International Journal of Hospitality Management 35 (2013) 59–67
Contents lists available at SciVerse ScienceDirect
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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R. Oliveira et al. / International Journal of Hospitality Management 35 (2013) 59–67
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)
R. Oliveira et al. / International Journal of Hospitality Management 35 (2013) 59–67
61
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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R. Oliveira et al. / International Journal of Hospitality Management 35 (2013) 59–67
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
R. Oliveira et al. / International Journal of Hospitality Management 35 (2013) 59–67
63
(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 )
(7)
1 + 2
˜ it +
(
˜ it )
,
˚(
˜ it )
˜ it =
−εit
(14)
where (·) and ˚(·) are the density and the conditional distribution
function of standardized normal distribution for the truncated normal model the result is obtained by replacing ˜ it by ˜ it + u2 / 2
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
and therefore, since εi = vi − ui :
fe,u (ei , ui ) = fu (ui )fv (ei + ui )
(8)
which allows to obtain the marginal density of εi :
∞
fe (ei ) =
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
2
ln ˚
−ε i
−
2 1 εi
2 (11)
(u2
where
=
+ 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 , εit )
f (uit )f (εit |uit )
=
=
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
E(uit |εit ) =
∞
uit fu (uit )fv (εit + uit ) duit
0
∞
0
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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R. Oliveira et al. / International Journal of Hospitality Management 35 (2013) 59–67
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.
R. Oliveira et al. / International Journal of Hospitality Management 35 (2013) 59–67
65
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%.
66
R. Oliveira et al. / International Journal of Hospitality Management 35 (2013) 59–67
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.
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