Container Port Output

IS PORT THROUGHPUT A PORT OUTPUT?

5. Container Port Output

Rather than using TEU interchange service as the amount of output provided by a container port, the literature heretofore has instead used TEU throughput. However, what are the impacts in doing so on the estimation of container port’s economic production and cost functions for investigating container port technical and cost inefficiencies?

5.1. TEU Throughput and the port production function

Theoretical economic production functions utilized heretofore in the esti- mation (via econometric and frontier analysis procedures) of port economic production functions are those that have appeared in the literature in the estimation of economic production functions of firms that produce a tan- gible product rather than provide a service. Specifically, these production functions relate the maximum amount of a product (or output) produced by a firm to the levels of resources utilized, i.e.,

Output =g1(Ri) i= 1,2, . . . M (3) Port studies where estimates of economic production function (3) are found include, for example, studies by Chang,¹ Bendall and Stent,³ Liu,⁵ Dowd and Leschine⁴ and Cullinane and Song.⁸ In the estimation of economic production function (3) for container ports, output is measured as TEU Throughput.

Criticisms in using function (3), where output is measured as TEU Throughput, to investigate the technical efficiency of container ports include: a) container ports provide a service as opposed to producing a tangible product, b) economic production function (3) unlike interchange service economic production function (1) does not capture the fact that

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the number of TEUs received by ports are not determined by the ports but by carriers through their port-choice decision making process and c) interchange service economic production function (1) no longer exists if interchange service is measured as TEU Throughput (see Proposition 1 below).

Proposition 1: Interchange service economic production function (1) no longer exists if interchange service is measured as TEU Throughput.

Proof. If TEU Interchange Service in function (1) were replaced with TEU Throughput, a problem would arise, i.e., from the fact that TEU Throughput = TEUs Provided by Carriers^tor TEUs interchanged by the port are the same TEUs provided to the port by carriers. Port output (a dependent variable) cannot be a function of itself and the function be a port economic production function. A function by definition denotes the relationship between a dependent variable and one or more independent variables. A function does not denote the relationship between a dependent variable and a set of variables that includes the same dependent variable.

Alternatively, a variable cannot be both a dependent and an independent variable in the same relationship and the relationship be a function.

5.2. TEU Throughput and port cost functions

A port will be cost efficient in the provision of its output if it provides its output at the least cost, given the prices that it pays for the resources employed. The relationship between the least or minimum costs and the amount of output provided is the port’s economic cost function. In order to be cost efficient, it is necessary that the port be technically efficient in the provision of this output. Otherwise the port could provide the same amount of output with at least a lesser amount of one resource and therefore incur lower cost in providing this output (for given resource prices).

5.2.1. Long-run total cost function

The long-run is a time period that is sufficiently long enough so that amounts of all resources employed can be varied. To be cost efficient in

tIn practice, i.e., once a time period is specified (say a year), this equality may not hold exactly. For example, containers that are received by a port at the end of the year may not depart from the port (and therefore become port throughput) until several days into the next year.

providing output in the long-run time period, a port will minimize its long-run total cost (LTC) in the provision of technically efficient output (represented by the interchange service economic production function (1)), i.e., minimize LTC subject to interchange service economic production function (1). Further, LTC will be minimized subject to resource function (2), since the latter represents the minimum amount of a given resource to be utilized the port given the amount of TEUs provided by carriers and the levels of the port’s operating options. LTC is the sum of the products of the amounts of resources (R_i) utilized by the port and the prices (P_i) incurred in their utilization, whereP_i is the price incurred by the port for theith resource.

From the above discussion, the port’s long-run total cost function will be derived by:

Minimizing LTC = P_iR_i subject to

TEU Interchange Service =f(R_i; TEUs Provided by Carriers) (4) R_i=R_i(OPTION₁,OPTION₂,OPTION_n. . .OPTION_N;

TEUs Provided by Carriers) i= 1,2, . . . M

The choice variables in the optimization of equation (4) are the port’s operating options. That is to say, the port would select the levels of its operating options (or quality of service). This selection in turn determines, given the TEUs provided by carriers, the port’s minimum levels of resources to be employed — which are also the levels to be employed that minimize the port’s long-run costs (LTC). From this optimization, the port’s long- run economic total cost function can also be derived, where LTC is a function of the prices of the resources employed by the port, the port’s TEU Interchange Service and TEUs Provided by Carriers, i.e.,

LTC = LTC(P_i, TEU Interchange Service,

TEUs Provided by Carriers) i= 1,2,3. . . M (5) Proposition 2: Port long-run economic total cost function (5) cannot be derived if TEU Interchange Service is measured by TEU Throughput.

Proof. By Proposition 1, interchange service economic production func- tion (1) does not exist if interchange service is measured as TEU

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Throughput. Hence, Eq. (4) cannot be optimized to obtain long-run

economic total cost function (5).^u

5.2.2. Short-run variable cost function

To be cost efficient in providing output in the short-run (a time period that is sufficiently short so that the amounts of one or more resources employed cannot be varied, i.e., are fixed), a port will minimize its short-run variable cost (SRVC) subject to interchange service economic production function (1),R_M amount of fixed resourceM and resource function (2), i.e.,

Minimize SRVC = P_iR_i subject to

TEU Interchange Service =f(R_i;R_M, TEUs Provided by Carriers) (6) R_i =R_i(OPTION₁,OPTION₂,OPTION_n. . .OPTION_N;

TEUs Provided by Carriers) i= 1,2. . . M−1

As for Eq. (4), the choice variables in the optimization of Eq. (6) are the port’s operating options. From the optimization, the port’s short-run economic variable cost function can be derived, where SRVC is a function of the prices of the variable resources (1 throughM −1) employed by the port, the port’s TEU Interchange Service, TEUs Provided by Carriers and R_M amount of fixed resourceM, i.e.,

SRVC = SRVC(P_i,TEU Interchange Service,

TEUs Provided by Carriers, R_M) i= 1,2,3. . . M−1 (7)

uCritics of the use of port aggregated cargo throughput (i.e., the aggregation of the throughput of two or more different types of cargo) as a measure of port output in the estimation of port economic production and cost functions note that port aggregated cargo throughput generates aggregation-bias estimates of technical and cost efficiencies for ports that handle more than one type of cargo, e.g., solid bulk, liquid bulk, general non-containerized and containerized cargoes. To avoid aggregation bias in such studies, Kim and Sachish² recommend that the port throughput of each type of cargo be used as port output measures rather than using a single aggregate throughput measure. In a port cost function estimation^studyby Martinez-Budria,⁹ aggregate throughput is used as the measure of port output. However, the study makes the restrictive assumption that the cost share of a ton of any type of cargo is independent of the activity where it is handled.

Proposition 3: Port short-run economic variable cost function (7) cannot be derived if TEU Interchange Service is measured by TEU Throughput.

Proof. By Proposition 1, interchange service economic production func- tion (1) does not exist if interchange service is measured as TEU Through- put. Hence, Eq. (6) cannot be optimized to obtain short-run economic

variable cost function (7).

5.2.3. Port cost function estimates

Estimates of long-run economic total cost functions for various types of ports are found in studies by Kim and Sachish,² Martinez-Budria,⁹ Jara- Diaz, Martinez-Budria, Cortes and Vargas,¹⁰ Jara-Diaz, Martinez-Budria, Cortes and Basso¹¹and Jara-Diaz, Tovar and Trujillo.¹²Port long-run total costs in these studies were expressed as functions of port throughput and the prices of the resources employed by ports — but not functions of port.

Interchange service.^v Measures of port throughput found in these studies include tons of: cargo, container general cargo, non-container general cargo, liquid bulk cargo, dry bulk cargo and roll-on roll-off (Ro-Ro) cargo.

As noted in Proposition 1, a port’s TEU throughput is also the TEUs provided by carriers to the port. This is also true for any type of port throughput — i.e., a port’s throughput of any type is also the amount of cargo of any type provided by carriers to the port (to be interchanged between arriving and departing carrier vessels and vehicles). Hence, the port long-run economic total cost functions used in the above cost studies may be alternatively stated as functions, where port long-run economic total cost is expressed as a function of the amount of cargo provided by carriers to the port and the prices of the resources employed by the port.

However, the derived long-run economic total cost function for a container port (function 5) has long-run total cost being a function of not only of TEUs provided by carriers and the prices of resources employed, but also of the port’s TEU interchange service. For a port handling any type of cargo, function (5) would be rewritten as port long-run total cost being a function of cargo provided by carriers, prices of resources employed and the level of cargo interchange service.

vThe one possible exception is the study by Jara-Diaz, Martinez-Budria, Cortes and Basso¹¹that includes the explanatory variable, index added of other activities that use part of the port infrastructure.

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Since the above port cost studies do not include the explanatory variable, cargo interchange service, in obtaining their long-run total cost function estimates, the studies’ estimated parameters are statistically biased due to specification error, i.e., from a relevant explanatory variable having been omitted from the estimation (see Pindyck and Rubinfeld.^16,w The studies conclude that ports exhibit economies of scale, i.e., port long- run total cost does not increase in proportion to the increase in port throughput. Would this conclusion hold if the explanatory variable, cargo interchange service, had been used in obtaining the long-run total cost function estimates?

6. Port Interchange Service Measures