Arbitrary inflation in fractional models

The analysis of subjective probabilities, that are fractional or share variables by definition, is becoming increasingly widespread in both economics and the social sciences in general. To avoid nonsensical predictions, empirical predictions for such variables must respect the fact that they are necessarily bounded on the 0 − 1 (or, 0 − 100, for percentage-type responses) interval. In addition, where the response variable of interest corresponds to a self-report on a fixed scale, individuals are often drawn to particular focal-point responses, resulting in distinct spikes in the empirical distribution. In this paper, we suggest a simple model that accounts for all of the nuances of such data, including its fractional and bounded nature as well as arbitrary inflation at such focal-points (which may appear at any point in the interval and are highly likely at the endpoints). We estimate our model using data drawn from the Italian Survey of Income and Wealth relating to an individual’s subjective marginal propensity to consume (MPC).