Learning Explanation of Prospect Theory
Why are people risk averse for gains and risk seeking for losses? Why does reactions to risk depend on a comparison to a reference level? Is the explanation to be found in Neuroscience? If so, why are similar results observed in data on firm performance?
In a paper published in Psychological Review 2015 I suggested that there is a simple alternative explanation of reference-dependent risk taking behavior; an explanation that emphasizes learning processes. I argue that behavior that seems to reflect an 's-shaped value' function may result from an algorithm that tries to make accurate predictions. The idea is that a s-shaped reference-dependent value function may reflect inferences about the reliability of observations: extreme observations are weighted less in predictions because they are believed to be less reliable.
If this theory is correct, then it implies that weighting outcomes according to the prospect theory value function might be functional in the in the sense that it leads accurate predictions about future values. So, in any setting where individuals or firms have learned to discount variable observations, reference dependent risk taking behavior will be observed and will also work well in the sense of predicting future expected values well. I test this hypothesis using data on corporate profitability, restaurant reviews, and citations. In each data set I examine how to weigh past outcomes to accurately predict future outcomes. The results show that combining past outcomes using an s-shaped value-function similar to that proposed by Kahneman and Tversky (1979) results in more accurate predictions than other linear and non-linear weighting schemes. These empirical results show that even a risk neutral individual who decides about which firm to invest in or what restaurant to visit based on data on past outcomes will behave as if she had an s-shaped value function. The theory also offers a simple explanation of the asymmetric effect of past corporate performance on future risk taking.
Abstract: Existing explanations of reference dependent risk sensitivity attribute it to cognitive imperfections and heuristic choice processes. This paper shows that behavior consistent with an s-shaped value function could be an implication of rational inferences about the expected values of alternatives. Theoretically, I demonstrate that even a risk neutral Bayesian decision maker, who is uncertain about the reliability of observations, should use variability in observed outcomes as a predictor of low expected value for outcomes above a reference level and as a predictor of high expected value for outcomes below a reference level. Empirically, I show that combining past outcomes using an s-shaped value function leads to accurate predictions about future values. The theory also offers a rationale for why risk sensitivity consistent with an inverse s-shaped value function should occur in experiments on decisions from experience with binary payoff distributions.