Estimation of the production profile and metafrontier technology gap: a quantile approach

Abstract

In this paper, a quantile function is suggested as an alternative description of a production technology. Since the quantile function may not share the same functional properties as the frontier function, it is argued that the quantile-based production function serves as a better benchmark for a firm’s production structure analysis. This argument is extended to the metafrontier analysis. The quantile metafrontier is defined as the envelopment of all groups’ quantile frontier at the same quantile level. The quantile technology gap serves as a more relevant indicator of efficiency in the adopted technology than the traditional measure of the metafrontier technology gap. The quantile approach is illustrated using survey data to estimate the earning profiles for men, and the impact of human capital on the industrial wage distributions in the service industry, the manufacturing industry, and all other industries in Taiwan.