# «By JONATHAN D. KETCHAM, NICOLAI V. KUMINOFF AND CHRISTOPHER A. POWERS* We develop a structural model for estimating the welfare effects of poli- cies ...»

** 3 ́ ́ ́.**

́ denotes the amount that person i expects to spend under plan j in terms of the premium plus out of pocket costs for prescription drugs, ́ is the variance of out of pocket costs, ́ is a vector of quality attributes, and is an idiosyncratic person-plan specific taste shock. The accents indicate that the variables reflect person i’s beliefs about plan attributes. Heterogeneity in beliefs is discussed below. Beneficiaries may also have heterogeneous marginal rates of substitution between expected cost, variance, and quality.

We model this heterogeneity as a linear function of observable demographics, some of which may evolve over time:, and similarly for and. Finally, people may lose utility from the time and effort required to learn about a plan and enroll in it. We assume that this cost is constant across plans so that it cancels out of betweenplan comparisons and can therefore be suppressed in (3).

We model heterogeneity in information by allowing suspect and non-suspect choices to be driven by different beliefs about PDPs. Non-suspect choices are assumed to be informed in the sense that decision makers’ beliefs about plan attributes coincide with the measures we collected. Put differently, we respect consumer sovereignty and invoke the standard assumption of full information in the absence of evidence to the contrary. In contrast, we do not observe the beliefs about plan attributes that led to suspect choices.

While the non-suspect (n) and suspect (s) groups may have different beliefs about plans, we assume that they share the same underlying preference parameters.

We dropped the accents in (5) to indicate that we are using objective measures of plan atPlans are occasionally discontinued, which can force people to make an active choice. In such case, we can revert to equation (3) to model the new enrollment decision.

26 Their expected PDP costs are defined as, their type-specific variance is defined as, and is a vector containing indicators for insurance companies and an index of overall plan quality developed by CMS. All variables are calculated using the techniques developed in prior studies of PDP choice as described in III.A.

When some decisions are misinformed, reforms that reduce information costs and/or simplify the choice process can, in principle, increase some consumers’ welfare. Consider a policy implemented between periods 0 and 1 that changes the set of available plans from to. Consumer welfare may be affected through three channels. First, the policy may change the menu of options by adding choices, removing choices, and regulating their costs or quality. Second, the policy may change how consumers or firms make decisions, e.g. by lowering the cost of switching plans. Finally, if the policy induces consumers and firms to adjust their behavior then those adjustments may feed back into the levels of endogenous attributes (e.g. premiums) through equilibrium sorting.

∑∈ 9 ∆, ∑∈

Welfare calculation is more involved for the suspect group. The observed part of (8) determines how PDP attributes affect their enrollment decisions, but their ex post realized utility from those decisions is determined by (5). This follows from our assumption that, conditional on prescription drug use and demographics, the suspect and non-suspect groups share the same underlying preference parameters. Therefore, a single plan’s contribution to expected utility is defined by integrating over the product of (5) and the probability of choosing that plan based on (8). Aggregating over the PDP menu prior to the policy yields the following general expression 10,…,, ∈ ∙ is the derivative of the joint CDF of the idiosyncratic taste shocks with rewhere spect to. Subtracting this expression from the post-policy measure of expected utility, dividing by the marginal utility of income, and integrating over the idiosyncratic taste shocks yields an expression for welfare that was first derived by Leggett (2002) as a way to describe decision making under misinformation.

21 ∑∈ ∑ ∑ 11 ∆, ∈ ∈ ∑∈

The first term inside braces in (11) is the standard log sum ratio evaluated at. The second and third terms adjust the log sum ratio to account for the welfare implications of the difference between and for each choice, weighted by the predicted probability of making that choice before and after the policy. In the special case where, equation (11) reduces to the standard welfare measure in (9).

** C. The Welfare Treatment of Inertia**

Equations (9) and (11) treat the non-suspect group’s inertia parameters as being directly relevant for welfare. This is consistent with interpreting inertia as a mixture of latent preferences and hassle costs of switching plans. However, Kling et al. (2002) argue that inertia is more likely to reflect downward biased expectations for the savings from switching plans along with other psychological factors such as status quo bias, procrastination, and limited attention. These mechanisms have no direct effect on consumer welfare; they affect welfare indirectly by lowering the rate at which consumers switch plans.

Our data do not allow us to distinguish the importance of psychological bias relative to latent preferences and switching costs. One can separate them, in principle, by adding assumptions on the form of statistical distributions for unobserved preference heterogeneity and switching costs (e.g. Heckman 1981, Dube et al. 2010, Polykova 2015). We prefer to avoid such assumptions by instead taking a partial identification approach similar to Handel (2013) and Bernheim, Fradkin, and Popov (2015). We calculate welfare for two extreme cases that provide bounds on the share of inertia that is welfare relevant. In the first case, inertia is assumed to be entirely welfare relevant (as in (9) and (11)) and in the second case it is assumed to be entirely irrelevant, e.g. due to psychological bias.

To calculate the change in expected welfare when inertia reflects psychological biases we replace equations (9) and (11) with (9’) and (11’).

Prospective welfare analysis also requires us to take a stance on whether a counterfactual choice architecture policy would induce consumers to behave differently. In principle, a policy designed to simplify the choice process could induce decision makers in the suspect group to update their beliefs about the market and behave more like decision makers in the non-suspect group. Or it could have no effect at all. In the absence of empirical evidence, we again take a partial identification approach and consider two extreme scenarios. One scenario assumes that the policy has no effect on behavior; the other assumes that the policy induces consumers in the suspect group to behave like those in the non-suspect group, conditional on demographics and prescription drug utilization. The second case involves replacing in equations (11) and (11’).

with and with In practice, we evaluate consumer welfare using the union of bounds on the policy’s effect on behavior and bounds on the treatment of inertia.

** E. Discussion**

Our welfare framework is consistent with divergent theories of consumer decision making. When it is costly for consumers to acquire information, to make a decision, or to negotiate a transaction they may choose not to become fully informed (Stigler and Becker 1977). Misinformation may also stem from psychological biases (Kahnemann, Wakker, 23 and Sarin 1997).27 Our framework requires observing which decisions are affected by some combination of these mechanisms, but it avoids the need to model them or take a stance on their relative importance. The disadvantage of being unable to disentangle these mechanisms in our data is that we only recover bounds on welfare. Whether the bounds are informative is an empirical question.

The bounds that we derive extend Small and Rosen’s (1981) welfare measure to recognize that consumers differ in the information they use to make decisions. Our adjustment for misinformation implements Bernheim and Rangel’s (2009) proposal for how to measure welfare when the analyst suspects that some choices will not reveal preferences.

This allows us to recognize that choice architecture may create winners and losers. As an extreme example, consider the partial equilibrium welfare effects of a hypothetical policy that eliminates consumer choice by simply assigning each consumer to a plan. Nobody can be made better off from such a policy within a model that assumes all consumers are fully informed (e.g. Lucarelli, Prince, and Simon 2012). At the opposite extreme, nobody can be made worse off within a model that assumes the policy is implemented by a benevolent regulator who knows consumers’ preferences better than they know their own preferences (e.g. Abaluck and Gruber 2011). Our approach provides a middle ground between these extremes. Equation (9) and its analogs recognize that informed consumers can be made worse off from restrictions on choice. Equation (11) and its analogs introduces flexibility so that misinformed consumers may gain or lose from restrictions on choice. Aggregating the gains and losses can yield criteria for policy evaluation consistent with the concept of asymmetric paternalism (Camerer et al. 2003).

Our framework also highlights the information needed to evaluate a prospective policy. First we must estimate parameters describing how suspect and non-suspect choice probabilities vary with plan attributes, and, in order to calibrate,,, and ∗. Then we must map the policy onto plan attributes and utility in order to calibrate ∗,,, and and calculate bounds on welfare.

27 To use the terminology from Kahnemann, Wakker, and Sarin (1997), one can think of as approximating the “hedonic utility” derived by consuming a good and as approximating the “decision utility” function maximized by people who are misinformed.

Table 5 presents the estimates that we use as the basis for policy experiments.28 The first column reports results for a naïve model that pools data on suspect and non-suspect choices. The main effects have the expected signs and are precisely estimated, with the exception of variance. Its insignificant coefficient mirrors the finding from Abaluck and Gruber (2011) and Ketcham, Kuminoff and Powers (2015) that in a naïve model of PDP choice the typical enrollee appears to ignore risk protection. Interacting variance with the MCBS college degree indicator suggests that college graduates are more risk averse.

Columns 2 and 3 repeat the estimation for non-suspect and suspect choices alone.

Comparing main effects across the three columns reveals that the insignificant coefficient on variance in the pooled model is driven by aggregating over suspect and non-suspect choices. Taken literally, the coefficient on variance for the suspect group implies they are risk loving. In contrast, the non-suspect group is risk averse at levels consistent with findings from prior studies (Cohen and Einav 2007, Handel 2013, Handel and Kolstad 2015).

For example, our results imply that enrollees in the non-suspect group would be indifferent between a 50-50 bet of wining $100 and losing between $94.2 and $96.3; and indifferent between a 50-50 bet of winning $1,000 and losing between $665.4 and $738.9.29 Further, the non-suspect group is more sensitive to price with the implication that the monetary value of inertia—defined by dividing the switching indicators by the expected cost coefficient—is nearly three times larger for the suspect group.

Focusing on non-suspect choices in column 2, the interaction coefficients are consistent with intuition. Interactions between cost and indicators for whether the beneficiary is in the top or bottom terciles of the claims distribution imply that the marginal utility of income declines as people become sicker. People who have previously taken the time to 28 We also estimated more flexible models that interacted PDP attributes with more comprehensive sets of demographic variables.

However the additional interactions tend to have small and statistically insignificant effects (Table A3), which led us to use the more parsimonious specification in Table 5. A notable result from the more comprehensive model is that enrollees who do and do not get help making health insurance decisions make choices that imply virtually identical marginal rates of substitution between cost, variance, and quality. The main difference between the two groups is that those who get help exhibit less inertia, as shown in Table 5.

29 These calculations are based on the fact that our specification for utility provides a 1st order approximation to a CARA model. Our calculations are additional discussion are provided in Table A4 and associated discussion in the supplemental appendix.

Note: The table summarizes logit models estimated from data on all choices; non-suspect choices only; and suspect choices only. All models include indicators for insurers. Excluded demographic interactions define the reference person as white and 78 years old with no college degree and annual income below $25,000. This person is in the middle tercile of the distribution of total drug claims, did not get help making an enrollment decision, and did not use the internet or 1-800-Medicare to search for information. Robust standard errors are clustered by enrollee. *,**, and *** indicate that the p-value is less than 0.1, 0.05, and 0.01 respectively.