Risk Aversion and the Value of Information

We use household survey data to construct a direct measure of absolute risk aversion based on the maximum price a consumer is willing to pay for a risky security. We relate this measure to consumer's endowments and attributes and to measures of background risk and liquidity constraints. We find that risk aversion is a decreasing function of the endowment—thus rejecting CARA preferences. We estimate the elasticity of risk aversion to consumption at about 0.7, below the unitary value predicted by CRRA utility. We also find that households' attributes are of little help in predicting their degree of risk aversion, which is characterized by massive unexplained heterogeneity. We show that the consumer's environment affects risk aversion. Individuals who are more likely to face income uncertainty or to become liquidity constrained exhibit a higher degree of absolute risk aversion, consistent with recent theories of attitudes toward risk in the presence of uninsurable risks.

Information about traffic conditions has traditionally been conveyed to drivers via radio, variable message signs, and, more recently, the Internet and advanced traveler information systems. This has spurred research on how travelers respond to information, how much they are willing to pay for it, and how much they are likely to benefit from it collectively. In this paper, we analyze the decisions of drivers on whether to acquire information and which routes to take on simple congested road networks. Drivers vary in their degrees of risk aversion with respect to travel time. Four information regimes are considered: no information, free information (publicly available at no cost), costly information (publicly available for a fee), and private information (available free to single individuals). Private information is shown to be individually more valuable than either free or costly information while the benefits from free and costly information cannot be ranked in general. Free or costly information can decrease the expected utility of drivers who are very risk averse; with sufficient risk aversion in the population, the aggregate compensating variation for information can be negative.

Due to the ever-changing and complex market environment, companies frequently face highly uncertain demand where data are so insufficient that the use of random or fuzzy variables, which are typically assumed in the literature, is impractical. Furthermore, companies are often risk-averse when making decisions. To address these two challenges, in this paper, we present the first study on a risk-averse newsvendor problem using the framework of uncertainty theory. To measure risk aversion, we adopt the measure of tail value-at-risk redefined based on uncertainty theory. We are able to analytically derive the optimal order quantity that maximizes the newsvendor's expected utility. We find that the optimal order quantity of a risk-averse newsvendor is less than that of a risk-neutral newsvendor. Furthermore, as the degree of risk aversion increases, the optimal order quantity decreases. Also, we show that the optimal order quantity may be independent of the risk confidence level when the degree of risk aversion is below a threshold. Moreover, we use numerical examples to illustrate how various parameters, such as the degree of risk aversion, salvage value, and unit ordering cost, affect the optimal order quantity.

The expected utility hypothesis predicts that, when the price of insurance is actuarially fair to the consumer, a risk-averse consumer will choose to fully insure against a potential loss. The only role that income can play in affecting the amount of insurance demanded at the actuarially fair price is to affect the size of the potential loss. This result is independent of the consumer's degree of risk aversion or how it varies with income. However, at a price of insurance above or below the actuarially fair level the consumer's degree of risk aversion and its relation to the consumer's income level must be considered if we are to usefully describe consumer behavior.' Mossin [10] showed, for a consumer with declining absolute risk aversion and at a price of insurance above the actuarially fair level but below the price at which no insurance will be purchased, the optimal amount of insurance demanded against a loss of a given size is inversely related to the consumer's income. Chesney and Louberge [2] noted that Mossin's result does not take into account the empirically plausible situation in which higher income consumers may have greater potential losses to insure against. They present results concerning the relationship between risk aversion and the level and composition of income (in terms of the proportion of income subject to loss) and the maximum premium the consumer would be willing to pay for full insurance coverage. Since their results are in terms of the maximum willingness to pay for full insurance,

Chapter 2This chapter examines the extent to which gender differences in risk aversion explain why women have a lower entrepreneurship rate, earn less, and work fewer hours than men. Data from the NLSY79 confirms previous findings that women are more risk averse than men. However, while less risk averse men tend to become self-employed, there is no significant effect of risk aversion on women's entrepreneurship decisions. Similarly, greater risk aversion increases earnings for male entrepreneurs, but it has no effect on female entrepreneurial earnings. More risk aversion lowers female wages, but the effects are of modest magnitude. On the contrary, more risk aversion raises male wages. Risk aversion does not explain variation in hours of work for either men or women. These findings and standard decomposition suggest that widely reported differences in risk aversion across genders play only a trivial role in explaining gender gaps in labor market outcomes.Chapter 3While more risk averse individuals are less likely to become entrepreneurs, theory predicts that more risk averse entrepreneurs pick ventures with higher expected returns and so they should survive in business longer than their less risk averse counterparts. Using successive entry cohorts of young entrepreneurs in the NLSY79, we find contrary to theory that the most successful entrepreneurs are the least risk averse. This surprising finding suggests that commonly used measures of risk aversion are not indicators of taste toward risk. Instead, measured risk aversion signals weak entrepreneurial ability--the least risk averse are apparently those who can best assess and manage risks. Indeed, our interpretation is consistent with recent experimental evidence linking cognitive ability with a greater willingness to accept risk.Chapter 4The fourth chapter investigates the stability of measured risk attitudes over time, using a 13-year longitudinal sample of individuals in the NLSY79. A variance decomposition shows that 57% of the total variance in measured risk aversion is attributable to variation in measured risk aversion within individuals and only 43% to variation across individuals. After removing variation attributable to socioeconomic factors, the proportion of within variance drops to 54%, strongly rejecting the presumption that measured risk attitudes are stable over time. We find that an individual's measured risk aversion changes systematically responding to personal economic circumstances. Measured risk aversion responds to fluctuations in employment: duration of employment spells and out of labor force increases risk aversion whereas length of unemployment spells decreases risk aversion. Previous labor market experience also increases risk aversion. Finally, risk aversion is quadratic in age and net family income with an inverted U-shape. Our analysis shows that measured risk aversion cannot be treated as a fixed attitude toward risk but rather a changing attitude that reflects changes in personal economic circumstances.Chapter 5In Lazear (2005)'s model of entrepreneurship, individuals with more diverse academic and occupational training are more likely to become entrepreneurs, while more narrowly trained individuals become employees. This chapter examines whether Lazear's model can also explain which individuals become nonprofit entrepreneurs. Information on successive cohorts of college graduates from a single university from 1982-2006 show that observed diversity of academic and occupational skills increases the probability of nonprofit sector entrepreneurship, consistent with previous findings of for-profit entrepreneurs. In addition, unobservable talents that increase probability of for-profit startups are positively correlated with the unobservable skills that lead to nonprofit start-ups, consistent with a presumed entrepreneurial skill that underlies the Lazear Jack-of-All-Trades model.

The value of weather forecast information to farmers is an important component of program evaluation of weather information systems. No empirical studies have attempted to provide this kind of information for Canadian producers. In this study, a farm level production economics model was used to characterize the value of precipitation forecast information to alfalfa (Medicago sativa L.) dry hay producers in the province of Ontario. This model was applied to precipitation forecast data from the Windsor and the London Environment Canada weather offices for the crop years of 1994 and 1995. Four forecast methods are compared. Precipitation damage relationships during harvest are estimated using an agronomic simulation model combined with expert opinion. The value of weather forecast information was found to vary considerably between 1994 and 1995. For the region served by the London Ontario weather station, our results indicate that the Environment Canada daily precipitation forecast was worth $30.23 (Cdn)/acre in 1994 and $26.39 (Cdn)/acre in 1995. For the region served by the Waterloo weather station, the 1994 forecast was worth $36.08/acre. In contrast, producers who followed the 1995 forecast would have been worse off by $5.72 (Cdn)/acre relative to what they would have been able to earn by naively assuming that precipitation over the next 4 d would be the same as the last 4 d. The level of risk aversion of the producer was not found to be an important determinant of the value of weather forecast information. Averages of the range of values of weather forecast information obtained in this study indicate that precipitation forecast information is of considerable value to producers at critical times in the production process for alfalfa dry hay. Research Question Weather forecast information has been made available to Canadian farmers at no cost, or for a nominal charge, for many years. Recent budget problems have prompted the federal government as well as most of the provincial governments to review the package of services that they provide. In this context, the value of weather forecast information has come under scrutiny. No estimates of this value are available. This paper reports the findings from an application of a farm level production economics model for characterizing the value of weather forecast information for alfalfa dry hay producers in southern Ontario. Literature Summary The available empirical studies of the value of weather forecast information to farmers have generally used an ex ante or an ex post approach. The ex ante approach generally employs farm surveys or interviews. It attempts to measure what farmers indicate they would be willing to pay for weather forecast information services. The ex post approach generally uses farm decision models based on production economics. These models are used to assess how much better off a representative producer would have been if he had known what the nature of a future weather event, say the amount of precipitation that would fall during the harvest period, was going to be before the decision to begin harvesting was made. Study Description This study uses the ex post approach. A farm decision model that incorporated various levels of aversion to risk was developed. This model was applied to alfalfa dry hay harvest decisions in the face of uncertainty about the timing and amount of precipitation during harvest. Data for two locations in southwestern Ontario for 2 yr were used. Was precipitation forecast information valuable to alfalfa dry hay producers in Ontario? The findings of this study indicated that precipitation forecast information was of considerable value to alfalfa dry hay producers in southwestern Ontario in most of the situations that were considered. For the region served by the London weather station, the estimated value of Environment Canada's precipitation forecast was $30.23 (Cdn)/acre in 1994 and $26.39 (Cdn)/acre in 1995. For the region served by the Waterloo weather station, the estimated value of the precipitation forecast was $35.08 (Cdn)/acre in 1994, but following the forecast would have lost the producer $5.72 (Cdn)/acre in 1995. Does intensity of risk preference matter in deriving a value of weather forecast information? It is often thought that information is more valuable to more risk averse people. It has been demonstrated theoretically, however, that this commonly held intuition is not generally true. So it is an empirical question in any given situation if the value of information varies inversely, directly, or not at all with the level of aversion to risk. We used sensitivity analysis to study the effect of variations in the level of risk aversion, from low to moderate risk aversion, on the value of weather forecast information. We found that this range of risk aversion did not change the estimated value of precipitation forecast information in alfalfa dry hay production in southwestern Ontario.

The need for low-carbon development has become a social consensus. Increasing numbers of enterprises implement carbon emission reduction by using carbon cap-and-trade mechanisms to cater to consumers and practice social responsibility. From the manufacturer’s perspective, they can implement carbon emission reduction investment by themselves or outsource it to the retailer or energy service company (referred as ESCO). To explore the best carbon emission reduction mode selection strategy, we built and compared three carbon emission reduction modes—manufacturer emission reduction, retailer emission reduction, and ESCO emission reduction—by using Stackelberg game models. The joint decisions of operation, finance, and environment were obtained by using the backward induction approach. The impacts of key parameters were analyzed, such as the retailer’s initial capital amount and the decision-makers’ risk aversion degree on the low carbon supply chain operation. Our results show that the optimal carbon emission reduction mode for the manufacturer is changed as the retailer’s initial capital amount changes. Carbon emission reduction by the ESCO (retailer) becomes the dominant strategy for both the economy and environment when the cost advantage (cash investment ratio) of the ESCO (retailer) carbon emission reduction mode is sufficiently high (low). Overall, decision-makers’ risk aversion is detrimental to both the economic and environmental developments of the supply chain. We also designed contracts to realize the coordination of risk-neutral, risk-averse, capital-adequate, and capital-constrained low-carbon supply chains. These results give guidance for decision-makers to better manage the low-carbon supply chain in the context of fully considering the influential factors of risk aversion and capital constraint.

Customer and retailer rebates under risk aversion

Risk aversion and asymmetry in procurement auctions: Identification, estimation and application to construction procurements

Consumers may overestimate the precisions of their valuation predictions. In this paper, we propose a decision model of this overconfidence in valuation and analyze a retailer's advance selling strategy in a two-period setting. The presence of overconfident consumers yields new insights in the retailer's selling strategy. We find that advance selling strategy is not always beneficial to the retailer. The retailer should practice advance selling when the difference of the regular consumers' expected valuation and expected surplus when not buying in advance is no less than a certain threshold. This threshold is weakly decreasing in overconfidence level given the same risk aversion degree, strictly decreasing in consumers' risk aversion degree if overconfidence level is high, and strictly increasing otherwise. When consumers become either more overconfident or risk averse with a high overconfidence level, the retailer becomes more likely to sell in both periods. We also show that, the retailer will set a higher price in the advance selling period in the market with overconfident consumers than that without overconfident consumers when selling in both periods.

Efforts to ensure that funded research represents "value for money" have led to increasing calls for the use of analytic methods in research prioritization. A number of analytic approaches have been proposed to assist research funding decisions, the most prominent of which are value of information (VOI) and prospective payback of research (PPoR). Despite the increasing interest in the topic, there are insufficient VOI and PPoR applications on the same case study to contrast their methods and compare their outcomes. We undertook VOI and PPoR analyses to determine the value of conducting 2 proposed research programs. The application served as a vehicle for identifying differences and similarities between the methods, provided insight into the assumptions and practical requirements of undertaking prospective analyses for research prioritization, and highlighted areas for future research. VOI and PPoR were applied to case studies representing proposals for clinical trials in advanced non-small-cell lung cancer and prostate cancer. Decision models were built to synthesize the evidence available prior to the funding decision. VOI (expected value of perfect and sample information) and PPoR (PATHS model) analyses were undertaken using the developed models. VOI and PPoR results agreed in direction, suggesting that the proposed trials would be cost-effective investments. However, results differed in magnitude, largely due to the way each method conceptualizes the possible outcomes of further research and the implementation of research results in practice. Compared with VOI, PPoR is less complex but requires more assumptions. Although the approaches are not free from limitations, they can provide useful input for research funding decisions.

This article analyzes a dynamic pricing and advertising model for the sale of perishable products under constant absolute risk aversion. We consider a time-dependent version of Gallego and van Ryzin’s dynamic pricing model with exponential demand and include isoelastic advertising effects as well as marginal unit costs. We derive closed-form expressions of the optimal risk-averse pricing and advertising policies of the value function and of the certainty equivalent. The formulas provide insight into the (complex) interplay between risk-sensitive pricing and advertising decisions. Moreover, to evaluate the optimally controlled sales process over time we propose efficient simulation techniques. These are used to analyze the characteristics of different degrees of risk aversion, particularly the concentration of the profit distribution and the impact on the expected evolution of price and advertising rates.

This paper studies the budget-constrained newsvendor problem under risk aversion with financing service and builds a two-stage supply chain decision model on the order quantity and wholesale price. The budget-constrained retailer as a newsvendor faces a nonnegative random demand and the financial institution provides the loan service for the retailer who is risk-averse. This paper first explores the impact of risk aversion on the decisions in financial supply chain. Different from the existing research, we analyze how the financing service of bank loan impacts the risk-averse newsvendor’s decision and how the risk-averse behavior of the retailer influences the optimal strategies in supply chain with CVaR risk measure criterion. It is found that the order quantity decreases in the degree of risk aversion. The optimal order quantity is decreasing in initial budget, wholesale price, and interest rate. It is worth noting that the financing service can improve the profit of the supply chain system when the retailer has a low initial wealth. Finally, to compare with the existing results the theoretical analysis and numerical examples are also illustrated.

Risk aversion typically erodes the value of an investment opportunity, often increasing the incentive to delay investment. Although this may be true when the decision maker has discretion only over the timing of investment, any additional discretion over the capacity of a project may lead to different results. In this paper, we extend the traditional real options approach by allowing for discretion over capacity while incorporating risk aversion and operational flexibility in the form of suspension and resumption options. In contrast to a project without scalable capacity, we find that increased risk aversion may actually facilitate investment because it decreases the optimal capacity of the project. Finally, we illustrate how the relative loss in the value of the investment opportunity due to an incorrect capacity choice may become less pronounced with increasing risk aversion and uncertainty.

This article considers an agricultural production model of sequential nitrogen application under risk. Because of random shocks between subsequent production stages, optimal fertilization decisions depend on the magnitude of farmers' risk aversion (risk premium), and the possibility for farmers to process information (value of information). We propose a joint estimation procedure of technology and risk aversion parameters, using a structural, simulation‐based econometric procedure. Parameter estimates allow to compute both the value of information and the risk premium, which account for about 30% of fertilizer cost for Midwest corn producers.