A Reexamination of Returns to Scale, Density and Technical Progress in U. S. Airlines

Abstract

The logic of protecting U.S. airlines from competition was initially founded on the belief that substantial economies of scale existed in the industry and that consumers would benefit through, among other things, regulation of fares, regulation of service network, and restrictions on entry and exit from the industry. However, studies [1; 7; 8; 12] have undermined the faith in economic regulation by showing that economies of scale were minimal and competition would promote efficiency. In a recent study, Caves, Christensen, and Tretheway [5] estimated returns to scale (RTS) and returns to density (RTD) for U.S. airlines. Based on a panel dataset for 1970-1981 containing trunk and local service airlines, they estimated RTD and RTS from a translog cost function for airline services. Like many other applied economists working with translog cost functions, they found that the neoclassical curvature or regularity conditions on the cost function are not satisified in almost half of the observations (105 out of 208). In general, concavity property is satisfied in the neighborhood of the sample mean (if it is chosen as the point of approximation for the cost function) but not at points further from the mean. Recently Diewert and Wales [6] suggested alternative flexible functional forms which are globally concave in input prices if the concavity property is satisfied at only one point. Thus if the concavity property is violated, imposition of it at a single point will make the function globally concave without destroying flexibility. Use of such functional forms can avoid violation of regularity conditions of the cost function at extreme points. The objective of this paper is to estimate a model of airline costs along the lines of Caves, Christensen, and Tretheway [5]. However, we extend their results in several ways. First, we consider a modest generalization of the Symmetric Generalized McFadden (SGM) cost function developed by Diewert and Wales by including network and control variables in the airline cost function. The SGM cost function is flexible and globally concave in input prices. Thus our estimates of parameters and measures of RTS, RTD, and technical progress are based on a cost function which is globally concave. Second, we estimate the system of input demand functions instead of the cost function and, while estimating these input demand functions derived from the cost minimizing behavior of the airlines, we incorporate firm- and input-specific effects. These effects capture possible differences in production technologies among airlines. Third, we intro