The Role of Unemployment Insurance in an Economy with Liquidity Constraints and Moral Hazard

Questions & answers

Q1. What is the model’s basic structure, and in what deliberate sense are its assumptions “extreme”?

The economy consists of a continuum of infinitely-lived, ex ante identical agents with preferences over consumption and leisure, facing an individual-specific two-state Markov employment-opportunity process; agents who are offered work can accept (working a fixed number of hours) or reject it, agents not offered work are unemployed, and the only asset available for self-insurance is a non-interest-bearing store of value – no borrowing and no private insurance markets are allowed. The authors describe this as deliberately chosen to generate an upper bound on the welfare benefits UI could provide in an actual economy, since real economies have at least some access to credit and informal (e.g., family) insurance that the model assumes away.

Q2. How is moral hazard introduced and parameterized in the model?

An agent who rejects an offered work opportunity nonetheless collects UI with exogenous probability π (and gets nothing with probability 1-π); the agent knows π when deciding whether to reject an offer, but not in advance whether they personally will receive UI. The authors motivate this as representing partial enforcement of a “work test” – every nonworking agent applies for UI, the government audits a fraction of applications, and a fraction π of undeserving (i.e., work-rejecting) applicants beat the audit and collect benefits anyway; varying π from 0 (strict enforcement, no moral hazard) to 1 (no enforcement, extreme moral hazard) spans the range of possible UI-eligibility regimes studied.

Q3. What do the results show about how moral hazard affects the economy’s employment rate and tax burden for a given replacement ratio?

With risk aversion ρ=1.5 and no moral hazard, raising the replacement ratio from 0 to 0.25 lowers the employment rate by only 1.9 percent (because even without moral hazard, a higher replacement ratio lowers the after-tax wage and so lowers labor supply at the margin); with extreme moral hazard (π=1) the same policy change lowers employment by 45 percent, and at a moderate moral-hazard level (π=0.15) employment falls by 6.5 percent. The tax rate needed to finance a 0.25 replacement ratio is about ten times larger under extreme moral hazard than under no moral hazard, since UI outlays scale with both the replacement ratio and the (much larger) number of people collecting it.

Q4. What is the paper’s central finding about the “optimal” replacement ratio, and how fast does it fall as moral hazard rises?

At risk aversion ρ=1.5, the welfare-maximizing replacement ratio is 0.7 with no moral hazard but falls to zero once moral hazard is extreme (π=1); the authors report the decline is especially sharp at small amounts of moral hazard – raising π from 0.05 to 0.1 drops the optimal replacement ratio from 0.6 to 0.2, and for π above about 0.25 the optimal level of UI is essentially zero. At higher risk aversion (ρ=3 or 5), the optimal replacement ratio is markedly less sensitive to small amounts of moral hazard, though it still eventually falls toward low single digits (reported as 10 percent even under extreme moral hazard at ρ=5) as π grows large.

Q5. What welfare-cost comparisons does the paper report between the liquidity-constrained economy, the social-planner optimum, and UI at its optimal level?

Using a welfare measure based on the percentage increase in individual productivity (equivalently, GNP) needed to make the liquidity-constrained economy’s average agent as well off as under the social planner’s optimal allocation, the authors find this baseline welfare cost is 0.76% of GNP (at ρ=1.5, no UI); introducing UI at its optimal replacement ratio (0.7, no moral hazard) reduces this cost to 0.29% of GNP, a 62% reduction. At higher risk aversion, UI can close the gap entirely with low moral hazard (welfare costs reduced to zero, i.e., matching the social planner’s allocation, at ρ=3 or ρ=5 when π is small), though even under extreme moral hazard some welfare benefit from optimal (near-zero) UI remains available (a 10% reduction in welfare cost at ρ=3, 26% at ρ=5).

Q6. What happens if the replacement ratio is fixed at an empirically realistic level (0.5) rather than set optimally, as moral hazard varies?

Setting the replacement ratio arbitrarily at 0.5 – described as a reasonable lower bound for actual U.S. UI replacement rates – the authors find UI improves welfare relative to having none only for very low moral hazard (π=0 or 0.05); for π at or above 0.1, this amount of UI actually reduces welfare, and the welfare cost grows “enormous” as π increases further. This result underlines that whether UI helps or hurts welfare, at realistic benefit levels, depends sensitively on how well the work test is actually enforced.

Q7. What potential biases does the paper itself flag in interpreting these results, and what does the paper’s conclusion emphasize about work-test enforcement?

The authors note several reasons the model may overstate UI’s potential benefits – most individuals have at least some access to credit and family-based informal insurance that the model assumes away, and if jobs differ in characteristics that make quitting costly (e.g., loss of job-specific human capital), the moral-hazard channel modeled here (agents freely rejecting/quitting for a chance at UI) may be overstated. The paper’s conclusion stresses that, because U.S. UI work-test disqualifications are reported (citing Clark and Summers 1982) to affect fewer than 0.1 percent of claimants, with eligibility instead controlled mainly through indirect requirements (minimum base-period earnings/weeks, limited benefit duration), replacement ratios above 0.5, as found in the actual U.S. system, are justified in this model’s terms only if the work test is strictly enforced in practice – and are called for only under a reasonable degree of risk aversion.