20  Prospect theory applications

20.1 Taxi drivers on rainy days

Camerer et al. (1997) studied the labour supply of New York City taxi drivers.

The taxi drivers in the study rent a cab for a 12-hour period for a fixed fee, plus petrol. Within the 12-hours, a driver can choose how long they keep the taxi out.

For many reasons, such as weather, subway breakdowns, day of the week and conferences, a taxi driver’s effective wage can vary. When they are busier, they have a higher effective wage (that is, more fares).

Camerer et al. found that:

  • The wage elasticity of drivers - that is, how their hours of driving respond to changes in their effective wages - was negative in two of the three samples. That is, drivers drove less when their effective wages were higher.
  • For inexperienced drivers, elasticities were negative in all three samples and significantly greater in magnitude than that for experienced drivers.

Camerer et al. argue that this result is because taxi drivers have a one-day time horizon for decision making, whereby they have an earnings target beyond which they derive little additional utility. This leads them to work until they reach their target, which they reach more quickly on days with a higher wage.

  • People have a tendency to engage in “narrow bracketing” when they make decisions, isolating them as single decisions (how much should I work today?) rather than thinking about them as a stream (how much should I work each day this week?)
  • Aversion to falling below the reference point is consistent with loss aversion, with a result below the reference point causing stronger feelings than a result a similar amount above the reference point.

There have been numerous follow-up studies of taxi-drivers:

  • Farber (2005) studied New York cabdrivers and found that the decision to stop work was primarily a function of how many hours had been worked up to that point in the day. He identified the difference between his and Camerer et al.’s result as being due to different empirical methods and measurement problems with the Camerer et al. data.

  • Farber (2008) found that a model of labour supply with reference-dependent targets has a better fit than a standard neoclassical model, but that there was substantial variation day-to-day in any given driver’s reference income level and that most shift ends before that reference income is reached.

  • Farber (2015) used a much larger dataset on New York taxi driver behaviour and found that, as standard economic theory would predict, taxi drivers drive more when they can earn more. Farber also found that drivers did not earn more when it was raining.

  • Martin (2017) examined taxi driver labour supply incorporating the S-shaped reference dependence of Prospect Theory (the reflection effect with risk seeking behaviour in the loss domain and risk aversion in the gain domain. Martin found evidence that taxi driver behaviour was consistent with this fully form of Prospect Theory. He differentiated from the other papers on the basis that they considered a narrower version of reference dependence focusing on loss aversion only.

20.2 The disposition effect

The disposition effect is the tendency for investors to sell stocks that are in the gain domain relative to the purchase price and to hold stocks that are in the loss domain (Shefrin and Statman (1985)).

While tax implications or portfolio rebalancing are both potential explanations for asymmetric behaviour relating to the sale of stocks, these factors have been shown to be insufficient to explain the observed behaviour.

Most behavioural explanations have turned to prospect theory.

For example, Shefrin and Statman (1985) argued that the disposition effect is driven by the reflection effect, whereby investors are risk seeking in the loss domain and risk averse in the gain domain. To demonstrate how it works, they present the following scenario:

[C]onsider an investor who purchased a stock one month ago for $50 and who finds that the stock is now selling at $40. The investor must now decide whether to realize the loss or hold the stock for one more period. To simplify the discussion, assume that there are no taxes or transaction costs. In addition, suppose that one of two equiprobable outcomes will emerge during the coming period: either the stock will increase in price by $10 or decrease in price by $10. According to prospect theory, our investor frames his choice as a choice between the following two lotteries:

A. Sell the stock now, thereby realizing what had been a $10 “paper loss”.

B. Hold the stock for one more period, given 50-50 odds between losing an additional $10 or “breaking even.”

For an investor who is risk seeking in the loss domain, option B would be attractive.

If we craft an alternative scenario where the stock is now selling at $60, selling would realise a $10 gain, while holding the stock would be a risky prospect with the same expected value. An investor who is risk averse in the gain domain will sell.

20.3 The housing market

Genesove and Mayer (2001) examined hosing data from Boston. They found that owners subject to nominal losses:

  • Set higher asking prices of 25-35% of the difference between the expected selling price and their original purchase price
  • Attain higher prices of 3-18% of that difference

This suggests sellers are averse to realising nominal losses.