A General Error Revenue Function Model with Technical Inefficiency: An Application to Norwegian Fishing Trawler

Abstract

In this paper we consider a revenue maximizing model and derive the revenue function from the transformation function where errors are parts of the outputs. First, we adapt McElroy’s additive general error model to the transformation function with multiple inputs and multiple outputs and derive the revenue function. The error terms in the output supply functions, derived from the revenue function, inherit their stochasticity from the error terms in the outputs. The second approach uses a multiplicative general error model (MGEM), in the spirit of Kumbhakar and Tsionas (J Appl Econ 26:270–297, 2011), with multiple outputs in which multiplicative errors are parts of the outputs. The MGEM is further generalized to accommodate output-oriented inefficiency. The translog revenue function with MGEM makes the intercept and the coefficients of the linear terms random (functions of the errors associated with outputs). The errors in the revenue share functions are linear functions of the errors associated with the outputs. Vessel level data for the Norwegian whitefish fisheries for the period 1995–2007 is used to showcase the application of the model. We also estimate a standard (off-the-shelf) revenue function with output-oriented technical inefficiency and compare technical change and technical efficiency results with the MGEM revenue function which is estimated along with the revenue share equations. Although the means are found to be somewhat similar, patterns of technical change and technical efficiency are found to be quite different across these models.