Tuesday, 21 March 2017

Myopia and Discounting

Gotta love any technical paper that opens with a Böhm Bawerk cite. 

Gabaix and Laibson have a new framework up in which patient Bayesian imperfectly informed agents display behaviour observationally equivalent to hyperbolic discounting.

The intuition of the model is pretty simple. Agents get noisy signals about the future state of the world, and so there's option value in deferring some decisions until you get more certainty. You consequently get things that look like preference reversals, but they're really just information updating by patient agents.

Their summary here is rather nice:
We provide an illustrative example of our framework in Section 2, where we study a binary choice problem: an actor chooses between an early reward and a mutually exclusive later reward. We show that when the variance of forecasting noise rises linearly with the event horizon, Bayesian agents will act as if they are hyperbolic discounters, even though their deep time preferences are perfectly patient.

In Section 3, we describe the broader implications of our framework, and identify predictions that distinguish our framework from time preference models. First, we show that our (perfectly patient) agents exhibit preference reversals of the same kind that are exhibited by agents with hyperbolic discount functions. However, these preference reversals do not reáect a self-control problem. The preference reversals arise because the agents obtain less noisy information with the passage of time. Accordingly, our agents do not wish to commit themselves; they act as-if they are naive hyperbolic discounters (Strotz 1957, Akerlof 1992, OíDonoghue and Rabin 1999) rather than sophisticated ones (Laibson 1997).

In the cross-section, our framework implies that agents with greater intelligence exhibit less as-if discounting - their superior forecasting ability enables them to make choices that are more responsive to future utility flows.

In addition, our agents exhibit as-if discounting that is domain specific. They exhibit less as-if discounting (i) when they have more overall life experience, (ii) when they are more experienced in the specific choice domain, (iii) when they have more time to think about an intertemporal choice (e.g., Imas, Khun, and Mironova, 2016), and (iv) when they have more cognitive bandwidth to think about their choice (e.g., Benjamin and Shapiro, 2015).

In Section 4, we generalize our example by making the action set continuous. We provide sufficient conditions that imply that perfectly patient agents who are imperfect forecasters will act as if they are naive hyperbolic discounters.
And the Böhm Bawerk quip:
Diminishing sensitivity to future utils is also explained by imperfect information. For example, Böhm-Bawerk (1889) wrote that "we possess inadequate power to imagine and to abstract, or that we are not willing to put forth the necessary effort, but in any event we limn a more or less incomplete picture of our future wants and especially of the remotely distant ones. And then, there are all of those wants that never come to mind at all."
Hyperbolicy behaviour is a reasonably common justification for behavioural economics type interventions. Where the problem is information rather than self-control, providing information may well be the better solution.

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