representing each type of risk aversion are considered and then some of MS functions that
have been adopted such as the linear mean-variance (LMV) model and the linear
mean-standard deviation (LMS) model are discussed in the context of LS condition. Thirdly,
an attempt is made to specify MS function so that it nests several types of risk aversion under
the LS condition. The flexible MS function proposed in this study provides an alternative
interpretation of the nonlinear mean-standard deviation (NLMS) model. Finally, the
implication to the empirical approach “joint analysis of risk preference structure and
technology” is discussed.
Preliminary discussion
In this section, the full set of conditions that MS function has to satisfy under LS condition is
prepared for the upcoming sections. The important thing that we have to be aware of when
we consider the specification problem is that the MS framework established by Sinn (1983)
and Meyer (1987) is by nature an EU theory (more precisely, a special case of EU theory) and
utterly relies upon the EU-based analytical tools. For example, the definition of risk aversion
and the degree of risk aversion are exactly those of EU theory. In other words, the theoretical
fundamentals and the analytical tools of EU theory impose restrictions on the MS function.
The sources of restrictions this study focuses on are categorized into three kinds, which are,
(a) cardinal property of vNM utility function, (b) behavioral hypotheses that are translated
from EU theory to MS approach, and (c) relationship between Arrow-Pratt's risk aversion
measures.
Firstly, the existence of vNM utility, the core of EU theory, is guaranteed by von
Neumann and Morgenstern’s axioms, which implies that the utility is cardinal function that is
transformable only by a positive linear function. This cardinal property is transformed into
the MS approach in a straightforward manner. Suppose that under some condition on vNM
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