A model of the effect of affect on economic decision making

Abstract

The standard economic model of decision making assumes a decision maker’s current emotional state has no impact on his or her decisions. Yet there is a large psychological literature that shows that current emotional state, in particular mild positive affect, has a significant effect on decision making, problem solving, and behavior. This paper offers a way to incorporate this insight from psychology into economic modelling. Moreover, this paper shows that this simple insight can parsimoniously explain a wide variety of behaviors.

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Fig. 1

Notes

  1. 1.

    See, for example, Damasio (1995) on the role of emotions on behavior and evidence from how injuries to the areas of the brain responsible for emotions affect decision making. For instance, subjects with damage to the ventromedial frontal cortex make different decisions when gambling than normal subjects (Bechara et al. 1994). Loewenstein (1996, 2000) reports on how “visceral” influences—hunger, thirst, sexual desire, moods, emotions, and physical pain—affect behavior. For a survey on experimental manipulations of positive affect and consequent effects on decision making see Isen (2000). Slovic et al. (2002) provide another survey.

  2. 2.

    Some recent economic work in this area includes Loewenstein (1996, 2000), Kliger and Levy (2003), and Loewenstein and O’Donaghue (2004).

  3. 3.

    Other related work on evolving preferences, such as Benhabib and Day (1981), also relate today’s preferences to yesterday’s choices rather than yesterday’s utility or affect.

  4. 4.

    Condition (4) is more general than the assumption that if u > u′, then \(U_t\left(\mathbf{x},u\right) >U_t\left(\mathbf{x},u'\right)\). Observe that assumption would imply Eq. 4 by revealed preference:

    $U_t\left[\mathbf{x}_t^{\ast}(u),u\right] \ge U_t\left[\mathbf{x}_t^{\ast}(u'),u\right] > U_t\left[\mathbf{x}_t^{\ast}(u'),u'\right]$

    .

  5. 5.

    It also seems inconsistent with results that show that positive affect appears to build resources and facilitate coping, problem-solving ability, and smooth social interaction (see e.g., Aspinwall 1998; Erez and Isen 2002; Fredrickson and Joiner 2002; Gervey et al. 2005; and Isen 2000), all factors that support the idea that mood today will be better, all else equal, if it was good yesterday rather than bad yesterday.

  6. 6.

    As one reviewer noted, this precludes the consideration of certain context effects in the basic model; that is, for example, the idea that satisfaction with current income or consumption could be a negative function of the previous period’s income or consumption. Related concepts such as habituation and addiction are also beyond the scope of the basic model. The discussion of savings behavior below suggests, however, how lagged effects could be incorporated into the analysis.

  7. 7.

    Assume the support of ε t is such that \(\Pr\{u_t\le 0\}=0\).

  8. 8.

    Barring, of course, external shocks, such as those resulting from actions of others. For instance, harmful acts, even neglect, by others could be a shock to the dynamic system.

  9. 9.

    Since we’re considering a single-dimensional choice set of actions, we’re abstracting from the possibility of actions on other dimensions (e.g., going to an enjoyable film or giving oneself a treat to self-induce positive affect). But the point carries over to a vector of activities. That is, “happy” people could tend to choose the vector x, while “unhappy” people tend to choose the vector \({\hat{\mathbf x}}\), \({ \hat{\mathbf x}\neq {\mathbf x}}\). Yet this difference is not the cause of happiness or unhappiness, but merely a correlate.

  10. 10.

    This is roughly consistent with actual medical practice. Informal discussions with physicians indicate that “accepted practice” for first-time treatment with selective serotonin reuptake inhibitors (ssris) is to put someone on them for 6 to 12 months and, then, wean him or her off them. For many patients this is sufficient (i.e., u t is now greater than \(\hat{u}_{2}\) ), and future medication is not necessary. Other patients cycle on and off them, suggesting that their brain chemistry or life experiences are such that they are periodically and randomly thrown well below \(\hat{u}_{2}\), necessitating intervention to escape. Of course, intervention by others (e.g., taking the person to an enjoyable film or giving her a treat) can also be effective in many cases.

  11. 11.

    In what follows, we make the standard assumption that the constraints x t  ≥ 0 are not binding. Allowing this assumption to be relaxed is not particularly interesting in this analysis.

  12. 12.

    Note that there is an important difference between positive affect’s appearing to lead to a lack of control and it actually leading to a lack of control. Recall actors in our model are behaving rationally. Moreover, as noted earlier, empirical evidence suggests that positive affect does not lead to a loss of self-control, dangerous risk-taking, impulsive behavior, or failure to consider important negative information when there is good reason to pay attention to it. There is convincing evidence that positive affect does not foster such behavior (e.g., Aspinwall 1998; Isen et al. 1988; and Trope and Pomerantz 1998), even though, all else equal, people in positive affect will prefer to engage in and enjoy something pleasant, and do enjoy it more than do people in a neutral feeling state (e.g., Erez and Isen 2002; Isen and Reeve 2005).

  13. 13.

    But, as previously noted, this does not imply impulsiveness or loss of self-control.

  14. 14.

    Laibson (2001), Loewenstein (2000), and Romer (2000) are some notable exceptions.

  15. 15.

    See, for instance, Bell (1982) and Loomes and Sugden (1982) on the role of potential regret on decision making. Mellers (2000) and Mellers et al. (1999) also examine the role of anticipated emotions on decision making.

  16. 16.

    MacLeod turns to emotions to justify his model of heuristic problem solving versus the standard optimization techniques that economists typically model decision makers as using. He argues, based on clinical observations of brain-damaged individuals reported in Damasio (1995), that people’s heuristic problem-solving abilities are tied to their emotions. MacLeod does not, however, consider how different emotional states affect decisions, as we do. Kaufman, building on the well-known work of Yerkes and Dodson (1908) on arousal, suggests that emotional state can enhance or inhibit cognitive function: People who are completely uninterested in a problem or who are panicked over it are less able to solve it (or solve it less efficiently or effectively) than people exhibiting less extreme emotions.

  17. 17.

    Ashby et al. (1999), for instance, note that release of the neurotransmitter dopamine into frontal brain regions is associated both with positive affect and the ability to perform cognitive tasks. Increased dopamine in frontal brain areas, and activation of those areas, thus, could serve as a biological explanation for a link between affect and cognition.

    Relatedly, Erez and Isen (2002) find experimental evidence that positive affect increases the components of expectancy motivation: preferences (how well liked the reward is), but also perceptions (the estimated strength of the link between effort and reward, the likelihood of reward given a reasonable level of effort, etc.). Our paper concerns only the first effect, the impact on preferences.

  18. 18.

    Indeed, as our discussion of uncertainty indicates, we do not require that our decision makers be perfect forecasters, although some aspects of the model might not carry over if they were biased forecasters.

  19. 19.

    The idea that guilt is, for some, a persistent emotion is borne out by numerous anecdotes of people who devote large portions of their lives seeking to atone for their misdeeds or the misdeeds of their family or people.

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Correspondence to Benjamin E. Hermalin.

Additional information

Financial support from the Willis H. Booth Professorship in Banking and Finance is grateful acknowledged. The authors also thank Ulrike Malmendier, Barb Mellers, Matt Rabin, Bernard Sinclair-Desgagnes, Miguel Villas-Boas, and seminar participants at Stanford,

UC Berkeley, UC Davis, USC, and Vanderbilt University for helpful comments.

Appendices

Appendix 1: Comparison of affect with rational addiction

The rational addiction literature (see, e.g., Pollak 1970; Becker and Murphy 1988; and, for a survey, von Auer 1998) would seem related to the model of affect presented here. This appendix provides a brief comparison.

In a rational addiction model, utility at time t is given by the formula:

$$ u_t = V\left(x_t,S_{t-1}\right)\,, $$
(23)

where x t is time-t consumption of the addictive good and S t − 1 is some “stock” of the addictive good consumed to the beginning of period t. The stock follows the process:

$$ S_t = x_t + \rho S_{t-1}\,, $$
(24)

where 0 < ρ < 1. The key behavioral assumption is that the cross-partial derivative of V is positive: A larger stock of the addictive good raises the marginal utility of consuming it today.

Observe that instead of working in terms of per-period consumption, one can work in terms of the stock: Using Eq. 24, Eq. 23 can be rewritten as

$$ u_t = V\left(S_t - \rho S_{t-1},S_{t-1}\right)\,. $$
(25)

Given an initial stock, S 0, the rational addict chooses \(\{S_t\}_{t=1}^{\infty}\) to maximize the discounted utility flow of Eq. 25 subject to the constraint that S t  ≥ ρS t − 1 (i.e., negative consumption is not permitted). For a constant discount factor (i.e., \(\omega_t = \delta^t\)), the optimal S t solves

$$ V_1\left(S_t-\rho S_{t-1},S_{t-1}\right) - \delta\rho V_1\left(S_{t+1}-\rho S_t,S_t\right) + \delta V_2\left(S_{t+1}-\rho S_t,S_t\right) = 0 $$
(26)

if the constraint does not bind and equals ρS t − 1 otherwise.

The affect model also has a stock variable. But in the affect model it is utility itself. That is, loosely, in the affect model, expression (23), with u t − 1 substituted for S t − 1, defines both the flow of utility and the transformation of the stock variable (i.e., it is as if it combines Eqs. 23 and 24 in one expression). It is this difference—combined with the fact the affect model requires no particular sign on the cross-partial derivative of V—that distinguishes these models. It also explains why the dynamic programming problem in the affect model is so much more straightforward than in the rational addiction literature.

Appendix 2: Dynamics without monotonicity

As discussed in the text, the never-regret-a-good-mood assumption, expression (4), served to vastly simplify the dynamics in our model. While we believe it to be a reasonable assumption, we briefly consider, to be complete, what would happen were it not to hold. Let \({\mathbf{x}^{\ast\ast}_t(u_{t-1})}\) denote the optimal decision rule. Observe, by the envelope theorem, that a change in x τ , τ < t will not have an impact on future utility through \({\mathbf{x}^{\ast\ast}_t(u_{t-1})}\). Hence, the \({\mathbf{x}^{\ast\ast}_t(u_{t-1})}\) satisfy

$$ \left(\omega_t + \sum_{s=t+1}^T \omega_s \prod_{n=t+1}^s \frac{\partial U_n\big(\mathbf{x}^{\ast\ast}_n(u_{n-1}),u_{n-1}\big)}{\partial u}\right)\frac{\partial U_t\big({\mathbf{x}^{\ast\ast}_t(u_{t-1})},u_{t-1}\big)}{\partial x} = 0\,. $$
(27)

We can, thus, conclude

Proposition 1

Assume that a solution, \(\mathbf{x}_t^{\ast}\left( u\right) \), exists for the program (3) for all possible u. Assume further that U t (·,u) is strictly concave for all uand all t. Finally, assume that a solution\({\mathbf{x}^{\ast\ast}_t(u_{t-1})}\)exists to the decision maker’s dynamic programming and that solution satisfies

$$ \left(\omega_t + \sum_{s=t+1}^T \omega_s \prod_{n=t+1}^s \frac{\partial U_n\big(\mathbf{x}^{\ast\ast}_n(u_{n-1}),u_{n-1}\big)}{\partial u}\right) > 0 $$
(28)

along the equilibrium path. Then\({\mathbf{x}^{\ast\ast}_t(u_{t-1})} = \mathbf{x}^\ast_t(u_{t-1})\); that is, the optimal path involves maximizing per period utility.

Proof

If Eq. 28 holds, then the first-order condition (27) can hold if and only if

$$ \frac{\partial U_t\big({\mathbf{x}^{\ast\ast}_t(u_{t-1})},u_{t-1}\big)}{\partial x} = 0\,. $$

But given that U t (·,u) is strictly concave, this implies \({\mathbf{x}^{\ast\ast}_t(u_{t-1})} = \mathbf{x}^\ast_t(u_{t-1})\). Given that t was arbitrary, this completes the proof.□

For example, suppose T = ∞ and \(\omega_t=\delta^{t-1}\), where δ is a constant discount factor. Further assume \(U_t(x,u) = x-ux^2/2\) (observe this utility function does not satisfy expression (4)). It is readily shown that \(x^\ast_t = 1/u_0\) if t is odd and \(x^\ast_t = 2u_0\) if t is even. Substituting these values into Eq. 28 we have that the sign of Eq. 28 is the same as the sign of

$$ 1+\delta \frac{\delta - 2u_0^2}{1-\delta^2} $$

if t is even and

$$ 1+\delta \frac{2u_0^2\delta - 1}{2u_0^2(1-\delta^2)} $$

if t is odd. Both expressions are positive if \(\max\{\frac{1}{2u_0^2},2u_0^2\}<1/\delta\). This condition would hold, for instance, if u 0 = 1 and δ < 1/2. Observe that if this condition holds, then utility oscillates period to period between u 0 and \(\frac{1}{2u_0}\). Similarly, x oscillates between 1/u 0 and 2u 0. Such a “yoyo”-path with regard to the choice of x seems at odds with observed behavior with regard to many decisions and is one reason for questioning models that do not satisfy condition (4).

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Hermalin, B.E., Isen, A.M. A model of the effect of affect on economic decision making. Quant Market Econ 6, 17–40 (2008). https://doi.org/10.1007/s11129-007-9032-6

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Keywords

  • Affect
  • Morale
  • Emotion

JEL Classification

  • B41
  • D99
  • C70
  • C73
  • D81