Gain-loss Utility Research Articles

How Much to Work: Evidence of Reference Dependence in Taxi Drivers

This paper presents new evidence of labor supply behavior consistent with workers having reference points in daily income. Moreover, consistent with a model of gain-loss utility, I find that workers with flexible labor supply exhibit increasing marginal utility in income over the loss region and diminishing marginal utility in income over the gain region. The setting is taxi drivers, a group which faces a substantial degree of uncertainty in their hourly earnings but control over when to stop working within a shift. Previous papers studying taxi drivers have found mixed evidence for reference dependent behavior. Using a driver's propensity to stop working within a shift, I show not only the existence of a reference point in a large proportion of drivers, but I am also able to estimate what the reference point is without explicit functional form or ex ante assumptions about existence. Furthermore, I show that drivers are less likely to stop working the closer they are to their reference point, indicating their preferences for daily income have a Prospect theoretic S-shape.

Why you Can’t Find a Taxi in the Rain and Other Labor Supply Lessons from Cab Drivers*

Abstract I replicate and extend the seminal work of Camerer et al. (“Labor Supply of New York City Cabdrivers: One Day at a Time,” Quarterly Journal of Economics, 112 [1997], 407–441), who find that the wage elasticity of daily hours of work for New York City taxi drivers is negative and conclude that their labor supply behavior is consistent with reference dependence. In contrast, my analysis of the complete record of all trips taken in NYC taxi cabs from 2009 to 2013 shows that drivers tend to respond positively to unanticipated as well as anticipated increases in earnings opportunities. Additionally, using a discrete choice stopping model, the probability of a shift ending is strongly positively related to hours worked but at best weakly related to income earned. I find substantial heterogeneity across drivers in their elasticities, but the estimated elasticities are generally positive and rarely substantially negative. I find that new drivers with smaller elasticities are more likely to exit the industry, whereas drivers who remain quickly learn to be better optimizers (have positive labor supply elasticities that grow with experience). These results are consistent with the neoclassical optimizing model of labor supply and suggest that consideration of gain-loss utility and income reference dependence is not an important factor in the daily labor supply decisions of taxi drivers.

A Unified Theory: Prospect Theory and Market Dynamics

We measure crowd’s decision weights in trading by cumulative trading volume distribution and determine a reference price about crowd’s assessment value of an individual stock by the maximal volume price in stock market. We assume that prospect theory traders derive behavioral utility in trading not only from the liquidity utility expressed in terms of final trading wealth but also from a trading weight utility and a gain-loss utility relative to the reference price. We find a mathematical relation between them, derive a price-volume differential equation, and obtain two sets of explicit trading volume distribution models. One is the models in crowd’s independent trading, and the other is the behavioral models of reference-dependent preferences in crowd’s interactive trading. Finally, we propose an explicit S-shaped value function in prospect theory from the models in crowd’s interactive trading. The unified theory is successful, consistent with empirical tests in high frequency data.

Newsvendor Selling to Loss-Averse Consumers with Stochastic Reference Points

We study a newsvendor who sells a perishable asset over repeated periods to consumers with a given consumption valuation for the product. The market size in each period is random, following a stationary distribution. Consumers are loss averse with stochastic reference points that represent their beliefs about possible price and product availability. Given the distribution of reference points, they choose purchase plans to maximize their expected total utility, including gain-loss utility, before visiting the store, and follow the plans in the store. In anticipation of consumers' purchase plans, in each period, before demand uncertainty resolves, the firm chooses an initial order quantity. After the uncertainty resolves, the firm chooses a contingent price depending on the demand realization, with the option of clearing inventory by charging a sale price, and otherwise, posting a full price. Over repeated periods, the interaction of the firm’s operational decisions about ordering and contingent pricing and the consumers' purchase actions results in a distribution of reference points, and, in equilibrium, this distribution is consistent with consumers' beliefs. Under this framework of endogenized reference points, we fully characterize the firm’s optimal inventory and contingent pricing policies. We identify conditions under which the firm’s expected price and profit are increasing in the consumer loss aversion level. We also show that the firm can prefer demand variability over no-demand uncertainty. We obtain a set of insights into how consumers' loss aversion affects the firm’s optimal operational policies that are in stark contrast to those obtained in classic newsvendor models. As examples, the optimal full price increases in the initial order quantity; and the optimal full price decreases, while the optimal sales frequency increases, in the procurement cost.

Newsvendor Selling to Loss Averse Consumers with Stochastic Reference Points

Motivated by the supermarket practice of marking down perishable products daily, we study a newsvendor who sells a perishable asset over repeated periods to consumers with a given consumption valuation for the product. The market size in each period is random, following a stationary distribution. Consumers are loss averse with stochastic reference points that represent their beliefs about possible price and product availability. Given the distribution of reference points, they choose purchase plans to maximize their expected total utility, including gain-loss utility, before visiting the store and follow the plans in the store. In anticipation of consumers' purchase plans, in each period, before demand uncertainty resolves, the firm chooses an initial order quantity. After the uncertainty resolves, the firm chooses a contingent price depending on the demand realization, with the option of clearing inventory by charging a sale price, and otherwise, posting a full price. Over repeated periods, the interaction of the firm's operational decisions about ordering and contingent pricing and the consumers' purchase actions results in a distribution of reference points, and, in equilibrium, this distribution is consistent with consumers' beliefs. We fully characterize the firm's optimal inventory and contingent pricing policies. We identify conditions under which the firm's expected price and profit can be increasing in the consumer loss aversion level. We also show that the firm can prefer demand variability over no-demand uncertainty. We obtain a set of insights into how consumers' loss aversion affects the firm's optimal operational policies that are in stark contrast to those obtained in classic newsvendor models. As examples, the optimal full price increases in the initial order quantity, and the optimal full price decreases while the optimal sales frequency increases in the procurement cost.

State-dependent congestion pricing with reference-dependent preferences

Demand and capacity fluctuations are common for roads and other congestible facilities. With ongoing advances in pricing technology and ways of communicating information to prospective users, state-dependent congestion pricing is becoming practical. But it is still rare or nonexistent in many potential applications. One explanation is that people dislike uncertainty about how much they will pay. To explore this idea, a model of reference-dependent preferences is developed based on Köszegi and Rabin (2006). Using a facility yields an “intrinsic” utility and a “gain–loss” utility measured relative to the probability distribution over states of utility outcomes. Two types of preferences are analyzed: bundled preferences in which gains and losses are perceived for overall utility, and unbundled preferences in which gains and losses are perceived separately for the toll and other determinants of utility. Tolls are chosen to maximize total expected utility plus revenues. With bundled preferences the toll is set above the Pigouvian level when usage conditions are good, and below it when conditions are bad, in order to reduce fluctuations in utility. With unbundled preferences the direction of toll adjustment is less clear and depends on whether supply or demand is variable. For both types of preferences tolls are sensitive to the strength of gain–loss utility. If gain–loss utility is moderately strong, a state-independent toll can be optimal.

Family Violence and Football: The Effect of Unexpected Emotional Cues on Violent Behavior*

We study the link between family violence and the emotional cues associated with wins and losses by professional football teams. We hypothesize that the risk of violence is affected by the “gain-loss” utility of game outcomes around a rationally expected reference point. Our empirical analysis uses police reports of violent incidents on Sundays during the professional football season. Controlling for the pregame point spread and the size of the local viewing audience, we find that upset losses (defeats when the home team was predicted to win by four or more points) lead to a 10% increase in the rate of at-home violence by men against their wives and girlfriends. In contrast, losses when the game was expected to be close have small and insignificant effects. Upset wins (victories when the home team was predicted to lose) also have little impact on violence, consistent with asymmetry in the gain-loss utility function. The rise in violence after an upset loss is concentrated in a narrow time window near the end of the game and is larger for more important games. We find no evidence for reference point updating based on the halftime score.

Modeling of Job Mobility and Location Choice Decisions

This paper presents a comprehensive framework for modeling continuous decisions about changing jobs that individuals make over the course of their lives. The key objective of the research was to develop disaggregate econometric models for decision making about job mobility and location choice to implement longitudinal job mobility behavior of people within a dynamic microsimulation-based integrated urban modeling system. The paper includes two behavioral model components: (a) a job mobility model and (b) a job location choice model. The models were implemented empirically with a retrospective survey of the greater Toronto and Hamilton area in Ontario, Canada. The first component investigated the timing of job mobility with the use of a competing risk duration modeling approach for four event types: a job switch, a return to school, short-term unemployment, and withdrawal from the labor force. The second component, job location choice, was empirically estimated by applying the discrete choice methodology. One of the key features of the model was that it examined the influence of current employment in making decisions about the next job location and specified a gain–loss utility structure by the prospect–theoretic, reference-dependent choice modeling approach. A mixed logit model was developed to account for unobserved heterogeneity in the location preferences. These models were expected to be implemented in the Integrated Land Use, Transportation, Environment (ILUTE) modeling system, which had recently been updated with comparable disaggregate behavioral residential location models.

Family Violence and Football: The Effect of Unexpected Emotional Cues on Violent Behavior

Family violence is a pervasive and costly problem, yet there is no consensus on how to interpret the phenomenon of violence by one family member against another. Some analysts assume that violence has an instrumental role in intra-family incentives. Others argue that violent episodes represent a loss of control that the offender immediately regrets. In this paper we specify and test a behavioral model of the latter form in which the strength of an emotional cue depends on outcomes relative to expectations and individuals exhibit loss aversion. Our key hypothesis is that negative emotional cues -- benchmarked relative to a rationally expected reference point -- make a breakdown of control more likely. We test this hypothesis using data on police reports of family violence on Sundays during the professional football season. Controlling for location and time fixed effects, weather factors, the pre-game point spread, and the size of the local viewing audience, we find that upset losses by the home team (losses in games that the home team was predicted to win by more than 3 points) lead to an 8 percent increase in police reports of at-home male-on-female intimate partner violence. There is no corresponding effect on female-on-male violence. Consistent with the behavioral prediction that losses matter more than gains, upset victories by the home team have (at most) a small dampening effect on family violence. We also find that unexpected losses in highly salient or frustrating games have a 50% to 100% larger impact on rates of family violence. The evidence that payoff-irrelevant events affect the rate of family violence leads us to conclude that at least some fraction of family violence is better characterized as a breakdown of control than as an intra-family incentive system. More generally, the empirical findings suggest that gain-loss utility with a rational reference point could be a useful approach to modeling other cues and visceral influences.

Screening Loss Averse Consumers

Sellers often discriminate heterogeneous consumers with just a few products. This paper proposes an explanation for such coarse screening, based on consumer loss aversion. In our model, a seller oers a menu of bundles before a consumer learns his willingness to pay, and the consumer experiences gain-loss utility with reference to his prior (rational) expectation

Asset Prices Under Habit Formation and Reference-Dependent Preferences

This article explains the high level and the countercyclical variation of the equity premium in a consumption-based asset pricing model with low large-scale risk aversion. Investors have gain-loss utility over consumption relative to slowly time-varying habit. Stocks deliver low returns in recessions when consumption falls below habit; investors therefore require a high premium for holding stocks. The model's conditional moment restrictions are tested on consumption and asset returns data. The empirical estimate of large-scale risk aversion is low, whereas the estimate of loss aversion agrees with prior experimental evidence.

Reference-Dependent Risk Attitudes

We use Kőszegi and Rabin's (2006) model of reference-dependent utility, and an extension of it that applies to decisions with delayed consequences, to study preferences over monetary risk. Because our theory equates the reference point with recent probabilistic beliefs about outcomes, it predicts specific ways in which the environment influences attitudes toward modest-scale risk. It replicates “classical” prospect theory—including the prediction of distaste for insuring losses—when exposure to risk is a surprise, but implies first-order risk aversion when a risk, and the possibility of insuring it, are anticipated. A prior expectation to take on risk decreases aversion to both the anticipated and additional risk. For large-scale risk, the model allows for standard “consumption utility” to dominate reference-dependent “gain-loss utility,” generating nearly identical risk aversion across situations. (JEL D81)

A Model of Reference-Dependent Preferences*

We develop a model that fleshes out, extends, and modifies existing models of reference dependent preferences and loss aversion while accomodating most of the evidence motivating these models. Our approach makes reference-dependent theory more broadly applicable by avoiding some of the ways that prevailing models—if applied literally and without ancillary assumptions—make variously weak and incorrect predictions. Our model combines the reference-dependent gain-loss utility with standard economic “consumption utility†and clarifies the relationship between the two. Most importantly, we posit that a person’s reference point is her recent expectations about outcomes (rather than the status quo), and assume that behavior accords to a personal equilibrium: The person maximizes utility given her rational expectations about outcomes, where these expectations depend on her own anticipated behavior. We apply our theory to consumer behavior, and emphasize that a consumer’s willingness to pay for a good is endogenously determined by the market distribution of prices and how she expects to respond to these prices. Because a buyer’s willingness to buy depends on whether she anticipates buying the good, for a range of market prices there are multiple personal equilibria. This multiplicity disappears when the consumer is sufficiently uncertain about the price she will face. Because paying more than she anticipated induces a sense of loss in the buyer, the lower the prices at which she expects to buy the lower will be her willingness to pay. In some situations, a known stochastic decrease in prices can even lower the quantity demanded.

A Model of Reference-Dependent Preferences

We develop a model of reference-dependent preferences and loss aversion where “gain-loss utility” is derived from standard “consumption utility” and the reference point is determined endogenously by the economic environment. We assume that a person's reference point is her rational expectations held in the recent past about outcomes, which are determined in a personal equilibrium by the requirement that they must be consistent with optimal behavior given expectations. In deterministic environments, choices maximize consumption utility, but gain-loss utility influences behavior when there is uncertainty. Applying the model to consumer behavior, we show that willingness to pay for a good is increasing in the expected probability of purchase and in the expected prices conditional on purchase. In within-day labor-supply decisions, a worker is less likely to continue work if income earned thus far is unexpectedly high, but more likely to show up as well as continue work if expected income is high.