Non-positive data

The log transformation is popular in economics but has the drawback that the variable must take positive values. Yet in many applications some of the data take non-positive values. This includes applications in measuring poverty and inequality. Throwing out these values is hardly a good solution. An increasingly popular solution is to use the “inverse hyperbolic sine transformation.” However this has the serious drawback in poverty and inequality measurement that the IHS is not concave everywhere–indeed, it is convex for negative values. This leads to violations of the Pigou-Dalton transfer axiom.

In this paper, “Concave Log Like Transformation,” I propose a solution that delivers a strictly concave log-like transformation. And this Statistical Addendum to the paper provides some empirical applications.