Behavioural Economics

Weak Rank Dependent Utility and Risk Tradeoffs in Virtual Gain-Loss State Space (in progress)

There is no reason why probability weighting functions should be singled out in rank dependent utility theory for transformation into linear decision weights. In this paper, a splitting utility function over the distribution of ranked outcomes in an arbitrary choice set treats each outcome as a candidate reference point. This virtual change of coordinates induces a virtual gain-loss state space with a sense of loss for outcomes that are less preferred to the candidate reference outcome, and a sense of gain for more preferred outcomes. The reference dependent utility function induced by this set splitting process has many nonconvexities of the Friedman-Savage-Markowitz type. The weak rank dependent utility (WRDU) model, first introduced by Charles-Cadogan (2016) with one parameter extra compared to expected utility theory (EUT), generates inner (stochastic) and outer (deterministic) measures of loss aversion based on tradeoffs in risk. We construct a risk tradeoff matrix operator that transforms risk into perceptions of risk in the virtual gain-loss states. WRDU application to Holt-Laury (HL) multiple price list experiment data for safe lottery A, and risky lotttery B, shows that as candidate reference points run through the data, decision makers (DMs) engage in switching behaviour, within and between lotteries, for lottery pairs tradeoff when the virtual loss aversion (VLA) index associated with a simple lottery is greater than that for another within safe A or risky B or between safe A and risky B. The transitivity axiom is frequently violated, most switching behaviour occurs during risk seeking, and the least amount of switching occurs for stochastic measures of VLA.WRDU risk tradeoff operator has complex valued eigenvalues and it is almost periodic in the short run. It is asymptotically stable in steady state, where no switching occurs within safe A, and only one switch occurs in phase transition from safe A to risky B as predicted by theory. Furthermore, switching in the Holt-Laury MPL is caused by violation of second order stochastic dominance. SLIDES

Losses loom larger than gains and reference dependent preferences in Bernoulli's utility function JEBO, 2018, 154:220-237

Some analysts claim that Bernoulli's utility function is "reference-independent", so it is not able to generate a loss aversion index, and that the theoretical framework of Prospect Theory (PT) is required to achieve those results. This paper examines that claim and finds that the geometry of Bernoulli's original utility function specification either explains or implies key elements of PT: reference dependence and a loss aversion index. Theory and evidence show that the loss aversion index constructed from reference wealth in Bernoulli's utility specification is in the domain of attraction of a stable law. That is, its distribution is a slow varying function with a fat tail that decays like a power law. Additionally, the index can be tested with a modified Fisher z-transform test. Bernoulli`s utility function also sheds light on why loss aversion may be over-estimated under PT. In a nutshell, Bernoulli's utility function is alive and well.

Estimation and Inference for Loss Aversion in Cross Sectional Regressions of Happiness and Consumption on Economic Growth

We introduce an econometric test for mimicking myopic loss aversion (MMLA) to decline in standard of living, and correct for simultaneity bias in cross sectional regressions of subjective well-being (SWB) and happiness on economic growth. We show that extant models overestimate the impact of economic growth on SWB, and inference and policies based on those models may be misdirected. Our theory predicts clientele effects in risk attitudes toward growth, and we show how to recover consistent estimates of the MMLA index from cross sectional regressions on SWB with an identifying restriction on MLA. The asymptotic distribution of the MMLA index estimator is in the domain of attraction of a stable law. In particular, we show how location and scale parameters of a Lévy distribution can be used to extract an MLA index from data. We apply our theory to data from a published metastudy on loss aversion index, and our own metastudy of consumption, SWB and happiness data around the world. The theory is upheld in each case. Metastudy data support our stable law prediction, while our recovered MMLA index estimates are consistent with those reported in the behavioural and experimental economics literature. We find that high income countries have higher MMLA indexes than low income countries so they are more likely to report decline in SWB for a fall in income. Whereas, aggregation bias masks large disparities in MMLA index estimates within countries. slides and RES2018-Special-session