The Macroeconomic Dynamics of Labor Market Polices

It is trying to reconcile a tension in the literature: estimated elasticities of substitution across worker types are small at short horizons and large at long ones, and the authors state that, to the best of their knowledge, “our paper is the first to attempt to resolve such a puzzle within a quantitative framework.” The minimum-wage literature “has documented small employment effects of increases in the minimum wage in the year or two after an increase is introduced, suggesting a fairly small short-run elasticity of substitution among workers.” Meanwhile the literature on skill premia “has consistently found a fairly large longer-run elasticity of substitution” — Katz and Murphy (1992) estimate an elasticity across education groups of about 1.5, Card and Lemieux (2001) an elasticity within an education group between 4 and 6. Because the ultimate effect of a minimum wage or an EITC on employment, income and welfare “critically depend on firms’ ability to substitute across workers,” the horizon over which that elasticity is measured matters directly for policy evaluation.

Worker heterogeneity within and across education groups; imperfect long-run substitutability via nested CES plus putty-clay frictions; and firm monopsony power inside a search model. On the first: the authors use the 2017–2019 American Community Survey and stress that “within-education-group wage dispersion exceeds between-education-group wage dispersion by an order of magnitude” — wages in the top decile of the non-college wage distribution are about seven times those in the bottom decile, whereas the ratio of mean college to mean non-college wages “is less than two.” They note the median wage for both college and non-college workers in 2017 exceeded $15 per hour, “implying that the representative individual from both groups would not be bound by a $15 federal minimum wage,” while 40% of non-college workers earn less than $15 — so a representative-agent treatment would miss the policy entirely. On the second: putty-clay frictions “yield short-run elasticities of employment with respect to any change in policy that are close to zero, because workers who operate existing capital are highly complementary to each other in the short run.” On the third: monopsony captures the idea, “dating back to Robinson (1933), that policies may not only redistribute income but also help correct market inefficiencies,” formalised within a search model, which “avoids any ad-hoc rationing rules when policy-mandated constraints, such as the minimum wage, bind.”

Firms’ monopsony power arises from imperfect substitutability of jobs across firms in workers’ preferences, governed by a parameter ω, and is disciplined to match estimated wage markdowns. The disutility-of-work index aggregates employment across firms with elasticity ω; “the smaller ω is, the less substitutable jobs at the same firm are,” which yields an upward-sloping labour supply curve to each firm, “analogous to the downward-sloping consumer demand curve for each firm’s goods in models of monopolistic competition.” The setup follows Berger, Herkenhoff and Mongey (2022a). The authors discipline ω “so as to match the recent estimates of wage markdowns in Seegmiller (2021), Lamadon, Mogstad and Setzler (2022), Berger, Herkenhoff and Mongey (2022a), and Yeh, Macaluso and Hershbein (2022), which document that workers are paid between 65% and 85% of their marginal products.” The baseline targets a markdown of 0.75.

It makes production CES ex ante but Leontief ex post: “once a machine is built, it is clay-like in that it requires a fixed amount of labor of each type to operate at full capacity.” Given the installed stock of machines, “the demand for any type of workers is inelastic in the short run as long as total profits from operating the installed machines are positive, because a firm cannot substitute between existing capital and any type i of labor.” Over time new machines embodying different labour-to-capital ratios can be installed, so firms can substitute away from labour that has become more expensive. The speed of adjustment “is primarily governed by the depreciation rate of capital δ, because δ determines the rate at which the old, labor-intensive capital is replaced by new, less labor-intensive capital”; the baseline uses δ = 15%, consistent with aggregate NIPA data on equipment, and the results are reported as robust to a 10% rate that includes structures. The authors describe putty-clay as “a parsimonious way to capture a rich set of frictions to firms adjusting their entire input mix” rather than a literal technology.

Each worker type’s employment and labour income trace an inverted-U, or Laffer-curve, shape in the minimum wage, and a single minimum wage cannot correct monopsony distortions for all workers at once. For workers initially earning $7.50 per hour, whose wages “were inefficiently marked down due to firm monopsony power,” the minimum wage raises their employment up to about $8.50; past that point firms substitute away from them. The paper is explicit about which parameter governs which side of the hump: “the degree of monopsony power governs the upward-sloping part of the Laffer curves, whereas the degree of labor-labor substitutability governs the steepness of the downward-sloping part.” With a 25% monopsony markdown, the upper bound on the peak for a $7.50 worker is “approximately $9.40 = 1.25 × $7.50.” Raising the minimum from $7.25 to $8.50 raises the employment of low-productivity workers while leaving higher-productivity workers unaffected; raising it to $15 “helps alleviate the monopsony distortions of only higher-productivity workers and at the cost of decreasing the employment of lower-productivity workers.” The paper calls this “the distributional paradox of too large a minimum wage policy: in the long run without any countervailing force such as inflation, productivity growth, or other corrective policy, it hurts precisely the lowest-earning workers whose income it is supposed to support.” Under a $15 minimum, employment falls for all non-college workers initially earning less than $11 per hour, “who account for 26% of all non-college workers and 62% of the workers for whom the minimum wage binds.”

Employment barely moves for the first two years under any of the increases considered, and for the largest increase “less than one-fifth of the ultimate employment decline materializes over the first two years.” In the two years after the increase, non-college employment rises by 0.5% for an $8.50 minimum, rises even less for an $11 minimum, and falls by 2% for a $15 minimum. For the $8.50 and $11 increases “these short-run effects are similar to the ultimate long-run ones,” so short-run estimates of small increases are informative about their long-run effects “according to our model.” Putty-clay frictions are what generate the gap for the large increase: with putty-clay capital, aggregate employment takes nearly twenty years to converge to the new steady state after a large increase, versus about two years with standard capital; after a small increase the corresponding figures are about eight years versus about four. The mechanism is that a putty-clay firm facing a large increase “continues to operate existing capital at full capacity until it depreciates” — since firms “still earn substantial profits on existing capital” even after paying the new minimum — and only gradually “invests in new capital that is less intensive in the services of low-productivity workers.” The model also generates “a near point mass in the wage distribution at the new minimum wage, reproducing the typical bunching of empirical wage distributions,” which shrinks along the transition though “some bunching persists as in the data.”

Under a small increase, income rises and stays up; under a large increase, income nearly doubles on impact and then falls below its initial level after about ten years. For a worker initially earning $7.50, an $8.50 minimum raises labour income “of about 20% upon impact,” mostly from the wage increase itself with some contribution from higher employment as monopsony distortions ease; a worker initially earning about $12 is unaffected because they are paid far above the new minimum. A $15 minimum “nearly doubles income for workers initially earning $7.50 with almost no impact on their employment” in the short run, but “after about ten years, such workers’ income falls below its initial level and remains low forever after.” A worker initially earning $12 sees monotonically rising income under the $15 minimum, because it corrects monopsony distortions for them. The paper adds a cohort dimension: “Cohorts of the lowest-paid workers who start their careers after the introduction of the new minimum wage enjoy less of the short-term benefits and bear more of the long-term costs — the more so, the later these cohorts enter.”

Accounting for the transition changes the answer substantially for a large minimum wage: only 6% of the current cohort of non-college workers is made worse off by a $15 minimum, whereas a steady-state-only comparison “substantially overstates the welfare losses.” Welfare change is measured as the consumption-equivalent ∆ᵢ that makes a household indifferent between staying in the initial steady state and living through the entire transition to the new one. For an $8.50 minimum, the static and dynamic welfare measures “are essentially identical because the economy transitions fairly quickly to the new steady state.” For a $15 minimum they differ, because the steady-state comparison “ignores their short-term gains in terms of higher labor income early in the transition.” The paper reports that all non-college workers weakly benefit from an increase of between $1 and $3 per hour, and that even for the increase to $15, “nearly 85% of non-college workers initially earning less than $15 benefit from such a policy.” Two scope conditions travel with this: welfare “depends on the distribution of profits across households,” which the authors assume are distributed in proportion to each household’s share of total labour income; and risk sharing is perfect within a family type, so “if we allowed for a lower degree of risk sharing, then the welfare losses from large minimum wage increases, or the gains from a large expansion of the EITC, would be even larger.”

The EITC’s short- and long-run effects “always work in the same direction,” because the government rather than the firm pays the marginal cost of raising low-wage workers’ pay, so firms substitute towards those workers rather than away. Under the minimum wage, firms bear the cost of the higher wage, so a sufficiently large increase pushes wages above the efficient level and creates an incentive to substitute away. Under the EITC “the government pays the marginal cost of increasing the wages of low-productivity workers and, hence, subsidizes their employment,” which “reduces monopsony distortions without creating an incentive for firms to substitute away from lower-productivity workers.” The paper also notes that “a portion of the subsidy paid to workers is appropriated by firms in the form of lower before-transfer wages,” which acts as an indirect subsidy to firms and further induces them to shift their input mix toward these workers. Putty-clay frictions still bite, but in the opposite direction: they “dampen the positive effects of the EITC on employment in the short run,” so “the short-run benefits of the EITC are smaller than their ultimate long-run benefits.”

It reproduces the three regions of the actual EITC and is made budget-equivalent to the minimum wage it is compared against, by financing it with a linear tax on firm profits equal to the implicit profit loss the minimum wage would cause. The schedule has a phase-in region with a marginal subsidy rate of 25%, a plateau with a zero marginal rate, and a phase-out with a marginal subsidy rate of −22% (equivalently a positive marginal tax rate). Investment and vacancy-posting costs are fully deducted from profit taxes, “which implies that the profit tax does not distort firms’ decisions.” Under this construction “both the minimum wage and the EITC transfer the same total amount of income from firms to households: the two policies only differ in how they distribute those resources across households.”

The EITC budget-equivalent to a $15 minimum wage raises long-run non-college employment by 5.9% in the baseline, with the gains concentrated among the lowest-wage workers, and reaches only 1.6% after one year and 4.0% after four. The lowest-wage workers sit in the phase-in region, so they gain both from the average subsidy on their wages and from the positive marginal subsidy’s effect on firms’ job creation. The aggregate 5.9% is smaller than the gain for the lowest earners for two stated reasons: “in the phase-out region in which the marginal subsidy rate is negative, the EITC acts as a tax on job creation reducing employment,” and “the subsidy eventually dies out and so it does not affect any worker initially earning more than $16.” Comparing directly against a $15 minimum wage, “the EITC is much more effective than the minimum wage at stimulating the employment and labor income of initially low-wage non-college workers in the long run.” Because of putty-clay frictions, “comparing steady states would lead to an overstatement of the benefits of the EITC — these patterns are the opposite of those implied by the minimum wage.” Results are reported as qualitatively similar for a smaller EITC budget-equivalent to a $10 minimum wage.

Long-run employment effects of the minimum wage become more negative when monopsony power is weaker or labour-labour substitutability is higher, and the sensitivity is much larger for the big increase. For an $8.50 minimum, non-college employment changes range from +2.3% (ϕ = 2, markdown 0.6) to −3.2% (ϕ = 6, markdown 0.9); the baseline (ϕ = 4, markdown 0.75) gives +0.8%. For a $15 minimum, the range runs from −0.1% (ϕ = 2, markdown 0.6) to −20.0% (ϕ = 6, markdown 0.9); the baseline gives −12.1%. The intuition offered: “when firm monopsony power is weaker, there is less room for minimum wage increases to induce efficient employment gains,” and “when labor-labor substitutability is higher, firms more readily substitute away from workers whose marginal product is lower than the minimum wage in the long run.” For the EITC, the sign never flips: employment gains range from +2.0% to +6.3% for the large EITC and +0.1% to +0.6% for the small one, and they increase with substitutability, because a given subsidy leads firms to shift their production mix towards subsidised workers all the more when workers are more substitutable. The paper reports the results as “largely insensitive to different estimates of capital-labor substitutability from the literature,” and states that changes in α, ρ and the labour-supply parameter, and in the search parameters, have much more muted effects.

The authors argue it can reproduce the range of estimates, and they present that range-matching as the test rather than a single point estimate. Neumark and Shirley (2022)’s meta-analysis of 109 studies finds roughly 80% report zero to small short-run employment declines within two years, with the rest reporting small positive increases; the model’s implied elasticities for a $1.25 increase run from +0.12 (larger markdown, i.e. more monopsony power) to −0.16 (higher substitutability) at four years, and are “always small in absolute value, but their sign depends on the values of our key parameters.” Clemens and Strain (2021) find insignificant short-run effects for both small and large increases and significant negative medium-run effects only for large increases — a pattern the paper states the model replicates. Cengiz et al. (2019), whose increases average about 10% or $0.75 and who follow employment for up to seven years, find small positive but statistically insignificant effects that persist; the paper states its framework “qualitatively replicates these findings as well.” It also points to Meer and West (2016) on slow-materialising employment effects, Lindner and Harasztosi (2019) on Hungarian firms substituting from labour to capital, and Clemens, Kahn and Meer (2021) on substitution towards higher-productivity workers.

For small to moderate minimum-wage increases and for the EITC, short-run responses are good predictors of long-run ones; for large minimum-wage increases they are not. The paper is direct: “for small to moderate increases in the minimum wage and for the EITC, researchers should feel comfortable using short-run labor market responses to forecast the corresponding long-run ones.” But “only about 20 percent of the ultimate long-run impact of a $15 minimum wage on the employment of non-college workers occurs in the first two years,” and for the lowest-wage workers “the short-run labor income response is small and positive whereas the long-run response is large and negative.” Two further cautions are attached. On duration, one must “take a stand on the extent to which firms and consumers expect the policy to be temporary or permanent in real terms,” since a small positive medium-run employment response is consistent with at least three distinct configurations of monopsony power, substitutability and perceived permanence. On geography, since monopsony power and local labour-labour substitutability likely vary across localities, “the estimates of effects from any one regional or cross-regional study would not be able to precisely predict effects at the national level.”

A large difference: because inflation and productivity growth erode the real minimum between legislated changes, firms do not find it worth re-tooling, so “large increases are highly beneficial for lower-productivity workers in the short run at virtually no long-run cost.” The authors model a temporary increase as a real minimum decaying at 5% annually, which they interpret as 2% productivity growth plus 3% inflation “that accounts for baseline inflation plus any additional inflation induced by the minimum wage.” The employment response to a temporary increase is “an order of magnitude smaller than the response to a permanent one,” partly because the present value of the increase is smaller, but also because “firms anticipate that any new capital they install early on in the transition will still be in use later on, when the decaying minimum wage will no longer bind.” The temporary path also produces non-monotonic dynamics: employment first falls below its initial level, then rises above it, then reverts. For workers initially earning $7.50, labour income is “strictly higher in every period under a large temporary minimum wage increase than under a small one.” The authors flag this as an illustration of mechanism, not a policy recommendation: they present it “rather than to suggest that this is a tool that policymakers could repeatedly exploit,” and note “a full analysis of such a scenario would require carefully modeling agents’ expectations about the duration of policies.”

Coupling a modest minimum wage with the EITC produces “a much larger increase in long-run wages and employment for non-college low-wage workers than the EITC alone,” and the paper attributes this mainly to efficiency rather than to the usual anti-appropriation argument. Adding a $9.25 minimum wage on top of an EITC budget-equivalent to a $15 minimum, holding the combined profit reduction fixed, delivers this result. The literature’s argument — that a minimum wage stops firms from lowering before-transfer wages to capture part of the subsidy (Neumark and Wascher 2011; Lee and Saez 2012; Vergara 2022) — is present in the model but “actually relatively muted”; “the much more important reason” is that “the minimum wage is effective at correcting the monopsony distortions faced by low-wage workers.” The same caveat about size applies: “too large an increase in the minimum wage (to $12) may end up hurting these workers for the same reasons highlighted throughout the paper.” The paper summarises that its framework supports a role for a moderate minimum wage alongside transfer programmes “but for different reasons than those usually mentioned, namely, for efficiency rather than purely redistributive considerations.” Adding the Heathcote–Storesletten–Violante (2017) progressive tax and transfer function with τ = 0.181 leaves all the main insights intact.

Skill acquisition, multi-good price pass-through, oligopsonistic market structure, and within-group risk sharing are all explicitly flagged as abstractions. On skills, the authors note the demand for low-skilled workers falls with a large minimum wage but rises with an EITC, so returns to skill change; “it is apriori ambiguous, however, if skill acquisition would reinforce or weaken the welfare effects of these policies,” since a minimum wage both compresses wages at the bottom (reducing the incentive to invest) and lowers job-finding probabilities (raising it). On prices, the one-final-good structure rules out pass-through to the prices of goods disproportionately consumed by low-wage workers, which “have been found to be empirically important (Aaronson and French (2007)).” The model also abstracts from the oligopsonistic market structure in Berger, Herkenhoff and Mongey (2022b), whom the authors describe as complementary. The general-equilibrium setting, in which capital markets clear, may not match empirical designs exploiting regional variation; the authors report that a small-open-economy version taking intertemporal prices as given gives “very similar results.”