Black Daniel and Sanders 2002 — The Impact of Economic Conditions on Participation in Disability Programs Evidence from the Coal Boom and Bust

Summary

Using the coal boom (1970s, Organization of the Petroleum Exporting Countries (OPEC)-driven) and bust (1980s) in Kentucky, Ohio, Pennsylvania, and West Virginia as a natural experiment, Black, Daniel, and Sanders (2002) estimate the elasticity of Disability Insurance (DI) and Supplemental Security Income (SSI) participation with respect to permanent labor market conditions. The instrument is the interaction of the log annual coal price (set on world markets) with the log of county coal reserves (a geological constant), producing county-year variation in permanent earnings prospects orthogonal to transitory income fluctuations. The headline results: two-stage least squares (2SLS) elasticity of DI payments per capita $\approx -0.35$ to $-0.41$ ; SSI $\approx -0.40$ to $-0.71$ . Ordinary least squares (OLS) is near zero in both cases. An Unemployment Insurance (UI) placebo test confirms the mechanism: the same instrumental variable (IV) has a near-zero effect on UI (a transitory-shock buffer), while DI and SSI respond strongly — exactly the predicted pattern if disability programs insure permanent, not transitory, earnings losses.

Key Claims

DI payments elasticity (2SLS): $-0.345$ (Table 3, col. 1; $t = 3.95$ ) to $-0.41$ across specifications; statistically significant in all.
SSI payments elasticity (2SLS): $-0.713$ (Table 3; $t = 5.33$ ) to $-0.71$ across main specifications; consistently larger in magnitude than DI.
OLS $\approx 0$ : OLS estimates for both DI and SSI are near zero and statistically insignificant — consistent with transitory noise dominating the annual earnings measure and attenuating the coefficient.
First-stage $F \approx 27$ : Instrument ( $\Delta$ log coal price $\times$ log coal reserves) is strong by conventional standards.
UI placebo: 2SLS for log UI payments per capita $\approx 0$ (near-zero and insignificant); OLS for UI is positive and significant. This is the key falsification: UI responds to transitory shocks (OLS strong) and not to permanent shocks (IV $\approx 0$ ); DI/SSI are the mirror image (OLS $\approx 0$ ; IV strong).
Steel replication (6 states, 1982–87): Using $\Delta$ (steel employment share) $\times$ post-1982 dummy as a second instrument confirms generalizability: DI elasticity $= -0.361$ ( $t = 4.03$ ), SSI $= -1.049$ ( $t = 4.82$ ).
SSI > DI elasticity: SSI's means-test creates a dual channel — changes in own earnings and in family income both shift SSI eligibility, making it more elastic than DI (which only operates through the own-earnings/replacement-rate channel).
Coal workforce demographics: $\approx 95\%$ male; $\approx 30\%$ without a high school diploma in 1990. The sample population is overwhelmingly men in heavy blue-collar work.
Coal price path: Rose from $\$7.35$ /short ton in 1969 to $\$28.13$ by 1982 (1987 dollars); fell to $\$15.35$ by 1987. Coal employment in KY+WV rose from $\approx 60{,}000$ (1969) to $\approx 95{,}000$ (1982), collapsed to $\approx 47{,}000$ by 1987.
DI is quasi-permanent: Approximately $1.6\%$ annual exit rate from DI rolls; typical time-to-benefit $\approx 2$ years. Workers optimize over permanent earnings prospects, not transitory fluctuations — which explains why the annual earnings regressor fails in OLS.
Disability-as-continuum: Authors explicitly reject the "malingering" framing. Workers are on a continuum of health capacity; economic conditions determine where the application threshold falls. A bad elbow that does not prevent light work may make coal mining unsustainable — without implying the worker is dishonest.
Aggregate county-level data: Dependent variables are log(transfer payments per capita) at the county-year level. Cannot distinguish individual-level program selection from aggregate participation changes.

Concepts Introduced or Extended

Entities Mentioned

Quotes

"Our results suggest that as economic conditions improve, the participation rates in disability programs fall significantly. The OLS estimates, however, are very close to zero. This divergence arises because OLS estimates use variation in annual earnings, which contains much transitory variation, while the IV estimates use only the permanent variation in earnings associated with the coal boom and bust."

"The theoretical underpinning of our empirical analysis is straightforward. If the worker is on a continuum of disability, then economic conditions may determine who, among those individuals with some disability, actually participate in disability programs."

"UI, a program designed to replace income during transient unemployment spells, is much more strongly related to year-to-year fluctuations in earnings than it is to the permanent component of earnings. DI and SSI, by contrast, are programs designed to insure against long-term income losses — and their participation rates respond to the permanent component."

My Take

Black et al. 2002 makes three foundational contributions to the DI literature.

1. Permanent income mechanism. The OLS $\approx 0$ / IV strong divergence is the paper's most important methodological lesson. Transitory fluctuations in annual earnings dominate the signal in OLS, producing attenuation bias toward zero. The coal-price IV purges transitory noise and isolates the permanent component of earnings prospects — the economically relevant quantity for a program that requires a 24-month commitment and has a $1.6\%$ annual exit rate. This explains why a generation of cross-sectional and short-panel DI research produced weak or zero income elasticities: it was regressing DI on the wrong earnings measure. The lesson generalizes beyond coal: any IV that shifts permanent labor market prospects (trade shocks, plant closings, industry-level technological change) will find elasticities an order of magnitude larger than OLS.

2. IV design that generalizes. The coal-price × reserves instrument is a genuine natural experiment: price is set on world markets (exogenous to any county), reserves are geological constants (fixed before the period). The steel replication — a structurally different industry, different states, different decade — confirms the mechanism is not coal-specific. Together, these two experiments establish a template for regional labor market shocks as IVs for permanent earnings, which Autor and Duggan (2003) exploit at the national level via the DI replacement rate measure and which Deshpande et al. (2025) extend via the Bartik shift-share design.

3. SSI > DI elasticity as structural evidence. The larger SSI response is not noise — it is mechanistic. SSI's means-test adds a second channel (family income threshold) to the own-earnings replacement-rate channel that DI also has. Both channels tighten when permanent earnings fall. The differential quantifies the importance of the means-test mechanism and predicts that population groups with high family-income sensitivity (concentrated low-income households, multiple earners below the SSI threshold) will have even larger SSI elasticities than the county averages suggest.

Limitations: County-level data cannot identify which workers within coal counties are driving the response — miners, service workers serving miners, or broader local economy. The sample is $95\%$ male, limiting external validity to women and non-heavy-industry economies. The paper predates the 2003 Autor-Duggan framework that connects the replacement rate mechanism to the specific compositional changes in the applicant pool — Black et al. establish the elasticity but not the micro-behavioral channels (conditional vs. inframarginal applicants) that later work will flesh out.