Abstract
<p>The question "did lockdowns work?" is under-specified. A stay-at-home order, school closure, gathering ban, isolation order, contact quarantine, nursing-home shielding program, and border control are distinct interventions with different targets, costs, and mechanisms. This paper develops a counterfactual break-even framework for evaluating pandemic nonpharmaceutical interventions. In its simplest prevention form, a compulsory intervention is justified when the fatality rate in the affected population exceeds B = C / (N * DeltaA * V), where C is incremental policy cost relative to the disease-and-voluntary-behavior baseline, N is the affected population, DeltaA is the absolute reduction in cumulative attack rate, and V is the value assigned to a death avoided. The fuller ledger adds hospital-overload deaths avoided, the option value of delaying infection until vaccines or improved treatment, morbidity effects, and distributional costs. Applied to COVID-19, the framework explains why reasonable analyses diverge: the result is highly sensitive to mortality valuation, marginal mandate effectiveness, timing, and age structure. With illustrative U.S. parameters — 330 million people, $2 trillion incremental cost, and a 20 percentage point reduction in cumulative attack rate — the break-even IFR is 4.7% under an output-accounting lower-bound value of death, 0.61% under an age-adjusted VSLY scenario, and 0.21% under the current DOT age-blind VSL scenario. Under the output-accounting scenario, when cost is expressed as a share of GDP, national income cancels algebraically from the threshold: B = c / (DeltaA * YLL). That cancellation is narrow but useful; it holds only when both cost and death valuation scale with national output. A reproducible descriptive regression using 100 countries with complete data finds that age structure, GDP per capita, diabetes prevalence, and population density explain about one quarter of the variance in cumulative excess mortality, while adding average 2020-21 Oxford containment-and-health policy intensity changes R-squared by +0.000. This ecological result is not a causal estimate of lockdown effectiveness. It supports only a limited descriptive claim: average cross-country stringency, measured this way, was not the variable that separated high-mortality from low-mortality countries once basic structural risk was included. The main contribution is therefore not causal identification; it is a decision framework that makes explicit the valuation, counterfactual, timing, and targeting assumptions that determine whether a particular restriction is justified.</p>