Estimating the reference frame: A smooth twice-differentiable utility function for non-compensatory loss-averse decision-making

Since the introduction of prospect theory, reference-dependence and loss-aversion have become widely acknowledged as important elements affecting decision-making. Nevertheless, establishing and determining reference frames are not extensively analyzed in the literature; rather, in most applications, it is simply assumed that the reference frames can be represented through the status quo. This assumption, however, may lead to biased results, as not only the status quo affects reference frames, but also previous experiences or expectations, among many others. Therefore, it would be more appropriate to estimate the reference frame directly as an unobserved latent variable. Unfortunately, current utility functions utilized to depict this kind of behavior are not useful for this purpose, as they are defined piecewise. This work proposes a smooth twice-differentiable utility function that indeed allows estimating reference frames. Further, this function satisfies all major properties of prospect theory. Finally, the approach is tested relying on three case studies. They show that in the context of semi-compensatory loss-averted decision-making reference frames may diverge from the status quo.