# **d. Application of Frontier Analysis in the Port Sector**

The application of frontier analysis in the port sector is relatively recent, starting with a study by Liu (1995), which measured the efficiency of 28 public and private ports in the UK for the period between 1983 and 1990. The author concluded that port ownership, one of the considered inputs, did not have a significant impact on output (turnover). Aside from port ownership, the study considered other input variables such as labor and capital. Similarly, Tongzon and Heng (2005) used SFA to shed light on the relationship between ownership and efficiency of 25 ports across Asia and Europe, using container throughput as the output variable, and terminal quay length, terminal surface, and the number of quay cranes as inputs. They concluded that private sector participation can improve the efficiency of port operations.

Coto-Millan et al. (2000) used SFA to measure the efficiency of 27 Spanish ports with a translog cost function, finding a negative relationship between port size and efficiency in the sample. More recently, to assess the evolution of Spanish port efficiency, Gonzalez and Trujillo (2009) used a translog distance production function with a panel data from 17 Spanish ports from 1990 to 2002, showing that the average technical efficiency had changed little over time. Similarly, Estache et al. (2002) used SFA to measure the efficiency of 13 Mexican ports following a port reform. The variables included in the study were the volume of merchandise handled (output), the number of workers and the length of docks (the last two as inputs).

Notteboom et al. (2000) is an example of a region-wide analysis of port efficiency (with 36 European terminals) using terminal quay length, terminal surface area, and terminal gantry cranes as inputs, and terminal traffic in twenty-foot-equivalent units (TEUs) as the output variable. The authors conclude that terminals of hub ports, on average, are more efficient than those in feeder ports. More recently, Trujillo et al _._ (2013) applied SFA to the Africa region, analyzing a total of 37 ports. Using interactions among several input variables, the paper concludes that landlord ports show the highest level of efficiency. The overall average port efficiency for the period was low, 30%.

To the best extent of our knowledge, Stochastic Frontier Analysis has never been used to analyze port performance across LAC, although other studies have discussed port efficiency in the region relying on partial performance indicators or on Data Envelopment Analyses applied to a limited group of ports, countries or sub-regions of LAC. For example, Kent (2011) and IADB (2013) present a review of a set of partial productivity indicators in Central America ports, such as port productivity or port delay. Moreover, a survey of 19 LAC ports by Sanchez et al. (2003) provides measures of port efficiency specifically focused on time performance and terminal productivity, associating these variables with country competitiveness (measured in terms of waterborne transport costs). The study does not seek to provide a relative assessment (ranking) of the region’s ports or a measure of the evolution of efficiency over time.

Ramos and Gastaud (2006) applied DEA to MERCOSUR using five inputs (number of cranes, number of berths, number of employees, size of terminal area, and amount of yard equipment) and two output variables (annual TEUs handled and average number of containers handled per hour/ship. By considering five inputs, three years (2002-2004) and twenty-three ports, the paper finds that 60% of ports in MERCOSUR are efficient during that three year period.

Wilmsmeier et al. (2013) applied DEA to analyze technical efficiency evolution in 16 container terminals in LAC and 4 container terminals in Spain between 2005 and 2011. The authors focused on evaluating the impact of the financial crisis on productivity and efficiency, concluding that these terminals were particularly exposed to demand shocks and have difficulty to react effectively to these changes.

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