76		STATUS QUO BIAS AND DEFAULT OPTIONS

EXAMPLE 4.5 Status Quo Bias and Health Insurance

Default option bias is a special case of the status quo bias. The status quo bias is a general preference for things to remain as is. If people have been in a particular state for a long time, they might take this state as the reference point. As in the default option bias, if the status quo is the reference point, a person requires substantial compensation for a loss in any dimension. In essence, the default option in most circumstances is to do nothing, thus remaining at the status quo.

William Samuelson and Richard Zeckhauser provide numerous illustrations of the status quo bias. One of the more compelling illustrations is their analysis of health insurance plan choices among employees at Harvard University. Over time, Harvard University had expanded the plan options available to staff. Of those who were continuing staff members, only a very small portion, about 3 percent, changed their plan in any given year. Yet, newer employees disproportionately selected options that had not been previously available. Samuelson and Zeckhauser found large disparities in enrollment rates in newer plans between newer employees and older employees. Those with longer tenure were more likely to remain with older health insurance options than the newer employees.

Rational Explanations of the Status Quo Bias

Some care must be given when invoking the status quo bias. In some cases, true and substantive switching costs exist. For example, switching health plans can result in needing to find a new primary care physician. In this case, the investment of time and resources in developing a working relationship with the previous physician would be lost. Indeed, the Harvard University employees were more likely to switch between plans that preserved their ability to continue with their current physician. The status quo bias is not always a result of switching costs. Samuelson and Zeckhauser mention one person who buys the same chicken salad sandwich for lunch every day. This may be an example of being unwilling to explore one’s preferences for other options owing to the status quo bias. It might also be due to a strong and observed rational preference for that particular sandwich. If preferences are stable over time, the rational model would predict continuing with the same choices repeatedly when faced with the same decision.

History and Notes

The status quo bias was discovered and named by Samuelson and Zeckhauser in the late 1980s. More recently, since Eric Johnson’s work, there has been tremendous excitement among policymakers about the possibility of using default options to shape public well-being. However, some caution is necessary. Although default options are effective in shaping behavior, they also appear to be effective in shaping preferences. In this case, there is a serious question regarding the proper role of the

Reference Points, Indifference Curves, and the Consumer Problem		77

policymaker. Is it reasonable for the policymaker to be taking action to shape the people’s preferences about rather mundane issues? Additionally, whereas defaults as presented here offer relatively costless ways to shape choice without limiting the choices available to the individual, this would not be the case if the default options were relatively onerous, if there were some hassle involved in switching options, or if the use of defaults was so pervasive as to become an annoyance. For example, you might become annoyed if, by default, your account was debited $10 and you were delivered a chicken salad sandwich every day at noon if you did not call by 7:00 A.M. to express your wish for a different item (though Samuelson and Zeckhauser found at least one person who might be happy with the arrangement). Further, defaults are primarily effective where there is no strong preference between the options, or more especially where no preference has been formed. This could limit the usefulness of defaults in more well-developed policy spheres where people have given thought to preferences and outcomes. For example, recent efforts to require grade school students to take a fruit or vegetable with their school lunch have resulted in a sharp increase in the amount of fruits and vegetables tossed in the garbage.

Reference Points, Indifference Curves, and the

Consumer Problem

In earlier chapters, we originally defined loss aversion in terms of a value of wealth function. We also made use of loss aversion in the creation of indifference curves, but we never formally identified the meaning of loss aversion in the context of trading off consumption of various goods. Consider that a person must choose among a set of consumption bundles. Standard economic theory assumes a preference relation exists that represents the person’s motivation for choice. We can represent preferences using the relation , where x y means that consumption bundle x is preferred to consumption bundle y. Similarly, x y means that bundle x is at least as good as y, and x y means that the person is indifferent between x and y. Rationality assumes that the preference relation is complete and transitive. Completeness requires simply that given any two bundles, the person will be able to assign a preference relationship between the two. Transitivity requires that for any three bundles x, y, z, with y x, z y it cannot be the case that x z.

If people have a set of preferences that satisfy completeness and transitivity, it is possible to represent their preferences in the form of a utility function, ux, over consumption bundles, with the person behaving so as to maximize this utility function. Violations of transitivity are often called preference reversals. The simplest case of a preference reversal occurs when we observe that a person strictly prefers one bundle in one case, x y, but in another strictly prefers the other, y x. This appears to be the case we observe with the status quo bias or the default option bias. Utility maximization is predicated on a set of stable rational preferences. Thus, without these basic relations, we lose the ability to use standard utility maximization to describe the behavior.

	78		STATUS QUO BIAS AND DEFAULT OPTIONS
			Amos Tversky and Daniel Kahneman propose overcoming this problem by sup-
		posing that people have reference-dependent preferences. Here we define a reference
		state (not a reference point) as some outside set of conditions that cause preferences to
		change. Thus, given a reference state, the person has a set of rational preferences.
		However, the preferences are not necessarily rational when the reference is allowed to
		change between choices. A reference structure is a collection of preference relations
		indexed by a reference state,		r. Consider two different reference states, r1 and r2, in the
		same reference structure. The preference relation r1 must be complete and transitive
		given any reference state r1. However, it could be the case that x				r1 y and y r2 x. If people
		behave according to a reference structure, then it is possible to find a set of utility
		functions indexed by the		reference state representing the	person’s preferences as
		a function of the consumption bundle and the reference state, vr				x . Further, the person
		will behave as if she maximizes the utility function given the observed reference state.
		Standard utility theory is a special case of the reference-dependent model, where the
		reference state has no impact on preferences.
			As we have employed this model thus far, we will assume that the reference state is
		embodied by a single consumption bundle, called a reference point. Suppose that a
		consumption bundle consists of a collection of n goods in various nonnegative amounts
		and that the consumption bundle can be written as x = x1,			, xn , where x1 represents

the amount of good 1 consumed (and so on). Then, given a reference point, we can define loss aversion in consumption space.

Let x and y be any two consumption bundles, with xi > yi and yj > xj. Further, let r and

sbe any two reference points in consumption space, with xi ≥ ri > si, si = yi, and rj = sj. A reference structure displays loss aversion if for any consumption bundles and reference points satisfying these conditions, xry whenever xsy.

An example of this condition for the two-good case is shown in Figure 4.2. When the reference point is either r or s, consumption bundle x is considered a gain in terms of good i but a loss in terms of good j. Consumption bundle y is considered a gain in good j for either reference point. However, when the reference point is s, consumption bundle y is considered neither a gain nor a loss in good i, whereas from the point of view of reference point r, consumption bundle y is clearly a loss in good i. Because y is a loss in good i when considering reference point r, it requires a greater amount of good j to compensate the loss in i than if the reduction in i were simply considered the reduction of a gain. Thus, r implies a steeper indifference curve through bundle x than does s because s implies the removal of a gain rather than a loss. This notion of loss aversion generalizes the principles we have thus far used to represent loss-averse indifference curves. However, this simple version permits a wide variety of behavior, reducing the clarity of behavioral prediction as well as allowing behaviors that seem to be contradicted in observation. Thus, further restrictions on the shape of the indifference curves seem necessary.

Prospect theory generally proposes both loss aversion and that people experience diminishing marginal utility of gains and diminishing marginal pain from losses, commonly resulting in the convex shape of the value function over losses and the concave shape over gains. This notion of diminishing sensitivity to distance from the reference

point can also be translated into consumption space.

Let x and y be any two consumption bundles, with xi > yi and yj > xj. Further, let r and s be any two reference points, with rj = sj and either yi > si > ri or ri > si ≥ xi. A

Reference Points, Indifference Curves, and the Consumer Problem		79

good j

y

s r

good j

y

r s

x	vs = k1
	vr = k2
	good i	FIGURE 4.2
		Loss Aversion in Consumption Space

	sˆ	rˆ
	x	vr = k2
		vs = k1

good i	FIGURE 4.3
	Diminishing Sensitivity in Consumption Space

loss-averse reference structure displays diminishing sensitivity if for any consumption bundles and reference points satisfying these conditions, xry whenever xsy.

A reference-dependent structure satisfying diminishing sensitivity for two different sets of reference points is displayed in Figure 4.3. Here, when considering from the point of view of either reference point r or s, both x and y are considered gains in terms of good i, y is considered a gain in terms of good j, and x is considered a loss in terms of good j. The difference is that the consumption bundles are a greater distance from r than from s in the dimension of good i. When moving from y to x one gains xi − yi of good i. Owing to diminishing marginal utility of gains, this gain should provide a greater impact on

	80		STATUS QUO BIAS AND DEFAULT OPTIONS
		utility when it is realized closer to the reference point. Thus, this gain is more valuable
		when evaluating from reference point s than reference point r. Because the gain from
		xi − yi is smaller evaluating from r, it requires less of good j to compensate a move
		from xi to yi evaluating from reference point r than from s. This leads the indifference
		curve for vr x to have a shallower slope than that of vs x . Such effects may be why the
		bait-and-switch approach is so effective. This common marketing technique usually
		advertises some good at a price well below some (potentially never truly employed)
		regular price. However, when the customer arrives, the advertised good is sold out or
		otherwise not available, but some similar (potentially better quality) good at a modestly
		higher price is available. Setting the reference point at regular price and the original good
		makes the customer less sensitive to changes in other aspects of the deal.
			If instead we evaluate from reference points r and s, we can find the same relationship.
		Here, the loss of xi − yi has a greater impact when evaluating from s than at r owing to
		diminishing marginal pain from loss. Thus, it requires greater compensation for the loss
		when moving from xi to yi evaluating from s than evaluating from r. This again leads the
		indifference curve for vs x to have a greater slope than that for vr			x .
			Alternatively, if the decision maker displays constant marginal pain from loss and
		constant marginal utility from gains, we would say the preferences display constant
		sensitivity. Let x and y be any two consumption bundles, with xi > yi and yj > xj. Further,
		let r and s be any two reference points, with rj = sj and either yi > si			≥ ri or ri	> si ≥ xi. A
		loss-averse reference structure displays constant sensitivity if for any consumption
		bundles and reference points satisfying these conditions, x		ry whenever x		sy.
			In this case, the indifference curves for r and s must be identical, because the loss in
		value for a reduction from xi to yi is the same whether evaluating at r or at s. The distance
		from the reference point does not affect the marginal pain of the loss. Constant sensitivity
		places limits on the types of preference reversals that could take place. Constant sen-
		sitivity implies that no preference reversal between a bundle x and y can occur when
		considering reference points r and s, unless at least one dimension of either bundle is
		considered a gain under one reference point and a loss under the other. Otherwise,
		preferences would satisfy transitivity even if the reference point changes between
		decisions. Under diminishing sensitivity, preference reversals can occur even without
		bundles changing their loss or gain status in any dimension.
			Tversky and Kahneman propose a special case of the preference structure that is
		particularly useful in exploring the shapes of indifference curves and preferences. First,
		define a reference structure as displaying constant loss aversion if the preferences can
		be represented as a utility function of the form vr x = U R1		x1 ,	, Rn xn	, with

	Ri xi	=	ui xi	− ui ri	if	xi ≥ ri	4 1
			ui xi	− ui ri λi	if	xi < ri.

Here ui is an increasing function, and λi is a positive constant representing the degree of loss aversion; thus each argument of the value function is akin to a prospect theory value function in good i. Without loss of generality, suppose that uiri = 0. Given a reference point, when in the gain domain for any good, the ui function represents the value of the gain. In the loss domain, this function is multiplied by the added factor