Assets Frontier Technology and Technical Efficiency in (k, y) Space

Abstract

Technical efficiency estimation is mean to measure how firm combine their inputs to produce output in an efficient way, it capture the distance between the level of its actual output and the maximal level of output that can be achieved in production possibility set, or called production technology, with inputs unchanged. Technical efficiency can be calculated by parametric method or by nonparametric method such as data envelopment analysis. Although some authors use inputs such as capital, total employment, material and energy to analyze the firm-specific efficiency, but total capital K, labor L and total added-value Y are sufficient indexes to describe the production process for efficiency evaluation. Despite this virtue, input indexes K and L can't identify embodied technology well, recently labor productivity and capital-labor ratio is used in parametric method to evaluate firm efficiency. In order to explore nonparametric method corresponding to such variable, constant returns to scale (cRTS) production technology in (K, L, Y) is projected into (k,y) space which constructed by labor productivity y and capital-labor ratio k . It is proved that the image of the conventional constant RTS production technology is a non-increasing RTS production technology in (k,y) space. Moreover the technical efficiency defined in (k,y) space equals the conventional constant RTS technical efficiency in (K, L, Y) space. This result have more advantage over conventional constant RTS technical efficiency estimated in (K, L, Y) space. First, conventional cRTS technical efficiency can be estimated more easily in (k,y) space than in (K, L, Y) space; second the maximal productivity that can be achieved in production technology given capital-labor ratio can be estimated in (k,y) space, which is the best approximation of the physical technology of the machine and equipment corresponding capital-labor ration k