Exam 11: Disagreeing With Ourselves: Projection and Hindsight Biases

Hindsight bias, projection bias and time inconsistent preferences can only occur in situations in which decisions are made in at least two time periods.

Consider the following inter-temporal choice problem, where $s^{\prime}$ is the state today and $s$ is the state tomorrow. $\max _{c_{1}} u\left(c_{1}, s^{\prime}\right)+\delta\left[(1-\alpha) u\left(w-c_{1}, s\right)+\alpha u\left(w-c_{1}, s^{\prime}\right)\right.$ . This problem reduces to the rational model of inter-temporal choice when $\delta=1$ .

Time inconsistent preferences are a bias.

Which of the following statements about the projection bias is true?

Suppose you wanted to write down a model of addiction, where $c_{1}$ is drug use today and $c_{2}$ is drug use tomorrow. You want to model the idea that more drug use today increases the utility of drug use tomorrow. One way to capture this relationship is to model $c_{1}$ and $c_{2}$ as complements.

In the college admissions example, which of the following describes a student who exhibits time inconsistent preferences?

Inter-temporal choice refers to

The hot state is today "today" in inter-temporal choice with projection bias, as the cold state is to "tomorrow" in inter-temporal choice with projection bias.

Using the utility function given in 11.35 , show that 11.34 is true.

All of the following are types of preferences and behaviors that can be attributed to the hotcold empathy except

Consider Figure 11.1. Billy has a utility function given by $u\left(c_{1}, c_{2}\right)=\ln \left(c_{1}\right)+\delta \ln \left(c_{2}\right)$ and a budget constraint given by $c_{1}+c_{2} \leq 100$ . Where $c_{1}=$ hamburgers today and $c_{2}=$ hamburgers tomorrow, and $p_{1}=p_{2}=1$ . a. What is the slope of Billy's indifference curve at any point $\left(c_{1}, c_{2}\right)$ ? b. What is the slope of Billy's budget line? c. At any optimal solution to Billy's utility maximization problem, it must be true that $\frac{c_{2}}{\delta c_{1}}=1$ . d. Suppose Billy spends all of his income on hamburgers today and tomorrow. If $\delta=1$ , what percentage of his income is spent on hamburgers tomorrow? e. If $\delta=.8$ , what percentage of his income is spent on hamburgers tomorrow? f. In general, as $\delta$ decreases, hamburger consumption tomorrow increases.

Rational models of addiction assume that the effect of today's consumption on tomorrow's consumption is predictable. This is in contrast to the projection bias models of consumption, in which the addictive property is not predictable.

Projection bias occurs when

In the college admissions example, projection bias occurs because the prospective student does not incorporate the utility of their future-self under alternative weather.

Consider equation 11.33 and the model presented above. The interpretation of equation 11.33 is that for $\left(\overline{x_{1}}, \overline{x_{2}}\right)$ utility decreases as the individual's state becomes hotter. That is, without adjusting consumption of $x_{1}$ and $x_{2}$ , the individual becomes worse off as they experience a hotter visceral state.

Consider equations 11.20 and 11.21. When $\alpha=1$ , which of the following gives a correct interpretation of the $x_{c, 1}$ and $x_{c, 2}$ ?

Using the utility function given in 11.35 , show that 11.33 is true.

Consider a model of inter-temporal choice, with utility function $u\left(c_{1}, c_{2}\right)$ . If $c_{1}$ and $c_{2}$ are substitutes then which of the following must be true?

One way to model the hot-cold empathy gap is to put the visceral state directly into the utility function as a continuous variable $s$ . As $s$ increases, the individual becomes "hotter."

Time inconsistent preferences means that $\delta<1$ .