 2008. The Measurement of Productive Efficiency and Productivity Change. Oxford University Press, New York. Greene, W., 2005. The econometric approach to efficiency measurement. In: Lovell, K., Fried, H., Schmidt, S. (Eds.), The Measurement of Productive Efficiency. , 2nd ed. Oxford University Press, Oxford. Hu, J., Chiu, C., Shieh, H., Huang, C., 2010. A stochastic cost efficiency analysis of international tourist hotels in Taiwan. International Journal of Hospitality Management 29 (1), 99–107. IAGTO, 2013. International Association of Golf Tour Operators, http://www.iagto.com./public/awards/ (website accessed on 20 February, 2013). Jondrow, J., Lovell, C., Materov, I., Schmidt, P., 1982. On the estimation of technical inefficiency in the stochastic frontier production function model. Journal of Econometrics 19 (2–3), 233–238. Khrueathai, K., Unthonh, A., Kaosa-ard, M., Andrin, R., 2011. Measuring operation efficiency of Thai hotels industry: evidence from meta-frontier analysis. In: International Conference on Applied Economics, Perugia. Kumbhakar, S., Lovell, C., 2000. Stochastic Frontier Analysis. Cambridge University Press, New York, EUA. Lovell, C., Schmidt, P., 1988. A comparison of alternative approaches to the measurement of productive efficiency. In: Dogramaci, A., Fire, R. (Eds.), Applications @Modern ZhducGon Theory. Kluwer Academic Publishers, Boston. McFadden, D., 1978. Cost, revenue and profit functions. In: Fuss, M., Mcfadden, D. (Eds.), Production Economics: A Dual Approach to Theory and Applications. North-Holland, Amsterdam.
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Meeusen, W., Van den Broeck, J., 1977. Efficiency estimation from Cobb–Douglas production. Functions with composed error. International Economic Review 18 (2), 435–444. Pavlyuk, D., 2010. Regional tourism competition in the Baltic States: a spatial stochastic frontier approach. In: The 10th International Conference Reliability and Statistics in Transportation and Communication (RelStat’10), 20–23 October, Riga. Transport and Telecommunication Institute, Lomonosova, Riga, Latvia. Pérez-Calderón, E., Milanés-Montero, P., Ortega-Rossell, F., 2011. Sensitivity of listed European hotels with the sustainable tourism. International Journal of Environment Research 5 (1), 57–66. Phillips, P., 1999. Performance measurement systems and hotels: a new conceptual framework. International Journal of Hospitality Management 18 (2), 171–182. Rodríguez, J., Gonzalez, E., 2007. Cost efficiency of the lodging industry in the tourist destination of Gran Canaria (Spain). Tourism Management 28 (4), 993–1005. SABI (Sistema de Automac¸ão de Bibliotecas from Iberian Balance Sheet Analysis System from Bureau van Dijk Electronic Publishing). Shang, J., Hung, W., Lo, C., 2008. Ecommerce and hotel performance: three stage DEA analysis. The Service Industry Journal 28 (3), 529–540. Thang, B., 2007. Analysis of technical efficiency for the hotel industry in Vietnam. In: Technical Efficiency and Productivity Growth in Vietnam. The Publishing House of Social Labour, Hanoi. Wang, Y., Lee, W., Wong, C., 2007. Productivity and efficiency analysis of international tourist hotels in Taiwan: an application of the stochastic frontier approach. Taiwan Economic Review 35 (1), 87–114. WTA, 2012. http://www.worldtravelawards.com/award-europes-leading-beachdestination-2012 (website accessed on 02.03.13). Yi-Hsing, L., 2011. Estimating cost efficiency and the technology gap ratio using the metafrontier approach for Taiwanese international tourist hotels. Cornell Hospitality Quarterly 52 (3), 341–353.
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International Journal of Hospitality Management journal homepage: www.elsevier.com/locate/ijhosman
Efficiency performance of the Algarve hotels using a revenue function Ricardo Oliveira, Maria Isabel Pedro ∗ , Rui Cunha Marques CEG-IST – Center for Management Studies, Av. Rovisco Pais, 1049 001 Lisbon, Portugal
a r t i c l e Keywords: SFA Revenue function Hotels Stars Location Golf
i n f o
a b s t r a c t The tourism industry, particularly the hotel sector, is becoming increasingly competitive and dynamic as a result of the pressures of globalized supply and demand in a context of uncertainty. The aim of this study is to discuss the efficiency of hotel companies in the Algarve (Portugal), a tourist destination of excellence in southwest Europe. In particular, we intend to assess the efficiency of the hotels in terms of star rating (four and five-star hotels), their location (Windward and Leeward), owning or not golf courses and owning just a single hotel or more than one. This analysis will be based on the parametric method of stochastic frontier approach using a revenue function. We found relevant levels of inefficiency. The results also point out the important role of the operational environment, particularly the hotel location and the existence of golf facilities. Star rating and owning multiples hotels do not seem to be so relevant. © 2013 Elsevier Ltd. All rights reserved.
1. Introduction The tourism industry, particularly the hotel sector, is becoming increasingly competitive and dynamic motivated by the pressures of globalized supply and demand (COM, 2010). However, it is also characterized by a context of uncertainty, despite the growth trend. This motivates the search for continuous and systematic improvement of processes and resources toward efficiency. Many authors have studied the efficiency, including Phillips (1999), Barros (2004) and Chen (2007), all pointing to the improvement of management practices. Differences in markets, tradable products, quality, location, differentiation and price, among other aspects, can generate the critical factors of success and survival of these organizations. Algarve is a tourist destination of worldwide excellence. It was considered two times the best worldwide golf destination in the last decade by the International Association of Golf Tour Operators (IAGTO, 2013). The Algarve golf courses were also distinguished by Rheingolf Magazine and by Golf Digest, putting San Lorenzo and Vilamoura Old Course between the 100 better golf courses of the world. Recently, in European Gala of World Travel Awards Europe (WTA, 2012), the Algarve was considered the best beach destination of Europe and Portugal was deemed the best golf destination. Also Hotel Quinta do Lago was considered the best hotel of the Mediterranean area, while Martinhal Beach was the best villa resort, the Dunas Douradas Beach Club, the best villas and apartments complex and Conrad Algarve Hotel (Hilton Group) the best new resort of the world. Graham Cooke, President of WTA,
∗ Corresponding author. Tel.: +351 912642544. E-mail addresses: [email protected] (R. Oliveira), [email protected] (M.I. Pedro), [email protected] (R.C. Marques). 0278-4319/$ – see front matter © 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ijhm.2013.05.005
underlined that the “Algarve is also one of the most beautiful coastline of the world”. The Algarve has an area of 5412 km2 with approximately 450 thousand inhabitants but receives an average of 7 million foreign tourists each year. Despite this, it is essential that hotel companies improve or, at least, maintain their performance levels, so that the Algarve will continue to be a desired place. This study aims to analyze the efficiency of hotel companies in the Algarve and simultaneously to assess the influence of certain exogenous variable on the efficiency of these companies. These variables are: location (Windward and Leeward), star rating (four and five-star hotels), owning golf courses or not and owning only one hotel or more than one. Taking into account the available data and the Algarve setting, we believe that these ‘explanatory’ factors might be the most determinant in the performance highlighted. On the one hand, there is no consensus if the existence of golf facilities, star-rating or the number of hotels of the same company influence positively the performance and, on the other hand, location is surprisingly very relevant with Windward and Leeward presenting significant differences and features. In this study, a revenue function was estimated through the stochastic frontier approach (SFA) methodology. As far as we know, it is the first study using a revenue function and also the first time that the hotel efficiency in the Algarve is analyzed using the SFA methodology, so this work is considered pioneer. The assessment and analysis of efficiency using the SFA methodology has been the target of a number of studies since the 80s to the more recent: Assaf et al. (2012), Assaf and Barros (2011) and Pérez-Calderón et al. (2011). A number of authors have been addressing this issue, but all of them estimate cost functions. The literature review carried out for this research, which will be presented in Appendix A, enabled us to find 20 studies worldwide, 10 in Asia, 7 in Europe, two in North America and one in Africa. From
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the 7 studies in Europe, 4 (57%) were made in Portugal and from the 10 in Asia 8 (80%) were applied in Taiwan. In this survey, the author with the largest number of publications was Barros, with 6 studies (2 individually), followed by Assaf with 3 papers. In this survey, the most used variables as inputs were the cost of labor (13), the number of employees (9), the capital (9), the number of rooms (7), the operating costs (6), the F&B costs (5) and the space of F&B (3). Regarding the outputs, the more used variables were the total revenue (7), the room revenue (4), the F&B revenue (4), the other revenue (4) and the sales (4). As referred to, no study was found in the hotel efficiency literature using the revenue function. Since the hotel sector is profit oriented, it makes sense to consider this specification and thus this paper can give a sound contribution to the literature. In addition, the case study is still little studied and it is important to investigate the influence of the explanatory factors on the performance. Following this introduction, the paper is organized as follows. Section two presents a literature review on hotel efficiency using the SFA methodology and a cost function, the third describes the methodology used, the fourth presents the case-study, the fifth shows the results and their discussion and, finally, the sixth draws the major conclusions and makes some considerations about future research.
2. Literature review According to the literature review, we found several studies related to hospitality and the SFA methodology to analyze efficiency. The specifications regarding the sample, methodology and the variables most commonly used in the studies are specified in Table 1. Several and different issues were investigated in the literature. For example, Assaf and Barros (2011) concluded that cost efficiency of the hotels of Luanda (Angola) is still low, although it increased over the period of study and reached an overall average of 67.11%. This study also presents market trends and mentions the need for investment and the management control and focuses on government policies to generate significant increases of cost efficiency. Assaf and Magnini (2012) studied the role of clients’ satisfaction on the efficiency of eight hotel chains in the United States of America. The conclusions suggest that including the variable “clients satisfaction” the average efficiency corresponds to 89.5%. Excluding that variable, it is just 80.2%. These authors say that “clients’ satisfaction” has an important influence on efficiency levels because it is associated with loyalty, thus allowing to reduce costs of future transactions and also price elasticity’s. Pérez-Calderón et al. (2011) studied the energy consumption of European hotels between 2004 and 2007. The hotels of higher dimensions presented high inefficiency, although better performances in 2007. They found no positive correlation between profitability of these hotels and efficiency. They concluded that hotels with higher scale have increased the sense of savings of energy and got better performances due to their higher level of resources. On the other hand, the investments made increased the level of efficiency in 2007, although with a negative impact on the economic and financial return. Yi-Hsing (2011) concluded that in contrast with previous studies, this study found no significant differences between average cost efficiency of metropolitan hotels of Taipe comparing them with non-metropolitans ones. However, the average cost efficiency of small-scale hotels is significantly higher than that of large-scale hotels. The average cost efficiency of domestic chain hotels is clearly higher than that of independent hotels, which is in turn higher than the average cost efficiency of international chain hotels. Khrueathai et al. (2011) studied the operational efficiency and technology gap
for hotels in Thailand. The findings suggest that the efficiency and the technological variation ratio is significantly different between hotels and within groups of hotels. The average operational efficiency of each hotel on the frontier, the group of hotels on the frontier and all groups are respectively 0.90, 0.83 and 0.53. The results suggest that to transfer technology and management technology on operations management of hotels with high efficiencies to the ones with low efficiency, requires organization. They concluded that the effectiveness of foreign hotel groups is higher than of domestic hotels and that hotels can get revenue from other sources of income, such as entertainment and F&B. Assaf et al. (2012) using a panel data sample of 78 Taiwanese hotels concluded that the hotel chains have significantly higher efficiencies than independent hotels. The average efficiency for chains and independent hotels is respectively 77.2% and 73.3%. They also concluded that the ratio of technology gap of independent hotels have achieved only 77.2% of its potential output, while the hotel chains have reached 87.5%. They also observed that large hotels have better returns than those of small size and in terms of average efficiency groups. Larger hotels have efficiencies levels of 73.2% and 70.1% while the small size ones have respectively 68.2% and 63.2%. In this study we investigate the efficiency of hotel companies in the Algarve (Portugal) using the parametric method of stochastic frontier with a revenue function. Particularly we observe the influence of the star rating (four and five-star hotels), the location (Windward and Leeward), the owning or not golf courses or just a single hotel or more than one hotel on efficiency. 3. Methodology 3.1. Overview The frontier methods have been increasingly used in the literature on the estimation of production or cost functions because they also enable us to estimate efficiencies of observations. These methods aim to find the best practice observations (that constitute the frontier) allowing then the estimation of the efficiencies of the other observations from this frontier. So, efficient decision units operate at the production or cost frontier with efficiencies equal to one, while inefficient ones operate below the production frontier or above the cost frontier and have efficiencies less than unity (Chen, 2007). The best known and widely used econometric methodology for estimating efficiency are the stochastic frontiers which had origin in the independent works of Aigner et al. (1977), Meeusen and Van den Broeck (1977) and Battese and Corra (1977). The major principle associated with the efficiency measurement derived from the work of Farrell (1957) on which it was proposed to measure the efficiency of a decision unit through the deviations from an isoquant curve – the idealized frontier. SFA is an econometric regression used to predict the behavior of a dependent variable from one or more independent variables, reporting on the margins of error of these forecasts. More specifically, concerning the efficiency estimation, the parametric methods aim to derive a relationship between the performance of an organization, the market conditions and the characteristics of the production processes. 3.2. Advantages and limitations According to Chen (2007), for example, the cost function of a company depend on the output vector (Y), the price of the input (w), the level of cost inefficiency (u) and a set of random factors (v). The cost function frontier is expressed by: C(y, w, u, v) = f (y, w) exp(u + v)
(1)
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Table 1 SFA studies in the hotel sector. Author
Methodology
Sample
Inputs
Outputs
Anderson et al. (1999)
SFA/Translog
48 hotels, USA
(1) Number of full-time equivalent employees; (2) Number of rooms; (3) Total gaming-related expenses; (4) Total food and beverage expenses; (5) Other expenses.
Total revenue.
Barros (2004)
SFA/Cobb-Douglas
42 hotels, Portugal
(1) Price of work; (2) Price of capital; (3) Price of food. Dummies: (1) Historical hotels; (0) Regional hotels.
(1) Sales; (2) Number of occupied nights.
Barros and Santos (2006)
SFA
15 hotels, Portugal
(1) Employees; (2) Physical capital. Input-prices: (1) Price of labor; (2) Price of capital.
(1) Sales; (2) Added value; (3) Earnings.
Barros (2006)
SFA/Translog
42 hotels, Portugal
(1) Labor; (2) Physical capital; (3) Nights slept; (4) Trend; (5) Historic; (6) Dimension.
Sales.
Chen (2007)
SFA/Cobb Douglas
55 hotels, Taiwan
(1) Cost of work; (2) Total costs of F&B; (3) Cost of materials.
Total revenue.
Rodríguez and Gonzalez (2007)
SFA, Cobb Douglas, Translog
44 hotels, Spain
(1) Annual operational expenses; (2) Ratio (Annual labor costs/number of full-time equivalent employees); (3) Ratio (annual assets depreciation/fix assets at current prices); (4) Ratio (annual financial expenses/debts).
(1) Annual operational revenue; (2) Exogenous specification for efficiency; (1) Time; (2) Work productivity.
Thang (2007)
SFA
474 hotels, Vietnam
(1) Number of employees; (2) Labor costs; (3) Net assets; (4) Total intermediary costs.
Total revenue.
Wang et al. (2007)
SFA/Malmquist
66 hotels, Taiwan
(1) Salaries; (2) Area of food and beverage; (3) Number of rooms; (4) Other operational costs.
(1) Number of occupied rooms; (2) Revenue of food and beverage; (3) Other revenues.
Shang et al. (2008)
SFA
57 hotels, Taiwan
(1) Rooms; (2) Capacity of F&B; (3) Employees; (4) Operational costs.
Rooms revenue.
Assaf et al. (2010)
SFA/Metafrontier
78 hotels, Taiwan
(1) Number of rooms; (2) Employees of rooms in full-time; (3) Drinks; (4) Other departments.
(1) Revenue of rooms, food & beverage and others; (2) Market share; (3) Number of guests for employee.
Bernini and Guizzardi (2010)
SFA/Translog
414 hotels, Italia
(1) Number of employees; (2) Book value of property; (3) Years of activity of the company; (4) Gross salaries of workers; (5) Ratio (total capital/material capital); Dummy: city by the sea; Dummy: art city.
Added value.
Chen et al. (2010)
SFA
57 hotels, Taiwan
(1) Number of guest rooms; (2) Number of employees; (3) Total space of catering division; Prices-inputs: (1) Average price of operational rooms; (2) Annual average price of salaries; (3) Mean price of F&B operations.
(1) Total F&B revenue; (2) Total revenue of rooms; (3) Other revenue; Operational ambience variables: (1) Number of guests by nationality; (2) Chain; (3) Distance to the airport; (4) Year.
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Table 1 (Continued) Author
Methodology
Sample
Inputs
Outputs
Hu et al. (2010)
SFA
66 international hotels, Taiwan
(1) Price of work; (2) Price of F&B; (3) Price of other operations.
(1) Rooms revenue; (2) F&B revenue; (3) Other operational revenues.
Pavlyuk (2010)
SFA
1606 beds hotels, Estónia, Letónia, Lituânia
(1) Infrastructures; (2) Employment; (3) Geographic position and natural attractions.
Factor of competitiveness.
Assaf and Barros (2011)
SFA/Bayesian
13 hotels, Angola
(1) Price of work; (2) Physical capital price.
(1) Revpar; (2) Occupation rate.
Assaf and Magnini (2012)
SFA/Bayesian e Distant Function
8 chain hotels, EUA
(1) Number of stores; (2) Number of full-time equivalent employees; (3) Other operational costs.
(1) Total revenue; (2) Occupation rate.
Khrueathai et al. (2011)
SFA/CobbDouglas/Metafrontier
1799 hotels, Tailand
(1) Number of rooms; (2) Room occupation rate by night; (3) Number of employees; (4) Operational expenses; (5) Assets.
Total revenue.
Pérez-Calderón et al. (2011)
SFA/Cluster Analysis
220 hotels, Europe
(1) Supply of materials; (2) Materials consumed; (3) Cost of employees.
Revenue.
Yi-Hsing (2011)
SFA/Meta-frontier
62 hotels, Taiwan
(1) Type of guests; (2) Dimension of the hotel; (3) Management network.
Sales revenue.
Assaf et al. (2012)
SFA/Metafrontier
78 hotels, Taiwan
(1) Number of rooms; (2) Number of full-time equivalent employees of room division; (3) Number of full-time equivalent employees of F&B division; (4) Number of full-time equivalent employees of other departments.
(1) Total room revenue; (2) Total F&B revenue; (3) Other revenue; (4) Market share of each hotel; (5) Performance of the employees.
or, on logarithmic form, as follows: ln C = f (y, w) + u + v
(2)
The SFA technique enables the decomposition of the error term (εi ) into two components: a component ui representing the inefficiency which is assumed to be a non-negative random variable, and a component vi that captures random shocks and the statistical noise influence to which the organizations are subject and which cannot be controlled (Coelli et al., 1998). It is assumed as having a normal distribution with mean zero and unknown variance. The two components reflect the idea that the efficiency depends first on a set of non-measurable variables, which has an unpredictable effect on efficiency, and a second set of measurable variables that allow for the specification of a statistical model of the efficiency expected value. The aggregate effect on the efficiency of non-measurable variables is assumed to be symmetrical around zero, while the dispersion of the individual efficiency around the expected value may have different expressions (probability distributions) (Battese and Coelli, 1995). The types of distributions for technical inefficiency that have been assumed are the half-normal, the exponential, the normal truncated and the gamma (Coelli et al., 1998; Kumbhakar and Lovell, 2000). The estimation of individual inefficiency can be obtained using the distribution of the inefficiency term conditioned to the estimation of the composite error term (Jondrow et al., 1982). The cost efficiency (CE) is defined by the ratio obtained by the division of the lowest possible cost for the observed cost, according to the following expression: CE =
c min c(y, w) exp(v) = c c(y, w) exp(u + v)
(3)
As CE takes values between 0 and 1, entities with CE = 1 are considered efficient and entities with CE < 1 are inefficient.
There are several advantages of the SFA methodology, particularly when compared with non-parametric benchmarking techniques, such as DEA (see Fried et al., 2008). The possibility of statistical inference analysis is the most noteworthy. These welldeveloped statistical tests allow for investigating the validity of the model specification (tests of statistical significance suggesting the inclusion or exclusion of factors) or the functional form. Another important advantage of the SFA methodology is that if an irrelevant variable is included, it will have a low or even zero weight in the calculation of efficiency indicators and their impact will be neglected (Barros, 2004). Furthermore, it copes easily with the operational environment and the extreme and outlier observations are less important and influent. On the other hand, the SFA methodology also has drawbacks. One of them is related to the large number of options that need to be defined a priori, namely the choice of type of function, the functional form used and the distribution to be followed by the error term ui . Lovell and Schmidt (1988) discuss several advantages and disadvantages of the SFA methodology in their works.
3.3. The revenue function While the (frontier) cost function is achieved for the minimum cost corresponding to a given level of outputs, the revenue function is associated with the revenue maximization for a given bundle of inputs. Two revenue functions can be distinguished depending on whether or not there is market power: the standard revenue function and the alternative revenue function. The revenue function was initially developed by McFadden (1978) and also by Diewert (1974) through a special case with a single input. The standard revenue function assumes that the inputs and outputs markets are perfectly competitive. Given the vectors input (p) and output-price
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(w) the hotel company maximizes revenue by adjusting the amount of inputs and outputs. The revenue function can be expressed as:
Jondrow et al. (1982) present the explicit results for the halfnormal model:
Ri (pi , wi , ui , vi ) = f (pi , wi ) exp(vi − ui )
E[uit |εit ] =
(4)
or on logarithm form: ln Ri = f (pi , wi ) + vi − ui
(5)
The revenue efficiency is defined as the ratio between the real revenue of the hotel company and the maximum that can be achieved by the most efficient hotel company, as shown in expression (6): RE =
R
(6)
Rmax
Assuming that (a) vi and ui are statistically independent of each other; and that (b) vi and ui are independent and identically distributed across observations, we are able to obtain the joint density of the components: fv,u (vi , ui ) = fv (vi )fu (ui )
(8)
which allows to obtain the marginal density of εi : ∞
fu (ui )fv (εi + ui ) dui
(9)
0
The estimation of the frontier is then performed by maximizing the log likelihood function, here the contribution of observation i to the log likelihood is: ln Li (a, b, u2 , v2 | ln Ri , pi , wi ) = ln fε (Ri − f (pi , wi )|u2 , v2 )
(10)
For the case of Normal–Half Normal Model, it is assumed: fv (vi ) = N[0, v2 ] = (1/v )(vi /v ), −∞ < vi < ∞ and ui = |Ui |, where fU (Ui ) = N[0, u2 ] = (1/u )(Ui /u ), −∞ < Ui < ∞ where (·) denotes the standard normal density. Resulting the log-likelihood function for the normal–half normal stochastic frontier model: ln L(˛, ˇ, , ) = −N ln − constant +
N i=1
ln ˚
−ε i
−
1 ε 2 i
2
(11)
where 2 = (u2 + v2 ); = u / v and ˚(·) the standard normal cumulative distribution function (CDF). 3.4. Exponential and gamma models On the estimation of technical inefficiency in stochastic frontiers, according to Greene (2005) are computed initially the error term (εi ) and then estimated uit . The standard estimator uit is performed from the estimation of the average of the function E[uit |εit ], formulating: f (uit |εi ) =
f (uit )f (εit |uit ) f (uit , εit ) = = f (εit ) f (εit )
∞ 0
fu (uit )fv (εit + uit ) fu (uit )fv (εit + uit ) duit (12)
It is used as estimator the conditional mean from the conditional distribution
∞ uit fu (uit )fv (εit + uit ) duit E(uit |εit ) = 0 ∞ 0
( ˜ it ) , ˚( ˜ it )
˜ it =
−εit
(14)
where (·) and ˚(·) are the density and the conditional distribution function of standardized normal distribution for the truncated nor˜ it by ˜ it + u2 / 2 mal model the result is obtained by replacing The corresponding expressions for the exponential and gamma models are, respectively: E[uit |εit ] = zit + v
(zit /v ) , ˚(zit /v )
zit = εit −
v2 u
(15)
and E[uit |εit ] =
q(P, εit ) q(P − 1, εit )
(16)
4. Case study 4.1. Sample
fe,u (ei , ui ) = fu (ui )fv (ei + ui )
1 + 2
˜ it +
(7)
and therefore, since εi = vi − ui :
fe (ei ) =
fu (uit )fv (εit + uit ) duit
(13)
The studied sample consists of observations (hotel companies) owning four and five-star hotels located in the Algarve that operated in 2005–2007 period. The sample is composed of 13 companies owning 20 five-star hotels and 15 companies owning 36 fourstar hotels, corresponding therefore to a sample with a total of 84 observations (28 observations per year). Table 2 summarizes the observations considered. The fourth column includes the total number of the four and five-star hotel existent in the Algarve. Table 3 describes the characteristics of the companies and the numbers of companies regarding the number of “stars”, “location”, “owner of golf” and “owner of more than one hotel”. All data used for this study relate to the years 2005, 2006 and 2007 and were collected from the database SABI (System for Library Automation) from the Bureau van Dijk Electronic Publishing and AHETA (Association of Hotels and Tourist Resorts of the Algarve). 4.2. Model specification Taking into account the literature review and the available data the model was defined. On the specification of the revenue function it was assumed as dependent variable the total revenue (TR), and as price of outputs the price of rooms (PR) and the price of F&B (PFB) As inputs, the number of rooms (NR), the number of employees (NE), the number of seats F&B (NFB), the other costs (OC) and the Capex (CAPEX) were adopted. To further characterize the revenue function it was also considered the following exogenous variables that reflect the surrounding operational environment: • Dummy “Star” to capture the effect of a hotel being rated five or four stars. The value 1 was assigned to five-star hotels and the value 0 to four-star hotels. • Dummy “Regions” aims to capture the effect of sub-regions “Windward” and “Leeward”, defining the Windward with value 1 and Leeward with a value zero. • Dummy “Golf” is intended to capture the effect of the companies with golf courses where value 1 refers to companies with golf and value 0 to companies without golf. • Dummy “Number” is intended to capture the effect of hotel companies owning two or more hotels or that only own one hotel, where 1 corresponds to the first case and 0 the second one. The specification of functional form chosen was the translog due to its flexibility, its ease of estimation and interpretation of
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Table 2 Sample and population of the Algarve hotel companies for the years 2005, 2006 and 2007. Stars
Companies (no.)
Hotels owned (no.)
Hotels at Algarve (no.)
Percentage of the total number of hotels (%)
Observations (no.)
5 4
13 15
20 36
28 141
71.33 25.53
39 45
Total
28
56
169
33.14
84
Table 3 Number of companies by criterion used. Variables
5 stars
5 stars 4 stars Windward Leeward With golf Without golf Only one hotel More than 1 hotel
13 – 7 6 3 10 7 6
4 stars – 15 13 2 4 11 6 9
Windward
Leeward
With golf
Without golf
– – 20 – 5 15 10 10
– – – 8 2 6 3 5
– – – – 7 – 5 2
– – – – – 21 8 13
results. Taking the revenue function, the following configuration is obtained: ln
RT = PFB
˛0 + ˇPR ln
Only 1 hotel – – – – – – 13 –
More than 1 hotel – – – – – – – 15
The results also suggest that regarding the Algarve criterion, which considers all hotel companies studied, the average revenue
PR + ˛LNR ln NR + ˛LNE ln NE + ˛LNFB ln NFB + ˛LOC ln OC PFB
+˛LCPX ln CAPEX 1 1 1 1 + ˛NR2 ln NR2 + ˛NE2 ln NE 2 + ˛NFB2 ln NFB2 + ˛OC2 ln OC 2 2 2 2 2 1 + ˛CPX2 ln CAPEX 2 2 +˛NRNE ln NR × ln NE + ˛NRNFB ln NR × ln NFB + ˛NROC ln NR × ln OC
(17)
+˛NRCPX ln NR × ln CAPEX +˛NENFB ln NE × ln NFB + ˛NEOC ln NE × ln OC + ˛NECPX ln NE × ln CAPEX +˛NFBOC ln NFB × ln OC + ˛NFBCPX ln NFB × ln CAPEX +˛OCCPX ln OC × ln CAPEX +DSTAR DSTAR + DREG DREG + DGOLF DGOLF + DNUM DNUM For the linear homogeneity in prices condition to be met the total revenue (dependent variable) and the price of rooms were divided by the price of F&B. Given the impossibility of estimating the translog function due to the wrong direction of the skewness of the ordinary least squares (OLS) residuals was considered a hybrid translog form.
can increase by 11.6% with the same level of costs, in both models. For other criteria, the ones suggesting greater potential for revenue growth are “owner of one hotel” and “four-star hotels”, the first one presenting a potential for growth between 15.9% and 13.8% and the second between 13.8%, and 14.5% respectively in the exponential and gamma models. The criterion “five-star” presents itself as the one with the least potential for revenue growth.
5. Results and discussion 5.1. Results Table 4 presents the estimates of average efficiency for various companies groups and for two cases where exponential and gamma probability distributions for technical inefficiency are assumed. Other distributions were considered, however, just for these two models reasonable results were found. The results obtained suggest that the magnitude of the average revenue efficiency, the dispersion, and the maximum and minimum values show no significant differences either by adopting an exponential or a gamma distribution to model the inefficiency. The variation of the average efficiencies in the exponential model compared to the gamma model concerning total revenue and the period 2005–2007, ranges between 0.064% in the Algarve criterion and 2.6% in the Leeward criterion.
Fig. 1. Average efficiencies SFA – exponential and gamma models.
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Table 4 Descriptive statistics of the exponential and gamma models. Variable
Algarve 4 stars 5 stars Windward Leeward With golf Without golf More than 1 hotel Only 1 hotel
Exponential
Gamma
Average
Maximum
Minimum
Standard error
Average
Maximum
Minimum
Standard error
0.884 0.862 0.909 0.869 0.920 0.900 0.878 0.921 0.841
0.996 0.996 0.994 0.996 0.996 0.996 0.995 0.996 0.994
0.206 0.522 0.206 0.522 0.206 0.681 0.206 0.522 0.206
0.149 0.155 0.139 0.143 0.158 0.110 0.160 0.105 0.179
0.884 0.855 0.918 0.880 0.894 0.923 0.871 0.903 0.862
1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000
0.163 0.472 0.163 0.472 0.163 0.653 0.163 0.472 0.163
0.160 0.165 0.149 0.152 0.182 0.089 0.176 0.132 0.187
As Fig. 1 shows the highest values of efficiency (0.923) occurred in companies with golf in the gamma model and companies with more than one hotel in the exponential model. The values of the lowest efficiency (0.841) occurred in companies with just one hotel in the exponential model and (0.855) in four-star hotels in the gamma model. From the results it is possible to take several conclusions. First, it can be concluded that the five-star hotels have higher efficiency than those of four-star. Several reasons can be pointed out for this result, such as the more and higher differentiated range of services and the more sophisticated and more purchasing power customer’s demand. A greater competitiveness of this kind of offer, in a much more globalized and international context, demands other management pattern. Second, the Leeward hotels have higher efficiency levels than the Windward ones. The higher concentration of fivestar hotels and golf courses and the brand image associated with golf product (e.g. Vilamoura and Quinta do Lago) along with the features of this region (e.g. the physical differences in the beaches and the proximity of the international airport) might justify this result. Third, the hotels with golf present higher efficiency than the hotels without golf. It seems logical since they involve customers with greater purchasing power and differentiation and added value created by the proximity between the golf course and the hotel. Finally, it can be concluded that companies with more than one hotel display higher efficiency than the ones with only one hotel, which can be justified by synergies gained with economies of scale and economies of scope and by the supply of several and differentiated products.
5.2. Estimation of results: exponential distribution Table 5 summarizes the results obtained in the model, which assumed an exponential distribution for technical inefficiency. The fact that most of the coefficients of the majority of the estimated function were statistically significant means that the selection is appropriate (Hu et al., 2010). The variables price and the number of rooms have positive coefficients suggesting that, on average, 1% increase in the price of room implies 0.82% on total revenue; 1% increase in the number of rooms will increase total revenue by 1.04%; 1% increase in “other costs” implies an increase of 0.18% in total revenue. The exogenous (environmental) variables (DREG and DGOLF) have a negative sign, meaning that companies located in the Windward and owners of golf courses influence negatively the revenue. The lambda value ( = u / v ) is very high (2006.49), meaning that the error term u has an important role in the composite error term, justifying the choice for the SFA methodology. The value = u2 /(u2 + v2 ) = 0.9984 close to 1 means that a significant proportion of the variance in the composite error is derived from the inefficiency effect, thereby justifying also the use of the SFA in this study.
5.3. Estimation of results: gamma distribution Table 6 presents the estimation of results for the gamma distribution. All variables are statistically significant at 1% level, including the operational environment (DSTAR, DREG, DGOLF and DNUM), so the model is considered appropriate. The variables number of employees and CAPEX have negative correlations with the total revenue. The negative correlation between total revenue and number of employees can be related to the excess of employees so that there is the possibility of increasing revenue without increasing the employees, meaning that the number of employees is too high given the level of revenue. Regarding CAPEX, the increases in revenue cannot influence this type of costs due to its nature. The lambda value ( = u / v ) has a high value (2.93), meaning that the error term u has an important role in the composite error term, also explaining the choice of the SFA methodology. The ϒ value equal to 1 also justifies the use of the SFA in this study.
Table 5 Results of translog estimations (exponential distribution). Variable
Coefficient
P[|Z| > z]
Constant PR ␣LNR ␣LNE ␣LNFB ␣LOC ␣LCPX ␣NR2 ␣NE2 ␣NFB2 ␣OC2 ␣CPX2 ␣NRNE ␣NRNFB ␣NROC ␣NRCPX ␣NENFB ␣NEOC ␣NECPX ␣NFBOC ␣NFBCPX ␣OCCPX ␥DSTAR ␥DREG ␥DGOLF ␥DNUM
−0.1091 0.8209 1.0441 −0.0559 0.1672 0.1825 −0.0245 0.2801 −0.5121 1.0684 0.0294 −0.1215 0.6464 −0.6824 −0.1914 0.0490 −0.8990 0.3170 0.0466 0.2821 −0.0492 −0.0089 0.1128 −0.1458 −0.2762 −0.0451
0.0003*** 0.0000*** 0.0000*** 0.2696 0.0270 0.0063* 0.4395 0.0796 0.0241 0.0000*** 0.7110 0.0410 0.0006*** 0.0002*** 0.0875 0.4599 0.0002*** 0.0064* 0.4087 0.0965 0.5831 0.8497 0.0290 0.0020** 0.0000*** 0.2619
Variance parameters for compound error: Theta 7.32769435 (0.0000***); Sigma v 0.00365257 (0.7415); Log likelihood function: 76.92515. Exponential frontier model; Sigma-squared (v) = 0.00001***; Sigma-squared (u) = 0.01862. * Statistical significance at 10%. ** Statistical significance at 5%. *** Statistical significance at 1%.
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Table 6 Results of translog estimations (gamma distribution). Variable
Coefficient
P[|Z| > z]
Constant PR ␣LNR ␣LNE ␣LNFB ␣LOC ␣LCPX ␣NR2 ␣NE2 ␣NFB2 ␣OC2 ␣CPX2 ␣NRNE ␣NRNFB ␣NROC ␣NRCPX ␣NENFB ␣NEOC ␣NECPX ␣NFBOC ␣NFBCPX ␣OCCPX ␥DSTAR ␥DREG ␥DGOLF ␥DNUM
−0.06821 0.8224 0.9908 −0.0870 0.2532 0.1542 −0.0133 0.1189 −0.1348 0.5542 0.0841 −0.1009 0.5173 −0.4622 −0.2808 0.0832 −0.9342 0.1061 0.0296 0.4216 −0.0100 0.0110 0.1158 −0.1458 −0.1621 −0.1209
0.0000*** 0.0000*** 0.0000*** 0.0000*** 0.0000*** 0.0000*** 0.0000*** 0.0000*** 0.0000*** 0.0000*** 0.0000*** 0.0000*** 0.0000*** 0.0000*** 0.0000*** 0.0000*** 0.0000*** 0.0000*** 0.0000*** 0.0000*** 0.1504 0.0000*** 0.0000*** 0.0000*** 0.0000*** 0.0000***
Variance parameters for compound error: Theta 2.49466868 (0.0000***); P 0.23732360 (0.0000***); Sigma v 0.851477 (0.9483); Log likelihood function 172.0464; Sigma-squared (v) = 0.00000***; Sigma-squared (u) = 0.03813. *** Statistical significance at 1%.
6. Concluding remarks This paper measures the revenue efficiency performance of hotel companies in the Algarve disaggregated into a set of criteria, including typology of hotels, location in the area of the Algarve, ownership of golf course as well as being owning one or more hotels. By applying SFA parametric method using a SFA revenue function with a translog specification interesting results were found. Extensive inefficiency was obtained in the Algarve hotels and most of the exogenous factors adopted were considered relevant. Best practices might be identified with this study as well as managerial considerations. Several models were tested but only exponential and gamma models were significant. The highest values of efficiency (0.923) took place in companies with golf in the gamma model and in companies with more than one hotel in the exponential model. The values of the lowest efficiency (0.841) occurred in companies with just one hotel in the exponential model and (0.855) in four-star hotels in the gamma model. Comparing both models by criteria, we found that, in general, higher efficiencies occurred more in five-star hotels than in fourstar hotels, in Leeward than in Windward, in companies with golf than without golf and in companies owning more than one hotel than in companies owning only one. The variation of efficiencies between the two distributions is low (between 0.064% and 2.6%) in the various criteria examined. In the two models there are three statistically significant variables: the price of rooms, the number of rooms and the other costs and all three variables have the expected sign (in this case a positive sign). With this result we can conclude that these variables are the main determinants of the revenue function. We can also conclude the important effect of the operational environment – dummies regions and golf, which are statistically significant and have a negative signal, meaning that total revenue is higher in companies located in the Leeward region and in companies without golf courses.
Summarizing, we can suggest the managers that if they intend to have higher levels of efficiency they must create synergies and develop economies of scope and scale that can be reached through alliances with other hotels (companies owning only one hotel) or through the exchange of services (hotels without golf can hire for their clients to use golf course of another hotel providing transport). Also important are the synergies developed through international communication and the promotion of the destination, as a whole and not individually, as it is done in the hotels of the Algarve. Focusing on the customer to identify clearly increase needs is also relevant. The implementation of the lean thinking in the hotels may reduce inefficient levels. Greater differentiation of services, especially the hotels located in the Windward (alternative forms of entertainment, food, leisure activities) and optimization of variables that contribute most to revenue (price and number of rooms and control the variable “other costs”) should also be considered. In these resilient times, managers must also be aware of the organizational culture to adjust it to the new contexts that require new attitudes and practices. Future research may consider other variables and other methodologies, allowing for comparisons of efficiency levels of national or international hotels. For example, it could be an interesting challenge to apply the same methodology to compare the results that were obtained with this study in hotels in cities located in other regions of Portugal or South Europe. The use of partial frontiers is another area that needs investment. Also the study of efficiency in functional areas and the chain value of hotels may prove important in understanding the causes of inefficiency. Studying I inefficiency in strategic implementation and organizational culture may be important challenges for managers. Investigating the correlation of the lean thinking and efficiency may also be interesting. Also inquiring the prospective customer about the company’s efficiency, particularly at the end of the tourist experience, may prove to be very useful in diagnosing inefficiencies which are not always observable by management. References Aigner, D., Lovell, K., Schmidt, P., 1977. Formulation and estimation of stochastic frontier production function models. Journal of Econometrics 6 (1), 21–37. Anderson, R., Fish, M., Xia, Y., Michello, F., 1999. Measuring efficiency in the hotel industry: a stochastic frontier approach. International Journal of Hospitality Management 18 (1), 45–57. Assaf, A., Barros, C., 2011. Bayesian cost efficiency of Luanda, Angola hotels. The Service Industries Journal 31 (9), 1549–1559. Assaf, A., Magnini, B., 2012. Accounting for consumer satisfaction in measuring hotel efficiency: evidence from the US Hotel industry. International Journal of Hospitality Management 31 (3), 642–647. Assaf, A., Barros, C., Josiassen, A., 2010. Hotel efficiency: a bootstrapped metafrontier approach. International Journal of Hospitality Management 29 (3), 468–475. Assaf, A., Barros, C., Josiassen, A., 2012. Hotel efficiency: a bootstrapped metafrontier approach. International Journal of Hospitality Management 31 (2), 621–629. Barros, C., Santos, C., 2006. The measurement of efficiency in Portuguese hotels with DEA. Journal of Hospitality and Tourism Research 30 (3), 378–400. Barros, C., 2004. A stochastic cost frontier in the Portuguese hotel industry. Tourism Economics 10 (2), 177–192. Barros, C., 2006. Analyzing the rate of technical change in the Portuguese hotel industry. Tourism Economics 12 (3), 325–346. Battese, G., Corra, G., 1977. Estimation of a production frontier model: with application to the pastoral zone of Eastern Australia. Australian Journal of Agricultural Economics 21 (3), 169–179. Battese, G., Coelli, T., 1995. A model for technical inefficiency effects in a stochastic frontier production function for panel data. Empirical Economics 20 (2), 325–332. Bernini, C., Guizzardi, A., 2010. Internal and locational factors affecting hotel industry efficiency: evidence from Italian business corporations. Tourism Economics 16 (4), 883–913. Chen, C., 2007. Applying stochastic frontier approach to measure hotel managerial efficiency in Taiwan. Tourism Management 28 (3), 696–702. Chen, C., Hu, J., Jern-Jou, L., 2010. Tourists’ nationalities and the cost efficiency of international tourist hotels in Taiwan. African Journal of Business Management 4 (16), 3440–3446. Coelli, T., Rao, P., Battese, G., 1998. An Introduction to Efficiency and Productivity Analysis. Kluwer Academic Publishers, Boston.
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