Title: A new family of copulas, with application to the estimation of a production frontier system
Authors: Artem Prokhorov - University of Sydney (Australia) [presenting]
Peter Schmidt - Michigan State University (United States)
Christine Amsler - Michigan State University (United States)
Abstract: A system of equations is considered where one equation is a production function and the other equations are the first order conditions for cost minimization. The equation representing the production function contains a one-sided error that represents technical inefficiency. Also, because the first order conditions for cost minimization will not be satisfied exactly, the corresponding equations contain errors that represent allocative inefficiency. If technical and allocative inefficiency are not independent, we encounter the issue that common copulas do not capture the type of dependence that the economic model implies. What we want is a positive correlation between technical inefficiency and the absolute value of allocative inefficiency, which says that firms that are more technically inefficient have capital/labor ratios that are more in error than more technically efficient firms. The same argument can apply in a non-frontier setting. Even if $u$ and $v$ are standard zero-mean errors (e.g. normal), it may be reasonable to assume that $u$ is correlated with $|v|$ rather than $v$, reflecting the view that firms that are better at using the correct input ratios also on average produce more output from a given set of inputs.