Health Savings Accounts: Consumer Contribution Strategies and Policy Implications (2024)

Data Description

Our dataset is from the Medical Expenditure Panel Survey,¹² a set of large-scale surveys of families and individuals drawn from a nationally representative subset of households in the United States. It is based on an overlapping panel design in which data on medical expenditures (and other information) are collected for two consecutive calendar years from each household. Henceforth, panel p will refer to year pair {tp−1,tp}. We limited our dataset to individuals who were in-scopeⁱⁱⁱ throughout the survey period, and for whom the relevant covariate values (described below) were present. This excluded less than 10% of all individuals.

As the unit of analysis, we used Health Insurance Eligibility Units (HIEUs), “sub-family relationship units constructed to include adults plus those family members who would typically be eligible for coverage under the adults’ private health insurance family plans.” For panel p, let {Xtp−1i,Xtpi} be the cost percentile transition for the ith HIEU. Collecting these percentile pairs across panels produced the dataset used to calibrate our cost evolution models.

We divided the dataset into three samples: Training (Panels 7 to 14, corresponding to year pairs {2002, 2003} through {2009, 2010}), validation (Panels 15 and 16, corresponding to year pairs {2010, 2011} and {2011, 2012}), and test (Panels 17 and 18, corresponding to year pairs {2012, 2013} and {2013, 2014}). The training set was used to estimate all model parameters described below, and exploratory analyses were performed on the validation set to arrive at the chosen model. The chosen model was then refit to the combined training and validation datasets, and then used to predict the second year costs in the test set. All data preparation and model estimation was performed using SAS.

We develop two versions of the cost evolution model described further below: basic and expanded. The basic version uses a small set of covariates and is well suited for long-term planning as it does not require modeling the evolution of a large set of demographic and clinical variables. The expanded version includes a broader set of covariates and is well suited for generating more accurate short-term predictions that could have other applications as well. The covariates are the following:

• Basic model: Household size, percentage of individuals within the HIEU of each insurance type (private, public, private + public, uninsured*). The values marked with an asterisk (*) denote the baseline values within each group.

• Expanded model: This model additionally includes the following: % of individuals within the household of each sex (male, female*), age group (0-19, 20-39*, 40-59, 60+), race (White*, Black, American Indian/Alaskan Native, Asian/Native Hawaiian/Pacific Islander, Multiple races), perceived health status (excellent*, very good, good, fair, poor), perceived mental health status (excellent*, very good, good, fair, poor), region (West*, East, South, North), % of individuals not receiving help or supervision with instrumental activities of daily living (IADLs), % of individuals not receiving help or supervision with activities of daily living (ADLs), % of individuals without any functional limitations.

Overall, our 2002–2014 dataset includes 176,205 individuals belonging to 90,359 HIEUs. The final training, validation, and test sets contained 57,701, 15,818, and 16,840 HIEU pairs, respectively.

Problem Formulation

In year t, a HSA-eligible plan can be characterized by three parameters: A deductible Dt, a coinsurance rate c (percentage of expenses exceeding Dt covered by the household), and a maximum limit Mt on household OOP expenses for that year.

The household begins each year t in health state Xt−1 with initial account balance Wt−1 (with initial values X0 and W0 at the beginning of year 1). The account balance increases by the investment return rate w and the household’s pretax contribution Ct is added to the account. The household then transitions to a new health state Xt, incurs actual total expenses Yt, and is responsible for OOP expenses Vt, which are deducted from the savings account. Therefore,

If the current account balance is insufficient to cover these expenses (i.e., Vt>(1+w)Wt−1+Ct), the household must pay the difference directly. The difference is paid with after-tax dollars, so if the marginal tax rate for the household is r, the pretax value of this payment is h(Vt−(1+w)Wt−1−Ct), where h=1/(1−r). In each year, the deductible and OOP maximum values are increased by the health care cost inflation rate I: Dt=I×Dt−1 and Mt=I×Mt−1. This process repeats in year t+1 through year T, the number of years in the contribution period. These dynamics are illustrated in Figure 1.

A household has the freedom to select a contribution amount Ct for years t=1,…,T, and the most economic choice is the one that minimizes the total expected discounted cost (in pretax dollars):

where δ=11+ρ is the household’s discount factor and ρ is the household’s discount rate.

The health state Xt is the percentile for the household’s total medical costs Yt in year t, and is a measure of how costly the household is when compared to all other households in the nation. Xt is a continuous random variable (Xt∈[0,1)), where Xt=0 and Xt=1− represent the least costly (healthiest) and most costly (sickest) households, respectively. The costs represent total payments to medical providers by the health plan and the household. The evolution of Xt and Yt from year to year are driven by the cost evolution model that is described later.

To select the investment return rate w for the HSA, we observe that the 30-year annualized rates of return on the 10-year US treasury note and the S&P 500 index are about 6% and 10%, respectively.¹³ A HSA adopter is likely to invest in a moderately conservative long-term asset allocation, so we choose a rate of 8% corresponding to a 50/50 split between equities and treasuries. We also choose a discount rate^iv of ρ=8%×(1−0.25)=6%. This represents the return on money outside of the tax-advantaged HSA, assuming a marginal tax rate of 25%. Finally, the health care cost inflation rate is estimated to be 3.4%, based on a statistical analysis presented later.

Candidate Contribution Policies

We investigate two types of contribution policies in this article. The first is a dynamic policy that optimizes (3) over a long time horizon (T=∞). It has a closed form solution that can be used to approximate the optimal policy for the finite horizon setting. The second policy is a simpler static one that strives to cover the OOP maximum in each year, subject to an annual contribution limit.

Cost Evolution Model

Our model for producing year to year forecasts of household health care costs uses as predictors: 1) the household’s health care costs in the prior year and 2) demographic information and a set of self-reported health variables^v described in Data Description. The use of prior year costs is based on evidence that their use alone can perform almost as well as models that employ a broader set of clinical/demographic variables.^7,9,18,19 Furthermore, using more than one year of prior information has been shown to add little predictive power.²⁰

Rather than directly predict cost or some transformation of it, a novel aspect of our approach is to model the transitions of a household’s health care cost percentile from one year to the next.^vi The rationale for modeling percentiles rather than actual costs is apparent from Figure 2: The presence of a linear association among cost percentiles in two consecutive years is apparent in the right panel. Indeed, the correlation among consecutive year percentile values is 0.70, much higher than the corresponding correlation among actual costs in consecutive years (0.39).

Specifically, we propose a four-stage model for evolving costs: 1) a binary outcome model for the event that a household incurs zero cost in the current year (a nonnegligible percentage of households have zero cost in a given year); 2) conditional on having positive costs, a continuous parametric model for the household’s cost percentile; 3) a mapping from cost percentile to actual cost; and 4) inflation adjustment of actual costs from year to year.

Some of the models can incorporate either the basic or the expanded covariates vt−1∈Rp described in Data Description. We report out-of-sample performances for both versions, and use the basic one to study the two key questions.

Evaluation of Model Performance

We test the performance of our cost evolution model against ones employed in industry. The comparative studies by the Society of Actuaries^24,25,26 report performances for these models in terms of out-of-sample (prospective) R2 and mean absolute prediction error (MAPE).^vii We therefore evaluate the accuracy of our model’s cost prediction for household i in year t,

using the same metrics for comparison. We also calculate the predictive ratio, the ratio of the sum of predictions divided by the sum of actual expenditures. For R2, higher values are better, while for MAPE, lower values are better, and for predictive ratio, values closest to 1 are best. In order to limit the impact of outliers, we adopt the approach used in the comparative studies to truncate the forecast year expenditure values at $100,000 and $250,000.

Recall that R2 measures how much variance a model (linear regression or otherwise) explains relative to the straw rule of using the average response as the one-size-fits-all prediction. For our model, we report R2, MAPE and predictive ratio on the out-of-sample data in the 2013–2014 test panels. Since the predictions are made for household observations that were not used to develop the model, they are not sensitive to overfitting by complex models the way that their in-sample counterparts are.

Evaluation of Contribution Policies

To compare the performances of the static and dynamic policies, we simulate the total expected discounted cost under each of these policies over a 30 year contribution period.

The results are calculated for an HSA-eligible family plan with a $3,500 deductible, $12,500 OOP maximum, and 20% coinsurance rate.^viii We focus on family plans because individual and family plans have different federal requirements on their HDHP parameters (minimum deductible, maximum OOP max). As such, we assume a family of size of 2.8 (the average size of family units of 2 or more individuals).^ix We further restrict attention to private (employer-sponsored) insurance holders, as this is the population most likely to use HDHPs, and therefore we assume all participants are covered by private health insurance.

Since the health care inflation rate I and investment return rate w are really time-varying random variables, we try to account for this qualitatively by using a basic random walk to capture their evolution over time: In each simulation of the 30-year contribution period, we randomly sample initial values for each of these parameters from within a range of ±50% of the default (I=3.4%, w=8%). Then in each year, each parameter is either increased by 5%, decreased by 5%, or left unchanged, with equal chance for each outcome.

The policies that we considered are the following: 1) dynamic policy; 2) static policy with annual contribution limit of $2,000 (static $2,000); 3) static $4,000; and 4) static $6,450.^x We use the static $2,000 policy as the comparison benchmark because it is close to the median annual contribution for HSAs with nonzero account balances,²⁷ and as such serves as a proxy for common HSA contribution behavior. Household costs are simulated using the basic model because modeling the evolution of household covariates in the expanded model is beyond the scope of this article. All computations were performed in R 3.3.2.

We also perform sensitivity analyses on the results as different parameters are varied. First, we focus on the parameters of the HDHP that vary the most in the marketplace. Specifically we examine the nine pair-wise combinations of deductible values ($2,500, $3,500, $4,500) with OOP maximum values ($7,500, $10,000, $12,500).^xi Second, we separately assess sensitivity to the discount rate by examining three discount rate values (4%, 6%, 8%).

Assessment of Tax Impact and Federal Contribution Limit

To determine if adopting the dynamic policy would lead to total contribution amounts exceeding what the federal contribution limit allows for over 30 years, we examine the distribution of inflation-adjusted contributions over this timeframe. To take a conservative approach in this analysis, we focus on households on the high end of the contribution spectrum. Specifically, we assume an initial cost percentile of X0=0.9 and the highest marginal tax rate of 40%. We also take the highest deductible ($4,500) and OOP maximum ($12,500) values from our sensitivity analysis. These parameter choices yield the highest consumer cost burden, which requires the highest levels of HSA contributions. If the inflation-adjusted sum is less than what is allowed, then the dynamic policy’s long-term tax impact will be within what is currently budgeted by legislation.

We also analyze the proportion of annual contributions that exceed the federal annual limit. A high proportion would indicate that the current federal limit needs to be raised to enable households to take full advantage of the dynamic policy. We perform this analysis using our default parameters of deductible ($3,500) and OOP maximum ($12,500). For this analysis, using $3,500 rather than $4,500 represents a more conservative approach, since it leads to a lower proportion of limit-exceeding contributions.

Performance of Cost Evolution Model

Table 1 compares our basic and expanded models to the commercial models detailed in the comparative studies.^24–26 On the basis of R2, we see that our parsimonious models are superior to those in the first study.²⁴ Compared to the more sophisticated models evaluated in the other two studies, our models’ performances are in the middle of the range when truncation is applied at $250,000, and are at the high end when truncation applied at $100,000. Of course, for our HSA application, it suffices to truncate at the much lower level of the OOP maximum. On the basis of MAPE, our models’ performances are at the better end of the range in the comparison studies.

Performance of Contribution Policies

Figure 5 presents boxplots representing the costs of the static $4,000, static $6,450, and the dynamic policies as a percentage of the cost of the static $2,000 policy. Each boxplot summarizes the distribution of outcomes across 10,000 simulations of the 30-year contribution period. The columns represent initial cost percentile (X0) values of 0.25, 0.50 and 0.75, while the rows represent marginal tax rates of 15%, 25%, and 40%. Figures 6 and ​and77 present the results of the sensitivity analysis on plan parameters and discount rate. Figure 8 shows how the mean total discounted costs for the static $2,000 and dynamic policies vary with X0 and with tax rate. The main qualitative results are the following:

1. Both the dynamic and static $6,450 policies consistently outperform the static $2,000 one. For example, at a marginal tax rate of 40% and X0=0.75, the dynamic policy costs 19% less than the static $2,000 one (based on median performance), with the static $6,450 policy not far behind (Figure 5).

2. The dynamic policy has just a moderate edge over the static $6,450 one, around 2 to 3 percentage points lower based on median performance (Figure 5).

3. The cost advantage of the dynamic and static $6,450 policies over the static $2,000 ones rises with marginal tax rate. For example, at X0=0.5, for marginal tax rates of 15%, 25%, and 40%, the dynamic policy is about 7%, 10%, and 17% less costly than the static $2,000 policy, respectively, based on median performance (Figure 5).

4. The advantage the dynamic policy has over the static $2,000 one is not sensitive to the parameters that define the HDHP. Across the nine combinations of deductible and OOP maximum tested, the cost advantage was 8% to 11% based on median performance, about the same as those for the default plan parameter values (Figure 6).

5. The advantage the dynamic policy has over the static $2,000 policy decreases moderately as the discount rate rises. When the discount rate doubles from 4% to 8%, the cost advantage of the dynamic policy fell from 13% to 9% (Figure 7).

6. The initial cost percentile X0 significantly impacts the total costs of all policies. For example, at a marginal tax rate of 25%, the mean costs under the dynamic policy for X0=0.75 is 17% greater than for X0=0.25, while the equivalent cost differential for the static $2,000 policy is 20% (Figure 8).

7. The impact of the marginal tax rate on total costs is highest for the static $2,000 policy, falls as contribution limit rises, and is negligible for the dynamic policy. For the static $2,000 policy, with X0=0.5, a 40% marginal tax rate results in 15% greater costs than at the 15% tax rate, while for the dynamic policy, this difference is 1%. This is because the dynamic save-up-to threshold is allowed to be as high as the OOP maximum, thereby keeping tax penalties to a minimum (Figure 8).

Tax Impact and Implications of Federal Contribution Limit

We compute the distribution of inflation-adjusted contributions over 30 years. The 25th, 50th, and 75th percentiles are $50,100, $71,400, and $96,300, respectively, in 2013 dollars. These are all significantly lower than the 2013 federal limit of 30×$6,450=$193,500.

We compute the proportion of annual contributions that exceed the federal annual limit, for combinations of initial cost percentiles (0.25, 0.50, 0.75) with tax rates (15%, 25%, 40%). We find that 9% to 11% of households in a given year have recommended contributions that exceed the federal limit. For these households, the mean amount ranges from $10,100 to $10,300 in 2013 dollars.

How Should a Household Budget for Its HSA Contributions?

Our recommended dynamic policy and the static $6,450 one both incur substantially lower costs than our proxy for common contribution behavior (the static policy with a $2,000 contribution limit). The cost advantage is explained as follows. In the first few years following HSA adoption, there is a risk that the account will have insufficient funds to cover OOP expenses. By recommending that the household make a substantial contribution in year 1, the dynamic policy optimizes against this risk. Similarly, the static $6,450 limit policy makes large contributions in the first several years to quickly bring the balance up to the OOP max, thereby reducing this risk substantially. By contrast, the static $2,000 policy grows the balance more slowly, and is at greater risk of account insufficiency early on. The same phenomenon applies in years immediately following large expenditures, when the account is depleted. The dynamic and static $6,450 policies can quickly replenish the account, while the $2,000 policy requires more years to do so.

Our results suggest that while the dynamic policy is the most cost efficient among the ones examined, the static $6,450 policy is a worthy alternative. In the absence of personalized analytic guidance, the latter policy is a sensible strategy: Households outside the top tax brackets can capture most of the cost savings of the dynamic policy while still operating within the federal contribution limit. Our findings also indicate that insufficient annual contributions can result in substantially higher total costs.

The advantage the dynamic policy has over the static policies holds true across a range of parameter values, and is greatest for households with lower discount rates—those who place greater weight on future outcomes.

Should Policy Makers Revisit the Current Federal Contribution Limits for HSAs?

The last portion of our results suggest that 9% to 11% of households in a given year will need to make a HSA contribution that materially exceeds the current federal contribution limit. To allow these households to make full efficient use of HSAs, we propose an alternative to the current approach of capping annual contributions: Permit households to contribute to their HSA without limit up to a certain account balance (the limit-free balance), and then impose an annual limit on contributions thereafter. The limit-free balance could be set equal to each plan’s OOP maximum. This two-tiered approach allows households to quickly save up to the threshold recommended by the dynamic policy. Importantly, our results suggest that the resulting impact on overall tax receipts will be well below what is currently allowed by legislation.

To our knowledge, this is the first article to develop rigorous guidelines for HSA contributions, and we view it as a promising first step. To improve the accuracy of the model, future research should examine some of the possible extensions described below.

• Health care costs during retirement. We might also factor into our objective health care costs during retirement, during which no contributions are made. For this objective, a preferred policy is likely to be a hybrid of the dynamic policy (to cover current costs) and a fixed contribution component (to cover estimated retirement costs), with the goal of attaining an account balance at the end of the contribution period that is sufficient to cover costs during retirement. We can leverage the modeling framework developed here to analyze this type of policy.

• HSA withdrawals for nonmedical expenses. A reviewer correctly pointed out that a household can withdraw money from its HSA for nonmedical expenses. Such a withdrawal would trigger a penalty on top of the tax due on the withdrawal amount, so our current model prohibits negative contribution amounts. This can be relaxed by developing an additional model for predicting whether a withdrawal may be needed, as a function of the household’s wealth and spending needs. Fitting such a model requires gathering additional household financial data, which we leave for future research. If the current dynamic policy is operationalized to provide contribution recommendations, we advise that users contribute the minimum of what is recommended and the amount they anticipate would not be needed for other purposes.

• Impact of HSAs and high-deductible plans on expenditure distribution. In this article, we did not attempt to model this because the Medical Expenditure Panel Survey dataset only has limited information about the insurance plan parameters of individuals, and only up to 2001 (before the implementation of HSAs). In the future our model could be recalibrated to data from households with multi-year enrollment in HDHPs. The results of the RAND Health Insurance Experiment suggest that increased cost sharing reduces the likelihood of visiting a physician, but has a smaller effect on the costliness per episode of care.²⁸ We hypothesize the effect might appear as an increase in the probability of zero costs, and/or as a shifting of the overall yearly cost distribution curve to the left.

• Switching to a low-deductible health plan. Some households have access to both HDHPs and low-deductible plans, and may choose to switch between them. Under this scenario, the optimal policy may be of the form^xii: If the household’s current cost percentile is below a certain level, use a HDHP and contribute the amount (4) to a HSA; otherwise, select the low-deductible plan. Further exploration of the choice between high- and low-deductible plans is left for future research, possibly along the direction discussed above.

• Time-dependent covariates in cost prediction. Our cost evolution model uses time-fixed covariates to produce long-term forecasts, whereas leading industrial models use the most recently available values of time-dependent variables to forecast a little ahead in time. To incorporate these variables into our model for long-term planning, we need to have a way to simulate the evolution of these variables over time. This itself is a complex problem that is worthy of a separate research question. We note however that the short-term predictive performance of our model is already on par with the industrial ones. Hence, feeding a household’s most recent covariate values into our model should provide contribution recommendations that approximate the more sophisticated model.

We anticipate that our policy (or a version of it built atop more elaborate versions of the same models) could in the future be turned into a web application that consumers can use to determine contributions on an annual basis. While the details of such an implementation are outside the scope of this article, we imagine the application would operate as follows: The user would be requested to submit parameter values such as household size, prior year health care spending, marginal tax rate, and current health savings account balance. The application would then display the recommended contribution amount.

To conclude, we have developed a new analytical framework for modeling a HSA balance over time. We used this model to formulate a contribution policy that enables a household to optimize their expected discounted costs. With the growth trend in consumer-driven health plans, we expect that evidence-based modeling will play an increasing role in consumer health care financial planning.

DS_10.1177_2381468318809373 – Supplemental material for Health Savings Accounts: Consumer Contribution Strategies and Policy Implications:

Supplemental material, DS_10.1177_2381468318809373 for Health Savings Accounts: Consumer Contribution Strategies and Policy Implications by David J. Lowsky, Donald K. K. Lee and Stefanos A. Zenios in MDM Policy & Practice

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

The author(s) received no financial support for the research, authorship, and/or publication of this article.

Author Note: DKKL is now affiliated with Goizueta Business School, Emory University, Atlanta, Georgia.

Supplemental Material: The online supplementary materials for this article are available on the Medical Decision Making Policy & Practice website at http://journals.sagepub.com/home/mpp.

ⁱIn 2013, the household limit was $6,450, and for 2017 it is $6,750. Individuals aged 55 and older and not enrolled in Medicare are allowed to make additional annual contributions of up to $1,000.

ⁱⁱMachine learning methods have also been applied to predict expected health care costs.^7-10 However, for our problem it is necessary to model the cost distribution instead, given that the optimal dynamic policy is a critical fractile solution.

ⁱⁱⁱ“In-scope” is defined as being a member of the US civilian noninstitutionalized population. We further include individuals who were born or died at some point during the survey period.

^ivWe also performed an analysis of the sensitivity of results to discount rate (see Results).

^vSelf-reported health variables, including perceived health status, have been shown to be a valuable predictor of health care costs.^14-17

^viThis is a continuous version of a similar approach for modeling transitions among discrete cost states: Low, Medium, High, and Very High.²¹

^viiMAPE is expressed as a fraction of the mean out-of-sample costs.

^viiiThe relative performance of the policies was insensitive to the deductible amount or OOP maximum, per the results of our sensitivity analysis reported in Results.

^ixFamily size is modeled as a continuous covariate in our cost evolution models.

^xThe 2013 federal annual contribution limit was $6,450.

^xiWe selected $2,500 as the lowest deductible and $12,500 as the highest OOP maximum. These correspond to the lowest and highest federal allowable limits, respectively, for all HSA-eligible plans in 2013.

^xiiThis follows from applying policy iteration once to the Bellman equation in the supplementary material used to derive (4).

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