Analyzing tourism productivity changes with complex configurations

Introduction

Efficiency and productivity is a research area widely investigated by tourism scholars (Assaf and Josiassen, 2016; Assaf and Tsionas, 2019). In the non-parametric approaches devoted to applied efficiency analysis, two-stage DEA (data envelopment analysis) is a popular method. In the first stage, the relative efficiency scores of a sample of units are calculated by linear programming. In the second stage, the efficiency scores are explained by contextual factors through various techniques (Tobit, truncated regression, etc.). Assaf and Josiassen (2016) and Assaf and Tsionas (2019) highlighted the use of these approaches in different aspects of the tourism sector, where the units compared are, for instance, destinations or hotels.

Another facet of production frontier theory that has been extensively employed in empirical tourism research is productivity measurement and its decomposition. By considering productivity changes between two time periods, tourism scholars mainly used the Malmquist productivity index (Assaf and Dwyer, 2013). A key advantage of such approaches is the opportunity to decompose productivity into several components such as efficiency change, technological change, or scale efficiency among others. An insightful result by looking at this part of the literature is the lack of investigation about the explanation of productivity changes. Indeed, to our knowledge, no tourism studies using two-stage approaches in order to explain productivity variations are available in the literature.

Furthermore, from an economic perspective, most empirical studies in the second stage are restricted to the identification of net effects derived from an average behavior, a point already outlined by Corne and Peypoch (2020) in the two-stage DEA framework. Tourism, as a complex phenomenon, cannot be summarized by symmetric relationships and then the explanation of productivity changes in the tourism sector by considering possible multiple realities and asymmetric links is of interest to both researchers and decision-makers.

This note aims to contribute to the tourism performance literature by extending the seminal work by Corne and Peypoch (2020) to the case of productivity indexes and indicators. In the first stage, the Malmquist productivity index is considered to measure productivity variations. In the second stage, fsQCA (fuzzy-set qualitative comparative analysis) is used to identify combinations of factors explaining the productivity changes. An illustrative example of the suggested approach is provided with the productivity change analysis of Chinese destinations at the provincial scale. The rest of the paper is as follows. The next section discusses the methodological approach. Then, an empirical illustration is proposed. Finally, the last section concludes.

Empirical strategy: Combining productivity measures and fsQCA

This section outlines how fsQCA, introduced by Ragin (2008), could be implemented in a second stage in order to explain the productivity scores obtained in a first stage. A Malmquist productivity index (MPI), in output orientation (Färe et al., 1994), is considered but possible adaptations to other productivity measures are also discussed.

It is well known in the fsQCA framework that the first step about the calibration of the data is very important (Pappas and Woodside, 2021). By combining DEA and fsQCA in the second stage, Corne and Peypoch (2020, p. 9) emphasized the difficulty to choose the ambiguity threshold when the efficiency score from DEA must be calibrated. Indeed, either in input or output orientation, what is a higher or lower relative efficiency level remains an open question. In the case of productivity measurement, which is the subject of the present note, it seems that a quite simple theoretical answer exists. The calibrated variable for the second stage here is the MPI score which can be greater or less than 1 corresponding respectively to a productivity improvement or a productivity deterioration. In that case, the rationale should be to fix the ambiguity threshold equals 1. Indeed, according to production frontier theory, a value of 1 signifies neither a positive nor negative productivity change. The same logic can be applied to each component of the MPI. Hence, this note advocates setting the maximum ambiguity to 1 in the calibration step, whereas some contributions are still using percentiles in a such context (Diao and Liu, 2021).

Possible extensions could be done to other productivity indexes and indicators and their decompositions. On the one hand, the same intuition could be applied to the Malmquist decomposition into efficiency change and technological change (Färe et al., 1994) or to the alternative one by Ray and Desli (1997). On the other hand, this framework can be also applied to other productivity indexes with a multiplicative structure like the Hicks-Moorsteen productivity index introduced by Bjurek (1996). Finally, for the productivity indicators with an additive structure like the Luenberger productivity indicator introduced by Chambers (1996), such kind of approach in the second stage could be adapted by setting the intermediate threshold to 0. ¹

Empirical illustration

To illustrate the combination of the Malmquist productivity index and fsQCA, ² we consider data on 30 Chinese provinces in star-rated hotels for the year 2015 that have already been used in previous contributions (Dong et al., 2020, 2023) for both first stage (construction of the production technology) and second stage (contextual factors). The reason for this choice is to permit a clearer comparison of the innovative findings obtained in the second stage. To save space, we refer to Dong et al. (2023) for the presentation in terms of descriptive statistics of the 3 inputs (number of rooms, fixed assets, and number of employees) and the two outputs (number of rooms sold and total revenue) used in the first stage in order to estimate the MPI. The same applies to the second stage where a description of the four contextual factors—internet index, marketization degree index, law index, and trade openness can be found in Dong et al. (2020).

By following Dong et al. (2020), a hierarchical MPI with constant returns-to-scale is calculated between 2014 and 2015 in the first stage and the scores are extracted. Supplementary Table 1 in Appendix presents these findings.

In the second stage, the scores from Supplementary Table 1 are first calibrated by following the approach by Ragin (2008). As discussed above, the ambiguity threshold or intermediate membership for MPI is fixed to 1. Thresholds for full membership and full non-membership are derived from a cluster analysis by using Tosmana software (Cronqvist, 2019). Regarding the calibration of the contextual variables, the three thresholds are derived from the 80%, 50%, and 20% percentiles because the data are skewed (Pappas and Woodside, 2021). Table 1 presents the thresholds used in this empirical illustration.

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Table 1.

Calibration of the data.

Variable	Thresholds
	Full non-membership	Intermediate membership	Full membership
MPI	0.85	1	1.28
Internet index	305.4	314.7	338.9
Law index	3.2	5.7	10.8
Marketization index	2.2	3.2	3.7
Trade openness	1238.9	2109.4	6663.6

After the calibration of the data, the next step is the necessity analysis. Supplementary Table 2 (see Appendix) presents the results. None of the variables appears as a necessary condition with all consistency indexes less than 0.9.

The sufficiency analysis of the MPI is then implemented and the findings are presented in Table 2. Three configurations or paths are sufficient to explain a high positive productivity change. In these three combinations of variables, it should be noted that the law index plays different roles depending on its association with other variables. Indeed, the presence of the variable related to the law index appeared in one configuration, whereas the absence of this variable appeared in the two other ones. In each case, it is considered as a core condition. The complex role of this variable is here clearly illustrated and permits to go further on the effect of the legal environment and institutions on tourism productivity and growth (Belgodere et al., 2022). Productivity changes in the tourism sector cannot be explained by only the net effects of some contextual factors and the reality seems more complex, as emphasized by Corne and Peypoch (2020) in the tourism efficiency framework. Other examples that play different roles here are the internet index and the marketization degree index. These results expand previous findings derived from symmetric tests (Dong et al., 2020).

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Table 2.

Sufficiency analysis—MPI.

Concluding remarks

This note emphasizes the interest in investigating complex and multiple realities in the explanation of productivity changes. To do this, the work by Corne and Peypoch (2020), mixing DEA and fsQCA, is extended into the Malmquist productivity index framework. The use of this combined approach is discussed and illustrated empirically, providing a guideline for future research. Possible extensions of this combined approach are also outlined in order to encompass the case of other productivity measurements.

Supplemental Material