The Frisch elasticity of labor supply — the percentage response of hours worked to a temporary wage change holding the marginal utility of wealth constant — is a core behavioral parameter of macroeconomics, yet microeconometric estimates (typically 0.1-0.5) and the values implied by aggregate, cohort-level estimation and by macroeconomic models (often 1-3 or higher) differ by roughly an order of magnitude. Peterman (2016) showed that jointly relaxing two restrictions of the classic micro estimation — sample composition (prime-age married men versus the whole population, including older workers near retirement) and the intensive margin only (hours per worker versus total hours including participation) — can move a conventional micro estimate of about 0.2 into the macro range of 2.9-3.1, but left open whether that reconciliation is causal or artifactual. The paper's conclusion poses exactly one explicit charge for future work: because the joint hours and wage declines of older workers may reflect chosen transitions into partial retirement rather than responses to wage shocks, its cohort-level macro estimates may be upwardly biased, and 'future work should aim to disentangle the strength of this bias.' This problem asks for that disentangling: quantifying the endogenous-retirement bias in the cohort-level macro estimates (2.9-3.1 for ages 20-65; 1.75 excluding ages 61-65; 0.81 excluding ages 51-65) and thereby determining, within the specification-conditional calibration guidance the paper itself delivers, which of its candidate values a given aggregate macro model should use. As of 2026, no work has quantified this bias: the literature has produced conflicting point estimates (meta-analytic total-hours elasticities near 0.25 versus structural aggregate estimates near 1.75 and Peterman's macro-concept estimates of 2.9-3.1), but the strength of the retirement-endogeneity component in the cohort-level macro estimates remains unsettled.

Background

The Frisch (or intertemporal-substitution) elasticity of labor supply is the percentage change in hours an optimizing worker supplies when the real wage temporarily rises, holding constant the marginal utility of wealth (so that income and wealth effects are shut down; the resulting response is purely a substitution effect). It is a load-bearing parameter in dynamic stochastic general equilibrium (DSGE) and real-business-cycle (RBC) models — the workhorse frameworks used to study business cycles, fiscal policy, and taxation — because it governs how strongly aggregate hours react to wage fluctuations, and hence the size of fiscal multipliers and labor-supply responses to tax changes. A long-standing puzzle is that the parameter's value depends drastically on where one looks. Microeconometric studies, following the life-cycle labor supply tradition of estimating hours regressions on wages with instrumental variables (two-stage least squares, 2SLS, in which a wage regression on instruments supplies the exogenous wage variation), typically find small Frisch elasticities around 0.1-0.5 for prime-age men; macroeconomic calibration practice and some aggregate estimates require values of 1-3 or more to reproduce observed business-cycle fluctuations in hours. Classic micro estimation rests on two restrictions: it uses a narrow sample (prime-age married men) and studies only the intensive margin (adjustments in hours per worker), whereas aggregate hours also move on the extensive margin (whether individuals work at all) and across the whole population. Peterman (2016), 'Reconciling Micro and Macro Estimates of the Frisch Labor Supply Elasticity' (Economic Inquiry 54(1):100-120; working-paper version FEDS 2012-75), re-estimated the classic micro model while relaxing these restrictions one at a time and jointly. Neither alone closes the gap; jointly they raise an estimate of roughly 0.2 to 2.9-3.1, in the macro range. Two features drive this: the estimate is highly sensitive to the age coverage of the sample — excluding ages 61-65 lowers the baseline macro estimate of 2.88 to 1.75, and excluding ages 51-65 lowers it further to 0.81, so the large estimates are primarily driven by older individuals — and the aggregate effect is amplified by interactions between demographic composition and extensive-margin participation. But the paper itself flags that this reconciliation may be artifactual, and its conclusion singles out one issue as the explicit charge for future work. First and centrally, endogenous retirement: the joint hours and wage declines of older workers may reflect chosen transitions into partial retirement rather than responses to wage shocks — Casanova (2012), cited in the paper, finds that once partial retirement is controlled for, the wage profile of older individuals no longer falls — so cohort-level ('macro') estimates that include those ages may be biased upward, and 'future work should aim to disentangle the strength of this bias.' Three further sensitivities appear in the paper as reported results and robustness analyses rather than as open questions. Identification: 2SLS estimates of the Frisch elasticity are known to be biased toward the corresponding OLS (ordinary least squares) estimate when the instruments (e.g., age and education polynomials) are weak — a point made in the broader literature by Lee (2001) — and Peterman reports robustness to alternative instrument sets (his own polynomials versus Fiorito-Zanella's lagged-wage instruments) and to the source of identifying wage variation (life-cycle predictable variation versus persistent aggregate shocks). Non-workers: estimating an unconditional aggregate elasticity requires imputing or predicting wages for people who do not work, and different imputation conventions change the estimate substantively (roughly 1.68-2.64 versus the 2.9-3.1 baseline). And the demographic interaction effects that amplify the aggregate response suggest structural heterogeneity whose microfoundations are not understood. Whether the true causal Frisch elasticity appropriate for a given macro model is small or large remains genuinely contested: the meta-analysis of Elminejad, Havranek, Horvath and Irsova (2023) finds, after correcting for publication bias, an intertemporal substitution elasticity near 0.2 on the intensive margin and a total-hours elasticity around 0.25, while the structural aggregation theory of Erosa, Fuster and Kambourov (2016) implies an aggregate elasticity to transitory wage shocks around 1.75, and calibrated DSGE practice spans roughly 0.5-2. The question is therefore not merely 'what is the number' but which of the candidate numbers applies to which model. On the latter, the paper's Section 5.1 already delivers specification-conditional guidance as a result: a parsimonious model that includes neither partial retirement nor age-varying leisure preferences needs the large value incorporating older individuals to replicate the observed wage and hours profiles, whereas a model that includes a partial-retirement decision and rising leisure preference with age should use the lower value estimated from younger individuals. The validity of that guidance hinges on the paper's open question: how much of older workers' observed hours-wage declines is exogenous wage-shock response versus chosen partial retirement.

Problem Statement

Determine the Frisch elasticity of labor supply appropriate for calibrating aggregate macroeconomic models by resolving the open question Peterman (2016) explicitly leaves: quantify the bias that endogenous life-cycle transitions — in particular chosen partial retirement and retirement-related wage declines — impart to the cohort-level 'macro' Frisch estimates that include older workers. Peterman's baseline macro-concept estimate is 2.9-3.1 (ages 20-65, including extensive-margin fluctuations); it falls to 1.75 when ages 61-65 are excluded and to 0.81 when ages 51-65 are excluded. Are the joint hours and wage declines of older workers a response to exogenous wage shocks, or chosen transitions into partial retirement? The open question has two components, each resolvable on its own: First, the strength of this endogenous-retirement bias in the Frisch-elasticity units of the estimates above — how much of the baseline cohort-level macro estimate reflects chosen partial retirement and retirement-related wage declines rather than exogenous wage-shock responses — with the identification evidence supporting it; the bias-corrected value may lie outside the paper's reported candidate values. Second, the resulting calibration recommendation for each aggregate macro-model specification under the paper's own Section 5.1 guidance: which of the paper's candidate values that specification should use. The paper's reported sensitivities — instrument choice and strength, the source of identifying wage variation, and non-worker wage-imputation conventions (unconditional estimates of roughly 1.68-2.64) — frame why the bias question matters for interpreting these estimates.

References

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