Productivity in the Hotel Industry: An Order-α Malmquist Productivity Indicator

Abstract

In the literature, it is highlighted that the deterministic nature of the data envelopment analysis–based productivity measures makes them sensitive to sample characteristics. However, the majority of the related empirical studies ignore the potential bias in their data envelopment analysis–based productivity estimations. This article illustrates how the order-α quantile-type estimators can be applied to construct a robust version of the Malmquist productivity indices. Using the order-α estimators, we construct a Malmquist productivity index alongside with two well-known decompositions. The proposed productivity indicator is less sensitive to potential outliers and extreme values. Then, as an illustrative example, we apply the quantile-type productivity index on a sample of 270 hotels operating in the Balearic Islands over the period 2004-2013. The productivity levels alongside with their components are analyzed during the global financial crisis period.

Keywords

Malmquist productivity index hotel productivity Balearic Islands robust measures quantile frontiers global financial crisis

Introduction

The service sector is an important element of countries’ economic growth strategy. As a result, there is a necessity for policymakers to be able to measure, monitor, and analyze service productivity (Lundberg, 1990). Especially, the measurement of hotels’ productivity is an open research challenge for scholars using different methodological tools, different sample sizes, different variables, and different assumptions regarding the estimated production function (Assaf & Josiassen, 2016; Assaf & Matawie, 2009; Assaf & Tsionas, 2018a, 2018b; Barros, 2005a, 2005b; Barros & Santos, 2006). Two main methodological approaches can be adopted to measure hotel productivity. The first one is the parametric approach, known also as the stochastic frontier approach, under which the estimation is based on the advances of econometric techniques. The second approach is known as the data envelopment analysis (DEA) and is based on the advances of mathematical programming. Both approaches exhibit several advantages and disadvantages, and their use is determined most of the time from the problem at hand. The focus of this article is based on the estimation of productivity through the DEA framework. Chatzimichael and Liasidou (2019) pointed out that the DEA-based productivity measures are more popular among the scientists measuring hotels’ productivity levels since they provide greater flexibility in terms of the assumptions imposed in relation to the estimated production function.

Based on the relative literature, Färe and coworkers’ (Färe et al., 1992, Färe, Grosskopf, Lindgren, & Roos, 1994; Färe, Grosskopf, Norris, & Zhang, 1994) Malmquist productivity decomposition is the most popular productivity measure. An essential part of the Malmquist productivity index (MPI) is the estimation of distance functions (DFs). The DEA approach for estimating DFs is very popular among scholars when measuring hotels’ efficiency and productivity levels (Brown & Ragsdale, 2002; Cordero & Tzeremes, 2017; Dolasinski et al., 2019; Goncalves, 2013; Walheer & Zhang, 2018). The studies by Hwang and Chang (2003) and Barros and Alves (2004) were the first to apply the DEA-based MPI in order to measure and decompose the productivity of different hotel sectors. Similarly, Assaf and Barros (2011) applied Färe and Grosskopf’s (1996) productivity decomposition to evaluate hotels’ productivity in the Gulf region. However, the flexibility provided by the DEA-based framework comes with several weaknesses.

As has been suggested by Assaf and Tsionas (2018a, 2018b), DEA-based productivity measures are subject to potential bias since the determinist nature of DEA estimators can be influenced from sample characteristics. Tzeremes (2019) asserted that different outliers, extreme and atypical values included in a data sample, can distort the estimated productivity levels providing the analyst with a pseudo productivity view. Even though such a limitation is well documented in the relative literature, empirical studies measuring hotel productivity avoid tackling such a potential source of bias (Assaf & Josiassen, 2016).

To minimize the potential measurement bias, Assaf and Agbola (2011) applied a bootstrapped-based MPI on a sample of 34 Australian hotels over the period 2004-2007. They applied Simar and Wilson’s (1999) bootstrap procedure to provide a statistical significance of their measurement. More recently, Kularatne et al. (2019) applied Simar and Wilson’s (2007) double bootstrap algorithm on a sample of 24 hotels operating in Sri Lanka over the period 2010-2014. Kularatne et al. (2019) applied the double bootstrap approach to obtain bias-corrected efficiency estimates. Furthermore, as in the case of Assaf and Agbola (2011), Kularatne et al. (2019) further applied a bootstrapped MPI, which was based on Simar and Wilson’s (1999) bootstrap procedure. By doing so, they created confidence intervals for the estimated productivity measures and their components. In both Assaf and Agbola (2011) and Kularatne et al. (2019), the measurement and the decomposition of the MPI was based on Färe, Grosskopf, Lindgren, and Roos (1994) assuming constant returns to scale (CRS).

Serra and Lansink (2014) argued that the main assumption of the estimates derived from the DEA frontier lies in the fact that all units belong to the attainable production set. Therefore, superefficient units act as outliers having a direct impact on the estimated efficiency scores. As a result, the DEA-based DFs used to construct and decompose the DEA-based MPIs will suffer from the same potential bias estimation that is attributed to specific sample characteristics. According to Serra and Lansink (2014), this potential problem can be resolved by applying robust (partial) frontiers that avoid enveloping all data points that are included in the evaluated sample. According to Daraio and Simar (2005, 2007), there are two well-known robust estimators. These are the order-m (Cazals et al., 2002) and the order-α (Daouia & Simar, 2007) estimators that have the ability to be less resistant to sample characteristics since they do not envelope all data points during the estimation. Based on the MPI decomposition introduced by Wheelock and Wilson (1999), the study by Wheelock and Wilson (2003) was the first study that applied the order-m estimators to create a robust (order-m) version of MPI. Recently, Tzeremes (2019) adopted the order-m estimators to construct a robust version of Luenberger productivity index.

This article contributes to the relative literature by creating an order-α MPI in order to evaluate hotel productivity. The idea of using order-α estimators for the creation of robust (quantile) MPI measures was first initiated by Wheelock and Wilson (2013). By using the productivity decomposition introduced by Wheelock and Wilson (1999), they developed a cost-based productivity index evaluating U.S. credit unions during 1989-2006. Supplemental Figure S1 (available online) illustrates in a simple case scenario both the DEA and the order-α frontiers in one input and one output. As can be observed in contrast to the DEA frontier, the order-α frontier is less sensitive to extreme values and potential outliers since it does not envelope all data points (Daouia & Simar, 2007).

Our article utilizes these estimators to construct order-α-based MPIs and evaluate the productivity levels of 270 hotels operating in the Balearic Islands over the period 2004-2013. Finally, it uses the Ray and Desli (1997) decomposition of the estimated productivity levels presenting robust (order-α) productivity components. Lovell (2003) argued that this decomposition in many cases can be more appropriate compared with the decomposition introduced by Färe, Grosskopf, Lindgren, and Roos (1994) and Färe, Grosskopf, Norris, and Zhang (1994), since it applies throughout the estimation the assumption of variable returns to scale (VRS). According to Podinovski et al. (2014), in most cases, the true (best practice) technology is assumed to be represented better under the assumption of VRS. Finally, in the MPI context, the VRS assumption leads to a “safer” choice in contrast to the CRS; however, the latter assumption leads to better discrimination power (Podinovski et al., 2014).

Methodological Framework

Let $x \in ℝ_{+}^{K}$ and $y \in ℝ_{+}^{M}$ denote the input and output vectors in hotel production. Then, according to Cazals et al. (2002) and Daraio and Simar (2005, 2007), the probabilistic framework of hotels’ production function is characterized by the joint probability measure of $(X, Y)$ , and the probability function can be represented as

ϑ_{X Y} (x, y) = Prob (Y \geq y | X \leq x) Prob (X \leq x) = Λ_{Y | X} (y | x) S_{X} (x) .

(1)

In expression (1), $Λ_{Y | X} (y | x) = Prob (Y \geq y | X \leq x)$ denotes the survival function (conditional) of the outputs. The distributional function of the inputs is denoted by $S_{X} (x) = Prob (X \leq x)$ . As a result, the output-oriented efficiency score can be represented as

φ (x, y) = \sup {φ | Λ_{Y | X} (φ y | x) > 0} = \sup {φ | ϑ_{X Y} (x, φ y) > 0} .

(2)

We can calculate $φ (x, y)$ by inserting the empirical survival function of ${\hat{Λ}}_{Y | X} (y | x)$ in (2) as

{\hat{Λ}}_{Y | X, n} (y | x) = \frac{{\hat{ϑ}}_{X Y, n} (x, y)}{{\hat{ϑ}}_{X Y, n} (x, 0)}, given that {\hat{ϑ}}_{X Y, n} (x, y) = \frac{1}{n} \sum_{i = 1}^{n} I (x_{i} \leq x, y_{i} \geq y) .

(3)

Daouia and Simar (2007) argued that the order-α production function can be represented as follows:

λ_{α} (x) = \sup {y | Λ_{Y | X} (y | x) > 1 - α} .

(4)

The production function expressed in (4) represents the level of output not exceeded by $(1 - α) \times 100$ percent of hotels among the hotels that are using less input factors than $x$ . Then, for the multivariate case, we can define the output-oriented order-α efficiency score of a hotel operating at the level $(x, y)$ as

φ_{α} (x, y) = \sup {φ | Λ_{Y | X} (φ y | x) > 1 - α} .

(5)

When $α \to 1$ , then $φ_{α} (x, y)$ provides a robust version of the Farrell–Debreu output efficiency measures. The measure $φ_{α} (x, y)$ takes values greater, equal, and less than unity and provides either the proportional reduction $(if < 1)$ or the increase $(if > 1)$ of outputs for the hotel that is operating at the level $(x, y)$ to reach the frontier. Daraio and Simar (2007) argued that the Order-α estimator is $\sqrt{n} - consistent$ and asymptotically normal distributed.

To construct the order-α MPI index (MPI_α) measures, let the production possibility set at time $t$ be defined as

Ω^{t} = {(x, y) | x can produce y at time t} .

(6)

Following Shephard (1970), the output DF can be expressed as

Δ (x, y | Ω^{t}) \equiv \inf {ψ > 0 | (x, \frac{y}{ψ}) \in Ω^{t}} .

(7)

Given that $Δ (x, y | Ω^{t}) \leq 1$ , let $ϱ (Ω^{t})$ denote the convex cone of the production possibility set defined in (6) having $Ω^{t} \subseteq ϱ (Ω^{t})$ . By replacing Ωt1 and Ωt2 with Ωt1a and Ωt1a (the production sets of order-α at $t_{1} and t_{2}$ , respectively), we can define the order-α MPI_α as

\begin{array}{l} M P I_{α} (x_{i}^{t_{1}}, y_{i}^{t_{1}}, x_{i}^{t_{2}}, y_{i}^{t_{2}} | Ω_{α}^{t_{1}}, Ω_{α}^{t_{2}}) = \underset{T E Δ_{C R S, α}}{\underset{︸}{[\frac{{\hat{Δ}}_{n}^{α} (x_{i}^{t_{2}}, y_{i}^{t_{2}} | ϱ (Ω_{α}^{t_{2}}))}{{\hat{Δ}}_{n}^{α} (x_{i}^{t_{1}}, y_{i}^{t_{1}} | ϱ (Ω_{α}^{t_{1}}))}]}} \times \\ \underset{T Δ_{C R S, α}}{\underset{︸}{{[\frac{{\hat{Δ}}_{n}^{α} (x_{i}^{t_{2}}, y_{i}^{t_{2}} | ϱ (Ω_{α}^{t_{1}}))}{{\hat{Δ}}_{n}^{α} (x_{i}^{t_{2}}, y_{i}^{t_{2}} | ϱ (Ω_{α}^{t_{2}}))} \times \frac{{\hat{Δ}}_{n}^{α} (x_{i}^{t_{1}}, y_{i}^{t_{1}} | ϱ (Ω_{α}^{t_{1}}))}{{\hat{Δ}}_{n}^{α} (x_{i}^{t_{1}}, y_{i}^{t_{1}} | ϱ (Ω_{α}^{t_{2}}))}]}^{1 / 2}}} \end{array}

(8)

Specifically, equation (8) represents an Order-α (robust) version of the original Färe, Grosskopf, Lindgren, and Roos (1994) MPI, which consists of two parts. The first part ( $T E Δ_{C R S, α}$ ) represents the estimated efficiency change (technological catch-up). Catching up refers to the movements away/toward the estimated technological frontier over the examined period. The second part ( $T Δ_{C R S, α}$ ) captures technological change (i.e., movements of the technological frontier) among the two periods. This order-α $M P I_{α}$ index is computed under the assumption of CRS. However, based on Färe, Grosskopf, Norris, and Zhang (1994), we can further decompose $T E Δ_{C R S, α}$ to $T E Δ_{V R S, α}$ and $S E Δ_{α}$ . As a result, the order-α $M P I_{α}$ can be redefined as

\begin{array}{l} M P I_{α} (x_{i}^{t_{1}}, y_{i}^{t_{1}}, x_{i}^{t_{2}}, y_{i}^{t_{2}} | Ω_{α}^{t_{1}}, Ω_{α}^{t_{2}}) = \underset{T E Δ_{V R S, α}}{\underset{︸}{[\frac{{\hat{Δ}}_{n}^{α} (x_{i}^{t_{2}}, y_{i}^{t_{2}} | Ω_{α}^{t_{2}})}{{\hat{Δ}}_{n}^{α} (x_{i}^{t_{1}}, y_{i}^{t_{1}} | Ω_{α}^{t_{1}})}]}} \\ \times \underset{S E Δ_{α}}{\underset{︸}{{\frac{[{\hat{Δ}}_{n}^{α} (x_{i}^{t_{2}}, y_{i}^{t_{2}} | ϱ (Ψ_{α}^{t_{2}})) / {\hat{Δ}}_{n}^{α} (x_{i}^{t_{2}}, y_{i}^{t_{2}} | Ω_{α}^{t_{2}})]}{[{\hat{Δ}}_{n}^{α} (x_{i}^{t_{1}}, y_{i}^{t_{1}} | ϱ (Ψ_{α}^{t_{1}})) / {\hat{Δ}}_{n}^{α} (x_{i}^{t_{1}}, y_{i}^{t_{1}} | Ω_{α}^{t_{1}})]}}}} \times \\ \underset{T Δ_{C R S, α}}{\underset{︸}{{[\frac{{\hat{Δ}}_{n}^{α} (x_{i}^{t_{2}}, y_{i}^{t_{2}} | ϱ (Ω_{α}^{t_{1}}))}{{\hat{Δ}}_{n}^{α} (x_{i}^{t_{2}}, y_{i}^{t_{2}} | ϱ (Ω_{α}^{t_{2}}))} \times \frac{{\hat{Δ}}_{n}^{α} (x_{i}^{t_{1}}, y_{i}^{t_{1}} | ϱ (Ω_{α}^{t_{1}}))}{{\hat{Δ}}_{n}^{α} (x_{i}^{t_{1}}, y_{i}^{t_{1}} | ϱ (Ω_{α}^{t_{2}}))}]}^{1 / 2} .}} \end{array}

(9)

In the expression (9), $T E Δ_{V R S, α}$ represents an order-α version of hotels’ efficiency change levels; however, this is obtained under the assumption of VRS. In addition, $S E Δ_{α}$ represents an order-α version of hotels’ scale efficiency measure. Scale efficiency captures hotels’ ability to operate at optimal scale. However, it must be mentioned that $T Δ_{C R S, α}$ represents, as previously mentioned, hotels’ technological change levels under the CRS level.

In contrast to the two previous decompositions, we utilized an order-α $M P I_{α}$ measure that is based on the decomposition proposed by Ray and Desli (1997). This decomposition provided us with a computation of the scale efficiency change factor for mixed periods (named as scale change factor $S Δ_{α}$ ). In our setting, the order-α $M P I_{α}$ index under the Ray and Desli (1997) decomposition can be presented as

\begin{array}{l} M P I_{α} (x_{i}^{t_{1}}, y_{i}^{t_{1}}, x_{i}^{t_{2}}, y_{i}^{t_{2}} | Ω_{α}^{t_{1}}, Ω_{α}^{t_{2}}) = \underset{T E Δ_{V R S, α}}{\underset{︸}{[\frac{{\hat{Δ}}_{n}^{α} (x_{i}^{t_{2}}, y_{i}^{t_{2}} | Ω_{α}^{t_{2}})}{{\hat{Δ}}_{n}^{α} (x_{i}^{t_{1}}, y_{i}^{t_{1}} | Ω_{α}^{t_{1}})}]}} \times \\ \underset{S Δ_{α}}{\underset{︸}{{\begin{cases} \frac{[{\hat{Δ}}_{n}^{α} (x_{i}^{t_{2}}, y_{i}^{t_{2}} | ϱ (Ψ_{α}^{t_{1}})) / {\hat{Δ}}_{n}^{α} (x_{i}^{t_{2}}, y_{i}^{t_{2}} | Ω_{α}^{t_{1}})]}{[{\hat{Δ}}_{n}^{α} (x_{i}^{t_{1}}, y_{i}^{t_{1}} | ϱ (Ψ_{α}^{t_{1}})) / {\hat{Δ}}_{n}^{α} (x_{i}^{t_{1}}, y_{i}^{t_{1}} | Ω_{α}^{t_{1}})]} \\ \times \frac{[{\hat{Δ}}_{n}^{α} (x_{i}^{t_{2}}, y_{i}^{t_{2}} | ϱ (Ψ_{α}^{t_{2}})) / {\hat{Δ}}_{n}^{α} (x_{i}^{t_{2}}, y_{i}^{t_{2}} | Ω_{α}^{t_{2}})]}{[{\hat{Δ}}_{n}^{α} (x_{i}^{t_{1}}, y_{i}^{t_{1}} | ϱ (Ψ_{α}^{t_{2}})) / {\hat{Δ}}_{n}^{α} (x_{i}^{t_{1}}, y_{i}^{t_{1}} | Ω_{α}^{t_{2}})]} \end{cases}}^{1 / 2}}} \times \\ \underset{T Δ_{V R S, α}}{\underset{︸}{{[\frac{{\hat{Δ}}_{n}^{α} (x_{i}^{t_{2}}, y_{i}^{t_{2}} | Ω_{α}^{t_{1}})}{{\hat{Δ}}_{n}^{α} (x_{i}^{t_{2}}, y_{i}^{t_{2}} | Ω_{α}^{t_{2}})} \times \frac{{\hat{Δ}}_{n}^{α} (x_{i}^{t_{1}}, y_{i}^{t_{1}} | Ω_{α}^{t_{1}})}{{\hat{Δ}}_{n}^{α} (x_{i}^{t_{1}}, y_{i}^{t_{1}} | Ω_{α}^{t_{2}})}]}^{1 / 2} .}} \end{array}

(10)

The last step of our analysis was the estimation strategy of the order-α DFs between the two periods. For our analysis, let ${\tilde{\ddot{y}}}_{i}$ denote the projection of $(x, y)$ onto the order-α frontier in the output direction. Finally, the DFs that are needed to calculate the order-α $M P I_{α}$ and the components (equation 10) can be defined as

{\hat{Δ}}_{n}^{a} (x_{i}^{t_{1}}, y_{i}^{t_{1}} | Ω_{a}^{t_{1}}) \equiv \inf {ψ > 0 | (x_{i}^{t_{1}}, {\tilde{\ddot{y}}}_{i}_{i}^{t_{1}} / ψ) \in Ω_{a}^{t_{1}}},

(11)

{\hat{Δ}}_{n}^{a} (x_{i}^{t_{2}}, y_{i}^{t_{2}} | Ω_{a}^{t_{2}}) \equiv \inf {ψ > 0 | (x_{i}^{t_{2}}, {\tilde{\ddot{y}}}_{i}^{t_{2}} / ψ) \in Ω_{a}^{t_{2}}},

(12)

{\hat{Δ}}_{n}^{a} (x_{i}^{t_{1}}, y_{i}^{t_{1}} | Ω_{a}^{t_{2}}) \equiv \inf {ψ > 0 | (x_{i}^{t_{1}}, {\tilde{\ddot{y}}}_{i}^{t_{1}} / ψ) \in Ω_{a}^{t_{2}}},

(13)

{\hat{Δ}}_{n}^{a} (x_{i}^{t_{2}}, y_{i}^{t_{2}} | Ω_{a}^{t_{1}}) \equiv \inf {ψ > 0 | (x_{i}^{t_{2}}, {\tilde{\ddot{y}}}_{i}^{t_{2}} / ψ) \in Ω_{a}^{t_{1}}},

(14)

{\hat{Δ}}_{n}^{a} (x_{i}^{t_{2}}, y_{i}^{t_{2}} | ϱ (Ω_{a}^{t_{2}})) \equiv \inf {ψ > 0 | (x_{i}^{t_{2}}, {\tilde{\ddot{y}}}_{i}^{t_{2}} / ψ) \in ϱ (Ω_{a}^{t_{2}})},

(15)

{\hat{Δ}}_{n}^{a} (x_{i}^{t_{1}}, y_{i}^{t_{1}} | ϱ (Ω_{a}^{t_{1}})) \equiv \inf {ψ > 0 | (x_{i}^{t_{1}}, {\tilde{\ddot{y}}}_{i}^{t_{1}} / ψ) \in ϱ (Ω_{a}^{t_{1}})},

(16)

{\hat{Δ}}_{n}^{a} (x_{i}^{t_{1}}, y_{i}^{t_{1}} | ϱ (Ω_{a}^{t_{2}})) \equiv \inf {ψ > 0 | (x_{i}^{t_{1}}, {\tilde{\ddot{y}}}_{i}^{t_{1}} / ψ) \in ϱ (Ω_{a}^{t_{2}})},

(17)

{\hat{Δ}}_{n}^{a} (x_{i}^{t_{2}}, y_{i}^{t_{2}} | ϱ (Ω_{a}^{t_{1}})) \equiv \inf {ψ > 0 | (x_{i}^{t_{2}}, \frac{{\tilde{\ddot{y}}}_{i}^{t_{2}}}{ψ}) \in ϱ (Ω_{a}^{t_{1}})} .

(18)

Empirical Findings and Discussion

Following the relative literature of hotels’ efficiency and productivity measurements (Assaf & Agbola, 2014; Assaf & Barros, 2011; Assaf et al., 2011; Assaf & Josiassen, 2016; Cordero & Tzeremes, 2017; Tzeremes, 2019), we defined hotels’ production function having as inputs total employees and total fixed assets (measured in millions of euros). Moreover, our output is hotels’ total sales levels, which is also measured in millions of euros. According to Hwang and Chang (2003), an estimation of such a production function incorporates all the factors of hotels’ production process (manpower, input materials, capital, machines, and equipment). These factors are needed to produce hotels’ intangible and tangible services, and they are reflected in the volumes of total sales. Furthermore, the adopted estimated production frontier provides us with the advantage of minimizing the dimensionality problems that can influence the estimated DEA-based productivity indices (Charles et al., 2019; Dyson et al., 2001; Wilson, 2018). Although we do recognize that multiple outputs are present, we lack detailed data on them, and, despite this fact, revenue efficiency and productivity change are what hotel management is really interested in.

For the purpose of our analysis, we utilize a sample of 270 hotels operating in the Balearic Islands over the period 2004-2013. The data have been extracted from AMADEUS database having the majority of the hotels operating in the regions of Palma (95 hotels), Eivissa (23 hotels), Calvia (22 hotels), and in the region of Santa Margalida (20 hotels). According to Orfila-Sintes et al. (2005), these regions are within the group of regions that form the main holiday destinations in Spain. Table 1 presents yearly the descriptive statistics of hotels’ inputs/output used in our analysis. Even though we are using a balanced panel over the period 2004-2013, for the purpose of our analysis we analyze our findings based on five subperiods that are determining the overall global financial crisis (GFC) phenomena. Following Fiordelisi et al. (2014), we analyzed the estimation of hotels’ productivity measures over five distinct periods. Specifically, we focused our analysis on the precrisis period (2004-2007) and then on the U.S. subprime crisis period (2007-2008). Moreover, we analyzed hotels’ productivity levels during the GFC period (2008-2010) and through the sovereign debt crisis period (2010-2012). Finally, hotels’ productivity levels during the postcrisis period (2012-2013) were examined.

Table 1

Descriptive Statistics of the Factors of Hotels’ Production Function

Year	Statistic	Total employees	Total fixed assets	Total sales	Year	Statistic	Total employees	Total fixed assets	Total sales
2004	Mean	81	19726269.584	7156698.003	2009	Mean	80	16593936.036	6126260.683
2004	Standard deviation	130	88850434.974	11944895.044		Standard deviation	121	64071921.278	9123690.035
2005	Mean	78	19170468.721	6543620.506	2010	Mean	82	16160197.532	5809685.669
2005	Standard deviation	124	87631647.554	10559147.302		Standard deviation	125	68717450.652	8157972.124
2006	Mean	75	19204002.393	6399161.100	2011	Mean	78	12684491.861	5547516.901
2006	Standard deviation	120	93632203.352	10294564.199		Standard deviation	110	31697882.233	7552474.990
2007	Mean	75	18524487.151	5629971.434	2012	Mean	77	11914426.042	5266214.604
2007	Standard deviation	118	88878307.317	8825506.071		Standard deviation	108	29350768.639	7169945.184
2008	Mean	74	16866705.922	5426165.114	2013	Mean	76	11079195.261	5111459.572
2008	Standard deviation	119	67339156.686	8237749.661		Standard deviation	104	25340460.768	7307021.235

Figure 1 presents the density plots from the order-α MPI_α alongside the densities of the productivity components during the precrisis period (2004-2007). The results are obtained for two different values of α. Based on Daraio and Simar (2014), values equal to 0.5 (i.e., α = 0.5) provide us with estimates of the median of the distribution of hotels’ productivity levels (and the components) and corresponds to hotels’ “median” production frontiers. However, for values near to unity (α = 0.99), the estimators provided us with a robust version of the analysis for full (original) Malmquist productivity indices under the Ray and Desli (1997) decomposition. As in the original cases, the MPI_α alongside their comments can take values larger than, equal to, or less than unity. Values greater than unity suggest a progress of hotels’ productivity or/and their estimated components. In contrast, values less than unity signify a productivity decline, whereas values equal to unity signify a stagnation of the estimated productivity change over the examined period. Figure 1 indicates the mean values of the estimated measures; the observed densities are the dashed vertical lines, whereas the vertical solid line indicates unity. The results when set to both α = 0.5 and α = 0.99 reveal that during the precrisis period, hotels’ productivity levels are near unity. Moreover, the productivity decomposition analysis suggested that the productivity levels are attributed mainly to the hotels’ ability to operate at optimal scales ( $S Δ_{α} > 1$ ) alongside with their ability to increase their technological change levels $(T Δ_{V R S, α} > 1)$ . Our findings support the study by Fernández and Becerra (2015) suggesting that the Spanish hotel industry has benefited from its ability to operate at optimal scales through the investment in intangible and tangible assets. However, in both cases, it evident that during 2004-2007 hotels’ technological catch-up ability has been deteriorated $(T E Δ_{V R S, α} < 1)$ .

Figure 1

Density Plots of MPI_α and Components During the Precrisis Period (2004-2007)

Moreover, Figure 2 presents our findings during the subprime crisis period (2007-2008). It is evident that for the case of α = 0.5 (top panel), the picture remains similar compared with the precrisis period. However, when we examined the case of α = 0.99 (bottom panel), our findings revealed that the components of the estimated productivity levels have a platykurtic distribution. This finding suggested that the estimated values of the productivity components are less concentrated around the mean, due to larger variations in the estimated components. This phenomenon is even more pronounced during the GFC period (Figure 3). Our findings suggested that the ability of hotels to operate at optimal scale, to catch-up, and to innovate (technological change) has been under pressure over the two examined periods.

Figure 2

Density Plots of MPI_α and Components During the Subprime Crisis Period (2007-2008)

Figure 3

Density Plots of MPI_α and Components During the Global Financial Crisis Period (2008-2010)

As a result of such a pressure, hotels’ productivity levels have been decreased (at least for the majority of the cases) during the sovereign debt crisis period (2010-2012). Figure 4 reveals such a decrease (case α = 0.99); however, and in contrast to the previous subperiod, we observed a counter reaction indicated by an increase in hotels’ scale efficiency and technological change levels. This was more pronounced during the postcrisis period (2012-2013), under which hotels’ abilities to operate at optimal sizes and produce innovative services (technological change levels) has been increased (Figure 5). Both findings are supportive of the study by Devesa and Peñalver (2013), signifying that the Spanish hotel industry is based on training technologies. These policies are reflected both on the observed technological change levels and also on the estimated scale efficiencies. Our findings are also in line with the study by Orfila-Sintes et al. (2005), providing evidence of high technological investment on tourist accommodation in the Balearics. Similar findings were reported by several other studies (Baidal et al., 2013; Cordero & Tzeremes, 2017; Garay & Canoves, 2011; Tzeremes, 2019) that referred to different Spanish destinations, emphasizing that during the GFC period the Spanish hotel industry has been resistant, following different restructuring strategies. Such strategies enable the Spanish hotel industry to adapt to the GFC challenges by increasing their ability to innovate and operate at optimal scale levels. The outcome of those strategies is pictured in our results, especially in the analysis of the hotels’ estimated $S Δ_{α}$ and $T Δ_{V R S, α}$ levels. Finally, the reported hotels’ innovation capacity reflected on the increased technological change levels is supported by the relative literature (Campo et al., 2014; Guisado-González et al., 2013; Mattsson & Orfila-Sintes, 2014; Orfila-Sintes et al., 2005). In fact, our findings are an indication of the ongoing innovation-based investment strategy designed and applied by the Spanish hotel industry.

Figure 4

Density Plots of MPI_α and Components During the Sovereign Debt Crisis Period (2010-2012)

Figure 5

Density Plots of MPI_α and Components During the Postcrisis Period (2012-2013)

Finally, Supplemental Figure S2 (available online) presents the density plots of the estimated MPI_α measures for four main regions. It is evident that between 2004 and 2013 the productivity levels measured with both values of α have been decreased. Regardless, the most productive region appears to be the region of Calvia. This is since the larger area of the estimated productivity densities lies to the right of the solid vertical line (i.e., unity). Our findings support those presented by Ortega and Chicón (2013) suggesting that hotels’ efficiency and productivity levels can be affected by different regional aspects.

Concluding Remarks and Policy Implications

The necessity for efficiency and productivity measures that are less sensitive to sample characteristics has been highlighted in the relative literature (Assaf & Josiassen, 2016; Assaf & Matawie, 2009; Assaf & Tsionas, 2018a, 2018b). This article, by applying quantile frontier measures (Daouia & Simar, 2007), uses the probabilistic framework of frontier estimation (Cazals et al, 2002; Daraio & Simar, 2005, 2007) to present robust (order-α) Malmquist productivity measures. By doing so, we presented quantile MPI measures that are less sensitive to potential bias from extreme values and outliers. Furthermore, we applied Ray and Desli’s (1997) MPI decomposition producing robust productivity components. We applied the order-α MPI_α measures alongside their robust components to a sample of 270 hotels operating in the Balearic Islands over the period 2004-2013. In our order-α analysis, we used different values of α to check the validity of our findings. It is evident that that the GFC had a negative effect on hotels’ productivity levels; however, the results suggested that during the postcrisis period, the hotels recovered from the GFC’s negative effect. The increased productivity levels during the postcrisis period were mainly from the hotels’ ability to operate on optimal scales and being able to enhance their innovation capacity (technological change levels). Finally, our findings confirmed the relative literature (Baidal et al., 2013; Cordero & Tzeremes, 2017; Garay & Canoves, 2011; Tzeremes, 2019) suggesting that the Spanish hotel industry rarely suffered from the GFC. This is mainly attributed to the industry’s adaptation to the new demand changes and being able to produce innovative services. In fact, the reported positive changes on the estimated technological change levels in the Balearic region suggested the adoption of different innovation policies and practices (Campo et al., 2014; Guisado-González et al., 2013; Mattsson & Orfila-Sintes, 2014; Orfila-Sintes et al., 2005). Moreover, the increased technological change levels can lead to differentiation and customization of tourism demand (Stamboulis & Skayannis, 2003). In addition, the effects that are derived from the adoption of new innovative processes enable policymakers to construct attractive destination images (Pike, 2010; Sainaghi et al., 2019; Stylos et al., 2016; Stylos et al., 2017; Tasci et al., 2007) that are resistant to negative demand shocks.

Supplemental Material

sj-docx-1-jht-10.1177_1096348020974419 – Supplemental material for Productivity in the Hotel Industry: An Order-α Malmquist Productivity Indicator

Supplemental material, sj-docx-1-jht-10.1177_1096348020974419 for Productivity in the Hotel Industry: An Order-α Malmquist Productivity Indicator by Panayiotis Tzeremes and Nickolaos G. Tzeremes in Journal of Hospitality & Tourism Research

Footnotes

Authors’ Note:

We acknowledge the useful comments made by the reviewers. Also, we would like to thank Professor Albert G. Assaf for his helpful suggestions and comments.

ORCID iD

Nickolaos G. Tzeremes

Supplemental Material

Supplemental material for this article is available online.

Panayiotis Tzeremes, PhD (e-mail: tzeremes@uth.gr), is an assistant professor in the Accounting and Finance, University of Thessaly, Larissa, Greece. Nickolaos G. Tzeremes, PhD (corresponding author; e-mail: bus9nt@econ.uth.gr), is an associate professor in the Department of Economics, University of Thessaly, Volos, Greece.

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