Estimating Preferences Toward Risk

What do investor utility functions look like? We show how returns on a stock and prices of call options written on that stock can be used jointly to recover utility of wealth function of the marginal investor in the stock. We study whether non-standard preferences have an impact sufficiently large that it is present in the stock prices. Using options on the stocks in the Dow Jones Index, we show support for non-concave utility functions with reference points proposed by Kahneman and Tversky, Friedman and Savage, and Markowitz. The evidence for Kahneman and Tversky Prospect Theory value function, and Friedman and Savage and Markowitz utility functions is much stronger than the support for the standard concave utility function. Together the utility functions with convex regions and with reference points account for 80% of the market capitalization of the sample stocks. This is the first study to report findings of these utility functions using the prices of individual stocks (nonexperimental data). We also investigate a closely related question of whether different assets reflect different risk preferences. We find evidence showing that different stocks reflect different types of investor utility function.

"We use a large data set of deductible choices in auto insurance contracts to estimate the distribution of risk preferences in our sample. To do so, we develop a structural econometric model, which accounts for adverse selection by allowing for unobserved heterogeneity in both risk (probability of an accident) and risk aversion. Ex-post claim information separately identifies the marginal distribution of risk, while the joint distribution of risk and risk aversion is identified by the deductible choice. We find that individuals in our sample have on average an estimated absolute risk aversion which is higher than other estimates found in the literature. Using annual income as a measure of wealth, we find an average two-digit coefficient of relative risk aversion. We also find that women tend to be more risk averse than men, that proxies for income and wealth are positively related to absolute risk aversion, that unobserved heterogeneity in risk preferences is higher relative to that of risk, and that unobserved risk is positively correlated with unobserved risk aversion. Finally, we use our results for counterfactual exercises that assess the profitability of insurance contracts under various assumptions"--National Bureau of Economic Research web site.

We survey the literature on estimating risk preferences using field data. We concentrate our attention on studies in which risk preferences are the focal object and estimating their structure is the core enterprise. We review a number of models of risk preferences -- including both expected utility (EU) theory and non-EU models -- that have been estimated using field data, and we highlight issues related to identification and estimation of such models using field data. We then survey the literature, giving separate treatment to research that uses individual-level data (e.g., property insurance data) and research that uses aggregate data (e.g., betting market data). We conclude by discussing directions for future research.

This document is an introduction, for non-economists, to standard and behavioral economic theories of risk and uncertainty. It describes some broadly-accepted results in economics that are determinant in decision-making under risk or uncertainty and in situations where we have to deal with losses and gains. To illustrate this point, the document presents a selection of theoretical results, ponctuated with examples taken from everyday life, and research studies in economics and psychology on the perception of risk.

In this paper, we estimate a rich model of college major choice using a panel of experimentally-derived data. Our estimation strategy combines two types of data: data on self-reported beliefs about future earnings from potential human capital decisions and survey-based measures of risk and time preferences. We show how to use these data to identify a general life-cycle model, allowing for rich patterns of heterogeneous beliefs and preferences. Our data allow us to separate perceptions about the degree of risk or perceptions about the current versus future payoffs for a choice from the individual's preference for risk and patience. Comparing our estimates of the general model to estimates of models which ignore heterogeneity in risk and time preferences, we find that these restricted models are likely to overstate the importance of earnings to major choice. Additionally, we show that while men are less risk averse and patient than women, gender differences in expectations about own-earnings, risk aversion, and patience cannot explain gender gaps in major choice.

We present a method that dynamically designs elicitation questions for estimating risk and time preference parameters. Typically these parameters are elicited by presenting decision makers with a series of static choices between alternatives, gambles, or delayed payments. The proposed method dynamically (i.e., adaptively) designs such choices to optimize the information provided by each choice, while leveraging the distribution of the parameters across decision makers (heterogeneity) and capturing response error. We explore the convergence and the validity of our approach using simulations. The simulations suggest that the proposed method recovers true parameter values well under various circumstances. We then use an online experiment to compare our approach to a standard one used in the literature that requires comparable task completion time. We assess predictive accuracy in an out-of-sample task and completion time for both methods. For risk preferences, our results indicate that the proposed method predicts subjects' willingness to pay for a set of out-of-sample gambles significantly more accurately, while taking respondents about the same time to complete. For time preferences, both methods predict out-of-sample preferences equally well, while the proposed method takes significantly less completion time. For risk and time preferences, average completion time for our approach is approximately three minutes. Finally, we briefly review three applications that used the proposed methodology with various populations, and we discuss the potential benefits of the proposed methodology for research and practice.

This article deals with specification and estimation of risk preferences, production risk, and technical inefficiency. It makes contribution in three separate areas of production economics. First, we model producers' attitude toward risk and derive risk preference functions (without assuming any parametric form of the utility function and any distribution of the error term representing production risk) when risk arises from production uncertainty and technical inefficiency. Second, the standard production risk model is extended to accommodate technical inefficiency and producers' attitude toward risk. Finally, the technical efficiency model is generalized to accommodate production risk and producers' attitude toward risk.

Estimating risk preferences is tricky because controlling for confounding factors is difficult. Omitting or imperfectly controlling for these factors can attribute too much observable behaviour to risk aversion and bias estimated preferences. Agents often modify risky decisions in response to dynamic wealth or asset thresholds, where such thresholds exist. Ignoring this dynamic risk response introduces an attribution bias in static estimates of risk aversion. We demonstrate this pitfall using a simple model and a Monte Carlo simulation to explore the implications of this problem for empirical estimation. While an approach that jointly estimates risk preferences and wealth dynamics may remedy the problem by extracting dynamic risk responses from observed behaviour, it is likely to be challenging to implement in broader empirical settings for reasons we discuss.