David Lowsky and Stefanos Zenios

Graduate School of Business, Stanford University

In this work, we explore two healthcare topics:

1. Healthcare cost prediction and
2. the viability of health savings accounts.

We present a new approach for healthcare cost prediction based upon percentiles of previous year’s costs.  Our model is based on the following observation:  While there may be low correlation between a household’s actual costs in two adjacent years, there is significant correlation between a household’s cost percentiles in two adjacent years.  Using longitudinal cost data for 37,000 households from 1996-2003, we create a probabilistic model to predict a household’s next year cost percentile based upon its previous year cost percentile.  Combining this model with a forecast of household costs by percentile, we are able to produce household cost predictions that are reasonably accurate compared to existing methods.  Our method has the advantage of requiring minimal additional (medical) information per household, although such data can be incorporated to improve predictive power.  Our approach demonstrates that previous year household medical costs alone can be used to produce fairly accurate predictions of future costs.

Using the same probabilistic model for healthcare cost shocks, we also explore whether health savings accounts (HSAs) can be relied upon to cover a household’s healthcare costs over time.  Proponents of health savings accounts (HSAs), one category of  consumer-driven health plans that have emerged as alternatives to traditional medical insurance, seek to place greater financial decision-making in the hands of individuals.  HSAs operate as follows:  A household makes an annual pre-tax contribution to the HSA, which is used to pay for annual medical expenditures up to a certain high deductible.  The household also pays for medical insurance to cover larger expenses.  The household retains unused funds in the account, which carry over from year to year.  We seek to answer the following question:  How long does a household have to utilize and contribute to an HSA before it can rely upon it to cover all future healthcare costs with great confidence?  Using a Markov probability model to simulate a household’s healthcare cost shocks, we simulate a health savings account balance over time for various combinations of contribution and deductible.  Our initial finding is that HSAs require upwards of 20 years for most households before they can be relied upon with great confidence to cover all future healthcare costs.