1. Keith Marzilli Ericson and Justin Sydnor April 2017
PRELIMINARY AND INCOMPLETE. PLEASE DO NOT CIRCULATE Liquidity Constraints and the Value of Insurance*
Keith Marzilli Ericson and Justin Sydnor April 2017

2. How do liquidity constraints affect the value of insurance?
Key Insights
Standard insurance demand models implicitly assume costless borrowing
Many people face liquidity constraints
Premiums are the same each month, while cost‐sharing expenses are lumpy and unpredictable.
Paper simulates effects of liquidity => Big effects!
Implications:
People may rationally buy dominated health plans
Liquidity causes more variation in the value of insurance than variation in risk aversion
Liquidity affects the value of the Affordable Care Act’s cost‐sharing reductions (CSRs) for Marketplace (exchange) enrollees.
Insurance values from the CSRs is clearly enough to outweigh modest costs of public funds
Liquidity affects optimal contract design.
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.
Survey results find that proxies for liquidity constraints are associated with higher demand for insurance

3. 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).

4. Alternative models Monthly consumption model Cash-on Hand Model
Premium
Income