The Decomposition of Hotel Productivity Change in Taiwan from Overall and Disaggregate Perspectives

Abstract

It is necessary for the allocation of resources to be more efficient, and making more adequate operational strategies to realize productivity change is contributed to by the kind of output sources in the hotel’s production process. This study tries to propose hotel productivity change models from overall and disaggregate perspectives by using the Luenberger productivity index based on directional distance function. Empirical findings briefly show that the overall productivity change of ITHs in Taiwan has a growing trend and is driven from a technical change rather than an efficiency change. Moreover, the disaggregate hotel productivity growth comes from the service of hotel facilities, but improving the performance of the catering service is more important to a hotel’s overall performance. Individual ITHs can grasp the contribution of disaggregate hotel productivity growth on the overall productivity change, maintaining or developing competitive advantages in the hotel’s operation and management. Therefore, the viewpoint of this study can not only be used to examine the hotel issues but also be applied to other issues in the hospitality and tourism industry that target overall and disaggregate productivity growth.

1. Introduction

The tourism industry has had a certain degree of influence on economic development in Taiwan. In 2005, the government negotiated with the China Tourism Association for Chinese mainland residents traveling to Taiwan, subsequently implementing “Administrative Measures for Mainland Residents Traveling to Taiwan” the next year. Great numbers of tourists from China and other countries have come to Taiwan for tourism during the period 2009–2015. In fact, the number of visitor arrivals with the purpose of tourism accounted for 44.36% of total visitor arrivals in 2007 but jumped to 70.73% of total visitor arrivals in 2016, for a growth rate of 1.59 times (Tourism Administration, 2016). Moreover, the number of Taiwan’s tourist hotels has risen from 87 to 118 during the period of 2005 to 2015. These phenomena show that it is indeed worth exploring the development of the hotel industry during this period, especially for ITHs.

How to survive in this highly competitive market has become a critical issue for general managers of ITHs. Anderson et al. (2000) mentioned that the performance of a firm is an important determinant of its survival in the long run. Phillips (1999) indicated that performance of any management process not only reflects the business situation in reality but also gives a competitive advantage for follow-up operations. As a result, the evaluation of hotel performances has received wider attention in the literature (Morey & Dittman, 1995; Tsaur, 2001; Hwang & Chang, 2003; Chiang et al., 2004; Barros, 2005a, 2005b; Wang et al., 2006a, 2006b; Hu et al., 2009; Yu & Lee, 2009; Chiu & Wu, 2010; Shieh, 2012; Higuerey et al., 2020; Yin et al., 2020; El Alaoui et al., 2023; Zhu et al., 2023; Vidali et al., 2024).

Taiwan’s international tourist hotels (ITHs) mainly provide several services, including lodging service, food and beverage (F&B) service, as well as other services provided by a hotel’s recreational facilities. Yu and Chen (2016) noted that hotel operators need more information regarding their performance to maintain or promote their competitiveness in the ITH industry. The performances are evaluated using productivity scores that allow one to understand only the relative efficiency of transforming inputs into outputs in the current period and contain more information regarding driving forces of inter-temporal improvement. Hence, each ITH should pay more attention to its productivity performance, especially for knowing which is the main source of productivity change.

Realizing a hotel’s productivity change is contributed to by the kind of output sources is helpful for allocating the resources to be more efficient and for helping hotel management to make more adequate business strategies. Traditionally, the total factor productivity (TFP) index, compared to the partial factor productivity index, commonly evaluates the productivity change that considers all dimensions of production resources in each decision-making unit (DMU) (Coelli et al., 2005). The Malmquist productivity index (MPI) and Luenberger productivity index (LPI) are widely adopted to evaluate productivity change in various industries, but Boussemart et al. (2003) and Managi (2003) indicated that MPI may overestimate productivity growth. C. P. Chen et al. (2013) indicated that MPI is derived from the proportional distance function that assumes all factors have the same distance to the frontier, preventing us from examining the various contribution of each factor on productivity change. More importantly, MPI and LPI are aggressive and do not simultaneously evaluate the TFP change and the productivity change of a single factor under the total factor framework (Chang et al., 2012).

To our best knowledge, the existing studies mainly focus on evaluating overall hotel productivity change but neglect to discuss the main source of productivity change from a hotel’s multiple activities. Barros and Alves (2004), Barros (2005b), Hwang and Chang (2003), Yu and Chen (2016), and Cordero and Tzeremes (2017), use MPI to investigate the hotel’s overall productivity change. Moreover, Wheeler and Zang (2018), Tzeremes (2019), El Alaoui et al. (2023), and Choi and Kim (2024) discuss the hotel’s productivity change by using advanced DEA methodologies under overall productivity perspective, but they still do not point out the relationship between overall and disaggregate hotel productivity change. The existing studies have mentioned that disaggregate productivity change offers more information for nations and industries (C. P. Chen et al., 2011; Chang et al., 2012; C. P. Chen et al., 2013), but scant attention has been paid to measure the productivity change from the overall and disaggregate perspectives, especially for the hotel industry.

The distinguishing features of this study’s analysis are provided in several points. First, this paper aims to simultaneously evaluate the overall hotel productivity change and the productivity change of an individual output factor under the total factor framework. Different from the concept of the traditional productivity change index, we extend the traditional LPI with a strongly efficient vector for each output and then evaluate overall and disaggregate hotel productivity change indices. Second, the proposed index from the overall perspective enables us to adequately evaluate the overall hotel productivity changes and its components. We show that the overall productivity change of ITHs in Taiwan has a growing trend and is driven from the technical change rather than the efficiency change. Third, the proposed index herein mainly shows that the overall hotel productivity change is the average of disaggregate hotel productivity changes. The previous studies ignored the contribution of disaggregate hotel productivity changes on overall hotel productivity change. This study explores the contribution (improvement or deterioration) of each output factor from different hotel activities to the overall productivity change in the hotel industry. Fourth, understanding hotel productivity change from overall and disaggregate perspectives not only provide theoretical contributions but also have managerial implications for hotel resource allocation and operational strategies. Therefore, this study provides a reference direction for academic research and industrial practice in the hospitality industry.

The remainder of this study is organized as follows. Section 2 reviews the relevant literature of performance evaluation on the hotel industry. Section 3 addresses the estimating methodology, in which we propose the concept of overall and disaggregate hotel Luenberger productivity indices and also show how to evaluate them. Section 4 displays and discusses the estimating dataset and results of productivity change in Taiwan’s ITHs. The concluding remarks are discussed in the Section 7.

2. Literature Review

When the existing studies discuss a hotel’s performance, its efficiency is usually one of the various indicators for any performance evaluation. An efficiency indicator can simultaneously take into account multiple inputs and outputs rather than other indicators that only consider the performance of a single factor, which fails to reflect the multidimensional nature of a hotel (Yu & Chen, 2016). Two main approaches are used to evaluate hotel efficiency. One is the stochastic frontier approach (SFA), which is a parametric approach (Lovell & Schmidt, 1993). Several existing studies evaluate hotel efficiency under the SFA framework such as Anderson et al. (1999), Anderson et al. (2000), Barros (2004, 2006), C. Chen (2007), Assaf et al. (2012), Hu et al. (2010), Kim (2011), Lin (2011), Salman Saleh et al. (2012), Assaf (2012), Assaf and Barros (2013), Arbelo et al. (2017), and Assaf and Tsionas (2018). However, with the development of newer methodologies, more recent research has increasingly addressed the limitations of SFA, especially its inability to account for nonlinearity and the diverse nature of hotel operations.

The second common method is a non-parametric approach, which is the famous data envelopment analysis (DEA). To the best of our knowledge, DEA has two main advantages over SFA. First, DEA is more flexible than SFA, as the latter cannot assume the functional form of the production function or distance function when evaluating efficiency scores. Second, the DEA methodology can consider multiple outputs and inputs in the analysis, especially for the multiple output features of a firm’s operations. DEA has been applied for performance evaluation in many industries including the hotel industry. The existing studies on this issue that used traditional or advanced DEA models include Morey and Dittman (1995), Tsaur (2001), Hwang and Chang (2003), Chiang et al. (2004), Barros (2005a), Barros and Mascarenhas (2005), Wang et al. (2006a), Barros and Dieke (2008), Hu et al. (2009), Yu and Lee (2009), Chiu and Wu (2010), Shieh (2012), Manasakis et al. (2013), Luo et al. (2014), and Ramanathan et al. (2016).

Recent studies have extended the application of DEA models to hotel efficiency evaluation, such as Tan and Despotis (2021) and Choi and Kim (2024), who explored new DEA-based approaches for assessing hotel performance. Vidali et al. (2024) highlight the strengths and weaknesses of both parametric and non-parametric methods in measuring hotel efficiency. However, the hotel efficiency indices in the existing literature can offer insight only into the relative efficiency of converting inputs into outputs at a specific point in time. This static index provides no information about the driving forces behind inter-temporal efficiency or technical improvement.

3. Previous Study Analysis

This section provides a comparison of the existing studies and summarizes key articles, their methodologies, aim, variables, findings, and contributions as shown in

Table A1. Summary of key studies for hotel’s efficiency and productivity.

Article	Method	Aim	Variables	Findings	Contribution	Conclusion
Tsaur (2001)	DEA	To assess hotel performance and efficiency using DEA	Input variables: labor, capital, operating costs; Output variables: revenue, room nights sold	Demonstrated how DEA offers detailed insights into hotel performance	Contributed to the application of DEA in hotel industry efficiency analysis	The study concludes that DEA is a powerful tool for evaluating hotel performance and can reveal inefficiencies that other methods may overlook.
Barros (2004)	SFA	To evaluate hotel efficiency and competitiveness across different regions	Input variables: labor, capital; Output variables: revenue, occupancy rate	Evaluated hotel efficiency and competitiveness	Contributed to the understanding of hotel performance in different regions	The study concludes that efficiency improvements are crucial for enhancing competitiveness but also emphasizes the need for region-specific strategies.
Barros and Mascarenhas (2005)	DEA	To evaluate hotel efficiency across different types of hotels	Input variables: capital, labor; Output variables: revenue, room occupancy, guest satisfaction	Applied DEA to evaluate hotel efficiency across different types of hotels	Provided evidence that different hotel types exhibit varying levels of efficiency	The study concludes that hotel efficiency is heavily influenced by hotel type, and thus, benchmarking needs to consider these differences to be meaningful.
Barros and Dieke (2008)	DEA	To assess hotel efficiency across various regions in Brazil	Input variables: rooms, labor, capital; Output variables: revenue, room occupancy	Applied DEA to evaluate hotel efficiency across different regions	Highlighted regional variations in hotel performance	The study concludes that there are significant regional differences in hotel efficiency, and a tailored approach is necessary to address these variations.
Cordero and Tzeremes (2017)	MPI	To analyze hotel productivity change over time using the Malmquist productivity index	Input variables: labor, capital, operating costs; Output variables: revenue, room occupancy	Analyzed hotel productivity change over time using MPI	Used MPI to evaluate hotel efficiency and productivity trends	The study concludes that while the MPI is useful for assessing overall productivity changes, it fails to account for the contribution of individual factors to productivity growth.
Wheeler and Zang (2018)	LPI	To evaluate hotel productivity changes using the Luenberger productivity index	Input variables: labor, capital, operating costs; Output variables: revenue, guest satisfaction	Evaluated productivity changes in hotels using LPI	Advanced the understanding of hotel productivity dynamics using LPI	The study concludes that LPI provides a more accurate and detailed measure of productivity change compared to traditional methods like MPI.
Tzeremes (2019)	LPI	To assess hotel productivity dynamics using LPI	Input variables: labor, capital, operating expenses; Output variables: revenue, room occupancy, guest satisfaction	Assessed hotel productivity dynamics using LPI	Contributed to the evaluation of productivity changes using a more flexible index	The study concludes that LPI captures productivity changes more effectively, offering better insights into individual factor contributions compared to traditional methods.
Higuerey et al. (2020)	DEA	To measure the efficiency of the hotel industry in Ecuador	Input: labor, capital, and resources; Output: hotel revenue, occupancy rates	The study found inefficiencies in resource utilization among hotels in Ecuador, with small hotels showing lower efficiency compared to larger ones.	Provides a comprehensive evaluation of hotel efficiency in Ecuador and suggests ways to optimize resource use for improved hotel performance.	The study concludes that improving operational efficiency, resource management, and adopting best practices are key for enhancing hotel performance in Ecuador.
Yin et al. (2020)	DEA	To analyze hotel performance from an internal cooperation perspective using a two-stage DEA model	Input: labor, capital, operational costs; Output: revenue, guest satisfaction	Internal cooperation within departments was found to significantly impact hotel performance. Hotels that promoted internal coordination showed better performance.	Introduces a new perspective on hotel performance by emphasizing internal cooperation, offering insights into how internal management can influence overall performance.	The conclusion highlights the importance of internal cooperation among departments for improving hotel performance. The study recommends strategies to enhance collaboration.
El Alaoui et al. (2023)	DEA	To analyze productivity, efficiency, and sustainability in the Tunisian hotel industry using a two-stage DEA approach	Input: resources (labor, capital); Output: revenue, productivity; Intermediate: service quality	Tunisian hotels showed mixed results, with larger hotels generally being more efficient. Smaller hotels, however, demonstrated better sustainability practices.	The study introduces a two-stage model to assess efficiency, sustainability, and productivity, particularly in developing economies like Tunisia.	The study concludes that sustainability practices should be integrated into productivity and efficiency evaluations for a more comprehensive performance measurement.
Zhu et al. (2023)	DEA	To measure the performance of Taiwan hotels using a hierarchical network DEA model that incorporates shared inputs	Input: labor, capital, resources (shared across departments); Output: revenue, occupancy rates, guest satisfaction	The study found that hotels using shared inputs across departments improved their efficiency and overall performance, especially in larger hotels.	Introduces the concept of shared inputs into the performance measurement model, providing a more accurate assessment of hotel operations.	The conclusion emphasizes that shared inputs contribute to better hotel performance, and suggests that hotels focus on optimizing shared resources to enhance efficiency.
Choi and Kim (2024)	DEA	To measure hotel service productivity	Input Variables: Labor, capital, operating costs, facilities. Output Variables: Revenue, room occupancy, guest satisfaction. Intermediate Variables: Service quality (measured through guest reviews and service metrics).	The two-stage network DEA model effectively highlights the importance of service quality as an intermediary variable in hotel service productivity analysis.	Provided empirical evidence on how hotels in different categories (based on star ratings) manage service quality and productivity.	The study concludes that a two-stage network DEA model incorporating service quality as an intermediary variable is more effective in measuring hotel service productivity.
Vidali et al. (2024)	Systematic literature review	To review the parametric and non-parametric methods for measuring efficiency in the hotel industry	N/A (Literature review)	The review highlights the strengths and weaknesses of both parametric and non-parametric methods (like SFA and DEA) in measuring hotel efficiency.	The paper systematically reviews and compares different efficiency measurement methods in the hotel industry, providing a clear overview of the existing research.	The conclusion discusses the need for a more integrated approach that combines parametric and non-parametric methods for a more accurate efficiency measurement.

. The hotel efficiency indices typically belong to a static measurement, but a productivity index belongs to a dynamic measurement, giving more information for understanding the intertemporal efficiency or technical improvement of hotel performance. Such an index would help hotel managers design appropriate strategies to improve resource allocation efficiently (Barros & Alves, 2004).

To address the limitations of traditional indices, this study adopts the Luenberger productivity index (LPI) to evaluate productivity changes in hotels. The LPI overcomes the main drawback of the Malmquist Productivity Index (MPI), which assumes all factors are equidistant from the frontier. The Malmquist productivity index developed by Caves et al. (1982) is widely adopted to analyze the nature of efficiency change in various industries. Several studies evaluate a hotel’s productivity change by using MPI such as Barros and Alves (2004), Barros (2005b), Hwang and Chang (2003), Yu and Chen (2016), and Cordero and Tzeremes (2017). However, recent studies have shifted to apply LPI to evaluate hotel productivity changes, such as Wheeler and Zang (2018) and Tzeremes (2019), indicating that LPI provides a more comprehensive view of productivity change by considering the contributions of individual factors.

This study fills the gap in the existing literature by evaluating productivity changes in hotels from both overall and disaggregate perspectives. By using LPI, we can simultaneously assess overall hotel productivity changes while also investigating the contributions (improvements or deteriorations) of each output factor to overall hotel productivity. This more granular approach allows for a deeper understanding of the dynamics of hotel performance. The existing research on hotel productivity largely focuses on overall efficiency or general productivity changes. However, few studies explore the contribution of individual factors to productivity changes, leaving a gap in understanding the specific drivers of hotel performance. This study aims to fill this gap by evaluating both overall and disaggregated hotel productivity changes by using the Luenberger productivity index (LPI), which provides a more precise and comprehensive assessment of each output factor’s contribution to overall productivity changes. The proposed model will be discussed in the next section.

4. Empirical Methodology

4.1. Overall and Disaggregate Hotel Luenberger Productivity Indices

This section introduces how to construct the disaggregate hotel productivity change by using the Luenberger productivity indicator. To model the production process, we assume that ${\mathrm{F}}^t$ is the production technology in which ITH k adopts multiple inputs, $x\in R_{+}^S$ to produce a vector of outputs, and $y\in R_{+}^M$ in time period t. Here, ${\mathrm{F}}^t$ for each ITH is defined as the set of all feasible input–output vectors:

$${\mathrm{F}}^t=\left\{(x^k,y^k):x^t\in R_{+}^S,y^t\in R_{+}^M,x \mathrm{can} \mathrm{produce} y\right\}.$$

(1)

After formally defining the production technology, we use the directional distance function (DDF) to construct the hotel Luenberger productivity indicator. Formally, the output DDF in period is defined as

$${\stackrel{⃑}{D}}_t\left(x^t,y^t;q_y\right)=\mathrm{m}\mathrm{a}\mathrm{x}\left\{\beta :\left(y+\beta q_y\right)\in {\mathrm{F}}^t\right\},$$

(2)

where $q_y$ is non-zero vectors in $R_{+}^M$. The output DDF directional allows decision-making units (DMUs) to simultaneously seek the maximum expansion of outputs (y) to optimize the production for any given production technology. The value of DDF equals zero if a country is technically efficient, whereas the value of ${\stackrel{⃑}{D}}_t\left(x^t,y^t;q_y\right)>0$ indicates the production is inefficient.

We finally can use the directional distance function in different time periods relative to the different period technology to measure productivity change by following Chambers et al. (1996). The hotel Luenbereger productivity indicator (HLPI) is set up as follows:

$$\begin{gathered} HLPI\left(x^t,y^t,x^{t+1},y^{t+1}\right) \\ =0.5\left[{\stackrel{⃑}{D}}_t\left(x^t,y^t,b^t;q\right)-{\stackrel{⃑}{D}}_t\left(x^{t+1},y^{t+1},b^{t+1};q\right)+{\stackrel{⃑}{D}}_{t+1}\left(x^t,y^t,b^t;q\right)-{\stackrel{⃑}{D}}_{t+1}\left(x^{t+1},y^{t+1},b^{t+1};q\right)\right]. \end{gathered}$$

(3)

If the value of the index is less than, equal to, or larger than zero, then it stands for productivity regress, no change, or progress between periods t and t + 1, respectively. Moreover, HLPI can be decomposed into hotel efficiency change (HEC) and hotel technical change (HTC) as follows:

$$HEC\left(x^t,y^t,x^{t+1},y^{t+1}\right)={\stackrel{⃑}{D}}_t\left(x^t,y^t,b^t;q\right)-{\stackrel{⃑}{D}}_{t+1}\left(x^{t+1},y^{t+1},b^{t+1};q\right)$$

(4)

$$\begin{gathered} HTC\left(x^t,y^t,x^{t+1},y^{t+1}\right)=0.5[{\stackrel{⃑}{D}}_{t+1}\left(x^{t+1},y^{t+1},b^{t+1};q\right)-{\stackrel{⃑}{D}}_t\left(x^{t+1},y^{t+1},b^{t+1};q\right)+{\stackrel{⃑}{D}}_{t+1}\left(x^t,y^t,b^t;q\right)- \\ {\stackrel{⃑}{D}}_t\left(x^t,y^t,b^t;q\right)] \end{gathered}$$

(5)

We note that HEC equals the difference in the directional distance function between two periods, while technical change equals the average ‘shift’ in the frontier. Efficiency change measures any changes in the position of the production unit relative to the best-practice frontier over time and represents the so-called ‘catching up’ effect—that is, convergence towards or divergence from the best practice. On the other hand, HTC equals the average ‘shift’ in the best-practice frontier from period to period and represents the ‘innovation’ effect—that is, improvement or deterioration in the performance of best-practice production units.

Our aim is to understand the role of individual output in hotel productivity. This study thus first uses the concept of Equation (3) to propose the disaggregate hotel Luenberger productivity index (DHLPI), which represents the output-factor hotel productivity index as follows:

$$\begin{gathered} DHLPIi={\displaystyle \frac{1}{2}}\left[{\stackrel{⃑}{D}}_{i\left(t\right)}\left(x^t{, y}^t\right)-{\stackrel{⃑}{D}}_{i\left(t\right)}\left(x^{t+1}{,y}^{t+1}\right)+{\stackrel{⃑}{D}}_{i\left(t+1\right)}\left(x^t{,y}^t\right)-{\stackrel{⃑}{D}}_{i\left(t+1\right)}\left(x^{t+1}{,y}^{t+1}\right)\right] \\ =\left[{\stackrel{⃑}{D}}_{i\left(t\right)}\left(x^t{, y}^t\right)-{\stackrel{⃑}{D}}_{i\left(t+1\right)}\left(x^{t+1}{,y}^{t+1}\right)\right]+{\displaystyle \frac{1}{2}}\left[{\stackrel{⃑}{D}}_{i\left(t+1\right)}\left(x^{t+1}{,y}^{t+1}\right)-{\stackrel{⃑}{D}}_{i\left(t\right)}\left(x^{t+1}{,y}^{t+1}\right)+{\stackrel{⃑}{D}}_{i\left(t+1\right)}\left(x^t{,y}^t\right)-{\stackrel{⃑}{D}}_{i\left(t\right)}\left(x^t{, y}^t\right)\right] \\ =DHECi+DHTCi. \end{gathered}$$

(6)

Note that if the value of DHPI is less than, equal to, or greater than zero, then it indicates that the productivity of the ith output regresses, does not change, or progresses from periods t to t + 1. Consequently, to measure the change in relative efficiency and the shift in the technology of the ith output, DHPI can be further decomposed into two components: disaggregate hotel efficiency change (DHEC) and disaggregate hotel technical change (DHTC).

We next convert the contribution of each DHPI in the overall HLPI by following the definition and its components of Equations (3)–(5). Since ${\stackrel{⃑}{D}}_t\left(x^t,y^t\right)$ is equal to the arithmetic mean of the distance functions of all outputs, we decompose the hotel productivity change into the productivity change of the individual output as:

$$\begin{gathered} HLPI=HEC+HTC={\displaystyle \frac{1}{Z}}\left[D{HEC}_1+D{HEC}_2+\dots +{DHEC}_Z\right]+{\displaystyle \frac{1}{Z}}\left[{DHTC}_1+{DHTC}_2+\dots +{DHTC}_Z\right] \\ ={\displaystyle \frac{1}{Z}}\left[{DHLPI}_1+{DHLPI}_2+\dots +{DHLPI}_Z\right]. \end{gathered}$$

(7)

Equation (7) indicates that the overall hotel productivity change is the arithmetic mean of the change in individual output-factor productivity. Moreover, the efficiency change and technical change in individual output can be aggregated as overall hotel efficiency change and overall hotel technical change, respectively. Under the disaggregate perspective, we are interested in the main source of hotel productivity—that is, to explore which output factor mainly contributes to hotel productivity growth, especially in ITHs.

4.2. Model Specification and Evaluation

After defining the hotel productivity index and all its decompositions, the question becomes how to evaluate these indices. To our best knowledge, we can apply the directional distance function to evaluate the output DDF from the above equations. However, this prevents us from examining the possible difference in productivity change across output rather than the proportional distance function that assumes all factors have the same distance to the frontier. Therefore, as the goal of a hotel’s productivity activities focuses on creating more output, we assume that the linear programming method of the directional distance function will maximize expanding outputs (y) given fixed inputs.

Let there be S inputs and W good outputs for each hotel in time t. The sth input and wth good output variable of the kth hotel are represented by $x_{sk}^t$ and $y_{wk}^t$ in time t, respectively. Therefore, the directional distance function for hotel k in time t can be evaluated by the following linear programming (LP) model:1

$$\begin{array}{ll}{\stackrel{⃑}{D}}_{k,t}\left(x^t,y^t\right)=& max{\displaystyle \frac{1}{W}}{\sum }_{m=1}^M{\beta }_w^y \\ & \mathrm{s}.\mathrm{t}.{\sum }_{i=1}^K{\theta }_i{x}_{si}^t\le x_{sk}^t,s=1,\dots ,S;\\ & {\sum }_{i=1}^K{\theta }_i{y}_{wi}^t\ge \left(1+{\beta }_w^y\right)y_{wk}^t, \mathrm{w}=1,\dots ,\mathrm{W};\\ & {\theta }_i\ge 0, i=1,\dots ,K; {\beta }_w^y\ge 0,\end{array}$$

(8)

where ${\theta }_i$ is the intensity variable that serves to form a convex combination of observed inputs and outputs. As shown in Equation (8), the variable ${\beta }_w^y$ is the inefficiency level of the disaggregate output. Consequently, the calculation of ${\stackrel{⃑}{D}}_{k,t+1}\left(x^{t+1},y^{t+1}\right)$ is similar to Equation (8), where t + 1 is substituted for t.

As for the evaluation of the two intertemporal directional distance functions, ${\stackrel{⃑}{D}}_{k,t}\left(x^{t+1},y^{t+1}\right)$ and ${\stackrel{⃑}{D}}_{k,t+1}\left(x^t,y^t\right)$, we obtain the measures by solving the following linear programming problems:

$$\begin{array}{ll}{\stackrel{⃑}{D}}_{k,t}\left(x^{t+1},y^{t+1}\right)& =max{\displaystyle \frac{1}{W}}{\sum }_{m=1}^M{\beta }_w^y\\ & \mathrm{s}.\mathrm{t}.{\sum }_{i=1}^K{\theta }_i{x}_{si}^t\le x_{sk}^{t+1},s=1,\dots ,S;\\ & {\sum }_{i=1}^K{\theta }_i{y}_{wi}^t\ge \left(1+{\beta }_w^y\right)y_{wk}^{t+1}, \mathrm{w}=1,\dots ,\mathrm{W};\\ & {\theta }_i\ge 0, i=1,\dots ,K; {\beta }_w^y\ge 0\end{array}$$

and

$$\begin{array}{ll}{\stackrel{⃑}{D}}_{k,t+1}\left(x^t,y^t\right)=& max{\displaystyle \frac{1}{W}}{\sum }_{m=1}^M{\beta }_w^y\\ & \mathrm{s}.\mathrm{t}.{\sum }_{i=1}^K{\theta }_i{x}_{si}^{t+1}\le x_{sk}^t,s=1,\dots ,S;\\ & {\sum }_{i=1}^K{\theta }_i{y}_{wi}^{t+1}\ge \left(1+{\beta }_w^y\right)y_{wk}^t, \mathrm{w}=1,\dots ,\mathrm{W};\\ & {\theta }_i\ge 0, i=1,\dots ,K; {\beta }_w^y\ge 0.\end{array}$$

(9)

Finally, we obtain HLPI from solving the above linear programming problems. All decompositions of HLPI and $DHPI$ can also be calculated from the results of the above linear programming problems.

5. Empirical Results

5.1. Data Descriptions and Sources

Since the hotel production process includes multiple decision-making activities, these ITHs not only provide accommodation services but also other services such as catering and entertainment from the hotel’s facilities (Wheeler & Zang, 2018). Only using number of rooms and number of employees, as well as total fixed assets, as inputs in the hotel production process is a common approach but not comprehensive. Several studies as shown in Table A1 have evaluated a hotel’s performance by employing a combination of flow and stock variables to represent the inputs and outputs, such as occupancy rate, revenues, number of rooms, expenditure, and number of employees, which may encounter double-counting problems.

In practice, most ITHs cannot immediately adjust the amount of fixed assets in the short run. A hotel general manager basically focuses on how to gain more revenue after paying those necessary operating expenditures. Therefore, the input–output variables of this study are adopted by the viewpoint of flow variables to show the operating conditions in each year of the current period when evaluating the hotel’s performance. Moreover, all resources required for the hotel production process can be comprehensively considered by using various expenditures as hotel production inputs, shown as the dotted line in Figure 1. Different from the existing studies, this alternative viewpoint for selecting the input–output variables when evaluating hotel productivity change are not only closer to the practical operations of hotel management but also provide another viewpoint for evaluating hotel performance as a future reference.

Existing studies using the combination of flow and stock variables to represent the inputs and outputs may have the double-counting problem and be less close to practical experience. This study selects three input variables: employee wage expenditure, food and beverage (F&B) expenditure, and other facilities’ operating expenditure. Employee wage expenditure mainly includes total expenditure for all hotel staff such as the salaries, insurance fees, etc. The number of employees affects the level of this expenditure. To avoid the problem of double-counting for labor input, one can use this flow variable method as it does not need to be added to the labor stock variable. F&B and other facilities’ operating expenses mainly represent things like F&B ingredients, room accessories and amenities, other facility maintenance fees, etc., which come from fixed assets. More fixed assets at a hotel will directly reflect the level of these expenses. Similarly, using these flow variables to replace stock variables of F&B and other operations can avoid the double-counting problem of these inputs. On the other hand, three major outputs in this study include room operating revenue, F&B revenue, and other facilities’ operating revenue. Room and F&B operating revenues account for approximately 80% of the total revenue. Other facilities’ operating revenue may include revenue from the swimming pool, laundry, rental service, etc.

All output and input variables utilized in this study belong to a panel dataset of 56 ITHs over the period 2005–2014. Output and input variables of each international tourist hotel are mainly collected from the Tourism Statistics Annual Report and Annual Report on the International Tourist Hotel Business Survey published by the Taiwan Tourism Administration.2 Since the data cover a time span of ten years, all variables in monetary units have been transformed into real variables in terms of million New Taiwan Dollars (NTD) in the year 2010.

Table 1. Descriptive statistics of input and output variables.

Name		Mean	SD	Min	Max
Input variable
x1	Wage expenditure	190.04	165.42	7.97	803.21
x2	Food and beverage expenditure	113.72	123.71	3.43	1241.82
x3	Other expenditure	271.08	295.54	20.39	2732.90
Output variable
y1	Room revenue	259.37	223.00	25.75	1312.17
y2	Food and beverage revenue	284.11	291.83	7.63	1630.80
y3	Other facilities revenue	107.30	418.61	0.09	9207.28

Notes: Data are collected from Tourism Statistics Annual Report and Annual Report on the International Tourist Hotel Business Survey. All variables are transformed into real variables in terms of million New Taiwan dollars in the year 2010. Data source is from Taiwan’s tourism statistics website: https://reurl.cc/VYad2n (accessed on 30 March 2024).

describes the summary statistics of these input and output variables. During the sampling period, Taiwan’s ITHs were facing a state of fierce competition, and it is worthwhile to investigate their productivity changes, especially from the overall and disaggregate perspectives. However, due to the limited official release of information, information in recent years has been restricted by the completeness of variable information disclosure, and there is no complete disclosure information about input variables. This limitation of the data period is a major difficulty facing this research. Despite such a limitation, it is still worth exploring the changes in hotel productivity from the overall and disaggregate perspectives.

Table 2. The correlation matrix of input and output variables.

Variable	Correlation Matrix
Input Variable
x1	1.0000
x2	0.6963 *	1.0000
x3	0.7224 *	0.5996 *	1.0000
Output Variable
y1	0.8644 *	0.6237 *	0.8012 *	1.0000
y2	0.9294 *	0.7790 *	0.7699 *	0.8522 *	1.0000
y3	0.2606 *	0.2430 *	0.2110 *	0.2178 *	0.2724 *	1.0000

Note: * represents significance at the 1% levels.

demonstrates the correlation matrix of input and output variables, whereby positive correlations exist between inputs and outputs, thus satisfying the isotonicity property that an output does not decrease with an increase in an input. These results not only confirm isotonicity between any input and both of the two outputs in the linear programming model but also can be applied to analyze HLPI and its components by our framework of inputs and outputs.

5.2. Overall Hotel Productivity Change Index and Its Components

Based on the framework of the Luenberger productivity index, this study develops the hotel Luenberger productivity index (HLPI) and solves the aforementioned linear programming problem by using LINGO software 20.0. It enables us to adequately evaluate the productivity change in ITHs and further decompose it into two components parts: hotel efficiency change (HEC) and hotel technical change (HTC). The former is the change in relative hotel efficiency, measuring how each ITH is getting closer to or farther away from its annual frontier (catch-up effect or fall-behind effect). The latter is the shift in the production frontier under the total-factor framework. An expanding technology frontier is generally contributed to by innovations, technology upgrading, diffusion, etc. This is the so-called innovation effect.

Table 3. Annual HLPI by operation type and region (%).

Year	2005/2006	2006/2007	2007/2008	2008/2009	2009/2010	2010/2011	2011/2012	2012/2013	2013/2014	Average
Chain	−0.1499	0.1487	−0.1201	−0.2446	−0.2678	12.5354	−7.0353	0.0896	−0.0109	0.5495
Independent	0.1387	0.2129	−1.6791	0.8385	−0.7081	27.9883	−22.7384	−1.1707	2.9716	0.6504
North	0.2510	0.1070	−0.3513	0.1989	−0.2171	16.0584	−18.6604	0.1266	0.4104	−0.2307
Central	−0.2958	0.1332	0.1100	−0.8013	0.4984	5.7685	−5.4718	−0.1681	−0.1609	−0.0431
South	−0.2969	0.2497	−1.9046	0.6068	−0.6227	19.4152	−2.3579	−1.8038	3.0350	1.8134
East	−0.2968	0.2694	−0.2594	0.0074	−1.5080	34.8967	−22.9647	0.4836	0.8421	1.2745
ALL	−0.0333	0.1736	−0.7325	0.1809	−0.4407	18.6061	−13.2043	−0.4055	1.1607	0.5894

Notes: Operation type mainly depends on whether or not the ITH is a domestic or foreign chain brand. North region refers to a hotel’s location in Taipei, New Taipei City, Taoyuan, Hsinchu, and Miaoli. Central region refers to a hotel’s location in Taichung City, Changhua County, and Nantou County. South region refers to a hotel’s location in Chiayi County, Tainan City, Kaohsiung City, and Pingtung County. East region refers to a hotel’s location in Yilan County, Hualien County, and Taitung County.

displays the empirical results of HLPI for each ITH during the 2005–2014 period, showing that the average HLPI reaches only a growth of 0.5894% for all sample hotels. In terms of operation type, the productivity of chain-operated hotels or independent-operated hotels averagely shows a positive growth trend, but the average productivity growth rate of independent-operated ITHs is higher than that of chain-operated ITHs. Table 3 also shows that the period of major productivity growth is from 2010 to 2011 and that there is a slight increase or decline in the remaining years. We also find that independent-operated ITHs on average have experienced a decline in the growth rate of productivity versus that of chain-operated hotels from 2011 to 2012.

In terms of regions, the ITHs in the south on average show a higher productivity growth trend than do the other regions, followed by those in the east. In contrast, the productivity of ITHs in the north and central regions shows a declining trend. Moreover, ITHs in the north and east regions have higher productivity growth from 2010 to 2011, but they also show a large productivity decline from 2011 to 2012. ITHs in the south region show a productivity growth trend from 2010 to 2011 but do not show productivity decline from 2011 to 2012. Therefore, the average productivity growth trend in the south region is more obvious than in the other three regions as there is a fluctuation in productivity changes during the sampling periods.

Table 4. Annual HEC and HTC by operation type and region (%).

	Year	05/06	06/07	07/08	08/09	09/10	10/11	11/12	12/13	13/14	Average
HEC	Chain	−0.3126	0.1605	0.0598	−0.1264	−0.0200	−18.2405	18.4187	0.0889	−1.4513	−0.1581
	Independent	−0.3993	−0.0782	−0.9261	1.2281	−0.6488	−32.2670	31.3995	−0.8440	−1.6210	−0.4619
	North	−0.0821	−0.0255	−0.1727	0.3807	−0.0733	−8.1190	7.1203	−0.0021	−1.6722	−0.2940
	Central	−0.5252	0.0283	0.3423	−0.8894	0.7272	−15.4994	15.6772	−0.2162	−1.9436	−0.2554
	South	−0.5875	0.1708	−1.1773	1.1748	−0.6280	−48.7666	49.2542	−1.0851	−1.2576	−0.3225
	East	−0.6637	0.1952	0.3664	−0.0795	−0.9203	−30.7121	31.2207	0.3963	−1.2179	−0.1572
	ALL	−0.3476	0.0676	−0.3275	0.4057	−0.2670	−23.7509	23.5182	−0.2776	−1.5179	−0.2774
HTC	Chain	0.1627	−0.0112	−0.1799	−0.1182	−0.2478	30.7759	−25.4540	0.0006	1.4403	0.7076
	Independent	0.5380	0.2911	−0.7530	−0.3896	−0.0592	60.2553	−54.1379	−0.3266	4.5925	1.1123
	North	0.3331	0.1326	−0.1786	−0.1818	−0.1438	24.1774	−25.7807	0.1287	2.0827	0.0633
	Central	0.2294	0.1049	−0.2323	0.0881	−0.2288	21.2679	−21.1490	0.0480	1.7827	0.2123
	South	0.2906	0.0790	−0.7273	−0.5680	0.0053	68.1818	−51.6121	−0.7186	4.2926	2.1359
	East	0.3669	0.0742	−0.6258	0.0869	−0.5877	65.6088	−54.1854	0.0873	2.0600	1.4317
	ALL	0.3142	0.1059	−0.4050	−0.2248	−0.1736	42.3571	−36.7226	−0.1279	2.6787	0.8668

Notes: Same as in Table 3.

displays the result of HEC for each ITH during the period 2005–2014. Drawn from results in Table 4, it is surprising to see that the average HEC is negative, indicating that those ITHs on average have a declining trend of 0.2774% in efficiency change during the sampling period. In terms of operation types, the efficiency change in chain-operated hotels or independent-operated hotels on average mainly shows a fall-behind effect, which means each ITH is moving far away from its annual frontier. Moreover, the average efficiency change in independent-operated ITHs is worse than those chain-operated ITHs. We further find that HEC of independent-operated ITHs during periods 2006–2007, 2008–2009, and 2011–2012 shows greater growth than those chain-operated hotels, implying that there exists a catch-up effect during these periods.

As for the result of HEC for a hotel’s region, each region on average shows a trend of decline in efficiency change, with the largest decline in the south, followed by the north. Moreover, we find that each region exhibits a larger decline trend from 2010 to 2011 during the sampling period, but a larger growth trend from 2011 to 2012. The result of HEC in the north region is also similar to that in the east region, presenting a relatively large growth trend from 2010 to 2011 but also a relatively large decline from 2011 to 2012. Overall, HEC of the south region on average shows an obvious decline trend relative to the other regions, while the other regions mainly show a slight growth or decline trend during these periods.

Table 4 lists the result of HTC for each ITH during the period 2005–2014. On average, we find that the average HTC is positive, indicating that those ITHs have a growth trend of 0.8668% in technical change during the sampling period. In terms of operation types, the technical change in chain-operated hotels or independent-operated hotels averagely shows that there exists an innovation effect representing the improvement in the performance of best-practice production units. Moreover, the average technical change in independent-operated ITHs is better than those chain-operated ITHs. We further find that HTC of independent-operated ITHs has experienced a larger decline trend than that of chain-operated hotels during the period 2011–2012, showing that this is the main determination in the performance of best-practice production units during this period. Combined with the result of a negative average HEC in Table 4, we conclude that the positive hotel productivity change is mainly contributed to by technical change rather than efficiency change.

As for the result of HTC for a hotel’s region, each region on average shows a growth trend in technical change, with the largest growth in the south, followed by the east. Moreover, we find that the average HTC of the south and east regions shows a larger growth trend from 2010 to 2011, but a massive drop from 2011 to 2012. The result of HTC in the north region is also similar to the above two regions. Overall, the result of HTC in each region on average shows an obvious growth trend representing that there exists the innovation effect among these regions, especially in the south.

5.3. Disaggregate Hotel Luenberger Productivity Change Indices

Under the framework of the Luenberger productivity index, the linear programming problem in this study not only estimates HLPI and its components among ITHs but also evaluates the LPI of each output factor among these ITHs. This disaggregate perspective is from us defining DHLPI in Section 4.1, including the room hotel Luenberger productivity index (RHLPI), food and beverage hotel Luenberger productivity index (FHLPI), and other facilities’ hotel Luenberger productivity index (OHLPI) in order to explore the contribution of each output factor productivity change on overall hotel productivity change in a hotel.

The result of RHLPI during the period 2005–2014 appears in

Table 5. Annual RHLPI by operation type and region (%).

Year	2005/2006	2006/2007	2007/2008	2008/2009	2009/2010	2010/2011	2011/2012	2012/2013	2013/2014	Average
Chain	−0.0567	−0.0246	0.5855	−0.9575	0.1919	−0.0695	0.2706	0.0007	−0.0360	−0.0106
Independent	−0.0245	−0.0394	0.4400	−0.4456	0.0934	−0.0027	0.1528	−0.0186	−0.0775	0.0087
North	−0.0264	−0.0091	0.2730	−0.6356	0.1371	−0.2087	0.2474	0.0294	−0.0619	−0.0283
Central	−0.0226	−0.3086	1.4001	−1.6242	0.2932	−0.1136	0.1714	−0.0101	−0.0601	−0.0305
South	−0.0709	−0.0206	0.6893	−0.8867	0.1466	0.2224	0.2254	−0.0723	0.0003	0.0259
East	−0.0689	0.0936	0.3823	−0.2375	0.1139	0.0158	0.1870	0.0086	−0.1201	0.0416
ALL	−0.0436	−0.0303	0.5283	−0.7564	0.1531	−0.0432	0.2243	−0.0068	−0.0522	−0.0030

Notes: Same as in Table 3.

. On average, RHLPI shows a slight decline trend of 0.0030% during the sampling period. In accordance with the type of a hotel’s operation, RHLPI of independent-operated ITHs on average shows a growth trend of 0.0087%, while the RHLPI of chain-operated ITHs shows a decline trend of 0.0106%. Moreover, RHLPI of chain-operated ITHs experienced a large decline from 2008 to 2009 but productivity growth from 2009 to 2010. As a whole, RHLPI of chain-operated ITHs has shown a declining trend since the growth rate is less than the rate of decline. In 2009, when a large number of visitors from mainland China came to visit in Taiwan due to the open policy of tourism, independent-operated or chain-operated ITHs in response to market competition will adopt various operation strategies or establish more marketing channels to attract more tourists in advance. As a result, RHLPI of ITHs between these two types has a growth trend from 2009 to 2010.

As for the result of RHLPI for a hotel’s region, ITHs in the east region on average show a higher productivity growth trend of 0.0416% than in the other regions. ITHs in the east region exhibit a growth trend of RHLPI during the periods 2006–2008 and 2009–2013. ITHs in the south region also on average show a productivity growth trend of 0.0259%. ITHs there have a growth trend of RHLPI during the periods 2006–2007, 2009–2012, and 2013–2014. On the other hand, RHLPI of the north and central regions on average shows a decline trend of 0.0283% and 0.0305%, respectively. ITHs in the north and central regions similarly have a larger decline trend during the periods 2008–2009 and 2010–2011. Although these two regions have a growth trend during the periods 2008–2009 and 2009–2010, the growth rates of RHLPI in the two regions are less than the rate of decline. Overall, the result of RHLPI in the east region has an obvious growth trend compared to other regions, since eastern Taiwan has many natural and beautiful sights such as Taroko National Park, which is always a famous destination for international tourists.

The result of FHLPI during the period 2005–2014 is in

Table 6. Annual FHLPI by operation type and region (%).

Year	2005/2006	2006/2007	2007/2008	2008/2009	2009/2010	2010/2011	2011/2012	2012/2013	2013/2014	Average
Chain	0.0135	0.0716	−0.1277	0.1605	−0.0020	−0.0443	−0.2243	0.1566	0.0753	0.0088
Independent	0.1231	0.0428	−0.1529	0.1344	−0.0014	−0.0340	−0.0049	−0.1250	−0.4576	−0.0528
North	0.1143	0.0655	−0.1439	0.1336	0.0006	−0.0750	0.0299	−0.0724	0.0807	0.0148
Central	0.0005	−0.0422	−0.1419	0.1740	−0.0507	−0.0897	0.0555	−0.0294	0.0240	−0.0111
South	−0.0191	0.1330	−0.1662	0.2107	0.0090	0.0048	−0.5494	0.3610	0.1154	0.0110
East	0.0582	−0.0149	−0.0566	0.0655	0.0056	0.0196	−0.0066	−0.1431	−1.4495	−0.1691
ALL	0.0577	0.0603	−0.1375	0.1502	−0.0017	−0.0402	−0.1381	0.0459	−0.1340	−0.0153

Notes: Same as in Table 3.

. On average, FHLPI shows a slight decline trend of 0.0153% during the sampling period. FHLPI of chain-operated ITHs on average has a slight growth trend of 0.0088%, while FHLPI of independent-operated ITHs has a decline trend of 0.0528%. Moreover, FHLPI of chain-operated ITHs has a productivity growth trend for almost the whole sampling period. Although there are three periods of productivity decline, the overall growth rate of FHLPI is larger than the decline rate for chain-operated ITHs. On the contrary, independent-operated ITHs have a tendency for their FHLPI to drop during the sampling period. Typically, chain-operated ITHs have more advantages in catering costs for food purchases and economies of scale and are also more flexible for the types of catering services and adjustments. Therefore, the performance of FHLPI for chain-operated ITHs is generally better than that of independent-operated ITHs.

As for the result of FHLPI for a hotel’s region, ITHs in the north on average show a growth trend of 0.0148%, while ITHs in the south on average show a growth trend of 0.0110%. The catering markets for ITHs in the north and south regions are much more competitive since these two regions include Taipei and Kaohsiung, which are the two most populous cities in the country. In such a highly competitive environment, ITHs located in these two regions must pay more attention to the control of catering costs and how to create more revenue, even for types of services or meals. On the other hand, FHLPI of central and east regions on average has a decline trend of 0.0111% and 0.1691%, respectively. Looking at the productivity trends in each period, the east region has experienced a drop in FHLPI since 2011. The central region has trends of growth or decline during the sampling period, but the growth is less than the decline. Overall, the result of FHLPI in the north region has an obvious growth trend compared to the other regions.

The result of OHLPI during the period 2005–2014 appears in

Table 7. Annual OHLPI by operation type and region (%).

Year	2005/2006	2006/2007	2007/2008	2008/2009	2009/2010	2010/2011	2011/2012	2012/2013	2013/2014	Average
Chain	−0.4066	0.3991	−0.8180	−1.2383	−0.9931	37.8696	−21.1523	0.0063	−0.0722	1.5105
Independent	0.3175	0.6352	−5.3244	4.2060	−2.2127	84.2629	−68.3425	−3.5315	9.4498	2.1623
North	0.6650	0.2647	−1.1830	0.6377	−0.7859	48.5536	−56.2584	0.3167	1.2125	−0.7308
Central	−0.8654	0.7505	−0.9281	−3.3282	1.2528	17.5830	−16.6424	−0.4790	−0.4466	−0.3448
South	−0.8007	0.6368	−6.2370	3.8558	−2.0236	58.4071	−6.7214	−5.9482	8.9893	5.5731
East	−0.8798	0.7296	−1.1039	−0.9842	−4.6436	104.8681	−69.0745	1.5414	4.0959	3.8388
ALL	−0.1141	0.4909	−2.5883	0.9005	−1.4722	56.0955	−39.6912	−1.3835	3.6685	1.7673

Notes: Same as in Table 3.

. On average, OHLPI shows a slight growth trend of 1.7673% during the sampling period. In accordance with the type of hotel operations, RHLPI of independent-operated and chain-operated ITHs on average shows a growth trend of 1.5105% and 2.1623%, respectively. Looking at the productivity trends in each sub-period, independent-operated ITHs have a relatively large growth trend from 2010 to 2011. Although OHLPI has been declining from 2011 to 2012, the growth is larger than the decline. Typically, the performance of other facilities is very important for international tourist hotels, especially for independent-operated ones, since the provision of other facilities’ services can make hotel operations more diverse, while at the same time creating unique hotel style characteristics. Therefore, the performance of FHLPI for independent-operated ITHs is generally better than that of chain-operated ITHs.

As for the result of OHLPI for a hotel’s region, ITHs in the south and east, respectively, show a growth trend of 5.5731% and 3.8388%. This finding represents that the ITHs located in these two regions put more emphasis on the performance of other facilities in their hotel. On the other hand, FHLPI of central and east regions on average shows a decline trend of 0.7308% and 0.3448%, respectively. In general, the facilities of Taiwan’s ITHs in the south and east regions are much richer and more diverse than those in the north and central regions, mainly due to these hotels having the characteristics of attractive sightseeing spots and abundant natural resources and taking the purposes of resort and leisure as their development features. Therefore, a hotel’s facilities not only are regarded as a marketing tool but also play a very important role in improving a hotel’s productivity, especially for ITHs in the south and east regions.

6. Summary and Discussions

Based on the above-mentioned empirical results, this section first summarizes our main finding in several points:

• Hotel productivity change in Taiwan slightly reaches a growth of 0.5894% during the sample periods. No matter what kind of operation-type, hotels show a positive growth trend, but the independent-operated hotels are averagely higher than chain-operated hotels.
• As for the changes in Taiwan’s hotel productivity change in different regions, the southern and eastern regions showed growth, while the northern and central regions showed a decline trend.
• The main source of growth in Taiwan’s hotel productivity is from technological progress rather than efficiency improvement, implying that the innovation effect dominates the catch-up effect, especially for independent-operated ITHs.
• Hotel productivity change based on the disaggregate perspective can provide more detailed information for the individual output’s productivity change. Productivity growth from hotel facilities’ service is more beneficial to the overall hotel’s performance, especially in Taiwan’s ITHs.
• Although accommodation service is still the main service for all hotels, independent operators need to pay more attention to the productivity growth from hotel facilities’ services.

Second, this study further explores the contribution of disaggregate hotel productivity on the overall hotel productivity change in each ITH. This study compares the above-mentioned four productivity indicators, HLPI, RHLPI, FHLPI, and OHLPI, as listed in

Table 8. Comparison with overall and disaggregate productivity indices.

Hotel No.	HLPI	Rank	RHLPI	Rank	FHLPI	Rank	OHLPI	Rank
1	0.1401	19	−0.0617	45	0.0064	24	0.4039	16
2	0.1445	18	−0.0760	49	−0.0294	47	0.3164	18
3	0.2900	13	−0.0306	38	−0.0190	42	0.8266	13
4	−0.1146	35	−0.0941	51	0.0017	27	−0.3887	34
5	−0.0439	26	−0.0436	40	−0.0182	40	−0.2612	29
6	−0.0802	31	0.0364	14	0.0160	19	−0.3648	32
7	−0.1287	38	−0.0413	39	0.0118	22	−0.5055	41
8	−0.4236	47	0.1100	5	−0.0108	36	−1.4750	48
9	−0.0633	27	−0.0142	33	0.0155	20	−0.2559	28
10	−0.1739	42	−0.0581	44	−0.0199	43	−0.4196	35
11	0.2800	14	−0.0960	52	0.0860	8	0.3877	17
12	0.0219	23	−0.0291	36	−0.0766	54	−0.0415	24
13	−0.2384	44	−0.0125	32	0.1038	4	−1.0277	46
14	0.1482	17	0.0140	21	0.0729	10	0.0537	22
15	1.2332	9	0.0039	25	0.0385	11	3.6967	8
16	−0.1404	41	0.0531	8	0.0324	12	−0.4991	40
17	−0.1213	37	−0.0093	31	0.0223	17	−0.3869	33
18	2.3517	5	0.0314	17	−0.0122	37	7.0912	5
19	−5.0371	56	−0.0006	26	0.0883	7	−12.1215	56
20	0.0183	24	−0.1074	53	−0.0053	30	0.1541	20
21	−0.0782	30	−0.0248	35	−0.0006	28	−0.3517	31
22	−0.0651	28	0.0122	22	−0.0226	44	0.1119	21
23	0.0062	25	−0.0672	47	−0.0091	34	−0.4329	38
24	−2.1291	54	0.0259	18	0.0912	6	−8.3534	54
25	−0.1125	34	−0.2468	56	−0.0050	29	−0.0901	26
26	−1.7205	52	−0.0209	34	0.0049	25	−5.2665	53
27	0.0436	21	−0.0047	27	0.0306	14	−0.0663	25
28	−0.0845	32	−0.1386	55	−0.0096	35	−0.6784	43
29	−0.1188	36	0.0323	16	−0.1095	55	−0.7137	44
30	−0.5603	49	−0.0477	41	0.0031	26	−2.0303	50
31	0.5945	12	−0.0814	50	−0.0122	38	1.8429	11
32	−0.1331	40	0.0571	7	0.0311	13	−0.4230	37
33	1.3280	8	0.3092	1	0.1701	1	3.3069	9
34	−0.2994	45	0.1435	4	0.0927	5	−0.1729	27
35	−0.0888	33	−0.0639	46	−0.0185	41	−0.4658	39
36	1.7858	6	0.2515	2	−0.0748	53	4.6726	6
37	1.5502	7	0.0359	15	−0.0587	52	4.2134	7
38	0.0254	22	−0.0499	42	0.0749	9	−0.0343	23
39	−0.4242	48	0.0412	12	0.0130	21	−1.8291	49
40	2.6671	4	−0.0718	48	−0.0562	51	7.7602	4
41	−0.1320	39	−0.0564	43	−0.0077	33	−0.5811	42
42	−1.8540	53	−0.0064	29	−0.0234	45	−5.2036	52
43	0.7048	10	−0.1307	54	−0.0390	49	2.4663	10
44	21.0092	1	0.0517	9	0.1328	2	66.6774	1
45	2.7590	3	0.0435	11	−0.0402	50	7.8919	3
46	0.6920	11	0.0063	24	0.0188	18	1.7987	12
47	−0.3320	46	−0.0086	30	−0.0069	32	−0.4217	36
48	0.2635	15	0.0116	23	0.0226	16	0.8100	15
49	−0.0676	29	−0.0048	28	0.0084	23	−0.2816	30
50	−3.0419	55	0.1045	6	−0.0321	48	−9.3453	55
51	−0.7922	51	−0.0304	37	−1.4335	56	−1.0314	47
52	14.7399	2	0.0399	13	−0.0285	46	43.3732	2
53	−0.7039	50	0.0462	10	0.0304	15	−2.0955	51
54	−0.2380	43	0.0201	19	−0.0171	39	−0.8487	45
55	0.0849	20	0.0160	20	0.1209	3	0.1858	19
56	0.2399	16	0.1488	3	−0.0067	31	0.8201	14
Average	0.5997		−0.0015		−0.0154		1.7928

below. On average, overall hotel productivity change exhibits a growth trend, in which disaggregate hotel productivity changes in rooms and food and beverages have slightly declined, while the disaggregate hotel productivity change in other facilities has increased. Therefore, the main source of productivity growth among the 56 ITHs is productivity growth from a hotel’s facilities, but the productivity decline from food and beverage service is detrimental to the hotel’s overall performance.

Finally, this study can provide the main sources of productivity changes in each ITH for reference in Taiwan’s hotel industry. From Table 8, we can take a look into those 25 of the 56 international tourist hotels that are showing overall productivity growth. There are seven ITHs in which all three disaggregate hotel productivities contribute to the hotels’ overall productivity growth, such as Numbers 11, 12, 33, 44, 46, 48, and 55. Six ITHs incur a contribution of disaggregate hotel productivity from rooms and other facilities on their overall hotel productivity growth, such as Numbers 18, 36, 37, 45, 52, and 56. Ten ITHs see a contribution of disaggregate hotel productivity from food and beverages or other facilities on overall hotel productivity growth such as Numbers 1, 2, 3, 11, 20, 26, 27, 38, 40, and 43. Therefore, an individual ITH can grasp the contribution of disaggregate hotel productivity growth on overall productivity and thus maintain or develop competitive advantages in its operations and management.

On the other hand, the empirical results show that 31 of the 56 international tourist hotels experience an overall hotel productivity decline. Ten ITHs have a deterioration in all three disaggregate hotel productivities on their overall hotel productivity changes, such as Numbers 5, 10, 20, 21, 25, 28, 42, 47, 48, and 51. Ten ITHs illustrate a deterioration of disaggregate hotel productivity from rooms and other facilities on their overall hotel productivity changes, such as Numbers 4, 7, 9, 13, 17, 19, 24, 26, 30, and 49. Eleven ITHs show a deterioration of disaggregate hotel productivity from food and beverages or other facilities on their overall hotel productivity growth, such as Numbers 6, 8, 16, 22, 29, 32, 34, 39, 50, 53, and 54. Therefore, an individual ITH with deterioration of disaggregate hotel productivity can relocate its hotel operating resources and formulate improvement strategies as a source of motivation for overall productivity improvement in the future.

7. Conclusions and Implications

With the rapid change in demand and a more competitive market in the global tourism industry, international tourist hotels (ITHs) must pay more attention to their productivity performance and whether their output has reached the optimum stage or not. The existing studies have mainly focused on evaluating overall performance with few discussing the contributions of ITH resources. Therefore, this study establishes an index to evaluate the productivity changes in ITHs from overall and disaggregate perspectives. Through these two perspectives, we are able to explore the productivity change in each hotel and also fully investigate the main source of productivity change from the types of output factors. The contribution of disaggregate hotel productivity changes can be used as a decision-making reference for ITH management.

This study utilizes a panel dataset of 56 ITHs in Taiwan during the period 2005–2014 to evaluate the main source of productivity change from overall and disaggregate perspectives by using the Luenberger productivity index based on the directional distance function. Our main findings are briefly summarized as follows. First, the overall productivity change in ITHs in Taiwan shows a growing trend and the main source of productivity change is technical change rather than efficiency change. Productivity growth mainly comes from the innovative effect, in which non-chain-operated ITHs have higher productivity growth than chain-operated ITHs. Second, from the disaggregate perspective, non-chain-operated ITHs show an increasing trend in the productivity of rooms and other facilities, while chain-operated ITHs have a growing trend in the productivity of food and beverages. Lastly, the productivity growth of other facilities plays an important role in the hotel’s overall productivity growth, but a decline in the productivity of food and beverage is detrimental to the hotel’s overall productivity growth among these 56 ITHs.

As for implications from this study, the proposed productivity indices in this study can firstly provide theoretical contributions relative to traditional productivity indices for researchers in the field of hospitality management in three points:

• This disaggregate hotel productivity index easily evaluates total factor productivity growth and decomposes overall productivity growth into the productivity change in each output.
• The overall hotel productivity growth is measured by the arithmetic mean of each output’s productivity change, implying it is the main force behind the hotel’s total factor productivity growth.
• The framework of this study can directly explore productivity changes by using financial data such as revenues and expenditure when more detailed hotel operational data are not available.

Second, while multiple inputs can produce various outputs in each decision-making unit of the hospitality industry, managerial implications inspired from this study can be provided in three points:

• Hotel managers should analyze the main source of hotel productivity growth for how to allocate their resources more efficiently and what is the best strategy in their hotel’s operations for improving productivity from the main output factor.
• Understanding the source of productivity growth is not only limited to the hotel industry. Similarly, the tourism and catering industry also need to pay more attention to the relationship between overall and disaggregate productivity growth.
• The results of overall and disaggregate productivity change are not only applicable to interpreting the Taiwan case but can also be extended to investigating other country’s cases.

Finally, since the issue of hotel productivity is important to researchers and managers, we can provide further research directions and limitations as follows:

• Since hotel performance has gradually been discussed through a dynamic framework in recent years, it is still less accurate to grasp the dynamic correlation of resource usage between the input and output factors across time periods in a hotel’s operation process. Thus, how to describe the dynamic framework of a hotel’s business performance still needs to be developed.
• The framework of this study does not take into account the sources or types of a hotel’s residents, especially in the face of the increasing number of visitor arrivals year after year for Taiwan. Due to the characteristics of different sources or types of a hotel’s residents, the performance of each hotel may seem to be different. Therefore, if this characteristic can be included in the analysis framework, then it will be more in line with practical needs.
• If detailed data are available, then examining the productivity change in general tourist hotels and comparing this to international tourist hotels can provide more insightful implications for the hotel industry within a country, especially for Taiwan’s case.