Estimate Risk Preferences Research Articles

Efficient learning of decision-making models: A penalty block coordinate descent algorithm for data-driven inverse optimization

Decision-making problems are commonly formulated as optimization problems, which are then solved to make optimal decisions. In this work, we consider the inverse problem where we use prior decision data to uncover the underlying decision-making process in the form of a mathematical optimization model. This statistical learning problem is referred to as data-driven inverse optimization. We focus on problems where the underlying decision-making process is modeled as a convex optimization problem whose parameters are unknown. We formulate the inverse optimization problem as a bilevel program and propose an efficient block coordinate descent-based algorithm to solve large problem instances. Numerical experiments on synthetic datasets demonstrate the computational advantage of our method compared to standard commercial solvers. Moreover, the real-world utility of the proposed approach is highlighted through two realistic case studies in which we consider estimating risk preferences and learning local constraint parameters of agents in a multiplayer Nash bargaining game.

Estimating risk preferences integrating insurance choices with subjective beliefs

This paper combines real-world decisions with experimental elicitations to estimate risk preferences by incorporating individuals’ subjective beliefs in the analysis of insurance data. Unlike most studies estimating risk preferences “in the field”, we refrain from making specific assumptions regarding expectations; rather, we elicit them directly from the respondents. This approach yields risk aversion estimates compatible with a variety of deviations from rational expectations, such as biased subjective risk perceptions. Our results reveal that agents tend to overestimate the probability of recent rare events happening again in the recent future, and that the standard assumption of rational beliefs can lead to biased estimates and policy recommendations. Our empirical application offers new insights into the current debate on crop insurance subsidies. Correcting biased beliefs appears to be an effective strategy to reduce government support and, at the same time, maintain a high level of enrollment.

The statistical power of individual-level risk preference estimation

Accurately estimating risk preferences is of critical importance when evaluating data from many economic experiments or strategic interactions. I use a simulation model to conduct power analyses over two lottery batteries designed to classify individual subjects as being best explained by one of a number of alternative specifications of risk preference models. I propose a case in which there are only two possible alternatives for classification and find that the statistical methods used to classify subjects result in type I and type II errors at rates far beyond traditionally acceptable levels. These results suggest that subjects in experiments must make significantly more choices, or that traditional lottery pair batteries need to be substantially redesigned to make accurate inferences about the risk preference models that characterize a subject’s choices.

Effects of Household Shocks on Risk Preferences and Loss Aversion: Evidence from Upland Smallholders of South East Asia

Avoiding risk in financial decisions is credited to be a key contributor to persistent poverty and poverty traps. In spite of this, the methods used to measure behaviour under risk rarely reflect an adequate representation of the lives of smallholders in low income economies. We estimate risk preferences and their determinants by including two key aspects: aversion to losses and exposure to long term risk and vulnerability. We examine risk preferences of 93 smallholders in Cambodia and 91 smallholders in Lao PDR with an incentivised lottery design under the framework of Expected Utility Theory (EUT), Rank Dependent Utility Theory (RDU) and Cumulative Prospect Theory (CPT). We find that CPT best explains our data, but parameter values vary to those most commonly found in the literature. We report that the experience of household shocks have a significant effect on choice behaviour in the loss domain, even when we control for a large set of socio-economic and demographic variables.

Measuring and Controlling for the Compromise Effect When Estimating Risk Preference Parameters.

The compromise effect arises when being close to the "middle" of a choice set makes an option more appealing. The compromise effect poses conceptual and practical problems for economic research: by influencing choices, it can bias researchers' inferences about preference parameters. To study this bias, we conduct an experiment with 550 participants who made choices over lotteries from multiple price lists (MPLs). Following prior work, we manipulate the compromise effect to influence choices by varying the middle options of each MPL. We then estimate risk preferences using a discrete-choice model without a compromise effect embedded in the model. As anticipated, the resulting risk preference parameter estimates are not robust, changing as the compromise effect is manipulated. To disentangle risk preference parameters from the compromise effect and to measure the strength of the compromise effect, we augment our discrete-choice model with additional parameters that represent a rising penalty for expressing an indifference point further from the middle of the ordered MPL. Using this method, we estimate an economically significant magnitude for the compromise effect and generate robust estimates of risk preference parameters that are no longer sensitive to compromise-effect manipulations.

Probability distortion, asset prices, and economic growth

In this paper, we link 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 (CPT) 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.

Efficient Estimation of Risk Preferences

AbstractRisk and the risk attitude of agents are two fundamental elements of decision making under risk and uncertainty. Recent developments in risk and risk preference analyses have raised questions on conventional approaches to estimating risk preferences. This study proposes an estimation procedure that employs a seminonparametric estimator to estimate the density function of risk without imposing distributional assumptions, as well as a numerical integration method to construct closed‐form expressions of conditional moment conditions for efficient estimation. The method achieves a substantial efficiency improvement relative to the conventional GMM approach in Monte Carlo simulations. The proposed approach is general and applies to the estimation of behavioral choice models under risk, or models that require expectation operations and closed‐form equations for estimation.

Children’s rationality, risk attitudes and field behavior

We investigate the relationship between risk attitudes, choice consistency and field behavior of children by conducting economic experiments with 1275 8th graders. Choices are not completely consistent with any of the economic theories we consider, however, they are not random either. We use our experimental data to structurally estimate risk preferences and correct for decision error. Using a measure constructed from the estimates and individual choices, we find that risk preferences do predict future field behavior. Children who are more risk averse are less likely to receive disciplinary referrals one and two years after the experiment and are more likely to complete high school, even controlling for economic rationality, family background, scholarly achievement and past misbehavior. Accounting for decision error turns out to be important as a simple aggregate measure of risk is not found to be correlated with field behavior.

A dual theory approach to estimating risk preferences in the parimutuel betting market

This paper introduces an alternative empirical approach to estimating risk preferences in the parimutuel betting market using a dual theory model which is amended to include bettors’ misperceptions of probabilities. We replicate previous empirical results and test our alternative empirical approach using parimutuel horse race betting data. Our results suggest that while bettors are risk-averse, they are also prone to misperceiving probabilities by overweighting low probabilities and underweighting high probabilities. As an application, these results replicate the choice patterns consistent with the Allais paradox.

Are You What You Eat? Healthy Behaviour and Risk Preferences

Abstract: We elicit and estimate risk preferences for a pool of young adults in the UK, and explore their links with healthy eating and risky health behaviours. We construct the Healthy Eating Index (HEI) as an overall indicator of nutritional quality, and we use it to complement the body mass index BMI. While for females we find no significant association between the BMI and risk preferences, males with high BMI appear more risk-seeking. However, this association disappears when controlling for the quality of the diet. For males, the HEI is significantly associated with risk preferences. Males smoking status is not associated with risk preferences.

Estimating Risk Preferences in the Field

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. ( JEL C51, D11, D81, D82, D83, G22, I13)

Controlling for the Compromise Effect Debiases Estimates of Risk Preference Parameters

The compromise effect arises when options near the of a choice set are more appealing. The compromise effect poses conceptual and practical problems for economic research: by influencing choices, it distorts revealed preferences, biasing researchers' inferences about deep (i.e., domain general) preferences. We propose and estimate an econometric model that disentangles and identifies both deep preferences and the context-dependent compromise effect. We demonstrate our method using data from an experiment with 550 participants who made choices over lotteries from multiple price lists. Following prior work, we manipulate the compromise effect by varying the middle options of each multiple price list and then estimate risk preferences without modelling the compromise effect. These naive parameter estimates are not robust: they change as the compromise effect is manipulated. To eliminate this bias, we incorporate the compromise effect directly into our econometric model. We show that this method generates robust estimates of risk preference parameters that are no longer sensitive to compromise-effect manipulations. This method can be applied to other settings that exhibit the compromise effect.

Estimating risk preferences of bettors with different bet sizes

We extend the literature on risk preferences of a representative bettor by including odds-dependent bet sizes in our estimations. Accounting for different bet sizes largely reduces the standard errors of all coefficients. Substituting the coefficients from the model with equal bet sizes into the model with odds-dependent sizes leads to a sharp decline in the likelihood which shows that accounting for different amounts is important. Our estimations strongly reject the hypothesis that the overbetting of outcomes with low probabilities (favorite-longshot bias) can be explained by risk-seeking bettors. Depending on the exact specification within cumulative prospect theory, the data can best be described by an overweighting of small probabilities which is more pronounced in the gain domain. Models allowing for two parameters for probability weighting each in the gain- and in the loss domain are superior.

Controlling for the Compromise Effect Debiases Estimates of Risk Preference Parameters

The compromise effect arises when options near the of a choice set are more appealing. The compromise effect poses conceptual and practical problems for economic research: by influencing choices, it distorts revealed preferences, biasing researchers' inferences about deep (i.e., domain general) preferences. We propose and estimate an econometric model that disentangles and identifies both deep preferences and the context-dependent compromise effect. We demonstrate our method using data from an experiment with 550 participants who made choices over lotteries from multiple price lists. Following prior work, we manipulate the compromise effect by varying the middle options of each multiple price list and then estimate risk preferences without modelling the compromise effect. These naive parameter estimates are not robust: they change as the compromise effect is manipulated. To eliminate this bias, we incorporate the compromise effect directly into our econometric model. We show that this method generates robust estimates of risk preference parameters that are no longer sensitive to compromise-effect manipulations. This method can be applied to other settings that exhibit the compromise effect.

Judging statistical models of individual decision making under risk using in- and out-of-sample criteria.

Despite the fact that conceptual models of individual decision making under risk are deterministic, attempts to econometrically estimate risk preferences require some assumption about the stochastic nature of choice. Unfortunately, the consequences of making different assumptions are, at present, unclear. In this paper, we compare three popular error specifications (Fechner, contextual utility, and Luce error) for three different preference functionals (expected utility, rank-dependent utility, and a mixture of those two) using in- and out-of-sample selection criteria. We find drastically different inferences about structural risk preferences across the competing functionals and error specifications. Expected utility theory is least affected by the selection of the error specification. A mixture model combining the two conceptual models assuming contextual utility provides the best fit of the data both in- and out-of-sample.

Estimating risk preferences in the presence of bifurcated wealth dynamics: can we identify static risk aversion amidst dynamic risk responses?

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. , Oxford University Press.

Estimating Risk Preferences in the Presence of Bifurcated Wealth Dynamics: Do We Misattribute Dynamic Risk Responses to Static Risk Aversion?

Estimating risk preferences is tricky because controlling for confounding factors is difficult. Omitting or imperfectly controlling for these factors can attribute too much observable behavior to risk aversion and bias estimated preferences. Agents often modify risky decisions in response to dynamic wealth or asset thresholds, where they 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. Joint estimation of risk preferences and wealth dynamics may remedy the problem, but can be empirically challenging.

The story of the moment: risk averse cypriot farmers respond to drought management

This article illustrates the importance of estimating risk preferences when evaluating water policy. Using agricultural production data from the Kiti region of Cyprus we estimate farmers’ risk preferences à la Antle (Journal of Business and Economic Statistics, 1, 192–201, 1983, American Journal of Agricultural Economics, 69, 509–22, 1987) and show sensitivity to higher order moments of profit, such as skewness. We show that farmers in the Kiti region are risk averse with risk premiums in the region of 20% of expected profit. We use these estimates to analyse the impact of a water quota from the perspective of three policy-makers who differ only in their understanding of farmers’ risk preferences. We show in the case of Kiti that policy-makers who model risk preferences incorrectly, that is, either; (a) assume risk neutrality or; (b) ignore down-side risk, wrongly predict the magnitude and direction of input responses and therefore the magnitude of welfare changes. This highlights the importance of accommodating preferences for higher order moments of profit in the evaluation of water policy.

Estimating Risk Preferences from Deductible Choice

We develop a structural econometric model to estimate risk preferences from data on deductible choices in auto insurance contracts. We account for adverse selection by modeling unobserved heterogeneity in both risk (claim rate) and risk aversion. We find large and skewed heterogeneity in risk attitudes. In addition, women are more risk averse than men, risk aversion exhibits a U-shape with respect to age, and proxies for income and wealth are positively associated with absolute risk aversion. Finally, unobserved heterogeneity in risk aversion is greater than that of risk, and, as we illustrate, has important implications for insurance pricing. (JEL D81, G22)

Empirical Estimation and Use of Risk Preferences: An Appraisal of Estimation Methods That Use Actual Economic Decisions

The topic addressed in this paper concerns the conceptual basis, estimation procedures, and resources required for implementation of methods for estimating risk preferences by observing behavior. An attempt is made to review and appraise previous literature as well as to explore some alternative approaches. To begin, it is important to contrast four general types of empirical settings of interest. These are micro (farm level), macro (market or other aggregations), descriptive (positivistic), and prescriptive (normative) studies. The prescriptive, or conditionally normative, studies seemingly have dominated agricultural economic studies of risk. These generally have been micro in nature and have focused on