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Theory and Decision

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01.02.2014

Stronger utility

verfasst von: Pavlo R. Blavatskyy

Erschienen in: Theory and Decision | Ausgabe 2/2014

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Abstract

Empirical research often requires a method how to convert a deterministic economic theory into an econometric model. A popular method is to add a random error term on the utility scale. This method, however, ignores stochastic dominance. A modification of this method is proposed to account for stochastic dominance. The modified model compares favorably to other existing models in terms of goodness of fit to experimental data. The modified model can rationalize the preference reversal phenomenon. An intuitive axiomatic characterization of the modified model is provided. Important microeconomic concept of risk aversion is well defined in the modified model.

Vorheriger Artikel Motivation and mission in the public sector: evidence from the World Values Survey

Nächster Artikel Decreasing higher-order absolute risk aversion and higher-degree stochastic dominance

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See Camerer (1989), Starmer and Sugden (1989), Hey and Orme (1994), Wu (1994), Ballinger and Wilcox (1997), Loomes and Sugden (1998), Hey (2001), Schmidt and Hey (2004), Schmidt and Neugebauer (2007).

If a decision maker has a strict preference over all outcomes (for any \(x, y \in X\) either \(x\succ y\) or \(y \succ x\)), then the second case is possible only when \(L = L^{\prime }\).

Alternatively, choice probability may be left undefined in this case.

Setting \(F(1) = 1\) is appealing on normative grounds. From a descriptive perspective, it may be desirable to set \(F (1)< 1\). This allows model (10) to account for rare violations of stochastic dominance that are observed in the data. See Loomes et al. (2002) for a more detailed discussion.

Note that Fishburn (1978) model with a power function coincides with Blavatskyy (2011a) model with a function \(\varphi (v)= v ^{\mu }\) for all \(v \ge 0\).

See also graphical representation in MacCrimmon and Smith (1986) and Butler and Loomes (2007).

This special case may be considered as nearly conventional economic theory based on a revealed preference relation: \(L^{\prime }\succsim L\) when \(P (L, L^{\prime })=0\), \(L\succsim L^{\prime }\) when \(P (L,L^{\prime })=1\), and \(L \sim L^{\prime }\) when \(P (L, L^{\prime }) = 0.5\). This is “nearly conventional” because in standard economic theory a choice probability \(P (L, L^{\prime }\)) is not defined when \(L \sim L^{\prime }\).

A popular class of QRE is logit QRE, which is based on model (6) with error term \(\xi \) drawn from the logistic distribution. This specification of strong utility is sometimes called Luce’s choice model (cf. Luce (1959).

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Titel: Stronger utility
verfasst von: Pavlo R. Blavatskyy
Publikationsdatum: 01.02.2014
Verlag: Springer US
Erschienen in: Theory and Decision / Ausgabe 2/2014
Print ISSN: 0040-5833
Elektronische ISSN: 1573-7187
DOI: https://doi.org/10.1007/s11238-013-9366-3

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