Efficiency drivers for the South Pacific West coast port terminals: a two-stage non-convex metafrontier dea approach


We measure technical efficiency of Peruvian and Chilean port terminals, to evaluate the influence of certain contextual variables in the terminals’ efficiency levels. The sample includes 14 port terminals from 2004 to 2014. Due to the potential differences, we have estimated a DEA model in a non-convex metafrontier framework. Afterwards, we estimated all the regression models proposed in the literature that could be used to explain not only the technical efficiency estimated with respect to the metafrontier (TE*) but also each one of its components: the technical efficiency with respect to the group-specific frontier (TEk) and the technological gap ratio (TGR). Results are robust across models.

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  1. 1.

    These authors reviewed published port literature between 1980 and 2000 to investigate how seaport research has been conducted from the methodological perspective. They found that the main techniques used were descriptive statistics (35.5%), regression (16.9%), DEA (10.2%), Logit model (5.1%) and SFA (4.8%).

  2. 2.

    Furthermore, the present paper complements a more recent paper (Chang and Tovar, 2017b), which evaluates, with the same dataset, how differences in the terminals' total factor productivity could be explained by certain explanatory variables. See also Tovar and Wall (2019).

  3. 3.

    A detailed analysis about the relative merits of all of these models is out of the scope of this article. For a general reference, see Fried et al. (2008) and for a port terminals' application reference, see Cullinane and Wang (2010).

  4. 4.

    To test the robustness of our TE results depending on the DEA model used, the DEA efficiency scores were calculated from four different models: The Pooled model, the Yearly model, and, finally, two Window DEA models, where DEA scores are calculated using moving 5-year and 3-year windows, respectively. We have decided to keep the results from the yearly model for the second stage for two reasons. First and foremost, we are interested in discovering which determinants explain the \(TE_{i}^{*}\), \(TE_{i}^{k}\) and \(TGR_{i}\) scores on a yearly base. (For a similar analysis regarding the changes in those variables, as opposed to the levels, interested readers are referred to our paper Chang and Tovar 2017b). The second reason is that due to the fact that the TE DEA scores are highly correlated across models, in this way we avoid the problem identified by Cooper et al. (2004) of choosing the width for a window and the theoretical implications of representing each port terminal as if it were a different one for each period in the window.

  5. 5.

    A systematic overview of contextual variables influencing on terminals’ efficiency is out of the scope of the present paper but could be find in Bichou (2009).

  6. 6.

    Data accuracy, imprecision and missing values are common problems. To the previously mentioned problems, a useful approach could be Imprecise DEA (Zahran et al. 2020).

  7. 7.

    However, there are a lot of papers that, due to the difficulties in accessing that data, ignore this variable or try to approximate it through another capital variable; for example, the number of cranes. It should be noticed that both capital and labour variables should be included in the estimation, unless it is demonstrated that there is a perfect complementarity between them. To the best of our knowledge this relationship has never been demonstrated.

  8. 8.

    The time trend shows the efficiency evolving in a period. If firms improved their efficiency the coefficient linked to this variable would be positive. The time trend squared variable is included to allow more flexibility when modelling the temporary pattern of TE. We included both in our model because we believe that, due to the effect of learning by doing, when time pass leads to a more efficient situation although to a diminishing rate. Therefore, we expect that the coefficient linked to time squared variable ends up being negative.

  9. 9.

    The data used was obtained from various sources and is the same that the one used in Chang and Tovar, (2017a). The reader interested in more details about the dataset, can find it there.

  10. 10.

    Chang and Tovar (2017a) found that Latent Class Stochastic Frontier Model, with two classes, fits the unobserved heterogeneity of the Peruvian and Chilean port terminals better than the other Standard Stochastic Frontier Models.

  11. 11.

    Peruvian terminals analysed in this paper manage three type of cargo: containerized cargo, general & rolling freight and bulk cargo.

  12. 12.

    Container index, bulk ratio, occupancy rate and dgest variables have been identified by Chang and Tovar (2014b) as specific explanatory variables that contribute to reducing the inefficiency of Peruvian and Chilean port terminals.

  13. 13.

    Another commonly used proxy for inter-port competition is the Herfindahl–Hirschman Index (Figueiredo De Oliveira and Cariou 2015). Nevertheless, the construction of this variable requires very comprehensive data to appropriately define the relevant market of each kind of cargo. This data is not available for each terminal for the whole period.

  14. 14.

    Remember that \({\mathrm{TE}}_{\mathrm{i}}^{*}\), \({\mathrm{TE}}_{\mathrm{i}}^{\mathrm{k}}\) and \({\mathrm{TGR}}_{\mathrm{i}}\) scores are calculated following the yearly model because in the second stage, as we explained in footnote 3, we are interested in analysing the drivers of the variable levels each year and not in analysing the drivers of the changes in variables between the years. (The latter could be done by computing Malmquist productivity indices using metafrontiers, as Chang and Tovar (2017b) have recently shown). Therefore, Fig. 2 should be understood as reflecting how the levels of those variables change regarding the frontier of each year.

  15. 15.

    This is the average technical efficiency with respect to the metafrontier and its value varies between 0 and 1.

  16. 16.

    It should be noted that TGR = 1 indicates that (\({TE}_{i}^{*})\) is the same as (\({TE}_{i}^{k})\), but this does not necessarily mean that the terminal is efficient.

  17. 17.

    Remember that this variable is equal to 1 when terminal belongs to class 2 and zero otherwise.


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This research was partially funded with Grant ECO2015-68345-R (MINECO/FEDER) from Ministerio de Economía y Competitividad and Fondo Europeo de Desarrollo Regional (FEDER).

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Authors contributed equally to the development of the present paper.

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Correspondence to Beatriz Tovar.

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Chang, V., Tovar, B. Efficiency drivers for the South Pacific West coast port terminals: a two-stage non-convex metafrontier dea approach. Oper Res Int J (2021). https://doi.org/10.1007/s12351-021-00626-5

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  • Two-stage DEA non-convex metafrontier
  • Fractional regression models
  • Bootstrap truncated regression
  • Port terminals
  • Technological gap ratio
  • Efficiency drivers

Mathematics Subject Classification

  • 90B30