Returns to experience and the elasticity of labor supply

Layer 1: Overview

Research question and motivation: A large empirical literature uses micro data to estimate the intertemporal elasticity of substitution (IES) of labor supply, a parameter crucial for understanding business-cycle fluctuations in hours and labor-supply responses to tax policy. Standard micro studies, which regress log hours on log wages, typically obtain small estimates (in the range of 0-0.4), leading much of the profession to conclude labor-supply elasticities are small. These studies assume wages evolve exogenously. The authors argue that when wages rise with work experience (learning-by-doing, LBD), the marginal return to an hour of work exceeds the wage because it also includes the discounted increase in all future earnings from added experience. Because the wage is only one component of total remuneration, a given percentage wage increase raises the total marginal return by a smaller percentage, so regressing hours on wages produces a downward-biased estimate of the IES. Critically, the omitted variable (the ratio of total remuneration to the wage) is mechanically related to the wage, so the bias cannot be corrected by instrumental variables or natural experiments.

Model and strategy: The authors extend a MaCurdy (1981) life-cycle model of consumption and labor supply to include LBD, where the wage equals marginal return to human capital times a human-capital stock that grows with experience. They derive a log-linear labor-supply equation with an extra term capturing future returns to work, which is negatively correlated with the wage. Their key insight: for individuals whose future returns to experience are negligible (the term F approaches zero, e.g., at end of working life or at very high human-capital stocks), the standard regression yields an unbiased IES estimate, allowing them to remain agnostic about the human-capital accumulation process.

Data: They use daily labor-supply records of Florida spiny lobster trap fishermen from the Florida Fish and Wildlife Conservation Commission, covering the 1986 through 2007 seasons (a 22-year panel), restricted to the first 70 days of each season. Analysis samples are drawn from fishermen active 2001-2005. Wage variation is exogenous and partly predictable because lobster catch rates rise around the new moon (and with rough weather). The moon phase is the key instrument. The preferred sample of “retiring fishermen” (at least 60 years old, at least 15 years of experience, exiting at season’s end) has 50 individuals. A “naive” full sample has 639 fishermen; an “entering fishermen” sample (new entrants remaining at least two more seasons) has 29 individuals.

Main findings: Estimating intensive (hours) and extensive (daily participation) margins via a type-2 Tobit and summing them, the preferred total IES for retiring fishermen is 2.65 (hours elasticity 0.249, participation elasticity 2.401). Across retiring-fishermen specifications, the total IES ranges roughly 2.3 to 3.1, and the headline estimate stated in the abstract and discussion is 2.7. The naive full-sample estimate is 1.27 (about 1.3), implying that accounting for LBD bias more than doubles the IES (relative bias factor about 2.1). For entering fishermen, the IES is approximately zero (-0.068). Earnings per hour are about 40% higher during a new moon than a full moon. Returns to experience are positive, significant, and plateau around 15 years.

Implications: Results support using relatively large labor-supply elasticities in representative-agent macro models and provide model-free evidence that LBD matters. Because LBD breaks the equivalence of IES, Frisch, Hicks, and Marshall elasticities, a Frisch estimate no longer bounds welfare effects of tax changes, and permanent tax changes can have larger short-run labor-supply effects than transitory ones, undermining transitory tax cuts as stimulus.

Layer 2: Deep Dive

What is the core theoretical mechanism generating the bias?

In a life-cycle model with learning-by-doing, the wage equals the marginal return to human capital times the human-capital stock (w = w-tilde times k), and human capital grows with hours worked. The intra-temporal first-order condition shows total remuneration for an hour of work is w + F, where F is the discounted marginal increase in all future earnings from one additional hour of experience. The log-linear labor-supply equation thus contains an extra term, omega times ln(1 + F/w). Since F is non-negative and negatively correlated with the wage, omitting it (the standard model, where gh=0 so F=0) produces omitted-variable bias that pushes the estimated IES downward. The Frisch elasticity equals omega times w/(w+F), which is weakly less than omega.

What is the identification strategy and what are the main threats to it?

Identification rests on (1) selecting fishermen for whom future returns to experience are negligible (F approximately 0), so the standard regression is unbiased, and (2) using the lunar cycle as an instrument for the wage, since catch rates and hence hourly earnings vary predictably with the moon phase but the moon plausibly does not affect tastes for or opportunity costs of work (fishermen fish in daylight, are not affected by tides, and other relevant fisheries are closed during the studied window). A type-2 Tobit (Amemiya 1984) corrects for selection because earnings and hours are observed only when fishermen participate; exclusion restrictions for the selection equation include weekend indicators, their interactions with age and age-squared, and a hurricane-preparation indicator. The main threat: that something other than returns to experience makes the samples respond differently to wage variation. Because the omitted variable is mechanical, IV cannot fix the bias in the biased samples, but it is not needed in the retiring sample where F is approximately 0.

How do they validate the key exclusion restrictions?

For weekend indicators, prices and landings must not vary with the day of week; they regress daily lobster prices on Saturday/Sunday indicators with season and dealer fixed effects and find the coefficients extremely small and insignificant. Landings are argued independent of day-of-week because trap catch does not depend on aggregate participation. For the hurricane-preparation indicator, they regress daily prices on hurricane indicators with season and dealer fixed effects and find the hurricane-preparation coefficient very small and insignificant. Lobsters being storable/transportable and Florida supplying only 4-7% of the global annual spiny lobster catch supports price exogeneity.

What is the evidence that returns to experience matter in this industry?

They estimate two restrictive wage specifications: one with years of experience, its square, and an indicator for having one or more years of experience; another with eighteen indicators for each experience level. Both (Figure 1) show returns to experience are positive and statistically significant, with cumulative returns plateauing around 15 years (consistent with the model’s assumption that gh approaches 0 at high human capital and with the 15-year experience criterion for retiring fishermen) and a sizable drop in marginal returns between zero and some experience.

What are the headline elasticity magnitudes?

Preferred retiring sample (15+ seasons): hours elasticity 0.249 (SE 0.062), participation elasticity 2.401 (SE 0.548), total IES 2.650. The 10+ seasons retiring sample gives total IES 2.309 (smaller because returns to experience may not yet be negligible below 15 years). Across specifications retiring estimates span about 2.3 to 3.1, with 2.7 as the headline. Full (naive) sample: hours 0.046, participation 1.226, total 1.272 (about 1.3). Entering fishermen (preferred): total -0.068, i.e., approximately zero; expanded entering sample also small and insignificant. New moon earnings about 40% above full moon.

How do they rule out that sample differences other than experience drive the results?

They re-estimate using a placebo sample of fishermen who meet the retiring-sample criteria (at least 60 years old, at least 15 years experience) but are at least two years from retirement, so they share age and career history but still have non-negligible returns to experience. Estimates for these older, experienced, non-retiring fishermen (Table 3) are very similar to the full sample and notably smaller than for retiring fishermen, indicating the elasticity difference is driven by returns to experience, not age or career history. They also note (footnote 27) that a flat cumulative return after 15 years is consistent with significant human-capital depreciation, so marginal returns can remain non-negligible until the final pre-retirement season.

What robustness checks address the wage-prediction (instrument) being estimated separately per sample?

Because estimating equation (11) separately per sample lets the moon-phase coefficient vary across samples, they run two pooled alternatives. Alternative #1 predicts earnings from the full sample of fishermen; the preferred retiring IES falls slightly (to about 2.06) because the moon coefficient is larger in absolute value, but entering-fishermen estimates stay small and insignificant. Alternative #2 pools entering and retiring fishermen in estimating (11), interacting all variables with an entering-fisherman indicator to limit selection-bias contamination; this raises retiring IES somewhat. Both confirm the cross-sample differences come from different responses to wage variation, not from different wage predictions.

How does the paper relate to and differ from prior structural and reduced-form work?

Beginning with Imai and Keane (2004), a literature jointly estimates labor supply and human-capital accumulation in fully structural models (Imai and Keane 2004 IES 3.8; Wallenius 2011 IES 1.1; Keane and Wasi 2016 IES 2). Structural models control for wage endogeneity and allow counterfactuals but require fully specifying the wage and choice environment, are complex, and it can be unclear which moments identify the IES. This paper’s complementary, largely model-free approach exploits negligible end-of-career returns to experience, remaining agnostic about human-capital accumulation. Their estimates lie within (at the high end of) the structural range. Their relative bias (2.1) nearly matches Wallenius (2011) and is below Imai and Keane’s 8-12 (whose sample of 20-36 year-old males has high returns to experience; bias falls to 3.2 for a 20-64 simulated sample with outliers removed). The closest prior approach is Rogerson and Wallenius (2013), who infer an IES lower bound from rationalizing retirement; both approaches are robust to LBD but use very different identification.

What alternative explanations do they consider and reject?

Two. (1) Borrowing/credit constraints (Domeij and Floden 2006) also bias the IES downward and could differ across samples if retiring fishermen are less constrained; but the authors study daily decisions, and fishermen own a collateralizable vessel and almost certainly have credit or liquid assets for day-to-day purchases, so daily credit constraints are implausible. (2) Reference dependence with daily income targets and loss aversion (Camerer et al. 1997; tested by Farber 2015 on NYC taxi drivers, who also finds elasticities rising with experience): reference-dependent behavior should appear only when realized wages deviate from expected wages, but here identification comes from the perfectly predictable lunar cycle, so it cannot drive the results. The much larger participation elasticity for retiring fishermen (a decision based on anticipated wages) further argues against it; moreover Farber (2015) and Haggag, McManus and Paci (2017) find LBD in NYC taxis, so the experience-elasticity correlation there may itself reflect LBD.

What are the policy implications and their scope conditions?

Results support relatively large labor-supply elasticities in calibrated representative-agent macro models (their IES falls within aggregate hours elasticities of 1.9 to 4 reported by Chetty et al. 2011). But extrapolation to macro requires care: the IES-to-labor-supply-elasticity link is broken under LBD, and aggregate elasticities depend on long-run labor-force participation and aggregation across life-cycle stages, not the daily participation margin estimated here; a fully structural model is still needed for life-cycle and aggregate predictions. On taxes, because LBD breaks the standard ordering (IES = Frisch, Frisch > Hicks > Marshall), a Frisch estimate no longer bounds welfare effects of tax changes. Permanent tax changes can have larger short-run labor-supply effects than transitory ones (which only affect the current wage), undermining transitory tax cuts as ideal short-term stimulus; permanent changes also have amplified long-run effects because reduced current labor lowers future wages.

What modeling choices and caveats accompany the estimates?

They model a daily period, so omega is the IES over hours within a working day; the total elasticity comparable to annual data is the sum of the hours elasticity (delta from the intensive-margin equation) and the daily participation elasticity (from the probit). For retiring fishermen, individual fixed effects equal individual-by-season fixed effects (each appears one season), flexibly controlling for the human-capital stock. They do not correct standard errors for the generated regressor (predicted log wage) but, citing Miles (1997) and Benito (2006), judge it unlikely to render estimates insignificant; standard errors are clustered by calendar date. A potential dynamic concern (lobsters accumulating in traps) is dismissed because catch per trap stops rising after a few days of soak time (and average soak times of 7-15 days exceed that), so daily catch depends on environmental conditions, not past fishing. The exit-date inference rule drops less than 3% of observations with virtually identical results.

Key Concepts