Frontier Analysis

Abstract

This article presents a comprehensive review of frontier studies in the tourism literature. We discuss the main advantages and disadvantages of the various frontier approaches, in particular, the nonparametric and parametric frontier approaches. The study further differentiates between micro and macro applications of these approaches, summarizing and critically reviewing the characteristics of the existing studies. We also conduct a meta-analysis to create an overview of the efficiency results of frontier applications. This allows for an investigation of the impact of frontier methodology on tourism research. The present review also highlights the limitations of existing studies and suggests an agenda for future research.

Keywords

frontier analysis review meta-analysis future directions

Introduction

Over the past decade, performance benchmarking using frontier methods has become very prevalent in the tourism and hospitality literature (Peypoch et al. 2012; Assaf and Josiassen 2012; Barros and Dieke 2008; Barros 2005). More than 50 studies have been published focusing on various sectors of the tourism industry and covering a broad set of tourism destinations. Because of a number of advantages over other indicators of performance, frontier methods such as data envelopment analysis (DEA) and stochastic frontier analysis (SFA) are increasingly being recommended by researchers/practitioners to assess the impact of operational strategies and policies on tourism performance. Frontier analysis is “an objectively determined quantitative measure that removes the effects of market prices and other exogenous factors that influence observed performance” (Bauer et al. 1998, p. 85). Frontier analysis allows the incorporation of multiple inputs and outputs in the measurement of performance and provides a benchmark (i.e., frontier) against which competitors can identify areas of “best practices” and “worst practices” associated with high and low measures of performance. Frontier analysis also allows managers to identify the gap between their actual performance and optimal performance (Coelli et al. 2005). As indicated by Berger and Humphreys (1997, p. 176), “frontier analysis will generally tell informed industry participants little they do not already know in a general, qualitative way. However, while the qualitative news may not be new, the quantification of it is.” Frontier methods provide a numerical value of performance (also known as technical efficiency) that is objective, easy to interpret, aids resource allocation, and helps firms and destinations measure the outcomes of their various strategies and policies.

Though tourism researchers now have a wealth of frontier studies at their disposal, the literature currently lacks a significant review and analysis of frontier studies. To this end, we review and compare the results of 57 tourism studies that utilize frontier analysis. We believe that such as review will greatly serve the tourism literature for three different reasons. First, despite the recent advances in the approach to tourism performance, there are still a number of major challenges and questions that remain unresolved. Most recent studies, for instance, seem to be replicating existing knowledge without significant contributions. In some cases, studies are repeated on the same country with only minor changes to the purpose, sample, method, or scope of the application. Hence, it is important to highlight areas of the current literature where potential contributions can be made.

Second, the literature also lacks evidence of careful comparison and selection among various methods. For example, we know from the economic literature that the benchmarking results derived from nonparametric frontier methods such as DEA or parametric frontier methods such as SFA can be different both in terms of average and ranking. Hence, a thorough review of the literature will provide additional insights into the impact of modeling choices on the estimated results of frontier studies in tourism. The review will also discuss the advantages and disadvantages of the different frontier methods and highlight the potential limitations of these methods in certain data contexts. Third and final, the review will discuss recent advances in frontier modeling techniques and their potential applications to the tourism literature. There are, for instance, many recent advances in the frontier literature that have not yet been used in tourism studies. We discuss the advantages of using such approaches and suggest ways in which they can be applied.

This article is divided into five parts. Prior to elaborating on the review of frontier methods, we first provide a brief literature review of the traditional performance methods used in the literature. The third section then provides a theoretical background of the concept of efficiency. The fourth section moves on to provide a background and description of the frontier approaches for efficiency estimation. This section also critiques the main parametric and nonparametric frontier methods. The applications of the different frontier methods are reviewed in the fifth section divided according to the purpose of the research, and covering both micro and macro aspects of the tourism industry. The fifth section also includes a meta-analysis to illustrate the impact of choice of frontier methodology on the efficiency results derived in frontier studies. The sixth section then highlights the gaps in the literature and suggests directions for future research, both in terms of methodological aspects and extending the focus of current frontier studies to enrich the implications and provide a stronger managerial focus. The final section provides some concluding remarks.

Traditional Approaches to Performance Measurement

Performance measurement has always been one of the key topics in the hospitality and tourism literature. As described by Assaf and Magnini (2012), performance measurement is important because it is key to strategy formulation and evaluation and is one of the main sources of sustained competitive advantages. Measuring performance can also help firms improve their market position by identifying areas of the value chain activities where competitors have stronger advantages (Barros 2005). At the tourism destination level, research has also discussed that tourism competitiveness is of little value unless it is linked to destinations’ performance (Mazanec, Wober, and Zins 2007).

Traditionally, the tourism and hospitality literature has relied on accounting-based indicators to measure overall performance (Phillips and Louvieris 2005). For example, measures such as average occupancy rates, average room/rates, revenue/wage cost, gross profit/revenue, number of tourism arrivals/receipts, net profit/revenue, and labor productivity (Baker and Riley 1994; Anderson et al. 1999) have been commonly used in the industry.

Realizing, however, that such measures are limited in focus and are sensitive to various accounting standards between firms, other studies have used more comprehensive methods for performance measurement and control (Sainaghi et al. 2013 ). The cost volume profit analysis, for example, has been useful in breakeven analysis, as it “does not only can it be used to analyze the performance of an individual firm, but it can be applied at a regional level for the purpose of comparing various types of firms” (Anderson et al. 1999, p. 47). Yield management also continues to be commonly used in the hotel industry for performance measurement (Barros et al. 2011). However, while yield management is useful in terms of maximizing revenue and using capacity efficiently, it brings some limitations. For example, it only works when there is a high level of demand and is more effective for four- and five-star hotel properties (American Hotel & Lodging Association 2005).

The balanced scorecard (BSC) method has also received strong attention in the hotel and tourism literatures (Evans 2005; Chen, Hsu, and Tzeng 2011). This method addresses the limitations of many business performance measurement systems, as it can capture both financial and nonfinancial performance measures (Phillips and Louvieris 2005). It “considers the tangible assets (financial) and three intangible assets and intellectual capital (customer, internal business process and learning and growth)” (Sainaghi et al. 2012, p.152). Such focus on both financial and nonfinancial aspects creates a stronger linkage with strategy implementation and evaluation (Evans 2005).

Other popular methods of performance include the importance–performance (IP) analysis method, which has been used across several contexts including travel and tourism (Go and Zhang 1997; Zhang and Chow 2004), hotels (Chu and Choi 2000), and leisure and recreation (Hollenhorst, Olson, and Fortney 1992). Its main advantages are that it is cost-effective, easy to use, and can inform management about the areas they need to devote more attention to as well as areas where they have unused resources or wastages (Martilla and James 1977).

To sum up, there are merits and limitations in each of the approaches mentioned above. The distinctive feature of the frontier methods for performance measurement is that they provide a measure of efficiency that reveals gaps between a firm’s actual and optimal performance. None of the above methods, for example, provide a measure of performance relative to optimal performance. In contrast to most of the above methods, the frontier methods are also capable of incorporating multiple inputs and outputs. We provide in the next section more theoretical background about the concept of efficiency, before we review the related literature on frontier methods.

Theoretical Background and Definition of Efficiency

Discussion of efficiency started with the work of Farrell (1957) and was later introduced more formally by Leibenstein (1976) in what he called X-(in) efficiency theory. In his theory, Leibenstein reformulated neoclassical micro theory to “explain why some firms in a given industry are more efficient than others” (Arndt 1988, p. 223). In particular, the X-(in) efficiency theory is concerned with the under-utilization of resources. For example, not all firms are equal in the way they transform their inputs to outputs. Some incur wastage as a result of factors such as poor management, lack of cost control, and poor selection of suppliers.

Hence, according to the X-(in) efficiency theory, technical efficiency refers to “the ability to avoid waste, either by producing as much output as technology and input usage allow or by using as little input as required by technology and production function” (Fried, Lovell, and Schmidt 2008, p. 5). The essential concept behind the definition of technical efficiency is to establish first the boundary of the production frontier, and then measure the distance between each point in the sample and the production frontier. To illustrate, let x and y be a vector of p inputs and q outputs such that $x \in R_{+}^{p}$ and $y \in R_{+}^{q}$ . The production possibilities of a firm can be summarized using the following production function, defined as follows in the Euclidean space $R_{+}^{p + q}$ :

Ψ = {(x, y) {x \in R_{+}^{p}, y \in R_{+}^{q} {x c a n p r o d u c e y}

The production set ψ should is “close” and “bounded.” The Farrell input- and output-oriented technical efficiency measures can be described on the basis of

θ (x^{0}, y^{0}) = \inf {θ {θ x^{0} \in X (y^{0})}

And

λ (x^{0}, y^{0}) = \sup {λ {λ y^{0} \in Y (x^{0})}

where $θ (x^{o}, y^{o})$ or $λ (x^{o}, y^{o})$ indicate the projections between $(x^{o}, y^{o})$ and the technical efficiency frontier.

If input prices are available, one can also obtain measures of cost-efficiency (i.e., the ability to produce a vector of outputs with the minimum cost possible). For example, if $w = (w_{1}, …, w_{N}) \in R_{+}^{p}$ is the vector of positive input price, and assuming that producers want to minimize the cost of producing the output vector y, with that cost being $w^{T} x = \sum_{p} x_{p} y_{p},$ , the cost frontier can be expressed as

c (y, w) = \min_{x} {w^{T} x : x \in X (y)}

Such frontier “provides a standard against which to measure the performance of producers for whom the cost minimization assumption is deemed appropriate” (Kumbhakar and Lovell 2000, p. 34 ). This cost frontier must all satisfy certain properties. For example, some of these properties are as follows:

c(y, w) is a concave function in w.

c(y, w) is a continuous function in w.

c(0, w) = 0 and c(y, w) > 0 for y ≥ 0.

Using this cost function, one can also derive interesting economic quantities. For example, one can obtain a measure of economies of scale as follows:

ε_{c} = {[\sum_{q = 1}^{Q} \frac{\partial \ln c (w, y)}{\partial \ln y_{q}}]}^{- 1}

where a firm is deemed to exhibit increasing, constant, or decreasing returns to scale if εc is greater than, equal to, or less than one, respectively.

It is also possible to derive a measure of economies of scope, which reflects “the cost savings from producing different number of outputs” (Coelli et al. 2005, p. 30).¹ This can be expressed as

S = [\sum_{q = 1}^{Q} c (w, y_{q}) / c (w, y)] - 1

where S > 0 indicates that it is better to produce all outputs as a group, while S < 0 indicates that it is best to produce all outputs separately (Coelli et al. 2005).²

Frontier Analysis

Estimation of efficiency starts mainly with the estimation of the production or cost frontiers. In practical terms, however, the main problem is how to obtain an estimate of this frontier from a random sample of inputs and outputs. The different methods that have been proposed in the literature can be classified into two categories: nonparametric and parametric frontier approaches. While both approaches are designed to estimate the frontier technology, the underlying assumptions they use to estimate the frontier technology are different in terms of “the functional form of the best-practice frontier (more restrictive parametric functional form versus a less restrictive nonparametric form), whether or not account is taken of random error that may temporarily give some production units high or low outputs, inputs, costs, or profits, and if there is random error” (Berger and Humphreys 1997, p. 177).

Before we elaborate on the use of frontier analysis in tourism, this section provides a short description of nonparametric and parametric frontier approaches. As mentioned, the main motivation for using frontier approaches is to provide objective measures of performance such as technical efficiency or cost efficiency. However, as cost efficiency has not been very common in the tourism industry,³ we focus in this review on the assessment of technical efficiency (TE) studies.

Nonparametric Frontier Approaches

The nonparametric approach to frontier estimation imposes limited structure on the estimation of the frontier technology. Different nonparametric methods are available in the literature, with the most popular being Data Envelopment Analysis (DEA) and Free Disposal Hull (FDH). The DEA method, first introduced by Charnes, Cooper, and Rhodes (1978), is known for its flexibility and simplicity; the method does not require a large sample size or any prior specification of a functional form for the production technology. It can also easily incorporate multiple inputs and outputs (Coelli el al. 2005). The frontier technology with DEA is constructed as a piecewise function over the data. Depending on the context or industry under analysis, DEA models can be estimated with either input or output orientation, and following either constant or variable returns to scale (CRS or VRS; see Coelli et al. 2005 for details).

FDH is another special variation of DEA (Deprins, Simar, and Tulkens 1984) that does not impose the convexity assumption on the frontier technology as with DEA. Such property is attractive as theoretically it is not always simple to justify or test that the frontier technology is convex. In cases when the frontier technology is convex, both DEA and FDH will lead to similar and consistent estimates. However, when the true frontier technology is not convex, DEA estimates become inconsistent (Fried, Lovell, and Schmidt 2008). Regardless of which method (DEA, FDH) is used, a main limitation of the nonparametric frontier approach is that it does not account for random error. As such, it is highly sensitive to outliers and sample size. Being nonstatistical, the nonparametric frontier method does not also provide the means for hypothesis testing or to conduct statistical inference on the efficiency results.

This last limitation was recently addressed in the literature with the use of a resampling technique, such as the bootstrapping approach. Bootstrapping is based on randomly selecting thousands of “pseudo samples” from the data in order to approximate the underlying sampling distribution and to conduct statistical inferences on the efficiency scores. Ferrier and Hirschberg (1997) were the first to introduce the bootstrap approach to DEA. However, their methodology was later criticized by Simar and Wilson (1998, 2000a, 2000b), who developed and tested a more advanced bootstrapping algorithm to deal with the possible inconsistency in the DEA efficiency scores.⁴

Parametric Frontier Approaches

The parametric methods take a totally different approach in estimating the frontier technology. There are three main parametric methods available in the literature: the stochastic frontier approach (SFA), the distribution-free approach (DFA), and the thick frontier approach (TFA). The SFA model can be expressed as follows:

y_{i t} = f ({x^{'}}_{i t}, β) + v_{i t} - u_{i t}, i = 1, …, n, t = 1, …, T

where y_it denotes the output variable, x_it is a vector of input and explanatory variables, and β_i is a vector of parameters. Here, v_it denotes measurement error, and u_it is a random error that measures the deviations (i.e., technical inefficiency) from the frontier technology SS′. As inefficiency cannot be negative, u_it follows an asymmetric distribution, usually the half-normal, truncated, exponential or gamma. The efficiency scores are calculated relative to the maximum feasible output provided by the stochastic frontier.⁵ To estimate the parameters of the model in (7), several estimation methods can be used such as the maximum likelihood (ML), generalized method of moment (GMM), and Bayesian. There is also a need to specify a functional form f(⋅) for the relationship between output and inputs. Several options for f(⋅) are available in the literature, with the most common being the Cobb-Douglas and the translog. For example, the Cobb-Douglas form can be expressed as

\ln y = β_{0} + \sum_{n = 1}^{N} β_{n} \ln x_{n}

while the translog can be expressed as follows:

\ln y = β_{0} + \sum_{n = 1}^{N} β_{n} \ln x_{n} + \frac{1}{2} \sum_{n = 1}^{N} \sum_{m = 1}^{N} β_{n m} \ln x_{n} \ln x_{m}

One of the main advantages of the translog relative to Cobb-Douglas function is that it “does not assume rigid premises such as: perfect or ‘smooth’ substitution between production factors or perfect competition on the production factors market” (Pavelescu 2011, p. 133). Also, the translog function introduces nonlinear relationships between the outputs and inputs.

Similar to the stochastic frontier approach, the distribution-free approach (DFA) also requires a specification of the functional form for f(⋅). However, the difference is that DFA does not impose strong distributional assumption on u_it or v_it. Rather it assumes that u_it is constant over time, and that v_it will become zero over time. The efficiency scores are derived as the difference between the average residuals and the residuals of firms on the frontier. Finally, the thick frontier approach (TFA) does not also any distribution on either inefficiency or random error, but it divides firms in the sample into four quartiles, where firms in the lowest quartile are assumed to be the least inefficient (most efficient). With TFA, it is therefore not possible to provide an efficiency inference for each firm in the sample; rather, only an overall average of efficiency of firms in the sample is provided.

Is There a Better Frontier Approach?

There is considerable debate in the literature about which frontier approach (parametric vs. nonparametric) is preferable. Each approach has its advantages and disadvantages. The nonparametric approach is more flexible in the sense that it does not require a specification of a functional form for the relationship between inputs and outputs. Its main limitation, however, is that it does not allow for random error. Hence, it is highly sensitive to noise in the data.⁶ The parametric approach, on the other hand, includes a random error, but imposes so much structure on the functional form f(⋅) in (7). Scholars, for instance, debate which functional form is the most appropriate one. The translog is known to be more flexible than Cobb-Douglas, but can also result in incorrect efficiency results for observations that are not close to the mean scale (Kumbhakar and Lovell 2000). The challenge also relates to the selection of the correct distribution of the inefficiency term u_it. As previously mentioned, there are several distributions available in the literature, such as the half-normal, gamma, exponential, and truncated. Findings from the literature have not always indicated that these different distributions lead to similar efficiency results (Kumbhakar and Lovell 2000; Murillo-Zamorano 2004). The half-normal and exponential distributions, for instance, both have a mode at zero that tends to inflate the efficiency results. The gamma models have also been criticized for imprecision (Ritter and Simar 1997; Murillo-Zamorano 2004).

The issue of selecting between the nonparametric and parametric approaches is not therefore simple and straightforward. Sometimes, “a careful consideration of them, of the data set utilized, and of the intrinsic characteristics of the industry under analysis will help us in the correct implementation of these techniques” (Murillo-Zamorano 2004, p. 63). There are also possible solutions that we propose later in this article to improve the results from both DEA and SFA methods. The next section summarizes the use of frontier methods in the tourism literature. We focus on the methods used and the area of study and conduct a meta-analysis to illustrate the effect of the frontier approach on the efficiency results in the tourism industry. The recommendations we propose are not only related to the selection of the frontier approach. We also address possible limitations in the current literature and suggest an agenda for future research.

Review of Frontier Studies in Tourism

We now move to the analysis of frontier studies in the tourism literature. We focus on how the efficiency results vary with the various frontier methods and highlight other important issues about sample characteristics and variables used. For this comprehensive review, we relied on leading tourism and hospitality journals: the Journal of Travel Research, Tourism Management, Annals of Tourism Research, Tourism Economics, Tourism Analysis, International Journal of Tourism Research, International Journal of Hospitality Management, and the Journal of Hospitality and Tourism Research. We also covered articles that appeared in management science, economic, and business journals such as the European Journal of Operational Research, Expert Systems with Applications, the Service Industries Journal, and the Journal of Business Research.

We divide this review into parts. First, we summarize the characteristics of the current studies in the literature, including both nonparametric and parametric studies. Second, we conduct a meta-analysis to examine the effect of the frontier methods and other related sample characteristics on the efficiency estimates in the context of tourism studies.

General Overview

Tables 1 and 2 summarize the current studies in the literature. The first table includes studies that focused on the efficiency analysis of hotels, travel agencies, tour operators, and restaurants. Hence, these studies took a micro-level approach. The second table presents studies that focused on the efficiency analysis of the whole tourism industry, using macro-level data. We divide the studies in each table according to the methodology used, starting with the nonparametric studies, and followed by the parametric studies. Tables 1 and 2 further classify each group of studies according to the model specification, samples of countries used, and the variables used. For each group of studies, we differentiate between two types of variables: 1, the input and output variables used to estimate the frontier technology, and 2, the second-stage variables used to explain the variations in efficiency between the various units under analysis.

Table 1.

Frontier Research in Tourism: Micro-Related Studies.

Method	Authors	Country	Input Variables	Output Variables	Second-Stage Variables
Input-oriented CRS DEA	Botti et al. (2009); Johns, Howcroft, and Drake (1997); Barros and Santos (2006); Ting and Huang (2012)	France, United Kingdom, Portugal, Taiwan	Number of room nights available, number of employees, total labor hours, total F&B costs, operating expenses, total utility costs, area of catering space, chain duration, book value of the assets	Sales, added value, earnings, occupancy rate, total covers served, total beverage revenue, total revenue	Ownership type
Input-oriented CRS DEA using bootstrapping	Oliveira, Pedro, and Marques (2013); Fuentes (2011)	Portugal, Spain	Number of rooms, number of employees, F&B capacity, annual expenditure, potential service, other costs	Total revenue, number of customers, average spending per customer	Hotels with golf course vs. hotels without golf course
Input-oriented VRS DEA	Wöber (2000); Wang, Hung, and Shang (2006a); Wöber (2007) ; Shang et al. (2008a); Shang, Hung, and Wang (2008b); Neves and Lourenco (2009); Pulina, Detotto, and Paba (2010); Tsai, Wu, and Zhou (2011)	France, Austria, Taiwan, Italy, World	Number of beds, number of seats (F&B), number of opening days, number of full-time employees, number of guest rooms, total area of F&B, total payroll and related costs, cost of goods and services, material-type expenditures, energy costs, cleaning costs, maintenance costs, communication costs, marketing costs, administration costs, other fixed and variable costs, average job experience of employees, territory coverage, chain duration, current assets, net fixed assets, shareholders’ equity	Sales, total revenue, total accommodation revenue, total F&B revenue, other revenue, gross value added, average annual bed occupancy, number of contracts, turnover, contribution margin, EBITDA	Ownership type, market condition, management style, hotel size, time the hotel has been operating, location
Input-oriented VRS DEA using bootstrapping	Oliveira, Pedro, and Marques (2013); Wang, Hung, and Shang (2006b)	Portugal, Taiwan	Number of rooms, number of full-time employees in room departments and F&B departments, F&B capacity, other costs	Total revenue, revenue from room department and F&B, other revenue	Foreign individual travelers, online transactions, franchising (hotel type), number of years a hotel has been operating, location, hotels with golf course vs. hotels without golf course
Input- and output-oriented Network DEA	Yu and Lee (2009)	Taiwan	Number of employees in the room service department and in the F&B department, number of rooms, total floor area in the F&B service department, total expenses for each service sector	Total revenue generated from rooms and from F&B, other revenue	–
Output-oriented CRS DEA	Tsaur (2001); Brown and Ragsdale (2002); Hwang and Chang (2003); Sigala (2004); Sigala et al. (2005); Reynolds and Biel (2007); Reynolds and Thompson (2007); Botti et al. (2009)	Taiwan, United States, United Kingdom	Number of employees, number of guest rooms, total area of catering division, number of employees in room division and in catering division, total operating expenses, total payroll, total nonpayroll expenses, front office payroll, administration nonpayroll expenses, other room division payroll, total demand variability, F&B payroll, F&B material and other expenses, cost of goods sold, employee satisfaction, rent, tax and insurance, parking	Sales, total operating revenues, total operating revenues of the room division and the catering division, other revenue, number of rooms occupied, average daily rate, number of room nights, nonroom revenue, controllable income, average production value per employee in the catering division, brand quality, guest satisfaction, ratio of banqueting to restaurant covers, retention equity, tips	Server count, server hours
Output-oriented CRS DEA using bootstrapping	Oliveira, Pedro, and Marques (2013); Barros and Dieke (2008); Salman Saleh, Assaf, and Son Nghiem (2012)	Portugal, Africa, Malaysia	Number of rooms, number of employees, F&B capacity, operational expenses, other costs, total costs, investment expenditure, labor, capital	Total revenue, RevPAR, gross profit	Hotel size, market share, type of ownership, hotels with an international strategy, hotels with golf course vs. hotels without golf course
Output-oriented VRS DEA	Barros (2005); Chiang (2006); Assaf (2012); Assaf and Cvelbar (2011); Assaf and Agbola (2011)	Portugal, Taiwan, Asia Pacific, Slovenia, Australia	Number of employees, cost of labor, number of rooms, costs of materials, amortization costs, cost of service, surface area, book value of the premises, operational costs, external costs, F&B costs, room expenses, number of rooms available	Sales, room sales, F&B sales, number of guests, number of nights spent, yielding index, room revenue, F&B revenue, miscellaneous revenue, revenue	Local vs. international, years in business, star rating, size, location
Output-oriented VRS DEA using bootstrapping	Oliveira, Pedro, and Marques (2013); Barros and Dieke (2008); Salman Saleh, Assaf, and Son Nghiem (2012); Assaf and Cvelbar (2010); Assaf and Cvelbar (2011); Assaf, Barros, and Machado (2011); Assaf and Agbola (2011)	Portugal, Africa, Malaysia, Slovenia, Australia	Number of rooms, number of employees, F&B capacity, operational expenses, other costs, total costs, investment expenditure, costs of materials, costs of service, amortization costs, book value of assets, room payroll, other payroll, F&B costs, number of rooms available	Total revenue, room revenue, F&B revenue, RevPAR, gross profit, room sales, F&B sales	Hotel size, market share, type of ownership, hotels with an international strategy, hotels with golf course vs. hotels without golf course, years in business, star rating, size, location
Slack-based measure DEA	Ashrafi et al. (2013); Sun and Lu (2005); Cheng, Lu, and Chung (2010)	Singapore, Taiwan	Room rate, visitor arrivals, GDP, total operating expenses, number of employees, number of guest rooms, total area of the catering department	Room revenue, F&B revenue, total operating revenues, occupancy rate, gross lettings, average daily rate, average production value per employee	Total area of the catering department, number of employees, number of rooms, proportion of foreign guests, management style of a hotel, hotel location
Cobb-Douglas SFA using ML	Barros (2004); Barros and Matias (2006);Chen (2007)	Portugal, Taiwan	Price of labor, price of capital, price of F&B, operational costs, price of materials	Sales, nights occupied, total revenue, occupancy rate, production value of united catering space	Location, M&A activities, historic vs. regional hotels
translog SFA using ML	Pérez-Rodríguez and Acosta- González (2007); Anderson et al. (1999); Hu et al. (2010); Barros (2006); Barros, Dieke, and Santos (2010); Kim (2011); Salman Saleh, Assaf, and Son Nghiem (2012)	Spain, United States, Taiwan, Portugal, Africa, Malaysia	Price of labor, price of capital, price of rooms, price of F&B, financial costs, number of employees, number of rooms, gaming-related expenses, F&B expenses, other expenses, quantity of tangible fixed assets	Annual operating revenue, total revenue, room revenue, other operational revenue, F&B revenue, sales, market share, RevPAR, gross operational profit, real value added	Location, ownership, distance from airport, number of tourist guides, star rating, availability of golf course, number of hotel rooms, training, skilled workers, university graduates, bought-in services, IT capital
translog SFA using Bayesian	Assaf and Barros (2013); Assaf (2012); Assaf and Magnini (2012)	World, Asia Pacific, United States	Number of outlets, number of rooms, number of employees, other operational costs	Market share, occupancy rate, market share, revenue, customer satisfaction	Location, ownership, local vs. international

Note: CRS = constant returns to scale; DEA = data envelopment analysis; F&B = food and beverage; VRS = variable returns to scale; EBITDA = earnings before interests, taxes, deductions, and amortization; RevPAR = revenue per available room; GDP = gross domestic product; SFA = stochastic frontier analysis; ML = maximum likelihood; M&A = mergers and acquisitions; IT = information technology.

Table 2.

Frontier Research in Tourism: Marco-Related Studies.

Method	Authors	Country	Sample	Input Variables	Output Variables	Second-Stage Variables
Output-oriented CRS DEA	Cracolici, Nijkamp, and Rietveld (2008)	Italy	103 destinations	Regional state-owned cultural patrimony and heritage standardized for population, tourist school graduates divided by working-age population, labor units employed in the tourism sector	Bed nights relative to population	–
Output-oriented CRS DEA using bootstrapping	Barros et al. (2011)	France	22 destinations	Tourist arrivals, accommodation capacity	Bed nights	Monuments, kilometers of beaches, museums, theme parks, ski, natural park
Output-oriented VRS DEA	Fuchs (2004); Bosetti, Cassinelli, and Lanza (2007); Botti et al. (2009)	Europe, Italy, France	21 destinations 150 hotels	Bed capacity, salaries for tourism employees, energy and recycling costs devoted to tourism business, tourism advertising expenditures, tourism development index, public expenditure in tourism management and advertising, public expenditure in environmental protection, market size, hotels, camping, parks, monuments, beach kilometers, museums, labor costs	Tourism sales, tourist satisfaction, tourist arrivals, total presence of tourists, homogeneity of tourism flows during the year, percentage of protected areas, index of efficiency in solid waste treatment, sales revenue, gross value added	–
Output-oriented VRS DEA using bootstrapping	Barros et al. (2011); Assaf and Josiassen (2012)	France, World	71 destinations	Tourist arrivals, accommodation capacity, number of employees working in the tourism industry, capital investments made by governments in the tourism industry, total number of accommodation establishments available	Bed nights, total number of international tourists, total number of domestic tourists, average length of stay of international tourists, average length of stay of domestic tourists	Monuments, kilometers of beaches, museums, theme parks, ski, natural park, economic conditions, infrastructure, security, health and safety, government policies, environmental sustainability, labor skills and training, natural and cultural resources
Cobb-Douglas SFA	Cracolici, Nijkamp, and Rietveld (2008)	Italy	103 destinations	Regional state-owned cultural patrimony and heritage standardized for population, tourist school graduates divided by working age population, labor units employed in the tourism sector divided by the total regional ULA	Bed nights relative to population	–

Note: CRS = constant returns to scale; DEA = data envelopment analysis; VRS = variable returns to scale; SFA = stochastic frontier analysis.

From looking at Tables 1 and 2, we can see that no study has used the nonparametric FDH approach or the parametric DFA or TFA approaches. Hence, our discussions will focus on the nonparametric DEA and the parametric SFA. We include in both tables the model specification for both DEA and SFA studies. For DEA we also indicate the following: (1) whether the study has used an input or output-oriented approach; (2) whether the model was estimated under CRS or VRS; and (3) whether or not the study has bootstrapped the DEA scores. For SFA, we focus on the type of functional form used to estimate the frontier technology (e.g., Cobb-Douglas, translog), the method of estimation (e.g., ML, Bayesian).

To simplify the analysis, we present in Table 3 a quantitative survey of all 57 studies using the classifications observed in Tables 1 and 2. We also add new details. For example, we further classify the studies based on the regions where they were conducted, and present the average efficiency for both nonparametric and parametric studies. In total we found 49 micro studies and 8 macro studies. Of the 49 micro studies, 35 used DEA and only 14 studies used SFA. We also observe the same trend in the macro studies, where 7 of 8 studies used the DEA method. In terms of the characteristics of the different methods, we observe that most DEA studies were output oriented with VRS specification, and only 11 studies bootstrapped the DEA scores. For SFA, most studies used the translog functional form, and half-normal distribution for the inefficiency term. Regarding the method of estimation for SFA, most studies used ML, while only three studies used the Bayesian approach. Out of all DEA and SFA studies, only 24 studies have conducted a second-stage regression to analyze the determinants of efficiency. In terms of the regions of study, most studies seem to be concentrated across European and Asian countries.

Table 3.

Summary of DEA and SFA Studies.

	Nonparametric	Parametric
No. of micro studies	35	14
No. of macro studies	7	1
Total	42	15
Average efficiency	79%	73%
Nonparametric Model orientation
Input-oriented	15	–
Output-oriented	24	–
No orientation	3	–
Nonparametric specification
CRS	16	–
VRS	25	–
Nonparametric bootstrapping	11
Parametric specification
Cobb-Douglas	–	5
Translog	–	10
Parametric distribution
Exponential	–	1
Half-normal	–	10
Gamma	–	2
Truncated	–	2
Parametric method of estimation
Maximum likelihood	–	12
Bayesian	–	3
Conducted second-stage analysis	16	8
Used panel data	15	11
Region of study
Europe	20	7
Asia and Oceania	16	4
Middle East and Africa	1	1
United States	3	2
World	2	1

Note: DEA = data envelopment analysis; SFS = stochastic frontier analysis, CRS = constant returns to scale; VRS = variable returns to scale.

Of course, one of the most interesting issues from this analysis is to provide an overview of how average efficiency differs with the method applied (DEA vs. SFA), and with the classification and model conditions in Table 3. From just observing the average efficiency from DEA and SFA studies in Table 3, we see that DEA studies higher average efficiency than SFA studies. The VRS also seems to have a higher average than the CRS specification; for SFA, the Cobb-Douglas studies seem to have a higher average than the translog studies. In terms of the geographical area of study, Europe seems to enjoy higher efficiency than the rest of the world.

We conduct next a more detailed analysis to emphasize the importance of these findings. The values in Tables 1 and 2 have been generated from studies with different foci (micro vs. macro) and using different frontier technologies. Even studies within the micro group have focused on different tourism sectors such as hotels, restaurants, and travel agencies. Hence, in order to provide a more accurate analysis, it is essential to account for some of this heterogeneity when comparing between the various studies. Also, for a more robust comparison, it is important to include only studies from similar sectors and to differentiate between micro and macro studies. We summarize in the next section the details of our meta-analysis.

Meta-Analysis of DEA and SFA Studies

In this meta-analysis, we restrict the comparison to studies from Table 1, as it is clear from Table 2 that there are not enough macro studies to make a valid comparison between nonparametric and parametric frontier methods. For example, the review only indicated 8 macro studies, where 7 of them used the DEA method. It is also clear from Table 1 that most studies were conducted on the hotel sector (i.e., 43 studies), and only a few studies focused on the travel agency and restaurant sectors. Hence, in order to provide more consistency, we only focused on studies from the hotel sector.⁷ Undoubtedly, the data structure for such meta-analysis is still complex as studies involved hotels from different regions, using different input and output variables, and different versions of the DEA and SFA methods.

The meta-model can be expressed as

E f f_{i} = β_{j} X_{i j} + ε_{i}

where Eff_i is the efficiency scores derived from the different studies, X_ij is a matrix that includes covariates representing the characteristics of the various studies (e.g., method used, orientation, etc.), and ε_i is an error term distributed as $ε_{i} ~ N (σ_{ε}^{2})$ . Note that the efficiency scores generated from both DEA and SFA are bounded between 0 and 1. Hence, the model we use in (8) is of Tobit structure, which can be rewritten as follows:

E f f_{i} = {\begin{cases} E f f_{i}^{*} if 0 \leq E f f_{i}^{*} \leq 1 \\ 0 if E f f_{i}^{*} < 0 or E f f_{i}^{*} > 1 \end{cases}

where (9) is a censored Tobit model, and Eff_i is the unobserved dependent variable. In such meta-analysis, it is also important to account for the presence of heteroscedasticity, as most samples involve multiple data points that are generated from the same study (Odeck and Bråthen 2012). To address this issue, we estimate the model using random effects. In a “random-effects Tobit model, the error term becomes a composite matrix that includes the stochastic disturbances associated with the fixed and random effects in the model’s design matrix” (Odeck and Bråthen 2012, p. 1580). This can be expressed as follows:

E f f_{i}^{*} = β_{j} X_{i j} + ω_{i j}

where $ω_{i j} = ε_{i} + u_{i j}$ ; εi is the residual.

From the various studies summarized in Tables 1 to 3, we focus on the characteristics that have been described in the literature (Berger and Humphreys 1997; Kumbhakar and Lovell 2000; Odeck and Bråthen 2012) to have an important influence on the efficiency derived from frontier research. Specifically, the random-effects Tobit model we estimate in this study as follows:

{\begin{cases} E f f_{i}^{*} = β_{0} + β_{1} n o o f o b s + β_{2} n o o f i n p u t s + β_{3} n o o f o u t p u t s + β_{4} n o n - p a r a m + β_{5} D E A C R S + β_{6} P a n e l + β_{7} B o o t s t r a p + β_{8} C o b b - D o u g l a s + σ_{ε} ε_{i} + σ_{u} u_{i j} \\ E f f_{i} = \max {E f f_{i}, 0} \end{cases}

where noofobs is the number of data points in each study, noofinputs is the number of input variables in each study, noofoutputs is the number of output variables in each study, non-param is a dummy variable that takes the value of 1 if the study used DEA and 0 otherwise, DEACRS is a dummy variable that takes the value of 1 if the study used a CRS formulation and 0 otherwise, Panel is a dummy variable that takes the value of 1 if the study used panel data and 0 otherwise, Panel is a dummy variable that takes the value of 1 if the study bootstrapped the DEA scores and 0 otherwise, and Cobb-Douglas is a variable that takes the value of 1 if the study used a Cobb-Douglas functional form and 0 otherwise. Note that because of limited observations, we were not able to include other variables such as the type of distribution (e.g., half-normal, truncated) or the method of estimation (e.g., ML, Bayesian) used in stochastic frontier studies. Neither did we include studies that assumed no orientation in the context of DEA.

As some studies provided only one data point, our total sample included 70 data points generated from 43 studies. The estimates from the Tobit regression expressed in Table 4 suggest the following sets of conclusions. The method does not seem to be an important factor in the efficiency results of tourism applications. For example, studies that used the nonparametric DEA do not seem to report on average higher efficiency scores than studies that used the SF parametric approach. Meta-analyses from other literature have been inconclusive about the impact of the frontier methodology. Some researches were consistent and some others were inconsistent with our finding (Thiam, Bravo-Ureta, and Rivas 2001; Bravo-Ureta et al. 2007). There seems, however, to be more consistency in the literature about the impact of the model specification on the efficiency results (Brons et al. 2005; Odeck and Bråthen 2012). Our results also indicate that model specifications in the context of DEA lead to different efficiency scores. For example, it is clear that there is a significant difference between the CRS and VRS models. Studies with input-oriented models also seem to report lower efficiency scores than studies with output-oriented models. The use of bootstrapping is also an important factor. For example, studies with bootstrapping seem to report lower efficiency scores than studies without bootstrapping. In the context of SF, the functional form (Cobb-Douglas vs. translog) does not seem to have a significant impact on the efficiency results. Further analysis, however, might be needed to confirm this issue as most studies in our sample used the translog functional form. Finally, an important issue we observe from Table 4 is that the characteristics of the data play an important role. For example, the efficiency scores seem to increase with the number of input and output variables. The use of panel data also seems to be an important factor. We provide in the next section more insights into these findings and directions for future research.

Table 4.

Tobit Regression Results.

Variable	Coefficient	T-Value
number of observations	0.00	0.85
number of input variables	0.14**	4.75
number of output variables	0.12**	2.74
Nonparametric	0.06	0.64
DEA-CRS	–0.18**	–2.16
Input-Oriented	–0.08*	–1.77
Panel	0.22**	2.60
Bootstrap	– 0.16**	–2.01
Cobb-Douglas	–0.07	–0.17

Note: DEA = data envelopment analysis; CRS = constant returns to scale. Sigma = 0.26.

p < 0.1, **p < 0.05.

Summary and Directions for Future Research

In line with the above results, and along with our careful consideration of each study in Tables 1 and 2, we highlight several limitations in the extant literature that should be addressed and suggest ways in which future research may improve the outcomes of frontier studies.

1. First, we recommend that future studies pay more careful attention to model specification. As it was clear from the results, there is a significant difference between the CRS and VRS models. Probably, it is important to rely on appropriate tests to specify the direction of the frontier model. There are several tests that can be used to determine the appropriate scale assumption prior to estimating the frontier model. Currently, most studies in the tourism literature have ignored such tests and have simply stated the use of VRS or CRS models without any prior justification. On the other hand, studies in the broader business literature seem to place more emphasis on this issue (Casu and Molyneux 2003; Luo 2003; Favero and Papi 1995). As indicated by Coelli et al. (2005), the issue of scale specification should not be taken lightly as it can have a significant impact on the efficiency results. For example, the CRS assumption is very restrictive and assumes that all firms in the sample operate at an optimal scale. Hence, it is only appropriate when there is perfect competition or monopolistic behavior in the market (Coelli et al. 2005). For example, across many hotel markets, it is hard to assume that this is the case given the intense competition and the strong differentiation that exist in the hotel industry (Assaf and Agbola 2011). Unfortunately, in most hotel and tourism studies (e.g., Barros et al. 2011; Botti el al. 2009; Barros and Dieke 2008), there is little or no discussion on the choice of scale used. Studies seem to indicate the use of VRS or CRS without any appropriate testing or discussion regarding why the selected scale is the most appropriate for the sample under study.

2. The same applies to the orientation (input vs. output oriented) of the frontier model. The results demonstrate that the choice of orientation can affect the efficiency results, and the researcher thus needs to carefully select the orientation which best suits the industry under analysis. There is no clear argument in the economic or business literature in regards to which orientation is the best because the optimal choice is highly dependent on the market conditions (Barros 2005). As a general rule of thumb, the output-oriented model seems to be a more realistic choice for firms in highly competitive industries as these are usually more motivated to maximize their outputs (Assaf and Josiassen 2012). Even within the same industry, firms can behave differently depending on their location, economic conditions, and the characteristics of the local markets they are operating in (Coelli et al. 2005; Fried, Lovell, and Schmidt 2008).

While in many business studies (e.g., Assaf and Gillen 2012; Luo 2003) we see authors providing a clear discussion about the choice of orientation before running the DEA model, it was clear that most studies (e.g., Shang et al. 2008a; Shang, Hung, and Wang 2008b) included in this review selected the orientation without any prior justification. For example, even within the same hotel markets (e.g., Portugal), studies have used both input and output oriented models (Barros 2004, 2005). While each orientation can be the correct choice, it is important to justify the choice of orientation before estimation. In other words, the choice of orientation should not just be data driven, but also based on theoretical and conceptual arguments.

3. Another issue of interest is the choice of inputs and outputs. Most studies reviewed in Table 1 and Table 2 seem to be driven by data availability rather than a thorough understanding of the industry under analysis. For example, even when studies used the same unit of analysis (e.g., hotels), there was high variability in the number of types of input and output variables. This problem is less common in other industries where there seems to be more consistency in the selection of input or output variables. For example, in the banking industry, the choice of inputs and outputs seems to be more standardized (Barros and Wanke 2014; Berger and Humphreys 1997). In other words, the literature is in relatively high agreement as to the types of inputs and outputs that are most appropriate to analyze the efficiency of banking operations (Berger and Humphreys 1999).

Unfortunately, in the hospitality and tourism management literatures, researchers typically have not supported the selection of input and output variables with theoretical arguments from the literature. As highlighted by Assaf and Josiassen (2012), there is a need for scholars to identify the key inputs and outputs in the hotel industry. Such study may also consider taking the opinion of managers and other stakeholders in the industry in order to provide a more standardized approach for the selection of input and outputs. As discussed, frontier studies that use different inputs and outputs are difficult to compare as the estimates of efficiency will automatically be different. Therefore, standardizing the selection of inputs and outputs will allow for more meaningful comparison among future frontier studies.

4. There is also a shortage of studies that discuss the determinants of efficiency in the industry across both micro and macro levels. For example, as previously mentioned, only 24 of all the studies reviewed had conducted a second-stage analysis. Also, most studies that regressed the efficiency results on a set of determinants only focused on a limited number of determinants without covering other important variables that might also explain variations in the efficiency results. For example, little research exists on the effect of destination management or government investments on the efficiency of the tourism industry. Such analysis might prove to be more important for destination managers than a simple frontier analysis. For example, the important issue is not just how efficient an industry is but what variables drive the efficiency (positively or negatively) in the industry. The frontier analysis hence becomes more useful when it is linked to variables affecting policy and strategy formulation in the industry. For example, in the marketing literature, many studies have started using the frontier methods to test several interesting hypotheses such as the impact of CRM, advertising spending, or stock value on firm efficiency (Krasnikov, Jayachandran, and Kumar 2009; Luo and Homburg 2008).

5. Importantly, there is a need for more variability in the geographical distribution of frontier studies. For example, most studies in Tables 1 and 2 seem to be replicating the analysis on specific countries (e.g., Taiwan) or regions (e.g., Asia Pacific) with different frontier models or different model specifications. We recommend that future studies focus more on analyzing the tourism industry in other countries or regions that have so far received little attention in the literature. For example, only a few studies focus on the United States despite the international importance of its tourism industry. There is also a shortage of macro studies. For example, most studies seem to focus on the hotel industry, while the tourism industry has received surprisingly little focus. Another important issue to address is the efficiency comparison between countries. As there are only a few studies focusing on cross-country comparisons, the results should be interpreted with caution unless the findings are validated using different frontier techniques on similar data sets.

6. Additionally, there are many important methodological innovations that may improve the accuracy of frontier analysis in the tourism literature. For example, in the context of DEA, future studies might consider relying more on the bootstrap approach to provide a statistical foundation for the DEA scores. As shown in our meta-analysis, bootstrapped studies reported different efficiency results from their nonbootstrapped counterparts. Across many industries such as banking, airlines, and airports (e.g., Merkert and Hensher 2011; Assaf 2010; Casu and Molyneux 2003), the DEA bootstrap is becoming the most common approach. As mentioned above, the use of the bootstrap provides several advantages over traditional DEA. For example, the bootstrap provides statistical properties of the DEA efficiency scores. It is also useful to assess the sensitivity of DEA efficiency scores to various sample characteristics. In addition, when the data have some outliers, the bootstrap performs better that the traditional DEA as it provides bias-corrected efficiency scores.

7. In the context of stochastic frontier, several methodological advances can also be used to add more flexibility to the estimation of these models. For example, in terms of the functional form of the SF model, several studies have recently suggested the use of the Fourier-flexible functional form as one way to avoid the limitations of the translog or Cobb-Douglas functional forms (Tsionas 2012). The Fourier, for instance, adds more flexibility to the frontier by introducing the orthogonal trigonometric terms which help provide better fit. Currently, all studies in the tourism literature have used either the translog or Cobb-Douglas functional forms. Hence, future studies might consider using the Fourier as one way to improve the robustness of the efficiency results.

Future research might also consider adding more flexibility to the SF models by imposing less restrictive distributions or assumptions on the inefficiency term. For example, recent research has suggested the use of the nonparametric Dirichlet distribution, which imposes little structure on the model in comparison to the half-normal or exponential models (Griffin and Steel 2004). In addition, instead of using static assumptions on the inefficiency term, it is possible to use less restrictive assumptions such as the dynamic assumption that allows inefficiency to adjust itself over time (Tsionas 2006; Tsionas and Assaf 2014). In addition, with the heavy competition in the tourism industry, inefficiency is more likely to follow a dynamic framework than a static framework.⁸ Surprisingly, the dynamic approach has not yet appeared in the tourism literature, despite gaining popularity in many business contexts such as airports, retail, and banking (Barros and Wanke 2014; Assaf et al. 2012). Finally, improvements can also be made in terms of the overall estimation of the SF model. For example, instead of using the maximum likelihood method, future studies might consider using the Bayesian approach. Recently, a few studies in tourism have applied this approach, and future studies are encouraged to continue in this direction. The Bayesian approach, for example, provides several advantages over classical methods (e.g., maximum likelihood). It is flexible in the sense that it incorporates prior information about model parameters. It also allows individual-specific parameters to be estimated while accounting for parameter uncertainty in such estimates. Specifically, the Bayesian methodology provides individual-specific estimates of the model parameters. Note that the Bayesian approach also makes it easier to impose the dynamic assumption on the stochastic frontier model we discussed above (Tsionas 2006)

Concluding Remarks

This study is the first to critically review the application of frontier studies in the tourism literature. Despite the growing popularity of these methods, the tourism literature currently lacks evidence on the characteristics and limitations of the various frontier applications.

We started this review by providing a background and description of frontier analysis and discussed the difference between the nonparametric and parametric frontier methods. We then summarized the characteristics of the various frontier applications in tourism, covering both micro and macro studies. We also reinforced this discussion by conducting a meta-analysis to illustrate the impact of methodologies and other related characteristics on the efficiency results derived from frontier studies. For example, we found that little difference exists between the efficiency results derived from nonparametric and parametric frontier methods. It was clear, however, that the results are sensitive to different specifications of these methods as well as the sample characteristics (i.e., number of inputs, number of outputs). We provided further discussion of these findings and highlighted the current limitations in the extant literature.

The review also provided important directions for future research. For example, it is clear there should be more focus on analyzing the determinants of efficiency in order to enrich the implications from frontier studies. Finally, future studies should also introduce some methodological advances in order to improve the flexibility of frontier methods and the robustness of the efficiency results.

Footnotes

Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

Notes

Author Biographies

A. George Assaf is an Associate Professor at the Isenberg School of Management, University of Massachusetts- Amherst. His work has appeared in several tourism, management and economic journals, such as Tourism Management, Journal of Travel Research, Annals of Tourism Research, and Journal of Retailing.

Alexander Josiassen is an Associate Professor at the Copenhagen Business School. His work has appeared in several marketing and tourism journals, such as Journal of Marketing, Tourism Management, Journal of Travel Research, Annals of Tourism Research, and Journal of Retailing.

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