Metafrontier analysis on productivity for West Coast of South Pacific terminals

Transportation Research Part A 103 (2017) 118–134

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Metafrontier analysis on productivity for West Coast of South Pacific terminals Víctor Chang a, Beatriz Tovar b,⇑ a b

Faculty of Economics and Business, Ricardo Palma University, Peru Infrastructure and Transport Research Group, Dept. Applied Economics, University Las Palmas de Gran Canaria, Spain

a r t i c l e

i n f o

Article history: Received 17 June 2016 Received in revised form 23 December 2016 Accepted 23 December 2016

Keywords: DEA-Malmquist Metafrontier Technology gap ratio Dynamic panel data method Sector reform Port terminals Productivity drivers

a b s t r a c t This paper measures productivity of port terminals in Peru and Chile, and evaluates the influence of the certain specific explanatory variables that may explain their differences in productivity. In the first stage, a DEA-Malmquist model in a metafrontier framework is used to obtain the productivity scores. This approach lets us take the possible technological differences among the port terminals into account. In the second stage, an ArellanoBond model was estimated, to explain the differences in productivity change. The empirical evidence shows that the Class 1 terminals produce output under certain less favourable technological conditions than the Class 2 terminals. Moreover, on average, both classes present positive evolutions of the catching up effect, which shows that the terminals as a whole are moving nearer to the efficiency metafrontier. We also observe a technological regress during 2004–2014 and that the terminals have been affected by the financial crisis which started in the United States in 2008. Finally, we identified that the container/bulk rate and that private management contribute positively to the change in productivity, whereas the bulk rate and the total factor productivity change lagged contribute negatively. Ó 2017 Elsevier Ltd. All rights reserved.

1. Introduction The importance of port infrastructure in the transport chain and the economic growth of the countries have increased. The Latin America countries with a Pacific coastline, particularly Peru and Chile which are the main Pacific trade gateways to South American, have undergone significant economic improvements. There has been an average economic growth of 5.0% approximately during last 20 years, mainly influenced by the growth of international trade. The Peruvian and Chilean ports extend along nearly 9500 km of coastline, and about 95% of both countries’ commercial activity is transported via these ports. Prospects for international trade in Latin American countries are encouraging. The Peruvian and Chilean port reforms and the Panama Canal expansion project may increase Asia-Pacific1 international trade; also, it may increase the competitiveness of existing lower volume trade routes (e.g. Trinidad and Tobago to Chile) or open up new ones (Peru to Europe).

⇑ Corresponding author at: Infrastructure and Transport Research Group, Dept. Applied Economics, University Las Palmas de Gran Canaria, Campus de Tafira, Modulo D, Despacho 2.20, 35017 Las Palmas de Gran Canaria, Spain. E-mail address: [email protected] (B. Tovar). 1 The Asia-Pacific destination has become the primary regional market for Peruvian and Chilean exports, with respective shares of 27% and 35%. http://dx.doi.org/10.1016/j.tra.2016.12.012 0965-8564/Ó 2017 Elsevier Ltd. All rights reserved.

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The objectives of the reform processes implemented in 1990s in both countries were to stimulate the rate of investment,2 increase the productivity and reduce the logistics costs at the ports. These reform processes were similar in both countries,3 and began at about the same time; nevertheless, they have been conducted more successfully and with greater agility in Chile (Chang and Tovar, 2014a, 2014b). This paper measures productivity of port terminals in Peru and Chile to evaluate the influence of certain specific explanatory variables that may explain productivity differences among them. We use data from the 14 terminal ports during 2004– 2014 that represents most of the total cargo moved by both countries. A key issue linked to productivity analyses in Peruvian and Chilean port terminals is to compare the performance between terminals during the period of analysis in order to identify if the type of management (public vs private)4 has a role explaining productivity differences between port terminals in both countries. This let us identify the best public policies used by the Governments and improve the regulatory mechanisms ex-ante and ex-post. Comparing the efficiency and productivity change of different terminals usually assumes that they operate under the same production technology; nevertheless, in presence of unobserved heterogeneity, the efficiency and productivity change measurements will be erroneous5. This issue becomes relevant in our case because potential differences due to the terminals belonging to different countries, having different ownership, different geographical and operational settings, and so on. To account for this heterogeneity problem, Battese et al. (2004) introduced the technology-gap ratio and O’Donnell et al. (2008) introduced the metatechnology ratio (TGR), which quantifies the efficiency of heterogeneous groups based on their distances from a common and identical frontier. With this in mind, the main purpose of the present study is to measure the productivity of port terminals in Peru and Chile, and to evaluate the influence of certain specific explanatory variables that may explain productivity differences among these port terminals. Due to potential differences among the terminals, in the first stage a DEA-Malmquist model in a metafrontier framework will be estimated; this lets us take the possible technological differences among the port terminals into account. Furthermore, in the second stage, in order to explain the differences in productivity change of port terminals, we will use a dynamic panel estimation of Arellano and Bond (1991). This paper’s contributions have been considered of relevance, since for the first time both a DEA-Malmquist model in a metafrontier framework and a dynamic panel estimation of Arellano and Bond (1991) are used. The former has been used to analyse the change in productivity of the port terminals, whereas the latter is used to explain the difference in the Malmquist productivity index in the port sector. The structure of the paper is as follows. After an introduction, the second section presents a brief review of the literature. In Section 3 the analytical framework is presented. Section 4 shows the source and descriptive statistics of data used and the empirical results are presented in Section 5. Finally, Section 6 draws the most relevant conclusions, and presents the possible policy implications. 2. A brief review of the literature focused on measuring TFP in ports through DEA6 Productivity is the ratio between the outputs obtained and the inputs used in production. Although there are several approaches to measuring productivity, a frontier approach should be used in order to take into account the contribution of efficiency change to productivity change. Moreover, one of the indexes most used for measuring TFP changes should be selected; i.e. the Fisher, Törnqvist or Malmquist index. As it has been recently shown by Wilmsmeier et al. (2013), by far the most popular for measuring port productivity is the Malmquist index. This is probably due to its well-known advantages; that is to say it does not need input prices or behavioural assumptions. Table 1 provides an overview of the papers using DEA-Malmquist to measure TFP change in the port sector. It can be seen that these vary widely in scope. With regard to the objectives of the studies, most have measured the TFP change on a port and then decomposed it, whereas relatively few studies have analyzed the influence of certain contextual variables on port productivity; 12 out of 22, including this one. The latter papers can be grouped into two main categories, in terms of whether or not a regression model is used to explain the TFP change. The first sets of studies are compounded by a number of heterogeneous papers which do not use regression models to explain the relationship between the TFP changes and some of the contextual variables; Wilmsmeier et al. (2013) and Medal-Bartual et al. (2016) to name but two. Wilmsmeier et al. (2013) analyzed the effect of the financial crisis on the container port productivity of twenty terminals in Latin America, the Caribbean and Spain for the period 2005–2011. Moreover, they also considered whether port productivity of different types of terminals, Gateway, transshipment and hybrid, is 2 Nevertheless, according to Instituto Peruano de Economía (2009), after twenty years, the deficit in Peruvian port infrastructure had risen to approximately U.S. $3.6 billion. 3 For a description of both process see Chang and Tovar (2014a, 2014b). 4 In recent decades the Latin American port sector in has undergone major changes. Several countries began a series of port reforms. One of the main objectives of the reform processes were to stimulate the sector’s investment rate. Many countries have chosen to do it through some type of private participation. Peru and Chile are among those which have done it through a concession scheme. 5 This issue has been analyzed in depth in a port context by Tovar and Rodríguez-Déniz (2015). 6 DEA has been used extensively in the economic analysis of ports efficiency. Due to our literature review intends to put our paper into the proper context, and to clearly show the paper’s contribution, the review has been exclusively focused on the estimations of TFP using the Malmquist index and coming from a DEA approach.

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affected differently by changing economic environments. In order to do so, they compared the average TFP changes in both the pre and post crisis periods and for the different types of terminals. Medal-Bartual et al. (2016), following the same approach as Wilmsmeier et al. (2013), analyzed the effect of the financial crisis on the productivity of Spanish port authorities. Moreover, they tested, through the non-parametric Mann–Whitney test, whether investment and productivity change were related. The second set is formed of only three studies which use a regression technique in the second stage; see Table 1. In two of them, Barros (2003) and Ding et al. (2015), the first step was carried out using a DEA-Malmquist Productivity Index (MPI), and the factors affecting productivity efficiency change were then estimated and quantified using a Tobit regression in a second stage. The former, Barro’s (2003) paper, measures the productivity changes and its components in ten Portuguese seaport during 1990–2000. The paper then tries to explain it through several variables: the European integration effect or trend variable, the existence of container services, the market share and the type of management either private or public). It found that efficient scores are explained by the trend variable, by handling containerized traffic which accounts for the scale effect, by the market share and the property status meaning being privately managed. The latter paper, Ding et al. (2015), evaluates productivity change in twenty-one small and medium sized costal port container terminals in China. The empirical results indicate that the terminals holding share of more than 50% of the Chinese state-owned shipping lines show the highest increase in productivity efficiency change. The results also indicate that manpower structure, Chinese state-owned shipping line shareholding, registered capital and shipping correlate positively with the terminals’ productivity efficiency change. Finally, the last paper of the second set is by Halkos and Tzeremes (2012). It measured the productivity of Greek seaports for the time period 2006–2010. In the second stage, through a nonparametric analysis and using a local linear kernel model, they identified the effect of a seaport’s size on its productivity levels. The results revealed that the number of terminals is a crucial determinant of a seaport’s level of productivity. In addition, it seemed that the considerable length of the Greek seaports has had a negative influence on their productivity levels over the years. This current paper, which belongs to the second group, proposes applying a dynamic panel data model to explain the changes in the TFP in the second stage, instead of using the two approaches found in the literature review. On one hand, the Tobit model is not suitable for explaining changes in TFP, because TFP changes do not suffer from the effects of boundary problems; thus there is no reason to use a censored model. On the other hand, the local linear kernel model does not take advantage of the panel data structure or even of the dynamic TFP change process. Therefore, the dynamic panel data model specified in this paper outperforms the other options found in the literature. Consequently, the present paper contributes to the literature. It is the first to apply a DEA-Malmquist model to a metafrontier framework which has been used to analyse port terminal productivity change; this has let us take their possible technological differences into account. Moreover, it is also the first time that an Arellano-Bond model, which takes the dynamic characteristics of the TFP growth into account, has been estimated in a second stage to explain the differences in the TFP change found in the port sector. 3. Analytical framework Recent papers, such as Battese and Rao (2002), Rao et al. (2004) and O’Donnell et al. (2005, 2008) have introduced the concept of the metafrontiers technique, in order to take the technology differences among the production entities into account. These differences in technology are due to the different availability of physical stocks, human and financial capital, economic infrastructure, resource endowments and other physical characteristics, and the social and economic environment in which production takes place. The metafrontier technique consists of enveloping the groups of frontiers estimated through another frontier, called metatechnology. This technique entails the estimation of the metatechnology and the frontiers of relatively homogenous groups (Rao et al., 2004). DEA-Malmquist productivity index can be understood in terms of distance functions. The distance function can take an input orientation or an output orientation. The choice is done on the basis of which set of variables, inputs or outputs, the firm has more control over. In empirical applications we find both orientation (Panayides et al., 2009). In this paper we adopt an output orientation as other authors who consider that ports are closer to being outputs maximizers rather than input minimizers (Cullinane et al., 2004; Trujillo and Tovar, 2007; Cheon et al., 2010; Chang and Tovar, 2014a, 2014b). Formally, let xt 2 RþM y yt 2 RþL denote the input and output vectors in time t, and t ¼ 1; 2; . . . ; T. The production technology is defined as capability of transforming inputs into outputs. If there are k technology possibility sets, and k ¼ 1; 2; . . . ; K, an output oriented technology set P k ðxÞ is defined as the ykt obtainable from xkt . O’Donnell et al. (2008), define a common metafrontier as the boundary of an unrestricted technology set, which could be potentially accessed by all firms. However, the restrictions derived from a lack of economic infrastructure, and/or other characteristics of the production environment, could cause some firms not to have access to the unrestricted technology and have to use restricted technology sets (one of the k technology possibility sets). The technology set for the k group can be represented by the following output-oriented distance function (O’Donnell et al., 2008).

 k  

 yt 2 Pkt xkt Dkt xkt ; ykt ¼ inf d d > 0 : d

ð1Þ

Table 1 Summary of previous papers on measuring TFP in ports using DEA-Malmquist. Author/Year

Data

Martín (2002)

27 Spanish ports 1990–1999

Barros (2003)

10 Portuguese seaports, 1990–2000 11 Mexican ports 1996–1999 21 Spanish ports 1994–1998

Estache et al. (2004) Díaz-Hernández et al. (2007)

Chang and Carbajal (2009) Guerrero and Rivera (2009) Lozano (2009) Bo-xin et al. (2009) Cheon et al. (2010) Barro et al. (2012) Halkos and Tzeremes (2012)

Guner and Coskun (2013)

Song and Cui (2013) Wilmsmeier et al. (2013)

Mokhtar and Shah (2013)

Ding et al. (2015)

22 container terminals in Middle East & East African 2000–2005 14 Peruvian and Chilean ports terminals 2002–2009 7 Mexican ports 2000–2007 28 Spanish port authorities 2002–2006 10 Chinese container ports 2001–2006 98 ports around the world 1991–2004 25 Brazilian ports 2004–2010 12 Greek seaports 2006–2010

4 passenger ports in Aegean and Mediterranean shores 2003–2010 21 Chinese container terminals 2006–2011 20 terminals in Latin America and the Caribean and Spain 2005–2011 6 container terminals in Peninsular Malasya 2003– 2010 21 Chinese container terminal 2008–2012

Measure TFP change and its components to evaluate the reform process. Analyzes the technical efficiency and technological change of Portuguese seaports. Measure TFP change and decompose it after reforms. Measure TFP change, its components and analize the efficiency to evaluate the reform process.

Is it explaining TFP changes? Contextual variables

Methodology

Time trend, Container services. Market share, Public managed port.

Tobit regression

Total traffic volume above the average. Mean type of cargo: CGC, NCGC and SB. Ports with specialized container terminals Ports with a majority of privately owned cranes.

Mann-Whitney test

Geographical location

Analyse the mean of TFP change and the CV ANOVA, Welch’s test and the Brown– Forsythe test

Measure TFP change and its components of seaports which are considered as the middle of the cord which links the East and West sides. Measure TFP change, its components and analize the efficiency. Measure TFP change and its components Measure TFP change and its components. Measure TFP change, its components and analize the efficiency, Measure TFP change and its components to evaluate the reform process. Measure TFP change and its components Measure TFP change, its components and explaining it through CV in a second stage

Reform process

Seaport size approaches through two variables: Seaport length Terminals’ number

Local Lineal Kernel Model

Terminal location Terminal ownership Financial crisis

Analyse the mean of TFP change and the CV Analyse the mean of TFP change pre and post crisis

Registered capitalManpower structure; Chinese state-owned shipping line shareholding; Shipping routes, Number of terminal operators

Tobit regression

Measure TFP change and decompose it.

Measure TFP change and its components. Measure TFP change and its components to evaluate the impact of the financial crisis.

V. Chang, B. Tovar / Transportation Research Part A 103 (2017) 118–134

Al-Eraqi et al. (2009)

Goal

Measure TFP change, its components and analize the efficiency. Measure TFP change, its components and analize the efficiency, Also, quantify the factors than influenced the TFP change in a second stage.

(continued on next page) 121

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Table 1 (continued) Author/Year

Baran and Górecka (2015) Suarez-Aleman et al. (2016)

Medal-Bartual et al. (2016) Nwanosike et al. (2016)

18 ports in Asia, EE.UU. and UE 1996–2012 203 ports in 70 developing countries 2000–2010 28 Spanish port autorithies 2005–2011 6 Nigerian seaports 2000– 2011 14 Peruvian and Chilean ports terminals 2002–2014

Goal

Measure TFP change, its components and analize the efficiency. Measure TFP change, its components and analize the efficiency, to evaluate, amongst other things, the financial crisis. Measure TFP change and its components to evaluate the impact of the financial crisis. Measure TFP change and its components to evaluate the reform process. Measure TFP change, its components and analize the efficiency in a metafrontier context. Also, quantify the factors than influenced the TFP change in a second stage.

Is it explaining TFP changes? Contextual variables

Methodology

Investment in the Port Authorities.

Mann-Whitney test

Reform process.

Analyse the correlation between preand post-concession TFP change and its descomposition Dynamic panel data model: Arellano-Bond estimador

The lagged of TFP change. Container/bulk ratio Bulk ratio. Reform process.

TFP = Total Factor Productivity Malmquist index; CV = Contextual variables, CGC = Containerized general cargo; NCGC = Non containerized general cargo, SB = solid bulk that uses no specialized facility.

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Present Study

Data

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It should be noted that technical efficiency with respect to k-th group ðTEkt Þin period t can be defined through the use of a distance function for the group k, Dkt ðxkt ; ykt Þ. Thus, in this case, for a output-oriented distance function, TEkt ðxkt ; ykt Þ ¼ Dkt ðxkt ; ykt Þ. The metafrontier envelops the group frontiers, and contains all input–output combinations that are technologically feasible; this implies a boundary whereby the technological differences among the groups are surpassed. Thus, the metafrontier can be represented by the following output-oriented distance function:

n y
o t Dt ðxt ; yt Þ ¼ inf d d > 0 : 2 Pt xt d

ð2Þ

Similarly as Eq. (1), technical efficiency with respect to the metafrontier in period t ðTEt Þ is defined an analogous way as TEt ðxt ; yt Þ ¼ Dt ðxt ; yt Þ. In this paper, in order to account for possible technological differences among the Peruvian and Chilean port terminals, we use the terminals’ classification obtained by the estimation of a Latent Class Stochastic Frontier Model7 (LCSFM, hereafter). Following the LCSFM two classes belonging to different technology sets can be distinguished. Therefore, port terminals in our sample are operating under distinct group frontiers but facing a common potential metafrontier. We can link the technical efficiency with respect to the group-specific frontier and the metafrontier by a ratio of the two technical efficiencies, called Technology Gap Ratio (TGR).

TGRkt ðxt ; yt Þ ¼

Dt ðxt ; yt Þ Dkt ðxkt ; ykt Þ

¼

TEt ðxt ; yt Þ
 TEkt xkt ; ykt

ð3Þ

The metafrontier envelops the group frontiers, therefore TGRt ðxt ; yt Þ 6 1. On the other hand, and following Färe et al. (1994) the Malmquist Productivity index (MPI) for ith firm is given by:

MPIt;tþ1 ðxt ; yt ; xtþ1 ; ytþ1 Þ ¼

1=2 Dtþ1 ðxtþ1 ; ytþ1 Þ Dt ðxtþ1 ; ytþ1 Þ Dt ðxt ; yt Þ ¼ TEC t;tþ1  TC t;tþ1   Dt ðxt ; yt Þ Dtþ1 ðxtþ1 ; ytþ1 Þ Dtþ1 ðxt ; yt Þ

ð4Þ

where the technical efficiency change (TEC) is a ratio of two distance functions which measures the change in the technical efficiency between the periods of change; and, the technical change (TC) measures the technological change in the production technology, that is, it is an indicator of the distance covered by the efficient frontier from one period to another. When Eq. (4) is the group frontier-based measure it is named the group Malmquist productivity index (GMPI, hereafter). Thus, the GMPI is equal to:

GMPIt;tþ1 ðxt ; yt ; xtþ1 ; ytþ1 Þ ¼

Dktþ1 ðxtþ1 ; ytþ1 Þ Dkt ðxt ; yt Þ

" 

Dkt ðxtþ1 ; ytþ1 Þ

Dktþ1 ðxtþ1 ; ytþ1 Þ



Dkt ðxt ; yt Þ Dktþ1 ðxt ; yt Þ

#1=2 ¼ TEC kt;tþ1  TC kt;tþ1

ð5Þ

On the other hand, the metafrontier-based MPI measure (MMPI) defined in Rao (2006) and O’Donnell et al. (2008) is equal to:

MMPIt;tþ1 ðxt ; yt ; xtþ1 ; ytþ1 Þ ¼

 1=2 Dtþ1 ðxtþ1 ; ytþ1 Þ D ðxtþ1 ; ytþ1 Þ D ðxt ; yt Þ ¼ TEC t;tþ1  TC t;tþ1  t  t  Dtþ1 ðxtþ1 ; ytþ1 Þ Dtþ1 ðxt ; yt Þ Dt ðxt ; yt Þ

ð6Þ

where TEC  and TC  are the efficiency change and technical change measure, respectively, regardint to the metafrontier.In order to explore the link between MMPI and GMPI, and following Rambaldi et al. (2007) we present an alternative decomposition of the MMPI from Eqs. (3) and (6). Regarding to Technical Efficiency Change, it is possible to depict the TEC t;tþ1 in terms of TEC kt;tþ1 , TGRkt and TGRktþ1 as:

TEC t;tþ1

¼

TEC kt;tþ1


 TGRktþ1 xktþ1 ; yktþ1 
 TGRkt xkt ; ykt

ð7Þ

Eq. (7) shows that technical efficiency change with respect to the metafrontier is equal to the product of technical efficiency change with respect to k-th group and a term interpreted as the ‘‘growth index of TGR” (GITGR). This growth index can be interpreted as the relative technological progress or regress of the firm in group k regarding to shifts in the metatechnology or global technology change (Rambaldi et al., 2007). About Technical Change, it is possible to depict the TC t;tþ1 in terms of TC kt;tþ1 , TGRkt and TGRktþ1 as:

" TC t;tþ1 ¼ TC kt;tþ1 

TGRkt ðxkt ; ykt Þ TGRktþ1 ðxktþ1 ; yktþ1 Þ



#1=2 TGRkt ðxktþ1 ; yktþ1 Þ TGRktþ1 ðxkt ; ykt Þ

ð8Þ

7 LCSFM, allow to account possible technological differences among the terminals. It can be viewed either as a discrete, semiparametric approximation to the random parameters model, or as a formal specification of a model for a population characterized by a latent sorting of members into discrete groups (Greene, 2005).

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Eq. (8) show that the technical change with respect to the metafrontier is equal to the product of technical change with respect to k-th group and a term interpreted as the inverse of geometric mean of two GITGR, one evaluated at each period’s input-output mix and the other evaluated at the other period’s input-output mix (Rambaldi et al., 2007). Turning now to the definition of MMPI in Eq. (6). This can be expressed as:

MMPIt;tþ1 ¼ GMPIt;tþ1 

TGRktþ1 ðxktþ1 ; yktþ1 Þ TGRkt ðxkt ; ykt Þ

¼ GMPIt;tþ1  ½catch  upt;tþ1 

" 

TGRkt ðxkt ; ykt Þ

TGRktþ1 ðxktþ1 ; yktþ1 Þ



TGRkt ðxktþ1 ; yktþ1 Þ

#1=2

TGRktþ1 ðxkt ; ykt Þ

1

ð9Þ

Where

" #1=2 TGRktþ1 ðxktþ1 ; yktþ1 Þ TGRktþ1 ðxkt ; ykt Þ GMPIt;tþ1  ¼ ¼ MMPIt;tþ1 TGRkt ðxkt ; ykt Þ TGRkt ðxktþ1 ; yktþ1 Þ

catch-upt;tþ1

ð10Þ

Therefore, the MMPIt;tþ1 can be depicted as the product of two terms. One of them is the group specific productivity index (GMPI), and the other is the inverse group catch-up from t to t þ 1. It should be noted that the catch  upt;tþ1 term is greater than unity when the group shows catch-up with the global technology over the period t to t þ 1 (Rambaldi et al., 2007). Furthermore, it is possible to identify the drivers that explain the productivity change of Peruvian and Chilean ports terminal in a context of different technology sets, which are operating under distinct group frontiers, but facing a common potential metafrontier. We took advantage of the panel data structure to specify a dynamic model in a second stage. Thus, we use the following specification:

DTFPki;t ¼

S X

J X

s¼1

j¼1

as DTFPi;ts þ

bi X j;i;t þi;t

ð11Þ

P P where DTFPki;t is the GMPIt;tþ1  1; Ss¼1 as DTFPi;ts is the lagged dependent variable; Jj¼1 X j;i;t is the sets of variables control and i;t is the idiosyncratic error. Since we were trying to identify the drivers that explain the total factor productivity (TFP) changes, we chose the change in the Group Malmquist Productivity Index (GMPI) as the dependent variable. This index does not suffer from boundary problems; nevertheless, according to Pompei (2013), the lagged of GMPI change is correlated by construction with panel level effects and the lagged idiosyncratic error. In addition, the presence of serial correlation causes lagged GMPI change to also be correlated with the contemporaneous error term. This problem can be solved by implementing a bootstrap procedure in the first stage (Simar and Wilson, 2007) or by using econometric methods such as the GMM estimator, in order to eliminate the problems of serial correlation. The econometric approach of Arellano and Bond (1991) that use a GMM estimator was chosen to solve these problems, since this methodology provides asymptotically efficient inference when assuming a minimal set of statistical assumption. 4. Data To estimate DEA-Malmquist productivity Index, we consider the principal public use marine terminals in Peru and Chile. This way, we obtained information related to fourteen terminals (see Table 2) during an eleven-year period, from 2004 to 2014. Sample size was determined both under the aim of providing a fair representation of both countries and data availability. The ports included in the sample coincide with the major commercial ports of each country. In 2014, these terminals in Peru mobilized close to 100% of the total traffic of cargo moved by public direct berthing terminals. In Chile this figure accounted up to 85% of its traffic. The sample comprises seven terminals in each country and we tried to get enough representativeness of the different types of multi-purpose terminals in terms of their specialization (mix of cargoes) and ownership. As we stated before, two classes belonging to different technology sets can be distinguished. Table 2 presents the groups formed by the estimation of LCSFM using the posterior probabilities of class membership.8 The characteristics of the analyzed terminals by class are shown in Table 3. It should be noted that Class 2 incorporates mainly large terminals (Callao North Terminal, San Antonio Terminal and Valparaiso Terminal) with more employees, more equipment and more infrastructure; these are represented as net stock of fixed assets (a monetary variable). Class 2 also present a higher value in other variables such as machinery, draughts, berths and length of berths. Thus, Class 2 terminals had a capital/labour ratio greater than the Class 1 terminals, i.e. Class 2 terminals are more capital-intensive than Class 1 terminals. On the other hand, the terminals grouped in Class 2 mobilize, on average, 5.1 million kilotonnes per year, whereas Class 1 terminals manage just over 2 kilotonnes annually. 8

For the sake of brevity, the estimate of LCSFM is not included but it is available from the authors upon request.

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V. Chang, B. Tovar / Transportation Research Part A 103 (2017) 118–134 Table 2 Class composition. Class 1

Located in. . .

Class 2

Located in. . .

Chimbote Terminal Iquique Terminal Matarani Terminal Salaverry Terminal San Vicente Terminal Arica Terminal

Peru Chile Peru Peru Chile Chile

Mejillones Terminal Antofagasta Terminal Callao North Terminal Pisco Terminal Ilo Terminal Paita Terminal San Antonio Terminal Valparaiso Terminal

Chile Chile Peru Peru Peru Peru Chile Chile

Table 3 Characteristics of terminals analyzed, by class. Variables

Unit

Class 1

Class 2

Total cargo Container Bulk General & roll Labour Net stock of fixed assets Machinerya

(KT) (KT) (KT) (KT) (N° of workers) (US$ year 2000 = 100) Yard crane (N°), tractors (N°) and trucks (N°) Wharf cranes (N°),y ard crane (N°), tractors (N°) and trucks (N°) (Meters) (N°) (Meters) (capital per worker) – (%) (%)

2,316,339 1,183,753 898,405 234,181 203 12,672 18 16

5,146,597 3,034,039 1,675,478 437,080 207 19,663 24 21

10.4 4 228 82 3191 38.2% 58.2%

11.2 6 285 118 927,413 39.7% 67.8%

Draft Berth Length of berth Capital/labour Container/bulk Bulk rateb Container indexc

Note: All variable are measure from 2004 to2014, except machinery, draft, berth and length of berth, which are measure from 2004 to 2010. a Two variables ‘‘machinery ‘‘were developed through principal component analysis (PCA). b Bulk rate, is defined by dividing bulk cargo by the total cargo. c Containerization index, is defined by dividing containerized merchandise by the total general cargo.

Table 4 Eigenanalysis of the correlation matrix.

Component 1 Component 2 Component 3

Eigenvalue

Proportion

Cumulative

1.99 0.70 0.31

0.66 0.23 0.10

0.66 0.90 1.00

Additionally, Table 3 includes three other variables: container/bulk rate is defined by dividing the containerized merchandise by bulk cargo, the bulk rate is defined by dividing the bulk cargo by the total cargo, and the containerization index is defined by dividing containerized merchandise by the total general cargo. All are variables that account for the degree of mechanization at the terminals. The idea is to discern the differences in the degree of mechanization required, in order to manage bulk, containers, and general non-containerized cargo at ports terminals. As expected, the degree of mechanization influences the class selection criteria. The Class 2 terminals have a higher average value in all the aforementioned variables, when compared with Class 1 terminals. Since our aim was oriented to analyses the productivity change and its drivers, the variables of interest were mainly those associated with output, input and other important physical and technical data of the terminals. With regard to the output variables, and given the multi-product characteristics of our port terminals, disaggregated information about containerized cargo, general & rolling freight, as well as bulk cargo (kt) was obtained. With regard to the input variables we have chosen to define two variable inputs: labour and capital. In the case of labour, there was information about the number of workers. Then again, basic infrastructure, superstructure, machines and mobile equipment were grouped into a capital variable approximated by the stock of net fixed assets, obtained from each terminal. This data was then converted into MUS$ constant values; i.e. the year 2000 = 100. Thus, this variable only reflects variations in quantities.

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V. Chang, B. Tovar / Transportation Research Part A 103 (2017) 118–134 Table 5 Principal component (correlations). Variable

Component 1

Component 2

Component 3

Container Bulk Generall & roll

0.4861 0.6053 0.6303

0.8646 0.4382 0.246

0.1273 0.6645 0.7364

Although the specification of inputs and outputs is essentially ad hoc, the number of variables to be included should identify the multi-product process of our port terminals. In a nonparametric context, hypothesis testing of the inputs and outputs to be included in the estimation is not possible. However, that the omission of variables might have an adverse effect on the efficiency and productivity change estimate is taken into account. Likewise the number of variables cannot be increased indefinitely.9 Ideally, we would have liked to include those three output variables, but due to the number of terminals in each class this has not been possible. In fact, we have six and eight port terminals in Class 1 and Class 2, respectively. There would be a problem with the model’s discriminatory power, if we used a DEA-Malmquist with three outputs and two inputs. This is known as ‘‘the curse of dimensionality” and occurs in DEA when there is an excessive number of inputs and outputs in relation to the number of decision-making units. In order to solve the curse of dimensionality the combined use of Principal Component Analysis (PCA)10 and data envelopment analysis (e.g. Adler and Golany, 2002) has been recommended. In order to take the aforementioned into account and to avoid neglecting the multi-output nature of the port terminals analyzed, an aggregate output variable was built to reduce output variables: containerized cargo, general & rolling freight and bulk cargo. Table 4 shows the eigenvalues of each principal component, the explained variance (as a proportion) and the cumulative explained variance (cumulative). The explained variance11 is very important for knowing how many principal components should be used in our analysis. There is no definite rule about the number of components to be used. According to Kaiser’s method12 (1960) and Jolliffe’s rule13 (1972), which are perhaps the best known and most utilized in practice, only Component 1 is chosen. Component 1 explains 66% of the variance (see Table 5). On the other hand, and following Arellano and Bond (1991), we identify the drivers explaining the productivity change of Peruvian and Chilean port terminals. These were obtained by a metafrontier framework, as a function of the firm specific variables, which we consider may influence a terminal port’s productivity. The best model was obtained from the following specification:14

DTFPki;t ¼ a1 DTFP ki;t1 þ b1 þ b2 container=bulki;t þ b3 lnðbulkrateÞi;t þ b5 dgesti;t þi;t

ð12Þ

where dgest is a dummy variable that accounts for the type of management (public or private), taking the value 1 for private firms and 0 for public firms; container/bulk rate and bulk rate have already been defined. Descriptive statistics by classes of whole sample can be seen in Table 6.

5. Results A DEA-Malmquist output oriented productivity index has been estimated in a metafrontier context. The estimation provides a comparison between Class 1 and Class 2 port terminals. First, technical efficiencies and the Technology Gap Ratios (TGR) are shown in Figs. 1 and 2, respectively. Regarding the evolution of technical efficiency with respect to the metafrontier, the Class 2 terminals show higher technical efficiency than the Class 1 terminals for the whole period. Average technical efficiencies regarding the metafrontier were 53.3% and 76.7% for Classes 1 and 2, respectively. Nevertheless, the average technical efficiencies, when they are measured relative to their own frontiers, were 94.1% and 77.2% for Classes 1 and 2, respectively. These results imply that the average output of terminals in Class 1 and Class 2 are close to 94.1% and 77.2% of the possible output using the same input levels and the production technology available in their respective classes. 9 According to Boussofiane et al. (1991), the minimum number of decision making units (DMUs) would be approximately equal to the product of the number of outputs and inputs considered. On the other hand, Golany and Roll (1989) suggest that the minimum should be two times greater than the number of inputs plus outputs, while Charnes et al. (1994) recommend that this should be three times greater than the number of the inputs plus outputs. 10 PCA is a multivariate statistical technique widely used in social and behavioural science and other forms of analysis. This method has been used in productivity and technical efficiency analysis (Adler and Yazhemsky, 2001; Adler and Golany, 2002; Dong et al., 2015) because it allows for the summarizing of the major variation or information that is contained in many dimensions into a reduced number of uncorrelated dimensions without much loss of information. 11 PCA explains the variance structure of a matrix of data through linear combinations of variables. In this way, the data are reduced to a few principal components. Generally, those components describe between the 80 and 90% of the variance in the data. When most of the population variance can be assigned to those components identified, they can be used in substitution of the original variables with a minimum loss of information (Adler and Golany, 2002). 12 According to this rule, only the factors that have eigenvalues greater than one are retained for interpretation. 13 This author suggests, based on simulation studies, that eigenvalues lower boundary of 0.7 is roughly the correct level. 14 Other drivers were considered: ‘‘Container rate”, ‘‘ln(Container rate)” and ‘‘ln(container/bulk)” variables, however, the results were not satisfactory.

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V. Chang, B. Tovar / Transportation Research Part A 103 (2017) 118–134 Table 6 Descriptive statistics by classes. Variable

Mean

Standard deviation

Coefficient of variation

Class 1 Labour Capital Aggregate output container/bulk Bulk ratio dgest

203 12,672 1,260,977 3191 0.38 0.7

175.2 10277.7 881259.7 10664.9 0.36 0.5

0.86 0.81 0.70 3.34 0.95 0.71

Class 2 Labour Capital Aggregate output container/bulk Bulk ratio dgest

207 19663 2,753,578 927,413 0.4 0.6

221.1 18910.7 2,823,008 2,571,236 0.27 0.5

1.07 0.96 1.03 2.77 0.68 0.83

1.0

Technical Efficiency

0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 2004

2005

2006

2007

2008

2009

Class 1

2010

2011

2012

2013

2014

Class 2

Fig. 1. Average Technical efficiency, by class, 2004–2014.

TGR 2014

1.0

2004

0.8 0.6

2013

2005

0.4 0.2 2012

Class 1 2006

0.0

2011

Class 2

2007 2010

2008 2009

Fig. 2. Evolution of Average Technology Gap Ratio (TGR), by class, 2004–2014.

Note that the technical efficiency of Class 1 terminals is high when measured with respect to their frontier (TEk=1 = 94.1%), but low when measured against the metafrontier (TE⁄Class1 = 53.3%). This difference causes a low technology gap ratio (TGR)15 showing that there exists a technology gap in the terminals of this class. Indeed, the latter figure (TE⁄Class1 = 53.3%) indicates that

15

This ratio is defined by dividing technical efficiency with respect to the metafrontier by technical efficiency regarding the frontier of k-th group.

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20.0 15.0

MMPI change (%)

10.0 5.0 0.0 -5.0 -10.0 - 15.0 - 20.0 - 25.0 - 30.0 2004 -2005

2005-2006 2006-2007 2007-2008 2008-2009 2009-2010 2010-2011 2011-2012 2012-2013 2013-2014 Class 1

Class 2

Mean

Mean

Fig. 3. Evolution of Average MMPI, by class, 2004–2014.

Index 1.6

Index 1.4 2014

2014

1.2 1.0

1.0 0.8 2013

0.8

2013

2006

0.6

2006

0.6

0.4

0.4

0.2

0.2

0.0

0.0 2012

2007

2011

2008

2010

2005

1.4

2005

1.2

2009

(a) Class 1

2012

2007

2011

2008

2010

2009

(b) Class 2

Fig. 4. Decomposition of average MMPI, by class, 2004–2014.

the maximum feasible output using the Class 1 technology is only approximately 53.3% of the output that could be achieved using the technology represented by the metafrontier. Fig. 2 shows that Class 1 terminals had a lower level of TGR than Class 2 terminals. A TGR value less than 1 implies a technology gap in the terminals of this class. In contrast TGR equal to 1 means that terminals in this class are using the best available technology. However, a TGR equal to 1 does not necessarily mean that the terminals are efficient. The average TGRs of terminals from 2004 to 2014 for Class 1 and Class 2 were 57.2% and 99.4%, respectively. The terminals in Class 2 have been using the best available technology in almost all the whole period, except for 2011, 2013 and 2014, where the TGR was close to 98%. On the other hand, the TGR Class 2 terminals were 53.8% in 2004. Since that year, the TGR has grown by around 10%, reaching a TGR of 63.6% in 2014. Thus, it is observed that terminals in Class 2 have evolved their TGR positively; i.e. the terminals of this class have been catching up with the best available technology. The results obtained regarding the technical efficiency and the TGR of the Class 1 and Class 2 terminals suggest that, on average Class 1 terminals produce outputs under conditions that are less favourable from a technological point of view than those of Class 2; the latter Class 2 mainly composes the metafrontier. However, Class 1 terminals have improved their TGR during the period 2004–2014; i.e. there was relative technological progress of the terminals in Class 1 regarding the shifts in metatechnology. In addition, the average TGR of Class 1, 57.2%, suggests that terminals of this class could, at best, produce only 57.2% of the outputs that could be produced using metatechnology.

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It should be noted that the majority of private terminals are Class 2. In the mid-1990s, each country began a series of reforms, which consisted of greater private sector participation and increased competition in the provision of services, as well as the rupture of the labour market monopoly and a redefinition of the port authority’s role.16 Probably, the greater private participation, through a concession scheme, explains the higher levels of efficiency achieved by Class 2 terminals, when compared to those of Class 1. It should be noted that Chang and Tovar (2014a, 2014b) assessed and compared the efficiency level and performance evolution of the same port terminals, but for a shorter period (2004–2010). They estimated a stochastic distance function, which included a country dummy. This country dummy was statistically significant, showing that there were differences between the terminals belonging to both countries. However, the inclusion of a country variable as a separating variable in the LCSFM, which our terminal classification is based on, was not significant. One possible reason for the latter result is that it could be attributed to the longer time span utilized in the present paper (2004–2014). In other words, the gap between Chilean and Peruvian terminals seems to have been reduced due to the ongoing reform process in Peru. Therefore, it seems that, currently, there are differences among terminals, other than whether they belong to one country or another, which determine their technological differences. Fig. 3 illustrates the evolution of average Metafrontier Malmquist Productivity Index (MMPI) by class, during 2004–2014. Fig. 4 shows the evolution of its decomposition in terms of technological change (TECHCH), the pure technical efficiency change (PECH) and the Scale Efficiency Change (SECH). The results show that the MMPI demonstrated an average annual reduction of 2.8% within Class 1. This reduction was due to the SECH and TECHCH components which decreased 0.5% and 2.4%, respectively; this compensated for the improvement of the PECH component (1.7%). Regarding the Class 2 terminals, an annual average increase of 0.4% was observed, and this was influenced by the increase of the PECH component (9.1%). However, the SECH and TECHCH components showed annual reductions of about 0.2% and 3.0%, respectively. The evolution of MMPI was rather mixed with increases and decreases in the MMPI in both classes. It is useful to remember that a value larger than one for the MMPI or any of its components indicates an improvement in that source of productivity; however, a value lower than one indicates a deterioration. With respect to Class 1, decreases in productivity are observed for every year, except for the periods 2006–2007, 2009–2010 and 2011–2012. By contrast, the Class 2 terminals show increases in productivity during 2005–2008, 2009–2011 and 2012–2013. Thus, this latter class shows decreases in productivity in only 4 out of 10 periods. The evolution of MMPI shows that there was a decrease in the productivity in the Class 1 terminals close to 8.8% annually between 2004 and 2006 (see Fig. 3). Then, between 2006 and 2007 the Class 1 terminals improved their productivity, compared to the previous year. Although in the following years (2007–2014), the MMPI is constantly fluctuating. The main decreases occurred during the years 2007–2009 and 2012–2014. The first is probably explained as a result of the international financial crisis, and the second by the loss of value in raw materials and the economic slowdown in China. With respect to the Class 2 terminals, their productivity declined by 13.5% between 2004 and 2005, but later these terminals recovered and their productivity on average grew 8.6% annually during the period 2005–2008. Afterwards, between 2008 and 2009, the productivity of these terminals decreased considerably (25.0%), as Fig. 3 shows. This is probably also due to the effects of the crisis, as there was a subsequent recovery in the following year. It should be noted that the largest terminals in both countries are in Class 2 (Valparaiso, San Antonio and Callao North). The financial crisis seems to have affected the Class 2 terminals more profoundly, due to their commercial dependence on the cargoes which experienced a significant reduction. Finally, in recent years, productivity has shown a downward trend, decreasing by an average of 3.0% per year for the period 2012–2014. This was probably influenced by the loss of value of raw materials and the economic slowdown in China, although the terminals in Class 2 were less affected than those in Class 1. The decomposition of MMPI (see Fig. 4) shows a technological regress in both classes; this is represented by the TECHCH component, which on average was down by 2.4% and 3.0% per year in Class 1 and 2, respectively. Technological returns were accentuated during the period of the financial crisis. In the case of Class 1, the TECHCH component decreased on average by 14.4% annually during the 2007–2009 period. Meanwhile, for Class 2 terminals we observed an even greater decrease of 17.4% in the TECHCH component between 2007 and 2009.17 Then again, the other components linked to the decomposition of the MMPI show a different behaviour during the period. The PECH increased, on average, 1.7% and 9.1% per year in Class 1 and Class 2, respectively. However, the SECH component decreased, on average, 0.5% and 0.2% annually in Class 1 and Class 2, respectively. It is evident that during the financial crisis (2007–2009), the biggest impact on Class 2 terminals is explained as the result of the greater impact of technological returns (TECHCH = 17.4%), despite these terminals having improvements in efficiency (PECCH = 6.2% and SECH = 8.6% average per year). However, it seems that the Class 1 terminals better offset the negative effects of the crisis (TECHCH = 14.6%). Thus, significant increases in efficiency are observed in these terminals (PECH = 7.0% y SECH = 4.1% average per year).

16

For a detail description of the reform process the interest reader is referred to Chang and Tovar (2014a, 2014b) These results are similar to results reported by Estache et al. (2004) regarding the analysis of productivity of Mexican ports during the East Asian Crisis and Chang and Tovar (2014a, 2014b) and Wilmsmeier et al. (2013) regarding the effect of the financial crisis on Peru and Chile port terminals and Latin America and the Caribbean container port productivity, respectively. 17

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Index 1.10 2014

2005

1.00 0.90

2013

2006

0.80 0.70

Class 1 Class 2

0.60 2012

2007

2011

No change

2008 2010

2009

Fig. 5. Catch-up values by class, 2004–2014.

Index 1.6 1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.0

2014

2013

2005

2014

2006

2012

2007

2011

2008 2010

Index 1.6 1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.0

2013

2005

2006

2012

2007

2011

2008 2010

2009

(a) TEC*/TEC k

2009

(b) TC */TC k

Fig. 6. Technical Efficiency Change ratio (TEC*/TECk) and Technical Change ratio (TC*/TCk) by class, 2004–2014.

Table 7 Arellano-Bond model estimation: The determinants of TFP growth. Variables

Coefficient

Standard deviation

z statistic

P-value

DTFPt1 container/bulk ln(bulk rate) dgest Constant Observation Wald chi2 (4) Instruments Arellano-Bond test: Ho is no autocorrelation Ar(1) p-values Ar(2) p-values Sargan test: p-value Ho: overidentifying restrictions are valid

0.19920670 0.00000012 0.07553720 0.29015570 0.51303340 112 6387.83 40

0.04421820 0.00000003 0.00109260 0.13700150 0.12370830

4.51 4.65 69.13 2.12 4.15

0.00 0.00 0.00 0.03 0.00

Nota : Remember that DTFP ki;t is the GMPIt;tþ1  1.

0.0034 0.1782 1.000

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Another aspect to emphasize, regarding the decomposition of productivity, is the increase of pure technical efficiency between 2009 and 2011 (PECH = 37.9%) in Class 2. The increase of this component is mainly explained by increased cargo products, such as copper and fishmeal, which were exported from the Ilo terminal.18 Regarding the relationship between the GMMPI and MMPI, we estimated a series of distance functions with respect to alternative technologies and input-output combinations; this was in order for each class to build the annual catch-up values (see Eq. (9)) and both the ratio of technical change component (TC⁄/TCk) and ratio of technical efficiency change (TEC⁄/TECk). These ratios allow us to compare the decomposition of catch-up values in relative terms.19 Fig. 5 shows the annual catch-up values for each class.20 We observe that Class 2 terminals have maintained their relative position and have kept up with the global frontier for the whole period, except from 2012 to 2014. The main reason of this result is that the Class 2 terminals have been determining the global frontier. Thus, for Class 2 there has been no catch-up for most of the period. From 2012 to 2014, Class 2’s average productivity decreased more when was measured with regard to its own frontier than it did when compared to the metafrontier.21 In contrast, in the Class 1 terminals catch-up has only occurred from 2007 to 2008. From 2004 to 2007, the performance of Class 1 terminals was heterogeneous. Most of the terminals presented no catch-up for this period, except the Iquique terminal (2004–2005), the Arica Terminal (2005–2006), the San Vicente Terminal (2006–2007) and the Chimbote Terminal (2006– 2007). Then, from 2007 to 2008 there was catch-up for all terminals except for the Iquique terminal. Thus, the productivity linked to the individual frontiers increased, while the productivity measured with respect to the metafrontier decreased in that period. Finally, from 2008 to 2014, most of the terminals showed no catch-up. Fig. 6 shows the evolution of the technical efficiency change ratio and the technical change ratio values for each class. Regarding both ratios (see Fig. 6), the main differences by class began in 2008, during the financial crisis and post crisis periods. Fig. 6 shows that the measures of technical efficiency change and technical change components, with respect to the frontier built by terminals in Class 2, are similar to those measured by the metafrontier, except from 2011 to 2014. This is explained by the fact that the Class 2 terminals have determined the global frontier in the majority of the years, except from 2010 to 2011 and during 2012–2014. Finally, an Arellano-Bond model was estimated, in order to explain the differences in the productivity change of port terminals. We used a robust GMM-dif estimator in the one-step procedure, in order to control for heteroscedasticity. We also carried out controls for instrument validity, using both the Sargan test and the Arellano-Bond test, for autocorrelation in the residual difference. Table 7 show the results of the best estimation. Firstly, the lagged rate of TFP growth was significant at the 1.0% level. It means that the TFP growth is partly explained by its past value. That is, it shows the dynamic characteristics of the TFP growth and justifies the use of a dynamic panel data method. Moreover, the estimated lagged dependent variable parameter is negative, as expected. This outcome is consistent with the findings of previous studies (Pompei, 2013; Nakano and Managi, 2008). That is, the TFP growth variable changes inversely to its first lag, showing a convergence process. There are several reasons for this, one being that the productivity gains may be greater for low-productivity firms than for more advanced ones. Regarding the variables linked to the degree of mechanization, the coefficient of container/bulk and bulk rate are significant, at a 1.0% level. The positive coefficient of the container/bulk shows that handling higher proportions of containerized cargo, compared to bulk cargo, contributes positively to increasing the productivity change. In the case of bulk ratio, the negative coefficient of this variable shows that handling higher proportions of bulk cargo relative to the total cargo, including container cargo, contributes to reducing the productivity change. The negative effect obtained by the variable ‘‘bulk rate” could be explained to by the fact that the change in productivity is related not only to the pure technical efficiency of the terminals, but also to the other two components: scale efficiency change and technical change. In that sense, it seems reasonable that technical change should explain these differences; i.e., the technical change of bulk cargo has been less than the technical change for containerized cargo in recent years. With respect to dgest (type of management), this is positive and significant at the 1% level, which indicates that private management contributes positively to the productivity change. This result could be related to the institutional environment under which the private and public firms operate in Latin America, rather than the type of ownership, either public or private22; i.e., the fact that Chile and Peru modernized most of its terminals, with greater private participation through a concessions scheme, has allowed them to reap the benefits of the implemented reforms.

18

Ilo terminal increased its total cargo about 1.5 times between 2009 and 2011. For example, if the technological gap is widening between the kth class and the global technology, this fact will be reflected in (TC⁄/TCk) ratio major than 1; i.e. the value for TC⁄ measured with respect to the metafrontier will be higher than that derived using the group frontier. Similarly, if the technical efficiency change components have grown (TEC⁄ and TECk), but technical efficiency change measured with respect to the metafrontier is higher than that derived using the group frontier, the ratio of technical efficiency change will be greater than 1. 20 Remember that a catch-up(t,t+1) term (see Eq. (9)) is greater than unity when the group shows catch-up with the global technology over the period t to t + 1. 21 From 2012 to 2014 the annual averages of MMPI and GMPI, were 0.972 and 0.946 respectively. Angamos Terminal and Antofagasta Terminal were not part of the Metafrontier during 2012–2014, and nor were San Antonio Terminal and Valparaiso Terminal from 2013 to 2014. 22 This outcome is consistent with the findings of other authors when analyzing these kinds of reforms in other Peruvian sectors (see for example, Pérez-Reyes and Tovar, 2009, 2010) for the electricity sector. 19

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6. Conclusion The aim of the first stage of this paper is to measure productivity of Chilean and Peruvian port terminals, and the second stage is to evaluate the influence of certain specific explanatory variables that may explain productivity differences among these port terminals. There are potential differences which are derived from the fact that those terminals belong to different countries, have different ownership, different geographical and operational settings, and so on; due to this, our paper estimates the productivity scores, and explains the differences in productivity change in a metafrontier framework. In fact, following a Latent Class Stochastic Frontier Model two classes belonging to different technology sets can be distinguished among the Peruvian and Chilean port terminals. It should be noticed that Class 2 are more capital-intensive and bigger (mobilize more cargos) than Class 1 terminals. The present article is a step towards an improved understanding in the empirical literature related to productivity issues in Latin America and Caribbean. Its contributions are considered to be of relevance, due to the Peru and Chile are the main Pacific trade gateways to South American that in recent years have undergone significant economic improvements. Regarding methodological issues, the paper is relevant due to fact that is the first time a DEA-Malmquist model in a metafrontier framework has been used to analyse port terminal productivity change; this has let us take their possible technological differences into account. Moreover, it is also the first time that an Arellano-Bond model, which takes the dynamic characteristics of the TFP growth into account, has been estimated to explain the differences in the productivity change found in the port sector. The empirical evidence shows that the Class 1 terminals produce output under certain less favourable technological conditions than the Class 2 terminals. While, the Class 1 terminals have improved the technology gap ratio during the period 2004–2014, the results suggest that Class 1 terminals could, at best with the same inputs, produce only 57.2% of the outputs that might be produced using the metatechnology. On average, both classes present positive evolutions of the catching up effect, which shows that the terminals as a whole are moving nearer to the efficiency metafrontier. Moreover, both also have undergone a technological regress and the change in scale efficiency was nearly neutral. However, regarding the productivity, while the terminals in Class 1 had an annual reduction of 2.7%, the terminals in Class 2 showed an improvement close to 0.4% by year. Although terminals in both classes had, on average, a positive evolution of the catching up effect, in the case of Class 1 this improvement was not enough to compensate for the decrease in the other components. Thus, the negative average productivity change of Class 1 was a consequence of the deterioration in technological change, while the average productivity growth of Class 2 was a consequence of the important increase of the pure technical efficiency change component; this was able to compensate for a more significant technological regress than Class 1 experienced. We observe a technological regress during 2004–2014 and that both classes of terminals were affected by the financial crisis which started in the United States in 2008. The evolution of productivity shows a mixed performance, with increases and decreases in productivity for both classes. With respect to Class 1, decreases in productivity for every year are observed, except for the periods 2006–2007, 2009–2010 and 2011–2012. By contrast, the Class 2 terminals show increases in productivity during 2005–2008, 2009–2011 and 2012–2013. This class shows decreases in productivity only in 2004–2005, 2008– 2009, 2011–2012 and 2013–2014. In addition, we observe that Class 2 terminals have maintained their relative position and have kept up with the global frontier for the whole period, except from 2012 to 2014. Thus, it provides evidence that the Class 2 terminals could be determining the global frontier with their specific observable mix of input. We can conclude that container/bulk ratio and the private management contribute positivity to the productivity change; This is therefore evidence that the reforms have been conducted successfully in both countries; i.e., the fact that Chile and Peru modernized most of their terminals, with greater private stake holding through a concession scheme, has allowed them to reap the benefits of the implemented reforms. On the other hand, the TFP growth variable changes inversely to its first lag as expected, showing a convergence process, and the bulk rate contributes negativity to the productivity change growth. This is probably due to the technical change in bulk, cargo, which has been less than the technical change in containerized cargo in recent years. Finally, the main policy lessons from the paper can be summarized as follows. First, the Peruvian government should avoid further delays in the reform process. The increases in TFP due to the reform process, and the higher levels of mechanization due to easier access to investment found should bring about further reductions in logistics costs, if conducted with greater agility. This would lead to increases in Peru’s level of competitiveness, which is currently low compared to other Latin American countries. Second, it would be advisable for the regulatory agencies of both countries to take into account the important issue of the heterogeneity when evaluating and comparing the productivity and efficiencies. This is in order to use these measures in incentive regulation such as price-cap regulation, or regulatory benchmarking. If this heterogeneity exists, and it is not explicitly picked up by the model, then the estimated efficiency would be erroneous; consequently, a terminal could be identified as inefficient, when it is not necessarily true. Moreover, due to it sometimes being difficult to achieve the large samples desirable to carry out sensible benchmarking exercises within one country, regulators from different countries could cooperate by interchanging information to build a larger dataset. From this, and taking advantage of the methodologies shown in this paper, they could identify homogeneous classes of firms which are therefore comparable.

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