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# **Table 2.2 Cost functions estimation for port sector**

|**Author**|**Activity**|**Functional**<br>**specification**|**Data**|**Variables**<sup>**(1)**</sup>|**Scale economies evaluated**<br>**in the approximation point**|<sup>**Other Measurements**</sup>|
|---|---|---|---|---|---|---|
||||**MONOPRODU**<br>Time series|**CTIVE COST FUNCTIONS**||Minimal efficient scale|
|Kin y Sachis<br>(1986)|Infrastructure and<br>services|<br>Translogarithmic|Annual observations (19)<br>(1966-1983)|CTLP(Y,L,K,Pl,Pk)|Increasing|<br>Factor demand price elasticity<br>Cross elasticities|
|Martínez Budría<br>(1996)|Infraestructure|Cobb-Douglas|Panel data<br>27 ports<br>Annual observations (5)<br>(1985-1989)|CTit(Qit,, Wit,, mit,, rit, di, dt, Di, Dt)|Increasing|Cost factor elasticities<br>Individual specific effects of each port<br>Second stage analysis|
||||**MULTIPRODU**<br>Panel data<br>|**CTIVE COST FUNCTIONS**<br><br><br>|||
|Jara Díaz et al.<br>(1997)|Infraestructure|Quadratic|27 ports<br>Annual observations<br>(1985-1989)|CTlpit(GLit,,<br>GSit,,<br>MGCit,,<br>MGNCit,, CANONit,, wit,, rit, mit)|Increasing|Marginal costs for each product<br>Economies of scope (ED> 0)|
|Martínez Budría et al.<br>(1998)|Activity<br>of<br>the<br>SEED (2)|<br>Translogarithmic|Panel data<br>24 SEED<br>Annual observations<br>(1990-1996)|CTit(GSit,, MGit,, Plit,, Piit, T)|Increasing|Marginal costs for each product<br>Costs product elasticities<br>Total factor productivity for a subsample<br>of 14 SEED|
|Jara Díaz et al.<br>(2002)|Infraestructure|Quadratic|Panel data<br>26 ports<br>Annual observations<br>(1985-1995)|CTlpit(GLit,,<br>GSit,,<br>MGCit,,<br>MGNCit,, CANONit,, wit,, rit, mit)|Increasing|Marginal costs for each product i<br>Economies of scope (ED> 0)|
|Tovar et al (2003)|Cargo handling|Quadratic|Panel data<br>3 Port Terminals<br>Monthly observations<br>(1990-1999)|CTlpit(MGCit,, MGitRODitWnpit<br>WlcitWleit,, mit,, rit, DtT)|Increasing|Marginal costs for each terminal<br>Marginal costs for each product<br>Economies of scope (ED> 0)|
|(1):<br>CTLP= Long<br>Y = Tons of c<br>L = Labor<br>K = Capital.<br>Pl, = Labor pr<br>Pk= Capital p<br>Tit= Total ann<br>Qit,= Tons of<br>Plit= Labor pr<br>Piit= Interme<br>T = Temporal<br>Wit,= labor pr<br>mit= interme<br>rit= Amortiza<br>di= Individua<br>dt= Individua<br>Di= Port-spe|term total annual cost<br>argo<br>ice<br>rice<br>ual cost, both in port i<br>cargo, both in port i ye<br>ice<br>diate input price<br>trend<br>ice, both in port i year t<br>diate input, both in port<br>tion, both in port i year<br>l specific effect to port<br>l specific effect to year<br>cific dummy variable|year t<br>ar t (thousands)<br> <br>i year t<br>t<br>i<br>t|Dt= Firm-specific dummy varia<br>CTlpit= Long term total annual<br>GLit= Tons of liquid bulks (tho<br>GSit= Tons of dry bulks (thousa<br>MGCit= Tons of containerized<br>MGNCit= Tons of non-containe<br>CANONit= Index added of othe<br>wit,= imput price, both in port i<br>Wnpit= Non port worker person<br>Wlcit= Ordinary port worker p<br>Wleit= Special port worker price<br>rit= Capial price both in port i y<br>mit= Intermediate input price<br>MGit,= Tons of general cargo fo<br>RODit= Tons of ro-ro cargo for|ble<br>cost, both in port i year t<br>usands), both in port i year t<br>nds) , both in port i year t<br>general cargo (thousands), both in port i ye<br>rised general cargo (thousands), both in po<br>r activities that use part of the infrastructur<br>year t<br>al price, both in port i year t<br>rice, both in port i year t<br>; both in port i year t<br>ear t<br>r port i in year t<br>port i in year t|ar t<br>rt i year t<br>e||

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