Paradoxes, prices, and preferences : essays on decision making under risk and economic outcomes

Abstract

This doctoral thesis contains three theoretical essays on the predictive power of leading descriptive decision theories and one empirical essay on the impact of stock market investors’ probability distortion on future economic growth. Chapter 1 provides an extensive summary and motivation of all essays. The first essay (Chapter 2, co-authored with Maik Dierkes) shows that Cumulative Prospect Theory cannot explain both the St. Petersburg paradox and the common ratio version of the Allais paradox simultaneously if probability weighting and value functions are continuous. This result holds independently of parametrizations of the value and probability weighting function. Using both paradoxes as litmus tests, Cumulative Prospect Theory with the majority of popular weighting functions loses its superior predictive power over Expected Utility Theory. However, neo-additive weighting functions (which are discontinuous) do solve the Allais - St. Petersburg conflict. The second essay in Chapter 3 (co-authored with Maik Dierkes) shows that Salience Theory explains both a low willingness to pay, for example $7.86 ($12.33), for playing the St. Petersburg lottery truncated at around $1 million ($1 trillion) and reasonable preference reversal probabilities around 0.33 in Allais’ common ratio paradox. Typical calibrations of other prominent theories (for example, Cumulative Prospect Theory or Expected Utility Theory) cannot solve both paradoxes simultaneously. With unbounded payoffs, however, Salience Theory’s ranking-based probability distortion prevents such a solution - regardless of parametrizations. Furthermore, the probability distortion in Salience Theory can be significantly stronger than in Cumulative Prospect Theory, fully overriding the value function’s risk attitude. The third essay in Chapter 4 (co-authored with Maik Dierkes) proves that subproportionality as a property of the probability weighting function alone does not automatically imply the common ratio effect in the framework of Cumulative Prospect Theory. Specifically, the issue occurs in the case of equal-mean lotteries because both risk-averse and risk-seeking behavior have to be predicted there. As a solution, we propose three simple properties of the probability weighting function which are sufficient to accommodate the empirical evidence of the common ratio effect for equal-mean lotteries for any S-shaped value function. These are (1) subproportionality, (2) indistinguishability of small probabilities, and (3) an intersection point with the diagonal lower than 0.5. While subproportionality and a fixed point lower than 0.5 are common assumptions in the literature, the property indistinguishability of small probabilities is introduced for the first time. The ratio of decision weights for infinitesimally small probabilities characterizes indistinguishability and is also an informative measure for the curvature of the probability weighting function at zero. The intuition behind indistinguishability is that, even though the ratio of probabilities stays constant at a moderate level, individuals tend to neglect this relative difference when probabilities get smaller. Finally, the fourth essay in Chapter 5 (co-authored with Maik Dierkes and Stephan Germer) links stock market investors’ probability distortion to future economic growth. The empirical challenge is to quantify the optimality of today’s decision making to test for its impact on future economic growth. Fortunately, risk preferences can be estimated from stock markets. Using monthly aggregate stock prices from 1926 to 2015, we estimate risk preferences via an asset pricing model with Cumulative Prospect Theory agents and distill a recently proposed probability distortion index. This index negatively predicts GDP growth in-sample and out-of-sample. Predictability is stronger and more reliable over longer horizons. Our results suggest that distorted asset prices may lead to significant welfare losses.