A Note on the Use of the Log-Logistic Functional Form for Modelling Saturation Effects.

This note suggests that the logistic function is often not suitable for modeling aggregate demand or ownership levels because of the fact that the independent variable is defined to lie between minus and plus infinity (unlike many economic variables which are positive). This imposes strictly positive (possibly large) levels of ownership when the independent variable is zero. The log logistic is proposed as an alternative functional form. This is shown to have logistic function properties as between the dependent variable and the log of the independent variable. The relation between the dependent variable and the independent variable is described, and conditions for this to have a sigmoid shape are given. The use of the two curves is illustrated for the relationship between real income and ownership levels for five consumer durables. Copyright 1993 by Blackwell Publishing Ltd