Expectation-based Loss Aversion Research Articles

Consumer loss aversion and scale-dependent psychological switching costs

We consider a model of product differentiation where consumers are uncertain about the qualities and prices of firms' products. They can inspect all products at zero cost. A share of consumers is expectation-based loss averse. For these consumers, buying products of varying quality and price creates disutility from gain-loss sensations. Even at modest degrees of loss aversion they may refrain from inspecting all products and choose an individual default that is strictly dominated in terms of surplus. Firms' strategic behavior exacerbates the scope for this effect. The model generates “scale-dependent psychological switching costs” that increase in the value of the transaction. They imply that making switching easier or costless for consumers would not motivate more switching.

Loss aversion in strategy-proof school-choice mechanisms

Evidence suggests that participants in strategy-proof matching mechanisms play dominated strategies. To explain the data, we introduce expectation-based loss aversion into a school-choice setting and characterize choice-acclimating personal equilibria. We find that non-truthful preference submissions can be strictly optimal if and only if they are top-rank monotone. In equilibrium, inefficiency or justified envy may arise in seemingly stable or efficient mechanisms. Specifically, students who are more loss averse or less confident than their peers obtain suboptimal allocations.

Multi-prize contests with expectation-based loss-averse players

We investigate the optimal prize allocation in a multi-winner nested Tullock contest model with symmetric contestants who exhibit expectation-based loss aversion. We show that (i) multiple prizes can be optimal when contestants are sufficiently loss averse; (ii) all prizes should be equal in the optimal contest; and (iii) the number of prizes increases as the degree of loss aversion increases.

Consumer Loss Aversion and Scale-Dependent Psychological Switching Costs

We consider the Salop (1979) model of product differentiation and assume that consumers are uncertain about the qualities and prices of firms’ products. They can inspect all products at zero cost. A share of consumers is expectation-based loss averse. For these consumers, a purchase plan, which involves buying products of varying quality and price with positive probability, creates disutility from gain-loss sensations. Even at modest degrees of loss aversion they may refrain from inspecting all products and choose an individual default that is strictly dominated in terms of surplus. Firms’ strategic behavior exacerbates the scope for this effect. The model generates “scale-dependent psychological switching costs” that increase in the value of the transaction. We find empirical evidence for the predicted association between switching behavior and loss aversion in new survey data.

Consumer Vulnerability and Behavioral Biases

A wealth of evidence shows that individuals are biased and firms can often exploit consumers' behavioral biases in their contract designs. In this paper, we study how vulnerable biased individuals are to their own behavioral biases in market equilibrium, and focus on the role of risk aversion and intertemporal elasticity of substitution (IES). We measure consumer vulnerability by the percentage loss in a consumer's equilibrium certainty equivalent from a market with non-biased consumers to that with biased ones. We examine several important behavioral biases that have been extensively studied in the literature, including the impact of biased beliefs (either over- or under-confidence) in an insurance market, the impact of present bias and naivete about present bias in a dynamic model of credit contract design, the impact of projection bias about habit formation, and the impact of expectation-based loss aversion on an investor's portfolio choice. We show that consumer vulnerability to all four commonly studied behavioral biases has a non-monotonic relationship with risk aversion or IES. This is in striking contrast to the deviations in the equilibrium allocations from the rational benchmark, which are often monotonic to the risk aversion or IES. We also consider a setting of biased agents with Epstein-Zin preferences to isolate the effect of risk aversion from that of IES. Institutional subscribers to the NBER working paper series, and residents of developing countries may download this paper without additional charge at www.nber.org.

Consumer Search and the Uncertainty Effect

We consider a model of Bertrand competition where consumers are uncertain about the qualities and prices of firms' products. Consumers can inspect all products at zero cost. A share of consumers is expectation-based loss averse. For these consumers, a purchase plan, which involves buying products of varying quality and price with positive probability, creates scale-dependent dis-utility from gain-loss sensations. Even if their degree of loss aversion is modest, they may refrain from inspecting all products and choose an individual default that is first-order stochastically dominated. Firms' strategic behavior can exacerbate the scope for this uncertainty effect', and sellers of inferior products may earn positive profits despite Bertrand competition. We find suggestive evidence for the predicted association between consumer behavior and loss aversion in new survey data.

Consumer Vulnerability and Behavioral Biases

A wealth of evidence shows that individuals are biased and firms can often exploit consumers' behavioral biases in their contract designs. In this paper, we study how vulnerable biased individuals are to their own behavioral biases in market equilibrium, and focus on the role of risk aversion and intertemporal elasticity of substitution (IES). We measure consumer vulnerability by the percentage loss in a consumer's equilibrium certainty equivalent from a market with non-biased consumers to that with biased ones. We examine several important behavioral biases that have been extensively studied in the literature, including the impact of biased beliefs (either over- or under-confidence) in an insurance market, the impact of present bias and naivete about present bias in a dynamic model of credit contract design, the impact of projection bias about habit formation, and the impact of expectation-based loss aversion on an investor's portfolio choice. We show that consumer vulnerability to all four commonly studied behavioral biases has a non-monotonic relationship with risk aversion or IES. This is in striking contrast to the deviations in the equilibrium allocations from the rational benchmark, which are often monotonic to the risk aversion or IES. We also consider a setting of biased agents with Epstein-Zin preferences to isolate the effect of risk aversion from that of IES.

School Choice And Loss Aversion

Evidence suggests that participants in direct student-proposing deferred-acceptance mechanisms (DSPDA) play dominated strategies. To explain the observed data, we introduce expectation-based loss aversion into a school-choice setting and characterize choice-acclimating personal equilibria in DSPDA. We find that non-truthful preference submissions can be strictly optimal if and only if they are top-choice monotone. In equilibirum, DSPDA may implement allocations with justified envy. Specifically, it discriminates against students who are more loss averse or less confident than their peers, and amplifies already existing discrimination. To level the playing field, we propose sequential mechanisms as an alternative that is robust to these biases.

Optimal task assignments with loss-averse agents

This paper studies optimal task assignments in a setting where agents are expectation-based loss averse according to Köszegi and Rabin (2006, 2007) and are compensated according to an aggregated performance measure in which tasks are technologically independent. We show that the optimal task assignment is determined by a trade-off between paying lower compensation costs and restricting the set of implementable effort profiles under multitasking. We show that loss aversion combined with how much the marginal cost of effort in one task increases with the effort chosen in other tasks determines when multitasking saves on compensation costs, but results in an implementation problem.

English Versus Vickrey Auctions with Loss Averse Bidders

Evidence suggests that people evaluate outcomes relative to expectations. I analyze this expectation-based loss aversion in the context of dynamic and static auctions, where the reference point is given by the (endogenous) equilibrium outcome. If agents update their reference point during the auction, the arrival of information crucially affects equilibrium behavior. Consequently, I show that - even with independent private values - the Vickrey auction yields strictly higher revenue than the English auction, violating the well known revenue equivalence.

Loss aversion leading to advantageous selection

Some insurance markets are characterized by “advantageous selection”, that is, ex-post risk and coverage are negatively correlated. We show that expectation-based loss aversion as in Kőszegi and Rabin (Quarterly Journal of Economics, 121(4), 1133–1165, 2006; The American Economic Review, 97(4), 1047–1073, 2007) provides a natural explanation for this phenomenon in environments in which risk aversion models do not, e.g., when agents face modest-scale risks and/or in absence of moral hazard. More exposure to risk has two competing effects on an agent’s willingness to pay for insurance: a positive effect, as in standard expected utility models; and a negative one, due to a reference effect. We determine conditions under which an insurance provider optimally sets a high price at which only low risk agents buy.

Incomplete contracting, renegotiation, and expectation-based loss aversion

We consider a simple trading relationship between an expectation-based loss-averse buyer and a profit-maximizing seller. When writing a long-term contract the parties have to rely on renegotiation in order to ensure materially efficient trade ex post. We show that if the buyer expects renegotiation to occur, the seller can opportunistically exploit the buyer's attachment to the expected outcome of renegotiation. In other words, incomplete contracts create a new type of hold-up problem. If credible, the buyer prefers to expect not to renegotiate, which gives rise to ex post inefficiencies. In a next step, we allow the buyer to undertake a non-contractible investment. We find that loss aversion can mitigate the traditional hold-up problem.

Expectation-based loss aversion and rank-order tournaments

Many insights regarding rank-order tournaments rest upon contestants’ behavior in symmetric equilibria. As shown by Gill and Stone (Games Econ Behav 69:346–364, 2010), however, symmetric equilibria may not exist if contestants are expectation-based loss averse and have choice-acclimating expectations. We show that under choice-unacclimating—i.e., fixed—expectations both symmetric and asymmetric equilibria exist for all degrees of loss aversion. Importantly, a symmetric equilibrium also exists if players follow their preferred credible plan and the weight attached to psychological gain–loss utility does not strongly outweigh the weight put on material utility. Hence, for fixed expectations a focus on symmetric equilibria seems justifiable even if contestants are expectation-based loss averse.

Expectation-based loss aversion and strategic interaction

By extending the equilibrium concepts of Kőszegi and Rabin (2006, 2007), this paper analyzes the strategic interaction of expectation-based loss-averse players. For loss-averse players with choice-acclimating expectations, the utility from playing a mixed strategy is not linear but convex in the probabilities they assign to their pure strategies. As a consequence, they are generally unwilling to randomize and an equilibrium may fail to exist. For players with choice-unacclimating expectations, by contrast, randomizing over their pure strategies may indeed constitute a credible best response and an equilibrium always exists. Building upon these insights, we delineate how expectation-based loss-averse players differ in their strategic behavior from their counterparts with standard expected-utility preferences, derive novel strategic effects, discuss equilibrium selection, and derive equilibrium play for some simple games.

Expectation-Based Loss Aversion and Strategic Interaction

Extending the equilibrium concepts of Kőszegi and Rabin (2006, 2007), this paper analyzes the strategic interaction of expectation-based loss-averse players. For loss-averse players with choice-acclimating expectations the utility from playing a mixed strategy is not linear but convex in the probabilities they assign to their pure strategies. As a consequence, they are generally unwilling to randomize and an equilibrium may fail to exist. For players with choice-unacclimating expectations, in contrast, randomizing over their pure strategies may indeed constitute a credible best response and an equilibrium always exist. Building upon these insights, we delineate how expectation-based loss-averse players differ in their strategic behavior from their counterparts with standard expected-utility preferences, derive novel strategic effects, discuss equilibrium selection, and derive equilibrium play for some simple games.

Incomplete Contracting, Renegotiation, and Expectation-Based Loss Aversion

We consider a simple trading relationship between an expectation-based loss-averse buyer and profit-maximizing sellers. When writing a long-term contract the parties have to rely on renegotiations in order to ensure materially efficient trade ex post. The type of the concluded long-term contract affects the buyer’s expectations regarding the outcome of renegotiation. If the buyer expects renegotiation always to take place, the parties are always able to implement the materially efficient good ex post. It can be optimal for the buyer, however, to expect that renegotiation does not take place. In this case, a good of too high quality or too low quality is traded ex post. Based on the buyer’s expectation management, our theory provides a rationale for “employment contracts” in the absence of non-contractible investments. Moreover, in an extension with non-contractible investments, we show that loss aversion can reduce the hold-up problem.

Loss Aversion Leading to Advantageous Selection

Some insurance markets are characterized by “advantageous selection,” that is, ex-post risk and coverage are negatively correlated. We show that expectation-based loss aversion as in K'oszegi and Rabin (2006, 2007) provides a natural explanation for this phenomenon when agents face modest scale risks. More exposure to risk has two competing effects on an agent's willingness to pay for insurance: a positive effect, as in standard expected utility models; and a negative one, due to a reference effect. We determine conditions under which an insurance provider optimally sets a high price at which only low risk agents buy.

Incomplete Contracting, Renegotiation, and Expectation-Based Loss Aversion

We consider a simple trading relationship between an expectation-based loss-averse buyer and profit-maximizing sellers. When writing a long-term contract the parties have to rely on renegotiations in order to ensure materially efficient trade ex post. The type of the concluded long-term contract affects the buyer's expectations regarding the outcome of renegotiation. If the buyer expects renegotiation always to take place, the parties are always able to implement the materially efficient good ex post. It can be optimal for the buyer, however, to expect that renegotiation does not take place. In this case, a good of too high quality or too low quality is traded ex post. Based on the buyer's expectation management, our theory provides a rationale for ``employment contracts'' in the absence of non-contractible investments. Moreover, in an extension with non-contractible investments, we show that loss aversion can reduce the hold-up problem.

The expectation-based loss-averse newsvendor

We modify the classic single-period inventory management problem by assuming that the newsvendor is expectation-based loss averse according to Kőszegi and Rabin (2006, 2007). We show that the expectation-based loss-averse newsvendor orders less than the profit-maximizing quantity. Moreover, the order placed by the expectation-based loss-averse newsvendor features plausible comparative statics of cost and price changes.

Binary Payment Schemes: Moral Hazard and Loss Aversion

We modify the principal-agent model with moral hazard by assuming that the agent is expectation-based loss averse according to Kőoszegi and Rabin (2006, 2007). The optimal contract is a binary payment scheme even for a rich performance measure, where standard preferences predict a fully contingent contract. The logic is that, due to the stochastic reference point, increasing the number of different wages reduces the agent's expected utility without providing strong additional incentives. Moreover, for diminutive occurrence probabilities for all signals the agent is rewarded with the fixed bonus if his performance exceeds a certain threshold. (JEL D82, D86, J41, M52, M12)