An information-based model for the differential treatment of gains and losses

Gigler et al. (2009, p.779) explicitly note that “we do not seek to characterize conservatism by modeling the actual measurement process ... Instead, we develop a reduced form statistical representation of conservatism.”

Kahneman (2011)’s subtler point is that it’s not just preferences that are evolutionary but also the survival games. Two firms fighting for market share may spill no blood today (at least in advanced countries), but the notions of winning/losing/gains/losses/signaling/threatening are all evolutionary in nature. And it is precisely because the human brain recognizes the evolutionary skeleton of these games that it activates the evolutionary response. Breiter et al. (2001) document how gains and losses trigger different responses in the amygdala, while Knutson et al. (2003) show that gains trigger increased neuronal activation in the mesial prefrontal cortex, while losses trigger activity in the hippocampus. In addition, Montague and Berns (2002) show that the human brain evaluates monetary and material rewards similarly, suggesting that the various asymmetries in investor attitudes toward financial gains and losses in modern stock markets appear to be emerging from an evolutionary timeframe. Chen et al. (2006)’s results lend further credence to this evolutionary survival conjecture, showing that capuchin monkeys also display various gain-loss asymmetries. Also see Williams (1966, pp.77-83).

Context-dependent preferences that do not yield traditional montonic utility functions have been extensively studied both in behavioral and mathematical economics (Chipman 1960), and this literature recognizes both the virtues and the mathematical cumbersomeness of such preferences, relative to traditional preferences that have other shortcomings but yield monotonic utility functions (Kreps 1990, Section 3.5).

In fact, there is no guarantee that preferences with such reference points can be built up into a utility function, for the existence of a utility function demands considerable mathematical regularities from the underlying preferences (Chipman 1960). Our goal however is not to build full-fledged utility functions but simply to construct endogenous preferences that we can use to compare lotteries and sure payoffs.

Note that it is essential that the joint distribution of x₁, x₂, y be correlated. Otherwise the conditional distribution of y given the future realization of {x₁, x₂} will be the marginal distribution of y itself and thus has no information content.

Our focus on the asymmetric treatment of gains versus losses is silent on the relative treatment of lotteries with smaller gains versus lotteries with larger gains, or lotteries with smaller losses versus lotteries with larger losses. If we follow Gigler et al. (2009) and exogenously posit the existence of a joint correlated distribution x₁, x₂, y with various statistical properties, we will have a mathematical answer for all possible ranges of x₁, x₂, y, but the question is if that is what the FASB’s definition of conservatism really means. In other words, the notion of conservation is not so precisely defined by the FASB or Basu (1997) so as to give an unambiguous mathematical answer for every lottery (Lambert 2010, p.294). We therefore view conservatism in the limited sense as any measurement system that imposes an asymmetrical treatment of probable gains versus probable loss. Also see footnote 4 where we argue that we build our endogenous preferences for this limited sense of conservatism.

We directly use the text in http://​www.​iasplus.​com/​en-us/​standards/​ifrs-usgaap/​contingencies#recoveries-of-contingent-losses--reimbursements- and www.​iasplus.​com/​en-us/​standards/​international/​ias/​ias37.

Over time, each lottery will pay off, and the clean surplus relation means the that the lottery will be finally recorded at its liquidation value. Our bias is therefore related to the set of lotteries that have not yet paid off at any given point in time. We acknowledge that our logic may not work when the sequence of transactions is not i.i.d. More interestingly, Gigler et al. (2009, p.784) explicitly eschew the timeliness argument and state instead that Basu’s statistical regularity is amenable to more than one interpretation and use an alternative explanation to fit Basu to their model. So we are not alone in not having nailed down the timeliness argument completely.

Every loss is the counterparty expropriating money from the agent without giving anything back in return.

In additional analysis, we have also checked robustness to the ESS criterion.

Throughout the model, both in the production stage and protecting the output from the stealer stage, we assume that the probability measure and the unit of output are such that maximizing the expected value of output maximizes the probability of survival for the entity.

The assumption of decreasing marginal returns is not controversial even in biological production games; the hunter may get too tired searching for a large catch (Laundre 2014). The convex function \(C(e)\) is one way to model this phenomenon.

Note that because the stealer and the producer are assumed to be strangers, a one-period analysis will suffice, even if the game is played repeatedly among strangers in the population.

The model allows for \(\phi \) to vary by stealer. There is nothing in the model that requires \(\phi \) to be the same for all stealers.

The strength of the producer is relative to the stealer, which depends from game to game. In each game, the producer has a pure strategy over the stealer, but over many games, the observed behavior of the producer will be either to let go or to keep the output but never to share a part of it.

The use of exogenous impartial third parties to generate better outcomes has precedence in standard game theory as well; see Kreps (1990, pp.411–412). Also note that k accrues to the impartial party and is therefore not a social loss like the fight costs.

Studying how trust and reputation for impartiality are built, either through repeated games or some other mechanism, is beyond the scope of this study (Alesina and Giuliano 2015); our more modest goal is to show how such trust, when present, can alter the nature of information asymmetry and thus preferences.

When preferences fail to satisfy the necessary mathematical regularities, the utility function that emerges is a not a typical function but a complicated vector-like object (Chipman 1960).

The fact that our model generates the asymmetry as a consequence of two different games mirrors the biological evidence that gains and losses are evaluated in a different manner by the brain (Breiter et al. 2001; Knutson et al. 2003; Dickhaut et al. 2010).

Note that these preferences are valid for both producers and stealers. The preferencetoward a surer gamble is typically defined in a setting where the individual’s information setdoes not change as he chooses among gambles. But as Fig. 2notes, the stealer’s informationsets and beliefs evolve in the game. The stealer’s decision to fight when he is more certainthat the producer is Weak is not inconsistent with his overall preference for a surer gaingamble, should such a gamble be available. As Proposition5 notes, the stealer will fight whenthere is no certification, because his information set at that point is that the producer isWeak with a probability of one.

Our approach of linking verification standards to user preferences raises the issue of userpreference heterogeneity (Kothari et al. 2010, Section 2.3). Our interest isnot in the fact that different users’ reporting preferences are different. Instead, our focusis that these preferences switch their sign at zero. On average therefore one should see anasymmetry in reporting standards for probable gains versus probable losses.

Basu’s empirical measure of conservatism, which almost all the above studies employ in some form or the other, relies not just on earnings but also on prices. And prices depend on both investor preference and investor information sets. We acknowledge that the representative investor from an accounting perspective may not necessarily be the marginal investor in the firm’s stock who determines the price; see footnote 5 in Barberis (2013). Gigler et al. (2009, p.784) explicitly list Basu’s assumptions on the investor information sets.

See, for example, Henrich et al. (2001), who show that individuals’ experience with markets is correlated with greater fairness in experimental games.

Interestingly, accounting research has examined the association between social capital and several accounting variables (Jha and Chen 2015), but we are not aware of any similar empirical analysis of conservatism.

The ideas of trust and culture have a rich history in economic thought. In his 1751 Enquiry concerning the Principles of Morals, David Hume notes: “It is sufficient for our present purpose, if it be allowed, what surely, without the greatest absurdity, cannot be disputed, that there is some benevolence, however small, infused into our bosom; some spark of friendship for human kind; some particle of the dove, kneaded into our frame, along with the elements of the wolf and serpent.”