Disentangling Moral Hazard and Adverse Selection in Private Health Insurance

Abstract

Moral hazard and adverse selection create inefficiencies in private health insurance markets and understanding the relative importance of each factor is critical for addressing these inefficiencies. We use claims data from a large firm which changed health insurance plan options to isolate moral hazard from plan selection, estimating a discrete choice model to predict household plan preferences and attrition. Variation in plan preferences identifies the differential causal impact of each health insurance plan on the entire distribution of medical expenditures. Our estimates imply that 53% of the additional medical spending observed in the most generous plan in our data relative to the least generous is due to adverse selection. We find that quantifying adverse selection by using prior medical expenditures overstates the true magnitude of selection due to mean reversion. We also statistically reject that individual health care consumption responds solely to the end-of-the-year marginal price.

1. Introduction

Moral hazard and adverse selection create inefficiencies in health insurance markets and result in a positive correlation between health insurance generosity and medical care consumption. The policy implications are very different, however, depending on the relative magnitudes of each source of distortion, though empirically isolating the independent roles of moral hazard and adverse selection for private health insurance is often difficult and is rare in the literature. This paper quantifies the importance of moral hazard and adverse selection for the health insurance plans offered by a large firm. Our method provides estimates of the effects of plan generosity on the entire distribution of medical care expenditures while also permitting us to characterize the full distribution of adverse selection.

Rising health costs have prompted interest in mechanisms to reduce health care spending. There is a large literature studying how health insurance design encourages medical care spending and there is evidence that cost-sharing reduces health care consumption (see Baicker and Goldman (2011) for a review). Many recent federal policies have focused on increasing cost-sharing as a means to pass costs to the consumer and discourage additional consumption of medical care. The Patient Protection and Affordable Care Act (ACA) of 2010 promotes cost-sharing in several ways, such as the planned introduction of a “Cadillac Tax” which taxes plans with high premiums and, presumably, generous cost-sharing arrangements. Health savings accounts, established in 2003, encourage the purchase of high deductible plans which have less generous coverage at low levels of annual medical expenditures. On the other hand, policies encouraging the purchase of generous health insurance plans have been shown to have meaningful effects on medical care consumption. The income tax exclusion for employer-provided health insurance promotes the purchase of generous plans and additional consumption of care (Feldstein (1973); Pauly (1986); Cogan et al. (2011); Powell (forthcoming)).

Adverse selection is another impediment to efficiency in health insurance markets and the ACA’s individual mandate was motivated by the efficiency gains of reducing systematic selection into insurance. A large literature documents the difficulties in separating adverse selection and moral hazard (Chiappori and Salanie (2000); Chiappori (2000); Finkelstein and Poterba (2004)). We use plan introduction as an exogenous shock to plan generosity and then estimate the medical expenditure distribution of each plan if enrollment were random. The difference in the observed medical care distribution and this estimated distribution driven solely by moral hazard quantifies the magnitude of selection. While existing research has provided mean differences as metrics of adverse selection, we estimate the entire distribution of adverse selection. The distribution is interesting from a policy perspective because the mean can mask important heterogeneity. For example, adverse selection could – in principle – be driven by a small share of enrollees in a plan who are very sick. We find that the population enrolled in the most generous plan is more prone to health care consumption throughout the entire distribution.

We analyze administrative health claims data from a large employer in the United States for 2005–2007. This employer offered only one insurance plan in 2005. In 2006, they introduced three different PPO plans to replace the 2005 plan. These plans varied in generosity based on their deductible, stop loss, and coinsurance rate. We estimate the impact of each plan on the entire distribution of medical care consumption. We use the availability of new plans and the differential preferences for plan generosity, determined by observable family characteristics, for identification. We estimate a discrete choice model to predict the probability of enrollment into the new plans based on household characteristics. The estimated preferences act as our instrumental variables and identify our model hazard effect. We condition on the same household characteristics to account for the independent effects of the covariates and we further condition flexibly on 2005 medical expenditures to control for individual and household heterogeneity in health care consumption. This strategy allows us to estimate the effect of the plan on medical care if selection into the plan were random. Once we have estimated the distribution of expenditures for each plan, we can compare the observed distribution that selected into the plan to the estimated distribution if enrollment were random, separately identifying a useful measure of adverse selection.

We estimate the distributions resulting from enrollment in each plan non-parametrically instead of assuming that individuals respond to a specific price in the plan. We map each estimated distribution directly to the non-linear budget constraint created by the health insurance plan and observe whether the medical spending distribution is especially responsive for annual expenditure levels above the deductible or stop loss. This mapping provides insight into which aspects of a plan, such as the deductible or coinsurance rate, impact health care decisions. While there are many possible mechanisms through which a plan with a lower deductible can encourage additional consumption, a basic first step is to study this mapping between the plan and the distribution of medical care.

There is a long-standing interest in how responsive people are to the generosity of their health insurance plan. The RAND Health Insurance Experiment (Manning et al. (1987)) estimates are still widely considered the standard in this literature. More recent studies have also estimated the relationship between insurance cost-sharing and health care consumption, but there is no consensus about how to parameterize a health insurance plan. The RAND estimates assume that individuals respond only to the spot price - the out-of-pocket portion of the next $1 of medical care consumed. Recent work has asked what the relevant price is in the presence of a non-linear health insurance plan (e.g., Aron-Dine et al. (2015)). A limited number of studies model households as potentially responding to the entire budget set generated by a health insurance plan. These studies (including Cardon and Hendel (2001); Einav et al. (2013)) often do not use variation across plans for identification, require strong structural assumptions, and assume perfect foresight.

In this paper, we study the impact of different health insurance plans on the entire distribution of medical care consumption. This approach allows us to circumvent parameterizing plans by potentially uninformative metrics, imposing restrictive behavioral assumptions, or requiring individuals to solely respond to specific types of prices. The results can be interpreted as the medical expenditure distribution that we would observe if each person in the data were enrolled in the plan or, put differently, if there were no systematic selection into the plan. This approach also permits us to directly test the assumption that individuals respond to the realized end-of-year marginal price.

We see our paper as making five contributions. First, this paper is the first to estimate moral hazard with respect to health insurance by estimating unconditional quantile treatment effects, studying the entire distribution of responses to different health insurance plans. Second, by estimating the causal effect of each plan, our method allows us to be agnostic about how benefit design impacts medical care consumption. We estimate the impact of each plan on the distribution of medical expenditures with no parameterizations of the plans. We compare these non-parametric distributions to the estimated distributions when we impose restrictions made in the literature. We test the equality of the two distributions, allowing us to implement a straightforward test of the usefulness and accuracy of the more restrictive assumptions.

Third, we directly account for attrition in our sample. Families opt out of employer-sponsored health insurance for a variety of reasons, such as job changes and shifts in preferences for health care. In the literature, it is common to select on individuals who are observed for the entire time period. Attrition in the data can often be quite severe and the sources of attrition are potentially not random. In our empirical strategy, we predict both plan choice and attrition to jointly estimate a selection instrument which statistically predicts attrition, permitting us to compare people with similar probabilities of remaining in the sample for the entire period. It is straightforward to extend the quantile estimator to account for selection, introducing a new method to condition on a nonseparable sample selection adjustment.

Fourth, we separate adverse selection and moral hazard, providing magnitudes and distributions for both. Bajari et al. (2014) estimates a structural model to separate adverse selection and moral hazard in the context of private health insurance by fitting a specified utility function. Keane and Stavrunova (2016) separates moral hazard from selection in the context of Medigap, using behavioral variables such as cognitive ability as instruments for insurance coverage. They find evidence of moral hazard as well as advantageous selection, consistent with prior evidence for the Medigap context (Fang et al., 2008). Generally, however, it is rather rare to provide evidence of the relative importance of these distortionary forces. We observe plans that are similar but with clear ranks in terms of generosity. Because we estimate the causal distribution for each plan, we can compare the observed distribution - which is a function of both moral hazard and adverse selection - with the estimated distribution that we would counterfactually observe if there were no adverse selection. This difference identifies the magnitude and distribution of selection. There is widespread interest in adverse selection in health insurance (Cutler and Reber (1998); Bundorf et al. (2012); Cardon and Hendel (2001); Carlin and Town (2010); Geruso (2013); Handel (2013)), and we are able to provide plan-specific estimates of the magnitude of adverse selection and its relative importance compared to moral hazard.

Finally, we also find that measuring adverse selection by using prior medical expenditures overstates the magnitude of selection into the most generous plan. Put differently, a “naïve” difference-in-differences estimate comparing medical spending changes for those enrolling in the most generous plan to those enrolling in the least generous understates the true magnitude of moral hazard. Given medical expenditures in a previous year for households selecting into new plans, we might expect that using prior medical expenditures may understate adverse selection if households have private information about changes in health or preferences for medical care. Alternatively, mean reversion would suggest that high-spending households will, on average, experience reductions in medical spending. If these high-spending households also tend to enroll in generous plans – because they are selecting plans based partially on minimizing out-of-pocket costs given prior health care consumption – then previous medical care spending may overstate the true level of adverse selection. We find that this mean reversion mechanism dominates. We are able to separate and quantify these two biases.

We estimate plan elasticities and find that the most generous plan encourages additional spending throughout the medical care distribution. Observed expenditures in the most generous plan are, on average, $3,969 more than the per person costs in the least generous plan. We estimate that if selection were random, that the most generous plan would lead to $1,862 in more spending than the least generous plan, implying that 47% of the observed differential can be attributed to moral hazard. We also estimate adverse selection magnitudes. We find that if everyone in the sample were enrolled in the least generous plan that the annual premium for that plan would increase by $1,300. We also statistically reject that the price elasticity, using the end-of-year price, is an appropriate parameterization to describe behavioral responses to benefit design.

In the next section, we briefly discuss the importance of estimating the roles of adverse selection and moral hazard. We also consider the merits of an approach that does not parameterize moral hazard by a response to a specific price. Section 3 discusses the data and empirical strategy. Section 4 details the estimator and the parameters that are estimated. Section 5 presents the results and we conclude in Section 6.

2. Theory

2.1. Moral Hazard and Adverse Selection

An influential theoretical literature links asymmetric information in insurance markets to inefficient outcomes. Rothschild and Stiglitz (1976) models selection into plans with different risk types. Pauly (1968) discusses the role of moral hazard in health insurance and mechanisms to reduce medical care consumption such as cost-sharing. Optimal policy depends on the relative importance of adverse selection compared to moral hazard in explaining the correlation between plan generosity and medical care costs. The policy implications for moral hazard are different than those required to confront adverse selection. Adverse selection typically requires risk-pooling, while distortions driven by moral hazard would motivate additional cost-sharing. These issues are discussed in further detail in Cutler and Zeckhauser (2000).

Addressing the distortions induced by either moral hazard or adverse selection often exacerbates the inefficiencies created by the other factor. For example, the ACA’s individual mandate encourages healthier individuals to purchase insurance, pooling risk across a more heterogenous population. At the same time, the mandate plus the insurance expansions increase the number of insured individuals, driving down the price of care to consumers. Understanding the magnitude of this tradeoff is a first-order concern for health care policy. The importance of isolating the role of these two factors has been noted in insurance markets more generally and methods to empirically identify each have been introduced (see Abbring et al. (2003)).¹

2.2. Nonlinear Budget Sets

There are many reasons to believe that the entire budget constraint, not just a single segment and price, potentially matters when studying the effect of health insurance plans on any given part of the medical care consumption distribution. It is common to parameterize behavioral responses to benefit design when estimating responsiveness to health insurance. A related literature has studied estimation of labor supply responsiveness given nonlinear budgets sets created by income tax schedules (e.g., Hausman (1985); Blomquist and Newey (2002)), often reducing the dimensions of the full budget set based on the implications of utility maximization given a convex budget set. Keane and Moffitt (1998) studies labor supply and program participation behavior when welfare programs potentially imply several possible nonlinear budget constraints, permitting households to maximize utility over all possible nonlinear budget sets. The application of this paper also involves households choosing between multiple nonlinear budget sets and then responding to the incentives implied by the chosen budget constraint.

In the literature studying the price responsiveness of medical care, health insurance plans are often summarized by one particular price. We highlight three reasons why these parameterizations are likely too restrictive, suggesting gains in estimating the effect of a health insurance plan without parametric assumptions. First, we consider a model with a standard utility function U(c, m) where both consumption of goods c and medical care m are valued and preferences are convex. Assume that the person has perfect foresight and decides at the beginning of the year exactly how much medical care to consume. We can draw the budget constraint generated by a typical health insurance plan. In Figure 1, we include a deductible which generates a kink in the budget constraint. A stop loss point would generate a similar kink. The shape of the indifference curve follows directly from convex preferences. In this basic setup, it is possible that there is not a unique optimum due to the non-convexity of the budget constraint. Say that we observe an individual on the second segment of the budget constraint (to the right of the kink). Given standard assumptions on preferences, we cannot rule out the possibility that small changes in the first segment of the budget constraint would change the individual’s optimal health care consumption. The implication is that it would be inappropriate to assume that an individual only responds to the marginal price. While non-convexities in the budget constraint appear in other contexts, health insurance poses a situation where they are the norm and should not be ignored.

Figure 1:

Indifference Curve and Non-Linear Budget Constraint

Notes: This figure graphs consumption of all other goods as a function of total annual medical expenditures. The indifference curve assumes convex preferences.

Second, episodes of care can generate consumption behavior which appears inconsistent with convex preferences. Individuals may decide between not receiving a specific treatment versus initiating an expensive set of treatments. Keeler et al. (1977) and Keeler and Rolph (1988) include arguments that any price of care variable must account for these episodes. Again, the implication is that changes in one segment of the budget constraint may impact behavior on other segments.

Third, nonlinear budgets sets generate variation in spot prices throughout the year. Perfect foresight is a strong assumption, especially in the context of medical care consumption, which is a function of unforeseen health shocks. Purely myopic behavior is also unlikely. It is difficult to model how the different prices interact and how that relationship changes throughout the year. Cronin (2016) uses structural restrictions to separate myopic behavior from responsiveness to end-of-year prices. Abaluck et al. (2018) uses nonlinearities in Medicare Part D to study prescription drug utilization and consumer responsiveness to spot and expected marginal prices.

We believe that the policy parameters of interest are the responses to the entire health insurance plan. A health insurance plan can encourage consumption through several mechanisms, such as reducing the marginal cost of care, reducing the spot price of care for part or all of the year, or reducing the price of larger episodes of care. While understanding the role of each mechanism is interesting, we are concerned here with estimating the overall impact of a plan. We take a necessary step back relative to the literature to understand the role of benefit design in impacting annual medical care consumption. It is difficult to parameterize plans in such a way as to independently isolate the above factors. For example, using variation in spot prices (or variation in the time exposed to a specific spot price) within the year is typically tied to variation in the location of the kinks, making it difficult to distinguish myopia from the behavior that we would expect given Figure 1. Conceptually, myopia and behavioral responses (with perfect foresight) to non-convex budget constraints cannot be independently isolated without additional assumptions. The cost of our approach is that we are limited in the inferences that we can make since we only observe a limited number of health insurance plans offered by our firm.

3. Data and Empirical Strategy

3.1. Background

We study the impact of employer-sponsored health insurance on medical care spending. Traditional employer-sponsored health insurance plans are defined by three characteristics: the deductible, the coinsurance rate, and the stop loss. Consumers pay the full cost of their medical care until they reach the deductible at which point they are only responsible for a fraction of their costs, referred to as the “coinsurance rate.” In our sample, we observe plans with coinsurance rates of 0.1 and 0.2. Finally, consumer risk is bounded by the stop loss - the maximum annual out-of-pocket payments by the consumer. After stop loss, the consumer faces a marginal price of zero for additional medical care.

These plans are defined by individual annual expenditures, but it is also common for plans to include a family deductible and family out-of-pocket maximum. In our analysis, we want to map the distribution of expenditures to the non-linear budget set created by the health insurance plan and these family-level parameters obscure this mapping. Consequently, we select on families with only one or two enrollees because they cannot reach the family deductible or stop loss for the plans that we study. For example, the individual deductible for the most generous plan is $200 and the family deductible is $400. By limiting our analysis to families with only one or two members, we can ignore family-level parameters. This is beneficial because we know that a person consuming $50 of medical care is below the deductible. If we included larger families, then this individual could be facing the coinsurance rate or even a marginal price of 0 due to high medical care consumption of family members and drawing the individual’s budget constraint is complicated by such family-level interactions.

In our data, we study a firm that offered only one plan in 2005, which we label as Plan A. In 2006, the firm offered three PPO plans of varying generosity, which we label as Plans B, C, and D. Plan B is the most generous 2006 plan with a low deductible, coinsurance rate, and out-of-pocket maximum. Plan C is less generous and Plan D is the least generous plan. In 2007, the deductibles and stop loss points for Plans B and C changed. Table 1 provides the relevant parameters for each of the plans in our data.²

Table 1:

Health Insurance Plans

	Plan (Year)	Plan A (2005)	Plan B (2006)	Plan C (2006)	Plan D (2006)	Plan B (2007)	Plan C (2007)	Plan D (2007)
Deductible	Individual	$0	$200	$400	$800	$250	$450	$800
	Family	$0	$400	$800	$1,600	$500	$900	$1,600
Stop loss	Individual	None	$1,000	$2,000	$4,000	$1,250	$2,250	$4,000
	Family	None	$2,000	$4,000	$8,000	$2,500	$4,500	$8,000
Coinsurance		20%	10%	20%	20%	10%	20%	20%
Plan Type		PPO	PPO	PPO	PPO	PPO	PPO	PPO

In Figure 2, we show the empirical non-linear budget constraints generated by our plans. Our goal in Figure 2 is to illustrate the shapes of the budget constraints for the first $18,000 of annual medical expenditures. While we do not observe premiums in our data, we estimate premium variation across plans using average insurer payment differences (i.e., assuming risk-neutrality for the insurer).³ This informs the starting point for each budget constraint. There are significant differences in the placement of the kink points relative to annual medical expenditures.

Figure 2:

Budget Constraints Generated by Plans in Data

Notes: This figure graphs the nonlinear budget set generated by each 2007 plan. We do not observe premiums, but we estimate premium differences using spending differences across plans. The variation in the starting points of the 3 budget constraints is due to estimated premium variation only.

3.2. Data

We use administrative claims data from a large firm included in the MarketScan Commercial Claims & Encounter and Benefit Plan Design Databases. The firm is a large manufacturing firm, and the employees reside in 44 different states.⁴ The workers are not unionized and are predominantly salaried (94%) and work full-time (84%). These data provide basic demographic information for each person and detailed information about inpatient and outpatient medical claims, including out-of-pocket and total costs. The data also provide information about plan choice and plan structure, though there is limited information on other plan features such as networks. We observe claims from the firm for 2005–2007 and we restrict our attention to employees for whom we observe spending in 2005. We model medical expenditures for those with a full year of reported expenditures in 2007. Because this is a selected sample, we adjust for attrition. The benefit of observing multiple years is that we can compare the distributions of expenditures in 2005 and 2007 to account for individual-level (and household-level) heterogeneity. We observe all individuals enrolled in a plan even if they do not consume any medical care.

Another benefit of this firm is that the plans are identical except for the deductible, coinsurance rate, and stop loss. Consequently, given exogenous variation in plan enrollment, we can attribute differences in consumption behavior to the differences in these plan parameters. Furthermore, there was only one plan in 2005 so we can control for 2005 medical expenditures as an accurate representation of 2005 demand for medical care as each person is equally treated by plan generosity.⁵

Summary statistics are presented in Table 2. We present the summary statistics by 2007 plan. We do this for our sample (family sizes of 1 or 2) and, for comparison purposes, the full sample (no restrictions on family size) in Appendix Table A.1. As one might predict, the most generous plan attracts an older population with higher mean medical expenditures in 2005. The mean age and 2005 medical expenditures decrease with plan generosity. Furthermore, the “No Plan” group (the attriters) do not appear to be randomly-selected.

Table 2:

Summary Statistics

Family Size ≤ 2
	Plan B	Plan C	Plan B	No Plan
2005 Medical Expenditures	$5,157.89	$2,521.67	$1,453.58	$3,821.29
	($12562.64)	($5462.58)	($3059.12)	($12226.04)
2007 Medical Expenditures	$5,441.79	$2,883.20	$1,559.35	-
	($13291.73)	($7827.91)	($5021.00)	-
Family Size	1.51	1.57	1.41	1.66
	(0.50)	(0.50)	(0.49)	(0.47)
Age	52.23	48.69	39.88	52.88
	(8.98)	(11.33)	(13.05)	(9.84)
End-of-Year Marginal Price = 0.1	67.52%	0.00%	0.00%	-
End-of-Year Marginal Price = 0.2	0.00%	45.72%	24.32%	-
End-of-Year Marginal Price = 0	9.54%	4.14%	0.63%	-
N	2,777	4,639	1,435	12,578

Notes: All dollar values are nominal.

It is worth noting that the changes in expenditures, comparing 2007 to 2005 expenditures, are relatively similar across all three plans. However, using the raw differences in means across different plans as a measure of moral hazard is problematic for two primary reasons. First, households have private information about changes in health or preferences for health care, which are not accounted for by looking at prior medical expenditures. In general, private information should increase the additional spending observed in the most generous plans, implying that using observed changes in medical expenditures would overstate the true magnitude of moral hazard. To account for this private information, we predict probabilities of plan enrollment based on fixed household characteristics and use these predictions as instruments instead of using actual plan enrollment for variation. Second, even holding plan enrollment fixed across households, we would not expect households to have similar spending to their prior levels. Instead, we likely expect mean reversion to play a role – households with high spending will, on average, incur lower spending in future years. To the extent that households enroll in new plans based partially on prior medical care spending, then mean reversion would suggest that the raw changes shown in Table 2 understate moral hazard for the most generous plan. To account for mean reversion, we will control flexibly for 2005 medical expenditures in our models. We will disentangle the magnitudes of these two effects – private information regarding changes in health care preferences and mean reversion. We find that mean reversion dominates, implying that the differences shown in Table 2 mask moral hazard.

3.3. Attrition

A common concern with the use of claims data is attrition, which may bias estimates if this attrition is systematic. Selection bias concerns extend throughout the literature on medical care utilization, including influential randomized experiments (see Nyman (2008); Newhouse et al. (2008) for discussion of attrition in the RAND Health Insurance Experiment and Finkelstein et al. (2012) for the Oregon Health Insurance Experiment). In firm-level claims data, attrition occurs because employees drop coverage, leave the firm, switch to a spouse’s plan at another employer, and so on. If we define attrition as individuals enrolled in 2005 but enrolled for less than 365 days in 2007, the attrition rate across plans in the MarketScan data (selecting on firms in the data in both 2005 and 2007) is 58.3%. Our sample has a 58.7% attrition rate.

We select on individuals that are enrolled for 365 days in 2005. Some individuals disenroll in 2005, but this disenrollment should be orthogonal to the introduction of the new plans. The plans begin on January 1 and there is little (differential) incentive to switch to a different source of insurance (or no insurance) before that date. Attrition in the latter part of 2005 is rare and unlikely to be systematic. In Section 5.10, we test the robustness of our results to this assumption.

Despite the high rates of attrition in the MarketScan data and claims data more generally, research using these data sets often ignore the potential problems caused by selection. Conditioning on 2005 medical expenditures and covariates alleviates this concern, but we account for selection explicitly. We consider anyone enrolled for less than 365 days of 2007 as “attriters.” This broad definition is necessary because we will study the distribution of medical expenditures in 2007, which we only observe for those enrolled for all of 2007. We predict selection in our sample (non-attrition) in the same manner as we predict plan choice, which is discussed below. Attrition is separately identified using our empirical strategy and the conditions for a valid selection instrument are equivalent here to those needed for our plan choice instruments: the estimated probability of non-attrition must (1) predict non-attrition and (2) not affect medical care expenditures except through selection. We show that (1) is true empirically. We assume that (2) holds for the same reasons that we assume our instruments are plausibly exogenous conditional on household covariates and flexible functions of 2005 medical expenditures for both the individual and spouse/dependent.

3.4. Identification Strategy

Our outcome variable is 2007 medical care expenditures. We study 2007 instead of 2006 for the possibility that the change in plan options caused individuals to shift care that they otherwise would have consumed in 2005 for coverage under their 2006 plan.⁶ We explore the importance of temporal shifting more in Section 5.10.

Our identification strategy relies on the introduction of plans with varying generosity and the differential effect that this introduction had on enrollees based on covariates. We use the following household information to predict 2007 plan choice: 2005 family size, employee age, employee sex, age of other household member, sex of other household member, and the other member’s relationship to employee (spouse or dependent).

We use the changes in plan options for identification. Each person in our sample was enrolled in Plan A in 2005. We can assume that many of these families would have preferred a plan with different generosity. In 2006/2007, they were given a different set of options and sorted according to their preferences. We use the household characteristics to predict the probability of enrollment in 2007 into each plan using a discrete choice model. The predicted probabilities from the estimation of this model are our instruments. Given that the covariates should also independently affect medical care consumption, we condition on the same covariates in our analyses to isolate the differential effect of plan availability for identification. Identification originates from the nonlinearities of the probability estimates. Because we are also concerned about systematic attrition, we jointly estimate the probability of enrollment into each plan and the probability of attriting. We do not include 2005 medical expenditures in the discrete choice model to predict 2007 plan choice (and attrition). The discrete choice model predicts plan choice based only on fixed household characteristics at the start of 2005, reducing concerns that factors related to mean reversion partially determine variation in our instruments.⁷

While we control for the same covariates used to generate the predicted probabilities, we are concerned that the nonlinearities identifying the model may predict individual medical care consumption. To account for possible confounding individual-level heterogeneity, we leverage the longitudinal nature of the data and condition flexibly on “untreated” 2005 medical expenditures. Since each person was enrolled in the identical 2005 plan, medical care expenditures reflect variation in health and preferences for medical care since the treatment (plan generosity) was the same for each person. In our analysis, we condition on a 5-piece spline in lnM_i,2005, the log of 2005 medical expenditures for person i (set to 0 if M_i,2005 = 0), and a dummy variable equal to 1 for individuals with no 2005 medical expenditures. Our results are robust to more flexible functions. We also condition on the 2005 medical expenditures of the individual’s spouse/dependent to account for differences across households, using a 5-piece spline in the log of 2005 expenditures for the person’s spouse/dependent (as well as an indicator equal to 1 if spouse/dependent had no medical expenditures in 2005). This approach accounts for differences in medical care consumption propensity when all households are “untreated,” effectively studying changes in medical care consumption due to plan enrollment while flexibly accounting for potential mean reversion concerns.

3.5. Sample Selection

We select our sample on families with two or fewer members and a full year of enrollment in 2005 as described earlier. We study the medical care expenditures of the employees only. Our analysis sample includes 21,429 people. A high fraction of these 2005 enrollees attrit at some point before the end of 2007. Many are not observed in the data because they left the firm or dropped insurance at some point before the end of 2007. We also consider individuals that change plans after January 1, 2007 as attriters since we cannot map their behavior to a single budget constraint. Moreover, some policies gain members due to spouses or dependents joining the policy or due to births. We label employees which originally had policies with two of fewer members but added members by the end of 2007 as attriters since, as described above, these employees are subject to the family deductible and out-of-pocket maximum. Our selection adjustment term is estimated with these attriters and should account for different sources of attrition. When estimating the quantile functions of interest, our sample is the set of employees enrolled in the same 2007 plan for the entire year. We adjust for the probability of remaining in the sample until the end of 2007 to account for non-random attrition.

4. Empirical Model and Estimation

We use a quantile framework in our analysis for three reasons. First, a significant proportion of our analysis sample consumes no medical care within a year, and this censoring can bias mean estimates. Quantile estimates are robust to censoring concerns without making strong distributional assumptions. Second, the distribution of medical expenditures is heavily-skewed. Mean regressions techniques may primarily reflect behavioral changes for people at the top of the expenditure distribution and, in general, mean regression estimates are not necessarily representative of the impact at any part of the distribution. Third, a primary goal of this paper is to understand how insurance plans affect medical care consumption. If individuals are responding to the end-of-year marginal price, then we should observe that plans have larger causal impacts in the parts of the distribution above the deductible than the parts of the distribution below the deductible. Estimating a distribution permits us to map the quantile estimates to the plan parameters and observe whether the plan has larger impacts at parts of the distribution where the end-of-year price is lower. We will use the quantile treatment effect (QTE) framework introduced in Powell (2018) and extend it to account for sample attrition. We discuss the estimator more generally first.

4.1. Quantile Estimation

4.1.1. Generalized Quantile Regression

This paper uses and extends generalized quantile regression (GQR) (Powell (2018)). In this section, we discuss GQR given instruments Z, treatment variables D, and control variables X. We will specify these variables for our context in proceeding sections but discuss the estimator more generally here. Let U* ~ U(0, 1) be a rank variable (normalized to be distributed uniformly). The specification of interest for outcome Y can be written as

$$Y=D^{\prime }\beta \left(U^{*}\right),U^{*}\sim U(0,1).$$ (1)

We are interested in estimating the Structural Quantile Function (SQF):

$$S_Y(\tau \mid d)=d^{\prime }\beta (\tau ).$$ (2)

The SQF defines the τ^th quantile of the outcome distribution given the policy variables if each person in the data were subject to the policy variables D = d. It is common and frequently necessary to condition on additional covariates. Conditional quantile estimators require those covariates to be included in the structural model, altering the SQF. Instead of including the covariates in the SQF, GQR lets the covariates provide information about the distribution of the disturbance term. An older person is likely to have a different conditional distribution for U* than a younger person. The GQR estimator uses this information, jointly estimating the probability that the outcome is less than the quantile function.

With instrumental variables quantile regression (IV-QR), it is possible to estimate the SQF of interest (equation (2)) under the assumption that U*|Z ∼ U(0, 1). GQR changes this assumption to U*|Z, X ∼ U*|X, which will be necessary with our empirical strategy since our instruments are only conditionally independent. The GQR estimator uses the following moment conditions:

$$E\left\{Z\left[\mathbf{1}\left(Y\le D^{\prime }\beta (\tau )\right)-{\tau }_X\right]\right\}=0,$$ (3)

$$E\left[\mathbf{1}\left(Y\le D^{\prime }\beta (\tau )\right)-\tau \right]=0.$$ (4)

where τ_X represents P(Y ≤ D′β(τ)|X) and is jointly estimated using

$${\tau }_X=\mathrm{\Phi }\left(X^{\prime }\alpha \right)$$ (5)

GQR uses the covariates to determine the probability that the outcome variable is below the quantile function given the covariates. To compare to conditional quantile models, note that equation (3) is equivalent to the condition for IV-QR when τ_X is replaced by τ.⁸ When there are no covariates, GQR reduces to IV-QR. Condition (4) ensures that the estimates refer to the τ^th quantile of the outcome distribution. The use of the probit model (instead of a semi-parametric estimator) in equation (5) is for computational convenience.⁹

4.1.2. Extension to Adjust for Sample Attrition

Because of attrition, we do not observe the full distribution of medical expenditures. Instead, we observe medical care only when S = 1, where S_i represents selection into the sample (i.e., not-attriting). We model selection into the sample as a function of observables and a non-additive selection term (ϵ):

$$S=F\left(W^{\prime }\delta ,ϵ\right),$$ (6)

where W′δ ≡ X′ϕ₁ +Z′ϕ₂ +R′ϕ₃. X and Z were defined above. R represents the selection instruments, variables which affect the probability of selecting into the sample but do not independently affect the outcomes. It is important that we have at least one variable that affects selection above and beyond the other instruments and covariates, which can be shown by rejecting the null hypothesis ϕ₃ = 0. In our context, we will use the predicted probability of not exiting the sample, as discussed in Section 4.4.

Buchinsky (1998, 2001) discusses sample selection adjustments for quantile regression. These estimators include an additive sample selection term which Huber and Melly (2015) shows assumes a homogenous treatment effect. As before, including an additive control undermines a primary motivation for using a quantile framework. It is straightforward to extend GQR to include a non-additive sample selection adjustment. The conditions of the model are:

Assumption 1 Outcomes and Monotonicity: ${\tilde{Y}}_i=D_i^{\prime }\beta \left(U_i^{*}\right),U_i^{*}\mid \left(S_i=1\right)\sim U(0,1)$ where $D_i^{\prime }\beta (\tau )$ is increasing in τ.

Assumption 2 Conditional Independence: $U_i^{*}\left|\left(Z_i,X_i,W_i^{\prime }\delta ,S_i=1\right)\sim U_i^{*}\right|\left(X_i,W_i^{\prime }\delta ,S_i=1\right)$.

Assumption 3 Selection: $S_i=F\left(W_i^{\prime }\delta ,{ϵ}_i\right)$ and $Y_i={\tilde{Y}}_i$ if S_i = 1 unobserved otherwise.

Assumption 1 is a standard assumption in the quantile literature, permitting the impact of the treatment variables to vary based on a nonseparable disturbance term. Assumption 2 states that the conditional distribution of the disturbance term for the observed sample is the same for all values of the instruments once we condition on the covariates and selection adjustment. Assumption 3 is a standard sample selection model formulation. These assumptions lead to the following moment conditions:

Theorem 4.1. Suppose Assumptions 1–3 hold. Then for each τ ∈ (0, 1),

$$E\left\{Z_i\left[\mathbf{1}\left(Y_i\le D_i^{\prime }\beta (\tau )\right)-P\left(Y_i\le D_i^{\prime }\beta (\tau )\mid X_i,W_i^{\prime }\delta \right)\right]\mid S_i=1\right\}=0,$$ (7)

$$E\left[\mathbf{1}\left(Y_i\le D_i^{\prime }\beta (\tau )-\tau \right)\mid S_i=1\right]=0.$$ (8)

The proofs are included in Appendix Section A.1. The model includes the sample selection adjustment as an additional covariate, accounting for selection while preserving the nonadditive disturbance term since $U_i^{*}$ is modeled as a function of $W_i^{\prime }\delta$. The model normalizes (unconditional) $U_i^{*}$ to be uniformly-distributed for the observed sample, which implicitly defines the τ^th quantile estimates as the estimates for the τ^th quantile of the observed outcome. There is little loss in our context for normalizing the quantiles in this manner. Alternatively, we could impose an identification-at-infinity assumption and generate estimates for the τ^th quantile of the full sample (including attriters) as if we observed the medical expenditure distribution for the full sample.¹⁰ We choose not to do this for several reasons.

First, the only difference between the two sets of estimates is which quantile that the estimates refer to (e.g., the 60^th quantile of the observed sample may refer to the 50^th quantile of the full sample, but the estimated parameters would be the same). Since we will map the estimates to specific medical expenditure dollar values, the values of the quantiles themselves are relatively uninteresting. Second, we are hesitant to impose the identification-at-infinity assumption.¹¹ Finally, the adverse selection literature typically defines adverse selection as differences in selection across plans (see Geruso (2013); Handel (2013) for two examples). This metric refers to the observed sample and does not include people unobserved in the data.

The sample equivalents of conditions (7) and (8) are used to estimate $\widehat{\beta (\tau )}$. $P(Y_i\le D_i^{\prime }\beta (\tau )\mid X_i,W_i^{\prime }\delta )$ is simultaneously estimated. Identification is discussed in Powell (2018) and holds here under the same conditions given that the extension to account for attrition simply involves adding a function of $W_i^{\prime }\widehat{\delta }$ to the covariates.

4.2 Plan Elasticity

Now that we have discussed GQR generally, we will introduce the models of interest specific to this paper. A primary motivation for this paper is to estimate individuals’ responsiveness to health insurance plans without parameterizing the plan in a restrictive manner. The quantile function of interest is

$$S_{\ln M}(\tau \mid \text{Plan})=\sum _{k\in \{B,C,D\}}{\beta }_k(\tau )\left[\mathbf{1}\left({\mathrm{Plan}}_i=k\right)\right],$$ (9)

where M represents 2007 medical expenditures. 1(Plan_i = k) represents an indicator for enrollment in Plan k in 2007. This quantile function provides the resulting distribution for each plan if everyone in the sample were enrolled in that plan. We can graph the resulting distribution for each plan while marking the deductible and stop loss for that plan to observe whether the distribution responds to these plan components. Conditional quantile estimators are uninformative in this context because we cannot map the quantiles to specific expenditure levels.¹² Conditioning on 2005 medical expenditures, which we believe is necessary for our identification strategy, exacerbates the problems associated with conditional quantile estimation. An individual at the top of the 2007 distribution conditional on 2005 medical expenditures may be at the lower end of the unconditional distribution.

4.3. Estimation Details

We implement the GQR estimator with a non-additive sample selection term. Our model is

$$\ln M=\sum _{k\in \{B,C,D\}}{\beta }_k\left(U^{*}\right)[\mathbf{1}(\mathrm{Plan}=k)],U^{*}\mid (S=1)\sim U(0,1)$$ (10)

$$\begin{gathered} \tilde{Y}=\max (\ln M,C), \\ Y=\tilde{Y}\text{if}S=1, \\ S=F\left(W^{\prime }\delta ,ϵ\right), \\ {U}^{*}|\left(Z,X,W^{\prime }\delta ,M^{2005},{\tilde{M}}^{2005},S=1\right)\sim U^{*}|\left(X,W^{\prime }\delta ,M^{2005},{\tilde{M}}^{2005},S=1\right), \end{gathered}$$ (11)

Equation (10) characterizes the log of individual medical care spending in 2007 as a function of plan enrollment. If plan enrollment and attrition were (unconditionally) randomly-assigned and everyone had more than $0 of medical care spending, then this equation could be estimated using quantile regression. However, plan enrollment is not exogenous so we use an instrumental variables approach while conditioning on a set of explanatory variables. Moreover, many individuals do not consume any medical care and we model these individuals as having censored medical expenditures, setting C to a small negative number. Quantile estimation is, generally, robust to censoring. We estimate the SQF for quantiles that are unaffected by censoring (i.e, quantiles where the SQF predicts M > 0).¹³ The covariates (X) are the household demographic variables listed previously: 2005 family size, employee age, employee sex, age of other household member, sex of other household member, and the other member’s relationship to employee (spouse or dependent). In addition, we also include $f(M_i^{2005})$ and $\tilde{f}({\tilde{M}}_i^{2005})$, where ${\tilde{M}}_i^{2005}$ refers to the 2005 medical expenditures of individual i’s spouse or dependent, as covariates (though these are not included in X).

We estimate the index in equation (11) using the monotone rank estimator introduced in Cavanagh and Sherman (1998), which does not require distributional assumptions. We use subsampling (Politis and Romano (1994)) for inference and implement the entire procedure for each subsample to account for the inclusion of an estimated control variable in the second step. We use a 10-piece spline in $W^{\prime }\widehat{\delta }$ to account for attrition.

4.4. Instrumental Variables

Our empirical strategy requires predictions of plan choice in 2007. These predictions act as our instrument variables to identify the moral hazard model (equation (9)). We estimate a nested logit model (McFadden (1978, 1984)) using household demographic information to predict the plans that the households will select. The nested logit model, consistent with a random utility model, is often a natural means of modeling health insurance enrollment decisions (e.g., Feldman et al. (1989); Short and Taylor (1989); Ericson and Starc (2015, 2016)). Our covariates include the head of the household’s age and sex and an indicator equal to 1 if the household includes another member (i.e., household size is 2). We also allow the other member’s age, sex, and whether they are a spouse (i.e., versus dependent) to affect plan choice. We assume an additive and linear utility function:

$$V_{ij}=X_i^{\prime }{\phi }_j+u_{ij},$$

where X_i represents the vector of covariates mentioned in Section 4.3 and j indexes the plan. As discussed in Section 3.4, we do not use 2005 medical expenditures to predict 2007 plan choice.

While we refer to “plan choice,” we also permit households to exit the sample. Households may exit because they leave the firm or they do not enroll in one of the firm’s health insurance plans. The estimated probability of not exiting the sample will be used as the selection instrument (R in Section 4.1.2). Figure 3 illustrates the nesting structure of our model. We assume that households select whether to enroll in a firm health insurance plan or exit the sample. Because of concerns that the offer of Plan C may affect the choice between Plan B and Plan D, we next allow for households to select between “Generous Coverage,” defined as Plans B and C, and the least generous plan, Plan D. For those selecting generous coverage, the household then selects between Plans B and C.

Figure 3:

Plan Choice

The variables included in X_i are also controlled for when estimating the moral hazard model. Thus, we exploit the nonlinearities inherent in the predicted probabilities even when the covariates enter the indirect utility function additively. Because we are concerned that these nonlinearities may independently predict medical expenditures, we control flexibly for 2005 medical expenditures, effectively studying changes in medical care spending.

4.5. Reported Parameters

We will present our results with graphs that show the parameters over the entire distribution. When applicable, our graphs will include the points where the distribution has passed the plan deductible and stop loss. Each point refers to the quantile in the distribution based on the end of the year expenditures. The estimates are not comparing the behavior of a person right before and right after that person hits the deductible. Instead, the estimates below the deductible refer to people that never pass the deductible in that year while the estimates above the deductible refer to individuals that pass the deductible by the end of the year.

4.6. Summary of Empirical Steps

We briefly summarize the empirical steps outlined above. First, we estimate our plan choice model (discussed in Section 4.4) to generate person-specific, based on observable household characteristics (X), probabilities of enrolling in each 2007 plan or attriting. The predicted probabilities of plan enrollment act as the instrumental variables. The predicting probability of attriting is the selection instrument. Second, we estimate the selection equation (equation (6)). Specifically, we estimate δ. Given these estimates, we construct $W^{\prime }\widehat{\delta }$ and include a flexible function of this index as additional covariates. This function accounts for systematic attrition. Third, we estimate the SQF of interest (equation (9)) using GQR, controlling for X, flexible functions of medical expenditures for the individual and spouse/dependent, and a flexible function of $W^{\prime }\widehat{\delta }$. The predicted probabilities generated in the first step are used here as instruments.

We report differences in the plan estimates, using one plan as a baseline.¹⁴ For example, we present a figure graphing the differences between the most generous and least generous plan, corresponding to β_B(τ) − β_D(τ). We graph the estimates by quantile and mark which quantiles correspond to the deductible and stop loss thresholds for each plan. Presenting the results in this way allows us to test visually whether plans encourage additional expenditures for certain parts of the distribution. We will also formally test whether households respond solely to end-of-year marginal prices.

5. Results

5.1. Plan Choice Model

Our instruments are constructed by predicting plan enrollment probabilities using a nested logit model. We present the plan choice model results in Table 3. Enrollment in Plan B is the baseline. In brackets, we present the change in probability resulting from adding 1 to that variable. When the variable is an indicator variable, we present the probability change from switching each observation from 0 to 1. We find that our covariates are statistically related to plan choice, suggesting that the predicted probabilities generated from this model should be appropriate instruments. We will test this “first stage” relationship explicitly below. We find that male employees and households with two members are predicted to exit the sample and are much less likely to enroll in Plan B. For those who stay enrolled in a plan, men are more likely to enroll in the least generous plan. Similarly, families with two enrollees are more likely to exit the sample and less likely to enroll in the most generous plan. Age of the other member predicts enrollment in the most generous plan.

Table 3:

Plan Choice Model

Outcome:	Plan B	Plan C	Plan D	No Plan
Household Head
Age	-	−0.003**	−0.133***	0.016***
	-	(0.001)	(0.013)	(0.003)
	[−0.002]	[−0.003]	[−0.003]	[0.008]
Male	-	1.004***	3.243***	1.736***
	-	(0.217)	(0.216)	(0.135)
	[−0.181]	[−0.040]	[0.021]	[0.200]
Other Members
Family Size=2	-	0.874***	−0.755	1.588***
	-	(0.248)	(0.578)	(0.222)
	[−0.153]	[−0.062]	[−0.065]	[0.281]
Spouse	-	0.433*	0.647	0.689***
	-	(0.259)	(0.690)	(0.254)
	[−0.061]	[−0.017]	[−0.005]	[0.084]
Age	-	−0.027***	−0.022	−0.049***
	-	(0.007)	(0.015)	(0.007)
	[0.004]	[0.002]	[0.001]	[−0.007]
Male	-	0.758***	1.999***	0.522***
	-	(0.196)	(0.439)	(0.161)
	[−0.045]	[0.060]	[0.040]	[−0.056]
Baseline Probability:	0.130	0.216	0.067	0.587

Notes: Standard errors presented in parentheses. In brackets, we present the probability change when 1 is added to the variable. For indicator variables, we present the change in probability of switching each observation from 0 to 1. All parameters in the table are estimated jointly.

We use this model to predict a household’s probability of enrolling in each plan. There is substantial variation in the predicting probabilities. For example, the predicted probabilities in our sample of enrolling in Plan C range from 0.05 to 0.57. The predicted probability for exiting the sample varies between 0.21 and 0.92. This variation is necessary to identify this paper’s moral hazard model. We control for these exact same covariates – as well as 2005 medical expenditures – included in the above nested logit model in our quantile models. Identification originates from the nonlinearities in the predicted probabilities relative to a linear specification of the covariates.

5.2. First Stage and Selection Equation

We create instruments which predict plan choice as discussed in Section 5.1. We use the demographic information in our data to predict which plan each family will select in 2007. In 2005, all families were constrained to choose Plan A. Identification originates from the availability of Plans B, C, and D in 2007 and the differential preferences for these plans.

We verify that our predicted probabilities are actually predictive of plan choice, conditional on the covariates. Appendix Table A.2 shows that there is a relationship. In Appendix Table A.3, we report estimates for the selection equation, normalizing the sum of the square of the coefficients (including for variables not shown) to 1. We present estimates using a probit estimator and a monotone rank estimator. We use the estimates from the latter to construct the selection adjustment term. We find that the selection instrument (the predicted probability of not attriting) is positively associated with remaining in the sample for all of 2007.

5.3. Plan Elasticity Estimates

This section presents our main results. We estimate the quantile function in equation (9) and then present the differences in the SQFs to show how the plans generate different distributions of medical care. In Figure 4, we present the differences in the distributions for the most generous plan (Plan B) relative to the least generous (Plan D). We also include markers signifying the deductibles and stop loss points for each plan. The figure shows the estimated distribution of Plan B (relative to Plan D) if there were no systematic selection into either plan, mapping that distribution to the kinks in the budget sets generated by the plans’ parameters. If people respond to the marginal end-of-year price, then we should observe the plan elasticity increase after the deductible.

Figure 4:

Difference in Expenditure Distribution: Plan B vs. Plan D

Notes: Using an instrumental variable quantile regression estimator, we estimate the distribution of Plan B and Plan D if enrollment into each plan were random. We graph the difference in these distributions here. Confidence intervals generated using subsampling.

In general, we find that Plan B encourages higher spending than Plan D throughout the entire distribution. Between quantiles 20 and 39 ($161 to $543 for Plan B), the estimated difference in log medical spending ranges from 0.35 to 0.6, implying 41%−82% increases in spending due to enrollment in Plan B instead of Plan D. Higher in the distribution, we find that the elasticity steadily increases, reaching a value of 0.88 at quantile 83 ($6,619), suggesting a 141% causal increase in spending at that point in the distribution. There is little visual evidence that the distributions are reacting to the plans’ deductibles or out-of-pocket maximums.

We estimate large elasticities even at the top of the medical care distribution when the marginal price is zero for both plans. Overall, Figure 4 provides evidence that the more generous plan appears to encourage additional medical care spending for most of the distribution, even in parts where the generosity differences are small or zero. There are several possible reasons for this such as differences in the prices of episodes of care for expensive treatments and reductions in spot prices early in the year.

The differences in the estimated distributions between Plans C and D are shown in Figure 5. We observe similar patterns as before. In general, the elasticities are smaller, consistent with the fact that the differences in generosity between Plan C and Plan D are smaller. The estimated coefficients after the Part C deductible (but before the Part D deductible) are between 0.3 and 0.6, implying increases in spending of 35%−82% due to enrollment in Plan C relative to Plan D. Similar elasticities are estimated after the Plan C maximum is reached but before the Plan D maximum is hit. Overall, we observe more graphical evidence of responsiveness to the deductibles and maximums in Figure 5.

Figure 5:

Difference in Expenditure Distribution: Plan C vs. Plan D

Notes: Using an instrumental variable quantile regression estimator, we estimate the distribution of Plan C and Plan D if enrollment into each plan were random. We graph the difference in these distributions here. Confidence intervals generated using subsampling.

We also compare Plan B to Plan C, though the conclusions can be inferred from the other comparisons. Appendix Figure A.1 presents these estimates.

5.4. Testing Parametric Price Assumptions

Our approach estimates the causal effect of each plan for the entire distribution of medical expenditures. However, the literature often assumes that households are responding to specific prices, such as spot prices or end-of-year prices, when making health care decisions. We introduce a simple test which compares the nonparametric distributions shown in the previous section to distributions generated by imposing more parametric assumptions. We assume that households respond solely to the end-of-year price and then test that assumption. Using the same instrumental variables and controlling for the same covariates and selection adjustment terms, we estimate a parametric quantile function which assumes that the log of medical expenditures is a function of the household’s end-of-year marginal price. We then generate a distribution of medical expenditures implied by this model and compare it to the distribution from the non-parametric model. This approach is discussed in further details in Appendix Section A.2.

We use a Cramér-von-Misses-Smirnov (CMS) test and simulate the distribution of this test statistic for inference using subsampling. The CMS test rejects the equality of the two distributions at the 5% level for both Plan C and Plan D.¹⁵

5.5. Adverse Selection

Next, we present estimates of adverse selection. Without adverse selection, the observed plan distributions and the causal distributions would be the same, implying that P(Y_i ≤ β_k(τ)) = τ for each k. The intuition behind our metric is that once we have estimated the causal distribution of a plan, we can compare the observed distribution to the estimated distribution for information about the magnitude of adverse selection. We present the empirical probability

$$\widehat{{\psi }_k(\tau )}=\frac{1}{N_k}\sum _{i\in \mathcal{K}}\mathbf{1}(Y_i\le \widehat{{\beta }_k(\tau )}),$$ (12)

where N_k is the number of people enrolled in Plan k. This equation represents the sample equivalent of the probability that an enrollee in plan k is below the τ^th quantile. $\widehat{{\psi }_k(\tau )}<\tau$ implies that the enrollees are consuming more medical care than expected and that the plan has adverse selection.

We present our adverse selection metrics in Figure 6. If the adverse selection metric is above the 45-degree line, then that is evidence of favorable selection. For example, Plan D appears to attract an especially healthy population. With no systematic selection, we would expect 20% of the Plan D enrollees to have expenditures below the estimated 20^th quantile of the SQF for Plan D, which is equal to $110.46. Instead, we observe that almost 31% of the enrollees have smaller expenditures than $110.46. This favorable selection extends throughout the distribution.

Figure 6:

Adverse Selection

Notes: We use the plan elasticities presented in Figures 4, 5, A.1 to estimate the empirical probability that an enrollee in the plan is below the estimate quantile function for that plan. Confidence intervals generated using subsampling. The 45 degree line represents a plan with no systematic selection.

Plan B shows evidence of adverse selection. We estimate that without selection, the 30^th quantile of the medical care distribution for Plan B would be $311.24. Only 18% of Part B enrollees have smaller expenditures than this amount. The systematic selection into Plan B increases higher in the distribution before converging to the 45-degree line. Plan C shows a mix of favorable and adverse selection throughout the distribution. We observe adverse selection close to the bottom of the medical care distribution but favorable selection for most of the distribution.

More formally, we compare the observed medical care distribution with the estimated causal distributions using the same CMS test as in Section 5.4. These distributions would be the same in the absence of systematic selection. We reject the equality of distributions at the 1% level for Plan B, implying that there is systematic selection.

5.6. Relative Importance of Moral Hazard and Selection

While we have presented several metrics involving the distribution of medical expenditures, we also look at the overall importance of the causal impact of the health insurance plans on mean expenditures and selection. Understanding the relative roles of moral hazard and adverse selection in explaining the correlation between plan generosity and medical care spending is critical for addressing the resulting inefficiencies. Given estimates of equation (9), we integrate over all quantiles to arrive at the mean medical expenditures for each plan if there were no systematic selection into the plan. These metrics are the expected per-person medical expenditures for a given plan if everyone in our sample were subject to that plan. The calculation for Plan B is the following:

$$\widehat{E}[\text{Per-Person}\text{Medical}\text{Expenditures}\text{in}\text{Plan}\text{B}\text{with}\text{Random}\text{Selection}]={\int }_{\tau }\left[\widehat{{\beta }_B(\tau )}\right]d\tau .$$ (13)

We label these “Moral Hazard” in Table 4, Panel A because all differences across plans are driven solely by responses to plan generosity. The first row is the actual per-person expenditures which includes moral hazard and adverse selection. For the sake of consistency, we calculate the actual expenditures in a similar manner by using the values of the quantile endpoints and integrating over τ. Consequently, the numbers are slightly different from those found in Table 2.¹⁶

Table 4:

Decomposition of Plan Effects

Panel A: Decomposition of Plan Effects
	Plan B	Plan C	Plan D
Per Person Expenditures	$5,507.19	$2,928.35	$1,537.83
	($274.45)	($114.94)	($160.96)
Per Person Expenditures with Random Selection	$4,675.80	$3,864.07	$2,813.45
	($358.52)	($217.19)	($302.42)
Adverse Selection	$831.39	−$935.72	−$1,275.62
	($402.48)	($189.56)	($280.95)
Panel B: Comparison Across Plans
	Plan B to Plan D	Plan C to Plan D	Plan B to Plan C
Per Person Expenditures	$3,969.36	$1,390.52	$2,578.84
	($304.70)	($203.27)	($287.68)
Moral Hazard	$1,862.35	$1,050.63	$811.73
	($378.68)	($426.52)	($455.60)
Adverse Selection	$2,107.01	$339.90	$1,767.11
	($431.62)	($407.65)	($532.29)
Per Person Expenditures	$2,125.56	$863.69	$1,261.87
(assuming conditional independence)	($291.69)	($222.70)	($257.79)
Panel C: Adverse Selection Metrics
	Plan B to Plan D	Plan C to Plan D	Plan B to Plan C
2005 expenditure differences	$3,704.31	$1,068.09	$2,636.22
2007 differences, assuming conditional independence	$1,843.80	$128.65	$1,715.15
2007 differences, accounting for moral hazard estimates	$2,107.01	$339.90	$1,767.11

Notes: Subsampling is used to generate the standard errors. “Adverse Selection” is equal to “Per Person Expenditures” minus “Per Person Expenditures with Random Selection”.

Panel B estimates are simply differences of the metrics shown in Panel A. “Moral Hazard” is the difference in “Per Person Expenditures with Random Selection”. “Per Person Expenditures (assuming conditional independence)” represents differences across plans when controlling for 2005 spending (plus household covariates) but not using instrumental variable approach.

Panel C provides different metrics of adverse selection across plans. “2005 expenditure differences” shows differences in 2005 expenditures by 2007 plan. “2007 differences, conditional on 2005 expenditures” shows differences in 2007 spending, conditioning on 2005 spending (i.e., accounting for mean reversion). “2007 differences, accounting for moral hazard estimates” uses the main estimates of this paper.

We also include “Adverse Selection” which eliminates the causal impact of the plan and describes the expenditures of the individuals selecting into the plan if the plan itself did not impact expenditures. We simply subtract the moral hazard estimate from the per-person expenditures estimate to estimate selection. In the previous section, we tested the equality of the observed and estimated (causal) distributions as a test for adverse selection. We also see evidence of selection in the mean estimates. Our selection estimates provide evidence about the ramifications of policies which change enrollment behavior. For example, the Cadillac Tax may encourage enrollment in less generous plans. Our estimates suggest that if our entire sample enrolled in Plan D that the annual premium would rise by almost $1,300.

Panel B repeats the results in Panel A but shows comparisons between plans. We estimate that enrollment in Plan B causally increases per-person medical expenditures by over $1,800 relative to Plan D and over $800 relative to Plan C. We estimate that 53% of the additional spending in Plan B can be attributed to adverse selection.

5.7. Discussion of Moral Hazard Estimates

In this section, we summarize our estimates in a manner comparable to methods used to generate elasticities in the literature. First, we use our price elasticity estimates generated from our parametric model (see Figure A.2a). Calculating the mean estimate by integrating over the estimated quantile treatment effects, we calculate a price elasticity with respect to end-of-year prices of −0.38.

Next, we adopt the approach used to calculate arc elasticities in Aron-Dine et al. (2013) (see Table 4 of their paper). We take the difference in expenditure estimates for two plans as a percentage of the average expenditures for those plans divided by the difference in price as a percentage of the average price. The measure of “price” for this metric is calculated by first calculating the share of total expenditures paid out-of-pocket for each enrollee. The average of this ratio is defined as the “price.” Comparing Plan B to Plan C, our estimates imply an elasticity of −0.20. We estimate an arc elasticity of −0.49 using Plans B and D; an estimate of −0.55 comparing Plan C to D.

In all cases, we find that our estimated elasticities are reasonable and in the range of similar estimates found in the literature. Aron-Dine et al. (2013) reports arc elasticities that are slightly smaller in magnitude than those estimated here while Brot-Goldberg et al. (2015) estimates larger elasticities in the range of −0.59 to −0.69 in their context.

5.8. Mean Reversion versus Changes in Health Care Preferences

We previously discussed why a simple comparison of changes in medical expenditures across plans does not isolate moral hazard from other confounders. There are two concerns. First, households have private information about changes in preferences for health care. Second, mean reversion would suggest that households with high 2005 medical spending may experience relative decreases regardless of plan enrollment. Households with high levels of prior spending may also disproportionately enroll in the most generous plan. We can isolate the biases related to each of these factors. We estimate equation (9) – for all quantiles – while assuming conditional independence of plan selection. Practically, we do not use the instrumental variable strategy and instead use actual plan choice for identification. We still condition on household characteristics and flexible functions of 2005 medical expenditures (in the same manner as before). We present the differences in mean expenditures (integrating over the quantiles as before) across plans in the final row of Table 4, Panel B. These estimates account for prior medical spending and mean reversion, but assume that plan choice is unrelated to any private (unobserved) changes in health.

The observed, unconditional difference-in-differences estimate comparing medical expenditure changes across Plan B and Plan D would imply a moral hazard effect of only $178.13.¹⁷ Accounting for mean reversion but ignoring concerns about changes in health care preferences, the moral hazard estimate for Plan B relative to Plan D increases to $2,125.56 (bottom row of Table 4, Panel B), implying a substantial bias due to mean reversion. The medical care spending for the Plan B population would have decreased in 2007 relative to the 2005 medical spending baseline in the absence of any plan changes, and it is important to account for this systematic change in baseline expenditures.

However, this “conditional independence” estimate includes some systematic selection into Plan B due to private information about changes in health and health care preferences that are not accounted for by controlling for prior medical expenditures. These changes should be part of the adverse selection dimension that we are interested in, but we are inappropriately attributing them to moral hazard due to the assumption of conditional independence of plan choice. Indeed, we observe a decrease in the moral hazard estimate to $1,862.35 (our main estimate) when using our instrumental variable strategy which addresses selection concerns due to active choices made by households with private information.

Our results suggest that mean reversion biases the unadjusted difference-in-differences estimate towards zero substantially, obscuring moral hazard. Private information also plays a role, but this bias is smaller. Each source of bias operates in the expected direction.

5.9. Comparing Adverse Selection Metrics

Our empirical strategy allows us to calculate precise estimates of systematic selection into each plan. It is useful to compare this method to an alternative metric of selection - previous year’s medical expenditures. To test for selection, it might seem reasonable to observe whether individuals with higher medical expenditures in 2005 choose Plan B. As shown in the previous section, however, this approach ignores that individuals with high 2005 expenditures are both more likely to enroll in the most generous plan and revert to lower spending in 2007.

Our results suggest that previous medical expenditures overstate the magnitude of adverse selection. We present these estimates in Panel C of Table 4. We find that the difference in 2005 medical expenditures between Plan B and Plan D enrollees is $3,704. However, the difference in selection in 2007 expenditures is only $2,107 (as shown in Panel B and repeated in Panel C). Assuming conditional independence of plan selection, which accounts for mean reversion but ignores changes in health care preferences over time, our adverse selection estimate would be smaller, $1,843.80, since we are ignoring a component of systematic selection. Similarly, the difference in 2005 medical expenditures between Plan B and Plan C enrollees is $2,636. But, in 2007 expenditures, selection accounts for only $1,767. These differences are economically meaningful and highlight the benefits of estimating adverse selection in the same year that the selection is occurring.

These results again highlight the importance of accounting for natural changes in health care spending over time due to mean reversion and health improvements. They also suggest that households partially select plans based on prior medical expenditures, even when they would be predicted to have different levels of spending in the next year. Individuals with high medical expenditures may, on average, expect to require less care in the next year due simply to mean reversion and health improvements, but may still value the additional financial risk protection of the most generous plan.¹⁸

5.10. Robustness Tests

We test the robustness of our estimates and present the results in Table 5. To make the comparisons straightforward, we only present the mean differences across Plans B and D. The corresponding estimates from Table 4, Panel B are included in the first column.

Table 5:

Robustness Checks

	(1)	(2)	(3)	(4)
	Main	First 11	More Flexible	Different Plan
	Results	Months	Age Controls	Choice Model
Moral Hazard	1862.35	1534.24	1721.78	1624.18
Adverse Selection	2107.01	2435.12	2247.58	2345.18

Notes: These estimates correspond to Column 1 of Table 4, Panel B.

In Column (1), we repeat the main estimates of the paper.

In Column (2), we exclude December 2005 and treat January-November 2005 as the initial year. Thus, the sample includes individuals that attrit in December 2005 (and those households are considered attriters) and the medical care controls refer to medical care consumed in the first 11 months of 2005. This tests for systematic anticipatory behavior.

In Column (3), we include indicators for the employee’s age group

In Column (4), we generate our instruments using a different plan choice model.

In our first test, we treat January-November 2005 as the initial “year.” In our main analysis, we study 2007, controlling for behavior in 2005, because the plans were introduced in 2006 and households may have engaged in intertemporal substitution of medical care between 2005 and 2006. However, temporal shifting of care would also imply that medical care at the end of 2005 may be differentially “treated.” For this test, we eliminate care consumed in the last month of 2005 from the analysis. Similarly, while systematic attrition at the end of 2005 is unlikely, this approach also tests for whether this attrition is driving our estimates. Our sample for this test includes households in the data for January-November 2005 and treats households that drop out of the data starting in December 2005 as attriters. The estimates in Column (2) suggest that anticipatory behavior is not affecting our estimates.

In Column (3), we test whether including more flexible covariates affect our estimates.¹⁹ We include indicators for 5-year age groups based on the employee’s age instead of just including age linearly as in our main models. Our estimates are similar, suggesting that our results are not driven by omitted factors.

In Section 5.1, we discussed how we lumped together Plans B and C as “generous plans.” Alternatively, we could models households as selecting between Plan B and the “less generous” plans, Plans C and D. The households selecting the less generous plans would then choose between Plan C and Plan D. If we generate our predicted probabilities using this structure, we arrive at similar estimates.

6. Conclusion

Understanding moral hazard and adverse selection in private health insurance is widely-recognized as critical to policy. While the literature has frequently estimated the effect of price on medical care consumption, it has typically resorted to parameterizing the mechanism through which individuals respond to cost-sharing. In this paper, we estimate the impact of different health insurance plans on the entire distribution of medical care consumption using a new instrumental variable quantile estimation method and extending it to include a nonseparable term to account for attrition. We use the introduction of new plans with varying generosity at the firm-level interacted with differential preferences for plan generosity for identification. The estimated medical expenditure distributions are the distributions caused by the plans in the absence of systematic selection into plans. We map these causal distributions to the parameters of the plans themselves and statistically reject that individuals only respond to the end-of-year price.

We also estimate the magnitude of adverse selection. We find favorable selection in the least generous plan and adverse selection in the most generous. We estimate that adverse selection is responsible for $831 of additional per-person costs in the most generous plan, implying that an individual enrolling in this plan would pay over $69 per month in additional premium payments simply to cover the expected costs of the population selecting into the plan. Similarly, a policy which resulted in our entire sample enrolling in the least generous plan would cause annual premiums for that plan to rise by over $1,200.

Interestingly, a simple comparison of changes in medical expenditures across plans and over time understates the magnitude of moral hazard. This simple comparison is subject to two opposing biases. First, it ignores that households have unobserved shocks to their preferences for medical care which inform plan selection. Second, it does not account for systematic mean reversion. Households with high spending in the baseline year will revert to lower spending regardless of plan enrollment but may be more likely to enroll in a more generous plan. We find that the empirical bias for each mechanism is the expected sign, but that the mean reversion concern dominates rather substantially.

One implication of this finding is that using the previous year’s medical expenditures as a metric of selection greatly overstates the amount of systematic selection into plans. While prior year’s health care costs is a natural “unused observable” (Finkelstein and Poterba (2014)) to test for the existence of adverse selection in this context, it does not provide an accurate estimate of the magnitude. Instead, health and preferences for medical care change over time, and this private information should also be incorporated into measures of adverse selection. We estimate a measure of medical care costs without the causal impacts of plan generosity for the same year in which the plan was selected and find smaller adverse selection magnitudes.

We estimate that moral hazard is responsible for 47% of the differences in expenditures between the most and least generous plans. Adverse selection also plays an important role, accounting for 53%. In the absence of moral hazard, the difference in average medical expenditures across the plans studied in this paper would be $2,107 instead of $3,969.