In addition to the container port database, we also collected other variables that are important to explain port throughput and technical efficiency. First, we identified which ports have landlord models, that is, have at least one terminal under concession to the private sector (these data were collected using the Containerization International Yearbook). The data show that, in 2009, 61% of the sampled ports have terminals with private operations; this percentage is the largest in the Caribbean (72%) and the lowest in Central America/Mexico (45%). Second, we collected information on whether a port is specialized in container traffic or serves as a multi-purpose facility, that is, also operates general cargo or bulk (collected using the Containerization International Yearbook). The data show that 40% of the ports in the sample mainly operate containers; this percentage is the largest in the Caribbean (57%) where most of the transshipment ports are located and is the lowest in South America (28%).

Regarding variables at the country level, per capita income (in constant US$) from the World Development Indicators (WDI) was collected, it measures average income levels. In addition, liner shipping connectivity (produced by UNCTAD), an index number in which the highest index in 2004 is equal to 100, measures how well countries are connected to the global shipping network. GDP (in constant US$), extracted from the WDI, measures the size of the economies. Trade openness (in GDP percentage), also collected in the WDI, measures the degree to which countries import and export merchandise with the rest of the world. Finally, as a measure of the perception of corruption in the public sector, we collected a corruption index from Transparency International, ranging from 0 (highly corrupt) to 10 (highly clean).

# **4. Model**

A starting point to assess port efficiency in LAC using an SFA methodology is the specification of a translog stochastic production frontier, such as in Liu (1995), Cullilane (2006b), and Trujillo et al. (2013), and described in Equation 1.

These variables are defined as follows:

- ∀i = 1, ... , N and t = 1, ... , T

Qit is the container throughput (in TEUs) handled by port i in period t; Ait is the total area (in squared meters) of the container terminals in port i in period t; Bit is the total length (in meters) of berths used for container handling in port i in period t; Cit is the number of container cranes owned by port i in period t; and Tt is a time trend that captures overall changes in productivity through time<sup>4</sup> . In the model, vit it, which is assumed to be a is a random error term assumed to be independent from u truncated-normal random variable associated with technical inefficiency, as detailed in Section 2.

Other noteworthy input variables not contemplated in this model are labor and energy consumption. In container terminals, nevertheless, these variables play smaller roles, since container handling is highly infrastructure intensive and, as a result, the throughput elasticities of inputs such as workforce and energy consumption are expected to be relatively low. In this regard, our production function assumes implicitly that workforce and energy consumption are fixed for each unit of

> 4 In the original specifications by Cullilane (2006b), and Trujillo et al. (2013), the model also included interaction terms between all independent variables. We have also estimated such specifications, but the interaction terms were not significantly different from zero, therefore we omit the presentation and discussion of such results.

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