PRELIMINARY AND INCOMPLETE. PLEASE DO NOT CIRCULATE
Liquidity Constraints and the Value
of Insurance*
Keith Marzilli Ericson and Justin
Sydnor
April 2017
How do liquidity constraints affect the
value of insurance?
Key Insights
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Standard insurance demand models implicitly assume costless borrowing
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Many people face liquidity constraints
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Premiums are the same each month, while cost‐sharing expenses are lumpy and unpredictable.
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Paper simulates effects of liquidity => Big effects!
Implications:
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People may rationally buy dominated health plans
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Liquidity causes more variation in the value of insurance than variation in risk aversion
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Liquidity affects the value of the Affordable Care Act’s cost‐sharing reductions (CSRs) for Marketplace
(exchange) enrollees.
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Insurance values from the CSRs is clearly enough to outweigh modest costs of public funds
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Liquidity affects optimal contract design.
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The standard (Arrow 1969) insurance model has consumers preferring full insurance after a deductible,
but with liquidity constraints, individuals can prefer a low deductible plus coinsurance cost‐sharing above
the deductible because it smooths risk across months.
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Survey results find that proxies for liquidity constraints are associated with higher demand for insurance
Typical model
The typical approach:
Individual has a risk averse utility function U defined over annual
realized wealth.
So the utility of a plan in this “Utility from Annual Wealth” is given by:
for some baseline level of wealth. When a CARA utility function is
used, the definition of baseline wealth is irrelevant for valuing
contracts. When other utility functions are used, wealth is often
defined as annual income or some annual consumption level. Like
most of the literature, we assume that the utility function is not
state‐dependent (e.g., depends on how sick you are).
Alternative models
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Monthly consumption model
Cash-on Hand Model
Premium
Income