Lindner 2016 — How Do Unemployment Insurance Benefits Affect the Decision to Apply for Social Security Disability Insurance

Summary

Uses Survey of Income and Program Participation (SIPP) data (1990–2007) matched to Social Security Administration (SSA) administrative disability records to examine whether Unemployment Insurance (UI) benefit generosity affects the decision to apply for Social Security Disability Insurance (DI). The core finding is a negative but imprecisely estimated substitution effect: Cox proportional hazard models suggest a $100 increase in monthly UI benefits reduces the hazard of DI application by ~~10% (significant at 5% in the fully controlled specification), while spell-level logit models produce a similar-signed but statistically insignificant coefficient (~~−6%). The discrepancy is diagnosed as unobserved heterogeneity inflating the hazard estimate. A cost-benefit calculation implies a $1.00 increase in UI benefits reduces DI program expenditures by 15 cents. An extended optimal social insurance framework (building on Chetty 2006) shows that incorporating this cross-program savings raises the optimal UI replacement rate by more than 20 percentage points.

Key Claims

Aggregate evidence: A state-year panel (1993–2008) regression shows a negative, weakly significant ( $p < 0.10$ ) association between states' monthly UI maximum benefit amount and DI applications per thousand adults. A $100 increase in the UI maximum monthly benefit is associated with 0.075 fewer DI applicants per thousand (average application rate: 6.1 per thousand).
Individual-level hazard model: Among 8,886 UI recipients in the sample, 176 (1.98%) apply for DI. In the full-control Cox proportional hazard specification, a $100 increase in monthly UI benefits decreases the application hazard by approximately 10% (coefficient $= -9.55$ , standard error $[s.e.] = 3.93$ , $p < 0.05$ ). The effect becomes significant only after including the Principal Insurance Amount (PIA) as a control, because PIA is positively correlated with both the UI monthly benefit amount (MB) and the DI application probability.
Logit model and heterogeneity diagnosis: Spell-level logit results are consistently negative (coefficient $\approx -6\%$ ) but not statistically significant. The hazard-vs-logit discrepancy implies the hazard model overstates the effect due to worker heterogeneity: workers who would never accept a job offer (or never qualify for DI) mechanically inflate the hazard denominator as unemployment extends, biasing the hazard coefficient when higher UI prolongs their spell duration.
Subgroup heterogeneity: Effects are larger for workers aged 50 and older (hazard coefficient $= -10.59$ , $p < 0.05$ ) and workers without a college degree (hazard coefficient $= -15.97$ , $p < 0.05$ ; logit coefficient $= -11.42$ , $p < 0.05$ ). The UI-DI substitution is concentrated among groups with the least human capital and the strongest incentive to exit the labor market.
Cost-benefit calculation: A $100/month UI benefit increase for all new claimants for one year (direct cost: ~~$3 billion) averts approximately 4,500 DI applications and 2,700 DI awards (assuming a 60% DI approval rate). Using the present discounted value (PDV) of an average new DI beneficiary (~~$191,000 in 2000 dollars, from von Wachter, Song, and Manchester 2011), total DI savings are ~$0.5 billion — implying $0.15 in DI cost savings per $1.00 of UI spending.
Optimal UI formula extension: Adding a UI-DI substitution term $(ap_d b_d / D)\bar{\varepsilon}_{p_d, b_u}$ to the Chetty (2006) optimal social insurance formula (where $\alpha$ is the DI acceptance probability, $p_d$ is the baseline DI application probability, $b_d$ is the PDV of DI benefits, $D$ is average unemployment duration, and $\bar{\varepsilon}_{p_d, b_u}$ is the semielasticity of the DI application rate with respect to UI benefits), the optimal UI replacement rate rises by >20 percentage points across coefficients of relative risk aversion $\gamma = 2$ – $5$ (e.g., for $\gamma = 3$ : from 17.1% to 36.1% without vs. with the interaction term).
Robustness checks: UI maximum benefit changes are not significantly predicted by states' unemployment rates or claimant composition ratios, supporting the exogeneity of benefit level variation. A placebo regression using UI non-recipients shows no UI effect on DI applications (coefficient small, positive, not significant), consistent with the causal interpretation.
Contrast with Mueller, Rothstein, and von Wachter (2016): That study, exploiting the uneven rollout of UI extensions during the Great Recession, finds no effect of UI exhaustion on DI applications — leaving the UI-DI substitution result unresolved. Lindner argues their design identifies effects only immediately post-exhaustion and during a single recessionary period.

Concepts Introduced or Extended

Disability Insurance Program — UI-DI substitution mechanism; transfer income explicitly excluded from the substantial gainful activity (SGA) earnings screen permits simultaneous UI and DI eligibility; cross-program cost-benefit implications
Optimal Social Insurance — Chetty (2006) optimal UI formula extended with DI-substitution term; recognizing cross-program savings raises optimal UI replacement rate by >20 pp for $\gamma = 2$ – $5$

Entities Mentioned

Quotes

"I find that higher UI benefits reduce applications for DI. This substitution effect is imprecisely estimated but economically significant, implying that a $1.00 increase in UI benefits reduces DI expenditures by 15 cents."

"Recognizing this cost-saving effect would increase the optimal UI benefit level by more than 20 percent for coefficients of relative risk aversion ranging from two to five."

My Take

The paper's core identification is credible but underpowered: 176 DI applicants out of 8,886 UI recipients generates very wide standard errors, and the key hazard model result hinges on including PIA as a control — a variable that is itself a function of past earnings and therefore not strictly exogenous. The hazard vs. logit discrepancy is the paper's sharpest methodological contribution: Lindner formally models how unobserved heterogeneity biases the hazard estimator and shows the spell-level logit avoids it. The optimal UI formula extension is elegant but the 15-cent savings figure rests on a coefficient that is not significant in the logit model — making the welfare-optimal calculation a useful order-of-magnitude benchmark rather than a precise policy guide. This is the published version (JHR 51[1], 2016) of Lindner's dissertation research on UI-DI substitution. The wiki retains the earlier working-paper/dissertation version separately as Lindner 2011 — How Does Unemployment Insurance Affect the Decision to Apply for Social Security Disability Insurance, which uses a narrower data window (SIPP 1990–2004), a semi-parametric correlated-random-effects (Heckman-Singer) hazard specification, and frames the mechanism as competing insurance-vs-search-effort channels — a distinct methodology and cost-effectiveness framing worth preserving alongside this published version. Together the Lindner (2011, 2016) and Lindner–Nichols (2012) trio provides the most thorough investigation of the UI-DI interaction in the literature.