J64 | Macro Paper Warehouse

Artificial intelligence and technological unemployment

Mon, 01 Jan 0001 00:00:00 +0000

Wang and Wong develop a continuous-time labor-search model to assess the dynamic effects of generative AI (GenAI) on labor productivity and unemployment. The paper is motivated by conflicting empirical evidence: micro studies find productivity gains of 14% (Brynjolfsson, Li, and Raymond 2025) and 55.8% faster coding (Peng et al. 2023), while macro estimates suggest modest TFP gains of at most 0.064% annually (Acemoglu 2024), and occupation-level evidence shows a 13% relative employment decline in AI-exposed jobs (Brynjolfsson, Chandar, and Chen 2025).

The model distinguishes GenAI from earlier automation technologies by its learning-by-using mechanism: AI capability grows at rate µ per employed worker (law of motion dAt/At = µHt − δ), raises employed workers’ productivity, and creates a displacement threat through renegotiation. When renegotiation fails, AI replaces the worker, generating technological unemployment. Firms renegotiate wages at a rate ρµAt proportional to AI’s learning rate and the job’s exposure ρ. The joint surplus condition governs whether replacement occurs: AI replaces a worker if and only if πA (AI’s net present value per output) exceeds the post-renegotiation joint surplus St.

The model admits three steady states: (i) a some-AI steady state with finite AI capability, persistent AI adoption (It = 1), expanded job creation but declining employment at H∞ = δ/µ; (ii) an unbounded-AI equilibrium with sustained endogenous growth, no displacement (It = 0), and employment at H∞ = α/(α+σ); and (iii) a no-AI equilibrium reverting to the Mortensen-Pissarides benchmark. In the benchmark model (exogenous job-finding rate, AI-augmented productivity), multiple steady states can coexist—global indeterminacy—when condition (28) holds. In the full model (endogenous job creation via free entry), both global and local indeterminacy are possible, and a continuum of oscillatory transition paths converge to the some-AI steady state.

Calibrated to U.S. data, targeting a pre-AI unemployment rate of 5%, AI elasticity of productivity εy = 1.069 (from Czarnitzki et al. 2023), initial AI productivity boost of 14% (Brynjolfsson et al. 2025), worker exposure ρ = 0.618 (Brynjolfsson et al. 2018’s machine learning suitability index), AI replacement cost ϕ = 0.0043 (from U.S. business GenAI spending), AI learning rate µ = 0.632, and AI error rate δ = 0.462 (Moore’s law half-life of 1.5 years), the model converges to a some-AI steady state. The long-run results are: a 23% employment loss (H∞ = 0.732 vs. H0 = 0.95), AI capability improvement of 321%, and labor productivity gain of 366%. Approximately half of the employment loss—11.5 percentage points—occurs within the first five years, alongside a 49.3% output gain and 45.5% AI capability improvement over that period.

Untargeted moments are validated: the model implies 7.08% labor productivity growth over the first 10 years (consistent with Briggs and Kodnani 2023) and an AI elasticity of vacancies averaging 0.16 over the first five years (consistent with Acemoglu et al. 2022).

On welfare, equilibria are inefficient even when the Hosios condition holds. AI introduces four externalities beyond standard matching frictions: job destruction via displacement, productivity enhancement for employed workers, feedback from AI learning depending on employment, and direct effects on matching surpluses. A constrained-optimal subsidy to jobs at risk of AI displacement is 26.6% in the short run and exceeds 50% in the long run. In the full model, the Hosios condition requires fixing firm bargaining power θ to the vacancy elasticity of matching ξ, but an additional per-output transfer T = µApωA to firm-worker matches is necessary to correct AI adoption inefficiency.

Q: What is the core mechanism by which AI generates unemployment in this model? A: AI capability grows through a learning-by-using process (dAt/At = µHt − δ), improving as it observes employed workers. As capability rises, firms gain a displacement option that arrives at rate ρµAt per matched pair. When renegotiation over wages fails—i.e., when the AI’s NPV πA exceeds the joint surplus—firms replace workers with AI, causing unemployment. This creates a feedback loop: higher employment accelerates AI learning, which increases displacement pressure and reduces employment.

Q: What are the three steady states and what distinguishes them? A: The some-AI steady state features finite AI capability, persistent displacement (It = 1), and long-run employment H∞ = δ/µ; it involves technological unemployment. The unbounded-AI steady state features infinite AI capability, no displacement (It = 0), endogenous productivity growth, and employment H∞ = α/(α+σ) as in the standard Mortensen-Pissarides model. The no-AI steady state has A∞ = 0 with the same H∞ = α/(α+σ) but no AI contribution. Employment is higher in the unbounded-AI equilibrium than in the some-AI equilibrium.

Q: What does the calibration imply for long-run employment and productivity? A: The calibrated full model converges to a some-AI steady state with a 23% employment loss (H∞ = 0.732), a 321% improvement in AI capability, and a 366% gain in labor productivity. The parameters yield a unique equilibrium under the baseline calibration (πA = 1.949 > sAI = 0.8735 confirms some-AI existence). These results reflect a large worker replacement effect under the calibrated AI learning and error rates, while the job creation effect is relatively modest.

Q: How fast does technological unemployment materialize? A: Approximately half of the total 23% employment loss occurs within the first five years; specifically, employment falls by 11.5 percentage points over that period. Over the same five years, AI capability improves by 45.5% and output rises by 49.3%. Over the first 10 years, AI capability improvement accumulates to 94.0% and output gain to 103% (approximately double the five-year output gain).

Q: How does the full model differ from the benchmark model in transition dynamics? A: In the full model, job-finding rates are endogenous: firms post vacancies until a free-entry condition (κyt = ftΠt) is satisfied, tying job-finding rate αt to the surplus ratio st via αt = α(st). This endogeneity implies that as AI raises labor productivity, firms create more vacancies, slowing the employment decline relative to the benchmark model with a fixed job-finding rate. At the same time, AI capability grows faster in the full model because higher employment accelerates AI learning.

Q: What is global indeterminacy and when does it arise? A: Global indeterminacy occurs when both the some-AI and unbounded-AI steady states coexist, so the long-run outcome depends on initial conditions or expectations. In the benchmark model this requires condition (28): 0 < r + σ + α(1−θ) − (1−b)/πA ≤ εy(µα/(α+σ) − δ). In the full model, global indeterminacy is plausible when firm bargaining power rises to θ = 0.95 given the baseline AI replacement cost ϕ = 0.0043. The region of global indeterminacy is larger when firm bargaining power is higher.

Q: What is local indeterminacy and what does it imply for transition paths? A: Local indeterminacy means there is a continuum of equilibrium paths converging to the some-AI steady state in the neighborhood of that steady state, rather than a unique saddle path. In the full model, under alternative parameters (θ = 1, ξ = 0.765, εy = 6), the eigenvalues feature a negative real root and two complex roots with negative real parts, yielding oscillatory local dynamics in employment and AI capability. This implies short-run cycles in productivity and unemployment, consistent with the wide range of empirical findings on AI’s labor-market effects.

Q: Why does the Hosios condition fail to deliver efficiency in this model? A: The Hosios condition eliminates the standard matching externality by setting firm bargaining power to the vacancy elasticity of matching. But AI introduces four additional externalities: (i) job destruction through displacement, (ii) productivity enhancement for employed workers, (iii) feedback from AI learning that depends on aggregate employment, and (iv) direct effects on matching surpluses and job-finding rates. These externalities mean the standard Hosios rule alone is insufficient; additional instruments are required.

Q: What is the constrained-optimal policy response? A: In the simple model, the constrained optimal AI adoption threshold differs from the equilibrium threshold because firm bargaining power θ distorts adoption decisions: AI is over-adopted when πA > (1−b)/(r+σ+α(1−θ)) and under-adopted when (1−b)/(r+σ+α) < πA ≤ (1−b)/(r+σ+α(1−θ)). In the full model, constrained optimality requires setting θ = ξ (Hosios) plus a per-output subsidy T = µApωA to firm-worker matches exposed to AI displacement. This targeted subsidy is 26.6% in the short run and exceeds 50% in the long run.

Q: How does AI compare to computers in this model’s counterfactual? A: The paper reports that exogenous productivity growth from computers reduced unemployment only modestly—by 0.16 percentage points. By contrast, AI’s learning-by-using and displacement features imply a nearly 20% long-run employment loss in a comparable counterfactual. The key distinction is that computers lack the self-learning improvement and associated renegotiation-triggered displacement that characterize GenAI in this model.

Q: How is AI exposure parameterized and what does it capture? A: The exposure parameter ρ captures the degree to which a job is subject to AI-driven replacement risk. It is calibrated using Brynjolfsson et al. (2018)’s suitability for machine learning (SML) index: on a 1–5 scale, SML averages 3.47 across 964 O*NET occupations, translating to (3.47−1)/(5−1) = 61.8%, so ρ = 0.618. The effective exposure measure is ρµ, which is higher when facing a faster-learning AI.

Q: What is the predator-prey analogy in the model’s dynamics? A: The dynamical system for AI capability (At) and employment (Ht) in the simple model resembles the Lotka-Volterra predator-prey system. Employment (prey) feeds AI learning; as AI capability (predator) grows, it displaces workers faster, reducing employment; lower employment then slows AI learning, causing capability to decay; and the cycle repeats with diminishing magnitude until the steady state is reached. This mechanism operates only when the AI learning rate µ is neither too high nor too low, with the convergence path being a spiral when µα < 4δ²(1 − δ(α+σ)/(µα)).

Q: What is the labor-share implication of the unbounded-AI equilibrium? A: In the unbounded-AI steady state, employment is higher than in the some-AI steady state (H^AJJ > H^AI) and labor productivity grows without bound. However, the labor share is lower in the unbounded-AI equilibrium if the firm’s bargaining power θ is sufficiently low. This implies that while workers are not fully displaced and rising AI-augmented productivity sustains employment, workers’ income share may still decline even in the more favorable unbounded scenario.

Technological unemployment: A phenomenon in which AI adoption raises labor productivity and expands job creation, yet still causes sizable employment losses because the worker displacement effect (driven by renegotiation failure when AI’s NPV πA exceeds the joint surplus) dominates the job-creation effect. In the calibrated model this amounts to a 23% employment loss despite a 366% productivity gain.

Learning-by-using AI: The model’s representation of GenAI as a technology whose capability At grows through reinforced learning from employed workers at rate µ per worker, so aggregate AI growth is µHt, offset by deterioration at rate δ. This distinguishes GenAI from earlier automation technologies (computers, robotics) that do not self-improve through usage.

Some-AI steady state: A long-run equilibrium with finite AI capability (gA∞ = 0), persistent AI adoption (It = 1), and employment pinned at H∞ = δ/µ—the ratio of AI’s error rate to its learning rate. Characterized by expanded job creation but lower employment than the no-AI benchmark, constituting the model’s primary calibrated outcome.

Unbounded-AI steady state: A long-run equilibrium with infinite AI capability (A∞ = ∞), no displacement (It = 0), and endogenous growth at rate gA = µH^AJJ − δ. Employment equals the Mortensen-Pissarides level H∞ = α/(α+σ), and labor productivity grows without bound, complementing Aghion, Jones, and Jones (2019)’s idea production framework.

Global indeterminacy: Coexistence of multiple steady states (some-AI and unbounded-AI) such that the long-run equilibrium depends on initial conditions or expectations rather than being uniquely determined. Arises in the benchmark model when condition (28) holds and becomes more likely with higher firm bargaining power θ.

Local indeterminacy: A continuum of equilibrium transition paths converging to a single steady state from nearby initial conditions, rather than a unique saddle path. Arises in the full model under certain parameter configurations (e.g., θ = 1, ξ = 0.765, εy = 6), implying oscillatory short-run dynamics in employment and AI capability.

AI exposure (ρ): A firm-level parameter capturing the degree to which a job-match is subject to AI-driven displacement risk. The displacement option arrives at rate ρµAt per matched pair; ρ is calibrated at 0.618 using the average suitability-for-machine-learning score across O*NET occupations. The effective exposure measure is the product ρµ.

Renegotiation-proof displacement: Proposition 1’s result that the joint surplus Snt is independent of the renegotiation round n, so the AI adoption decision It is also round-invariant. This simplifies the model to a single indicator function: AI replaces the worker if and only if πA exceeds the joint surplus St, regardless of how many renegotiation rounds have occurred.

Disincentive effects of unemployment insurance benefits

Mon, 01 Jan 0001 00:00:00 +0000

This paper isolates the disincentive effects of pandemic unemployment insurance (UI) benefits on employment recovery, separating them from the simultaneously operating stimulative (demand) effects that previous studies conflate. The authors study the largest UI expansion in U.S. history — the CARES Act of March 2020 — which introduced three simultaneous provisions: a $600 weekly income supplement (FPUC) through end of July 2020, a 13-week extension of maximum benefit duration (PEUC), and expanded eligibility to workers previously ineligible for UI (PUA), together raising the median replacement rate to 145% and more than doubling the number of UI recipients.

The empirical strategy uses high-frequency establishment-level data from Homebase (HB), a scheduling and payroll provider covering approximately 140,000 small U.S. businesses — predominantly restaurants and retailers — matched to Yelp price-tier data and Safegraph foot-traffic and spending data. The final estimation sample is 4,595 businesses within 1,195 local-industry cells, observed at weekly frequency from January 2019 to December 2020.

The identification rests on comparing employment recovery of low-wage versus high-wage businesses within the same narrow local labor market (four-digit zip code), industry (two-digit NAICS), and price tier. Because neighboring businesses largely share the local demand stimulus from UI, differencing within local-industry cells removes common demand effects. The key variation is the expiration of the $600 supplement, which differentially compresses the replacement-rate gap between low- and high-wage businesses depending on local average wages — labor markets where the gap falls more sharply are the treated group.

The main empirical finding is that a 100 percentage point decline in the replacement rate gap is associated with a 5.7 percentage point rise in low-wage business employment recovery relative to high-wage business employment recovery at 12 weeks after the $600 expiration. For the average labor market, the expiration of the $600 supplement decreased the replacement rate gap by 46 percentage points, implying a 2.6 percentage point closing of the low-versus-high-wage employment gap within 12 weeks. Importantly, hours per employee and hourly wages grew faster in low-wage businesses over the same period, consistent with a labor supply rather than a demand mechanism. When the comparison is conducted at the U.S. state level rather than within local-industry cells — as in Finamor and Scott (2021) — the effect disappears and reverses sign, illustrating how local demand effects obscure disincentive effects at broader geographic aggregations.

To quantify the aggregate employment impact, the authors build and calibrate a McCall-style labor search model with heterogeneous firm wages, a UI-eligible and non-UI unemployed pool, and equilibrium reservation wages. The model is extended to include a probability (calibrated at 16.5%) that workers lose UI eligibility upon refusing a job offer, which reconciles the model with the empirical estimates; without this feature the baseline model substantially overstates the differential employment effect of the $600 expiration.

The full model-implied aggregate employment loss from all CARES Act UI provisions combined is 3.4 percentage points on average between April and December 2020, representing approximately 20% of the average employment shortfall in the Leisure and Hospitality sector over that period. When each provision is implemented in isolation, the effects are modest ($600 supplement: 0.2 pp; extended duration: 0.2 pp; expanded eligibility: 1.0 pp), but their interaction generates the large combined effect. Expanded eligibility is identified as the most disruptive provision, particularly for low-wage businesses, because it depletes the pool of non-UI unemployed who are the primary source of hires for these firms. The unemployment duration elasticities implied by the model are modest and in line with the low-to-middle range of pre-pandemic estimates.

The paper’s scope is restricted to the disincentive channel and deliberately excludes the stimulative effects of UI; it studies small, in-person service sector businesses and the April–December 2020 recovery period only.

Q: What is the core identification challenge this paper addresses? A: Prior empirical studies find only modest net effects of pandemic UI on employment, but it is unclear whether this reflects small disincentive effects or the near-cancellation of two opposing forces — UI suppressing labor supply while simultaneously stimulating local consumer demand. Identifying the disincentive effect alone requires a design that neutralizes the demand channel. The authors accomplish this by comparing low-wage and high-wage businesses within the same narrow local market, industry, and price tier, so that common local demand shifts from UI are differenced out.

Q: What data does the empirical analysis use, and how is the sample constructed? A: The primary data source is Homebase, covering approximately 140,000 small U.S. businesses with daily employment, hourly wages, and hours worked. The estimation sample is restricted to 4,595 businesses present throughout 2019, matched to Yelp price-tier classification and Safegraph weekly foot traffic and credit-card spending. Businesses are grouped into 1,195 local-industry cells defined by four-digit zip code, two-digit NAICS industry, and Yelp price tier (inexpensive vs. expensive). Within each cell, businesses are classified as low-wage or high-wage, with high-wage businesses paying on average $1.80 per hour more — about 8% above the average hourly wage of $10.90.

Q: How is the replacement rate defined in the empirical framework? A: The business-specific replacement rate is the ratio of average UI receipts (state benefit plus the pandemic supplement, converted to hourly units) to the pre-pandemic average hourly wage of that business. Because the supplement is uniform across workers, businesses with lower pre-pandemic wages face higher replacement rates; the replacement rate gap between low- and high-wage businesses within a local market is therefore a function of both state benefit levels and the local wage dispersion.

Q: What does the event-study analysis around the $600 expiration show? A: The event study exploits cross-labor-market variation in how much the replacement rate gap between low- and high-wage businesses declined when the $600 FPUC supplement expired at end of July 2020. Labor markets with a larger decline in the gap see faster relative recovery in low-wage business employment after expiration. A 100 percentage point decline in the replacement rate gap is associated with a 5.7 percentage point rise in the low-versus-high-wage employment recovery gap at 12 weeks post-expiration. For the average labor market, the $600 expiration reduced the replacement rate gap by 46 percentage points, implying a 2.6 percentage point narrowing of the employment recovery gap.

Q: Why does the estimated effect disappear when broader geographic aggregations are used? A: When businesses are compared within U.S. state borders rather than within local-industry cells, the estimated coefficient on the replacement rate gap turns positive and statistically insignificant. This occurs because at the state level, low-wage areas benefit disproportionately from the purchasing power increase that generous UI provides to local unemployed workers, so demand effects swamp and reverse the supply-side disincentive. This finding explains why Finamor and Scott (2021), using Homebase data with state fixed effects, find no negative association between replacement rates and labor market re-entry.

Q: What evidence supports a labor supply rather than demand interpretation of the differential recovery? A: During the period of the $600 supplement, hours per employee and hourly wages grew faster in low-wage businesses than in high-wage businesses, even as low-wage businesses lagged in employment levels. If the differential recovery reflected demand deficiencies at low-wage businesses, hours per employee and wages should have grown faster at high-wage businesses instead. The observed pattern is consistent with labor supply shortfalls at low-wage firms.

Q: What is the structure of the quantitative labor search model? A: The model features a unit measure of workers and a fixed measure of firms, each posting a constant idiosyncratic wage drawn from an exogenous distribution. Unemployed workers receive job offers at a rate determined by labor market tightness and accept offers above their reservation wage. Reservation wages are equilibrium objects because UI benefits depend on the worker’s previous wage. The unemployed are split into UI-eligible and non-UI pools; the non-UI pool accepts jobs from lower in the wage distribution and is the primary supply source for low-wage firms. The model is calibrated to pre-pandemic U.S. service sector averages, with a pre-pandemic UI replacement rate of 0.51, a UI recipiency probability of 14%, and a non-UI replacement rate of 0.15.

Q: Why does the baseline model overstate the empirical effect, and how is this reconciled? A: The baseline model dramatically overstates the differential employment impact of the $600 expiration because the CARES Act’s expanded eligibility (modeled as a rise in the recipiency probability from 14% to 70%) nearly empties the non-UI unemployed pool, which is the dominant labor supply source for low-wage firms. In the data, the share of unemployed receiving UI nearly tripled for in-person leisure and hospitality workers, but not to the degree that the model’s implied employment collapse would require. The model is reconciled by introducing a 16.5% probability that a worker loses UI eligibility upon refusing a suitable job offer — consistent with UI law — which reduces the effective outside option and raises acceptance rates for low-wage firms.

Q: What are the aggregate employment losses implied by the model? A: When all three CARES Act provisions are implemented jointly, the model estimates that the disincentive effects held back aggregate employment recovery by 3.4 percentage points on average between April and December 2020 — approximately 20% of the average employment shortfall in the Leisure and Hospitality sector. Implemented in isolation, each provision generates only modest losses: the $600 supplement alone accounts for 0.2 percentage points, extended duration for 0.2 percentage points, and expanded eligibility for 1.0 percentage points. The large combined effect arises from the interaction of all three provisions, not from any single one.

Q: What are the conditional (interaction) effects of each provision when the other two are in place? A: Conditional on the other two provisions being active, the income supplement holds back employment recovery by 1.6 percentage points, the extended duration by 1.5 percentage points, and expanded eligibility by 2.9 percentage points. This interaction effect is the central quantitative finding: individually modest provisions combine to produce effects far exceeding their sum when implemented simultaneously.

Q: What are the implied unemployment duration elasticities, and how do they compare to the literature? A: The $600 supplement alone raises average unemployment duration by 8% against a 343% rise in the replacement rate, implying an elasticity of 0.02. Extended duration alone raises unemployment duration by 6% against a 150% increase in potential benefit duration, implying an elasticity of 0.03. Expanded eligibility alone raises unemployment duration by 19%, implying an elasticity of 0.04. When each provision is activated on top of the other two, the implied elasticities rise substantially: 0.24 for the $600 supplement, 0.43 for extended duration, and 0.28 for expanded eligibility. These are in the low-to-middle range of pre-pandemic estimates (Katz and Meyer, 1990: 0.3–0.5; Johnston and Mas, 2018: 0.4–0.8; Rothstein, 2011: 0.06; Farber and Valletta, 2015: 0.15).

Q: What is the role of expanded eligibility specifically? A: Expanded eligibility is identified as the most disruptive CARES Act provision, accounting for 1.0 percentage points of employment loss alone and 2.9 percentage points conditional on the other provisions. Mechanically, expanded eligibility converts non-UI unemployed workers into UI-eligible workers, draining the pool of workers willing to accept low-wage job offers. Because low-wage firms depend disproportionately on the non-UI pool for hiring, this provision disproportionately depresses their employment. Using CPS data, the authors document that the share of unemployed workers receiving UI in the in-person leisure and hospitality sector nearly tripled in 2020 relative to the pre-pandemic period.

Q: What are the scope conditions and limitations of the analysis? A: The empirical analysis is restricted to small, in-person service sector businesses (restaurants and retailers) in the Homebase sample, which may not be representative of the broader labor market. The quantitative model is explicitly focused on disincentive effects only and does not capture the stimulative or demand effects of UI. The model also abstracts from re-opening restrictions and other pandemic-specific confounders. The analysis covers April to December 2020; the 2021 pandemic UI extensions are not studied. The job-refusal probability (chi = 16.5%) is a reduced-form calibration target rather than a structurally identified parameter.

Replacement rate gap: The difference in business-specific UI replacement rates between low-wage and high-wage businesses within the same local labor market; defined as UI benefits (state benefit plus supplement) divided by the business’s pre-pandemic average hourly wage. Larger gaps indicate greater relative disincentive for workers to accept jobs at low-wage firms.

Disincentive effect: The negative impact of higher UI replacement rates on workers’ willingness to accept job offers and thus on business employment recovery, isolated from the simultaneous stimulative demand effect of UI spending.

Non-UI unemployed pool: Workers who are ineligible for or have exhausted UI benefits and therefore receive only social benefits at a lower replacement rate (calibrated at 0.15 in the model). This group has a lower reservation wage and constitutes the primary labor supply source for low-wage firms.

Local-industry cell: The paper’s unit of comparison — businesses sharing the same four-digit zip code (covering on average four neighboring zip codes), two-digit NAICS industry, and Yelp price tier. Within-cell differencing is the mechanism that removes common local demand effects.

Benefit recipiency probability: The probability that a newly separated worker enters the UI-eligible unemployed pool, combining UI eligibility and takeup. Pre-pandemic this is calibrated at 14%; under the CARES Act it rises to 70%, targeting the observed near-tripling of UI recipients in the CPS data.

Job-refusal eligibility loss: A probability (calibrated at 16.5%) that a UI-eligible worker who rejects a job offer loses UI status and transitions to the non-UI pool. Motivated by UI law prohibiting refusal of suitable work; reduces the effective outside option and reconciles the model’s predicted employment gap with the empirical estimate.

Equilibrium residual wage dispersion: The wage dispersion observed in equilibrium conditional on worker observables. The model generates realistic dispersion by calibrating the non-UI replacement rate to match the lower half of the wage distribution and the firm wage offer variance to match the upper half; the presence of the non-UI state substantially increases residual dispersion relative to standard search models.

Evaluating macroeconomic outcomes under asymmetries: Expectations matter

Mon, 01 Jan 0001 00:00:00 +0000

Layer 1 — Overview

Research Question

This paper investigates whether and how assumptions about household and firm expectations alter the macroeconomic implications of asymmetries commonly embedded in macroeconomic models. Specifically, it asks: when a model features a nonlinearity — such as an asymmetric monetary policy rule or a nonlinear Phillips curve — do the longer-run average outcomes and the distributional properties of inflation and unemployment depend on whether agents have rational expectations (RE, accounting for the possibility of future shocks) versus perfect foresight (PF, not anticipating future shocks)?

Methodology

The paper works within a standard three-equation New Keynesian model comprising an IS curve (linking the unemployment gap to the policy rate and the natural rate of interest via Okun’s law with coefficient c ≈ 2), a forward-looking Phillips curve, and a monetary policy rule. The model is parameterized at a quarterly frequency with β = 0.99, κ = 0.01, φπ = 1.5, φu = −0.25, shock persistence ρ_rn = 0.9, and shock standard deviation σ_rn = 0.0025 (calibrated to match a 1-percentage-point standard deviation of the unemployment gap under the symmetric baseline rule).

The key methodological distinction is the specification of the expectations operator. Under RE, agents use the true stochastic transition matrix for the natural rate (approximated via the Rouwenhorst method with 105 grid points). Under PF, agents instead use a transition matrix that always places probability one on the steady-state value of the natural rate next period — i.e., they do not anticipate future shocks. The model is solved globally with a discrete state space projection (parameterized expectations) method, applied identically to RE and PF cases. The authors first derive analytical results in a simplified three-state environment and then present numerical results from 3,000 simulations of 1,000 periods each.

Two types of asymmetry serve as case studies: (i) an asymmetric monetary policy rule — the “Shortfalls rule” — under which the central bank does not tighten in response to a tight labor market (negative unemployment gap), in the spirit of the FOMC’s 2020 framework update; and (ii) a nonlinear (kinked) Phillips curve that steepens by a factor of three when the labor market is tight (unemployment gap < 0), consistent with empirical evidence in Smith, Timmermann, and Wright (2025).

Main Findings

The core finding is that the sign and magnitude of longer-run average outcomes under asymmetric macroeconomic environments can differ substantially — and can even reverse — depending on whether agents have rational expectations or perfect foresight.

For the Shortfalls rule, under PF the model implies a longer-run tradeoff: average unemployment gap is −0.32 percentage points and average inflation gap is +0.25 annualized percentage points relative to the symmetric Deviations rule. PF thus suggests policymakers can lower average unemployment at modest inflationary cost. Under RE, however, this apparent tradeoff disappears entirely: the average unemployment gap is essentially zero (−0.05 percentage points) while average inflation is elevated by approximately 1.02 annualized percentage points. The gap in average inflation outcomes between RE and PF thus exceeds one percentage point, and the labor market benefit implied by PF is absent under RE.

For the nonlinear Phillips curve (under a symmetric deviations rule with φu = 0), the results again diverge across expectations assumptions, and the direction of the effects reverses. Under PF, the kinked Phillips curve implies average inflation of +0.41 annualized percentage points and a near-zero unemployment gap (+0.30 percentage points). Under RE, the average inflation gap is essentially zero while the average unemployment gap rises to +0.63 percentage points — the opposite directional pattern from PF.

The mechanism driving the RE–PF divergence is the interaction between forward-looking price-setters and an inflation-stabilizing central bank. Under RE, anticipated future episodes in which the asymmetry may bind (e.g., the Shortfalls rule providing accommodation, or the Phillips curve steepening) cause firms to set higher prices today. The central bank responds to the resulting pickup in inflation expectations with tighter policy, generating a persistent contractionary offset. This channel is absent under PF because agents expect no future shocks.

Robustness

The main conclusions are robust across three extensions: (i) Bounded rationality (following Gabaix 2020, with m_br = 0.97): outcomes move toward the PF case, confirming that what matters is the degree to which agents internalize the probability of future shocks; (ii) Cost-push shocks instead of natural rate shocks: the RE–PF divergence under a Shortfalls rule is broadly similar in direction and magnitude to the baseline; (iii) Alternative shock specifications: the qualitative conclusions are maintained.

Crucially, under the symmetric Deviations rule the RE and PF solutions are identical in all cases, confirming that the divergence is specific to models with macroeconomic asymmetries, not an artifact of the solution method.

Layer 2 — Q&A

Q1: What is the central methodological claim about perfect foresight solutions in asymmetric models?

The paper argues that in macroeconomic models with asymmetries or nonlinearities, perfect foresight solutions — in which agents do not account for the possibility that future shocks may occur — can yield longer-run average outcomes and distributions that differ from their rational expectations counterparts in magnitude and potentially in sign. The paper is explicit that this is not a critique of PF methods per se, as PF is often necessary for estimating larger models; rather, the point is that researchers should check the robustness of conclusions about longer-run averages using simplified models solvable under both approaches.

Q2: How is the difference between RE and PF operationalized in the model?

The sole technical distinction lies in the specification of the conditional expectations operator Et. Under RE, this operator uses the true stochastic Markov transition matrix for the natural rate (P^RE), which assigns positive probability to all feasible future states. Under PF, agents use a degenerate transition matrix (P^PF) that assigns probability one to the mean value of the natural rate next period regardless of the current state — effectively, agents expect no future innovations. The same global solution method (discrete state space projection with 105 Rouwenhorst grid points) is applied to both, so differences in equilibrium outcomes are entirely attributable to the expectation specification.

Q3: What are the analytical results for the Shortfalls rule in the simplified three-state model?

In the simplified environment with the natural rate taking three equiprobable values (low, steady-state, high) and no persistence, the analytical solution shows that under PF the average unemployment gap is −Δ/(1 + φπκ) < 0 and the average inflation gap is Δκ/(1 + φπκ) > 0, where Δ parameterizes the degree of additional accommodation in the high-demand state. Under RE, the average unemployment gap is exactly zero and the average inflation gap is Δ/(φπ − 1) > 0. The inflation gap under RE exceeds that under PF by Δ(1 + κ)/[(φπ − 1)(1 + φπκ)] > 0, and the unemployment gap under RE exceeds that under PF by Δ/(1 + φπκ) > 0. Thus, PF spuriously implies an exploitable long-run tradeoff that vanishes under RE.

Q4: What are the analytical results for the nonlinear Phillips curve in the simplified model, and how do the directions of the effects compare to the Shortfalls rule case?

Under PF with a nonlinear (kinked) Phillips curve, the average inflation gap is positive (= Δpc > 0) while the average unemployment gap is zero. Under RE, the signs reverse: the average unemployment gap is positive (= Δpc/κ > 0) and the average inflation gap is zero. The difference is ūRE − ūPF = Δpc/κ > 0 and π̄RE − π̄PF = −Δpc < 0. This sign reversal relative to the Shortfalls rule case illustrates that the directional error introduced by PF is not uniform but depends on the specific asymmetry — the key feature is always the absence, under PF, of the forward-looking price-setting channel interacting with monetary policy.

Q5: What is the quantitative magnitude of the RE–PF divergence in the numerical model for the Shortfalls rule?

In the fully parameterized numerical model (Table 2), under a Shortfalls rule the average inflation gap is 1.02 annualized percentage points under RE versus 0.25 annualized percentage points under PF — a difference of roughly 0.77 percentage points. The average unemployment gap is −0.05 percentage points under RE versus −0.32 percentage points under PF — a difference of 0.27 percentage points. The paper also notes that model-implied averages for inflation and nominal interest rates “under perfect foresight can easily differ by at least one percentage point from their rational expectations counterparts.”

Q6: How do the simulated distributions differ between RE and PF under a Shortfalls rule?

Under PF, the simulated distributions of unemployment and inflation gaps exhibit a pronounced kink near the steady-state value (zero gap), reflecting the asymmetric treatment of expansions and contractions. Under RE, the distributions are substantially more symmetric, shifted to the right for inflation (mean of 1.0 versus 0.25 under PF). Standard deviations of the unemployment and inflation gaps are somewhat larger under PF (1.42 and 1.10, respectively) than under RE (1.33 and 1.03), because under RE the contractionary force from inflation expectations moderates the amplitude of fluctuations. These distributional differences have direct implications for how policymakers interpret the risks associated with state-contingent policies.

Q7: What is the role of the forward-looking pricing–central bank interaction in generating RE–PF differences?

The key mechanism is as follows: under RE, the possibility that the asymmetry may bind in the future (e.g., a positive demand shock triggering more accommodation under the Shortfalls rule, or a tight labor market steepening the Phillips curve) causes forward-looking firms to raise prices today in anticipation of future inflation. This increase in current inflation leads the central bank — whose mandate includes inflation stabilization — to raise policy rates, generating a contractionary offset even when the economy is not currently in the high-demand state. Under PF, agents do not form these anticipatory expectations, so this channel is entirely absent, and the asymmetry affects outcomes only when it directly binds.

Q8: Does the RE–PF divergence arise under a symmetric Deviations rule?

No. The paper shows analytically and numerically that when the monetary policy rule is symmetric (the Deviations rule, responding equally to deviations above and below target), the RE and PF solutions are identical. Unemployment and inflation gaps are both zero on average under either expectations assumption, and the policy rate gap is essentially zero (0.01 annualized percentage points) in both cases. This equivalence result confirms that the RE–PF divergence is not an artifact of the solution method or parameterization but is specifically generated by the interaction between an asymmetry and agents’ forward-looking behavior.

Q9: What do the bounded rationality results imply about the mechanism?

The extension following Gabaix (2020), with a myopia parameter m_br = 0.97, produces results that lie between the full-RE and PF cases: the adoption of the Shortfalls rule yields average unemployment of −0.26 percentage points (intermediate between RE’s −0.05 and PF’s −0.32) and average inflation of 0.62 annualized percentage points (between RE’s 1.02 and PF’s 0.25). This gradient confirms that the key driver is the extent to which agents internalize the probability of future shocks: the more forward-looking agents are, the more strongly the anticipatory pricing channel operates and the less favorable (and more inflationary) the apparent policy tradeoff becomes.

Q10: What are the results for the nonlinear Phillips curve in the numerical model?

Under the numerically calibrated nonlinear Phillips curve model (Panel B.3 of Table 3, with the slope increasing by a factor of three when the unemployment gap is negative), the average unemployment gap under RE is 0.63 percentage points versus 0.30 under PF, and the average inflation gap under RE is essentially zero (0.01 annualized percentage points) versus 0.41 under PF. The authors note that “the average outcomes for both unemployment and inflation can differ by roughly 0.3 to 0.4 percentage points between rational expectations and perfect foresight” in this case.

Q11: What is the paper’s advice for researchers who must use perfect foresight methods?

The paper explicitly states that PF methods remain valuable, especially for estimating or simulating larger models with heterogeneity at the micro level where RE solutions are computationally prohibitive. The authors recommend that researchers relying on PF to solve larger models “check the robustness of their conclusions on longer-run averages and the distribution of outcomes using simplified models which can be solved under both perfect foresight and rational expectations.” To support this, the authors provide multiple versions of code for solving simple macroeconomic models under various asymmetries and expectations assumptions.

Q12: How does the paper position its contribution relative to prior work on RE vs. PF in asymmetric models?

The paper acknowledges that Adam and Billi (2007) and Nakov (2008) previously documented that, at the zero lower bound, households’ anticipation of future ZLB episodes leads to lower average inflation — an RE–PF difference in the spirit of this paper’s findings. However, the paper’s contribution is to show that the sign and quantitative implications of a given asymmetry can change depending on the expectations assumption, and to systematically characterize this sensitivity across multiple types of asymmetry (asymmetric policy rules and nonlinear Phillips curves). The paper also categorizes the existing literature by expectations assumptions in Table A.1, showing that many papers examining macroeconomic asymmetries use only one approach.

Key Concepts

Shortfalls Rule: A monetary policy rule, motivated by the FOMC’s 2020 Statement on Longer-Run Goals and Monetary Policy Strategy, under which the central bank responds only to shortfalls of employment from its maximum level — i.e., it does not tighten policy in response to a tight labor market (negative unemployment gap) during an expansion. Formally, it = φπ πt + φu ut when ut ≥ 0 (labor market slack), and it = φπ πt only when ut < 0 (labor market tight). Contrasts with the symmetric Deviations rule that responds to deviations of employment in both directions.

Deviations Rule: A symmetric monetary policy rule in which the central bank responds to the unemployment gap regardless of its sign — tightening in expansions and easing in contractions. Serves as the baseline against which the Shortfalls rule is compared, and as the case in which RE and PF solutions are identical.

Perfect Foresight (PF) Equilibrium: An equilibrium in which agents solve their optimization problems assuming that no future shocks will occur — they expect all endogenous variables to converge to their longer-run (steady-state) values next period, regardless of the current state. In the paper’s notation, the PF transition matrix P^PF assigns probability one to the mean state next period. In linear models, PF and RE yield identical outcomes; in models with asymmetries, they diverge.

Rational Expectations (RE) Equilibrium: An equilibrium in which households and firms correctly account for the full stochastic distribution of future shocks in forming their expectations. Agents use the true Markov transition matrix P^RE for the natural rate process. This allows forward-looking pricing behavior to incorporate the possibility that the economy may enter states in which asymmetries bind in the future.

Nonlinear (Kinked) Phillips Curve: A Phillips curve in which the slope coefficient κ̃t is state-contingent, increasing when the unemployment gap is negative (labor market is tight). In the paper’s numerical implementation, the slope triples (κ̃ = 3κ) when ut < 0, consistent with empirical evidence in Smith, Timmermann, and Wright (2025) on structural breaks in the Phillips curve. The nonlinearity generates an asymmetric inflationary response: a given level of unemployment produces more inflation when the labor market is tight than when it is slack.

Stochastic Steady State: The equilibrium to which the economy converges in the absence of additional shocks, taking into account the stochastic nature of the environment (i.e., accounting for the possibility of future shocks). Used as the initial condition for computing impulse response functions under RE. Contrasts with the deterministic steady state (zero gaps), which serves as the initial condition under PF.

Parameterized Expectations (Global Solution) Method: The numerical solution algorithm used in the paper to solve for equilibrium policy functions for unemployment and inflation gaps over the state space. Implemented identically for RE and PF cases, differing only in the transition matrix used. Applied with 105 Rouwenhorst grid points for the natural rate. The paper shows this method is orders of magnitude faster than the more common shooting algorithm (0.04 seconds vs. 10.8 seconds) while yielding identical policy functions.

Bounded Rationality (Gabaix 2020): An extension of the baseline model in which agents discount the influence of future expectations by a myopia parameter m_br ∈ (0, 1), applied to both the IS curve and the Phillips curve. The parameter m_br = 0.97 (following McKay, Nakamura, and Steinsson 2017) limits the degree to which distant future states affect current decisions. Produces outcomes intermediate between full RE and PF, confirming that the key dimension of variation is the extent to which agents internalize the probability of future shocks.

Firm dynamics and random search over the business cycle

Mon, 01 Jan 0001 00:00:00 +0000

Layer 1 — Overview

Research Question

How do aggregate economic fluctuations reallocate workers across the firm productivity distribution over the business cycle? In particular, to what extent do recessions impede workers’ movement up the job ladder toward more productive firms?

Model and Methodology

The paper develops a tractable random search model combining three features that had not previously been integrated in a single quantitative framework: (i) firm dynamics driven by idiosyncratic productivity shocks, with endogenous entry and exit; (ii) on-the-job search, generating a job ladder in which workers gradually move toward more productive firms; and (iii) aggregate productivity shocks. Multi-worker firms post employment contracts, choose hiring rates, and decide whether to continue or exit. The key tractability result — called “size-independence” (Result 1) — shows that, under a constant-returns hiring cost technology, firms’ optimal policies (contract value, hiring rate, exit decision) are all independent of firm size, so the relevant state space reduces from the full joint distribution of firm productivity and size to the employment-weighted distribution of firm productivity alone. A further result (“rank-monotonic equilibrium,” Result 2) guarantees, under a sufficient convexity condition on hiring costs (hc’’(h)/c’(h) ≥ 1), that the optimal employment contract is increasing in firm productivity, so the job ladder maps one-for-one onto the firm productivity ladder. The optimal wage contract then admits a closed-form solution.

The model is calibrated to British data for 1997–2018. Worker-level transition rates (unemployment-to-employment, employment-to-unemployment, and job-to-job) are drawn from the British Household Panel Survey (BHPS). Firm-level data on labor productivity (value added per worker) and employment costs per worker come from the Annual Respondents Database (ARD) and Annual Business Survey (ABS), merged with the Business Structure Database (BSD). The numerical solution adapts ideas from Krusell and Smith (1998), approximating the employment-weighted productivity distribution by a small set of moments and parameterizing value functions as polynomials in the aggregate state; standard linearization methods are inapplicable because endogenous firm entry and exit introduces a discontinuity in value functions.

Main Findings

Model validation via the OP decomposition. The paper’s central validation exercise uses the Olley-Pakes (OP) decomposition of a labor productivity index constructed from firm-level data. The aggregate employment-weighted labor productivity index is decomposed into (a) the unweighted average firm productivity and (b) an interaction term (the “OP term”), which captures the covariance between employment shares and productivity — i.e., how well workers are allocated to productive firms. In the British firm-level data, approximately 20 percent of the variance of the aggregate labor productivity index is accounted for by this interaction (OP) term, with the remaining ~80 percent attributable to the unweighted average of firm productivity. The baseline model, with this moment untargeted, successfully replicates this 80/20 split. By contrast, the leading benchmark model of Moscarini and Postel-Vinay (2016) (MPV2016), calibrated to the same British data, attributes nearly all of the variance of labor productivity to the OP/worker reallocation term, grossly overstating the importance of job-ladder dynamics.

Structural decomposition of labor productivity. Using the calibrated baseline model to decompose the variance of aggregate labor productivity over the post-war British business cycle (“GDP shocks” going back to 1955), the baseline model attributes approximately 30 percent to the direct effect of the aggregate productivity shock, approximately 50 percent to changes in the distribution of active firms (the “firm ladder” or firm selection component), and approximately 20 percent to the worker reallocation component (the OP interaction term). This result is robust to an alternative calibration with a lower curvature of the hiring cost function (c1 = 1).

Persistence and mechanisms. The impact of recessions on the job ladder is persistent: while the aggregate productivity shock is typically close to its pre-recession value four years after a typical recession onset, the overall allocation of workers to firms remains clearly worse relative to the pre-recession level at that same horizon. The Great Recession, viewed through the lens of the model, is a large but not unusually large recession.

Firm selection with multiple aggregate shocks. An unexpected finding concerns the direction of firm selection. With a single aggregate productivity shock, the model generates a standard “cleansing” mechanism: negative shocks raise the firm exit threshold, so surviving firms are on average more productive. However, when additional shocks to the exogenous separation rate (δ) and hiring cost scale (c0) are included — as required to match the volatility of labor market flows — firm selection instead amplifies the decline in labor productivity. The mechanism is a general equilibrium one: a higher separation rate lowers the optimal wage contract (since greater separation risk is passed on to workers), which in turn lowers the entry-exit threshold. Less productive firms become viable because their employees face higher unemployment risk and therefore accept lower wages; moreover, a larger pool of unemployed workers makes it easier for low-productivity firms to recruit.

Wage flexibility tension. The model implies a pass-through elasticity of wages to productivity shocks of approximately 0.7, well above the 0.05–0.2 range typically found empirically.

Scope Conditions

All calibration and quantitative results pertain to Britain for the period 1997–2018 (firm-level data) and 1955–2018 (GDP-based aggregate shocks). The model abstracts from decreasing returns to scale in production and from nominal rigidities. The tractability results rely on specific assumptions about the hiring cost function; the rank-monotonicity condition requires sufficient convexity (hc’’(h)/c’(h) ≥ 1).

Layer 2 — Q&A

Q1: What is the central tractability result and why does it matter for computational feasibility?

A: Result 1 (“size-independence”) shows that, because both the production technology and the hiring cost function are constant returns to scale, the firm’s present discounted value of profits is linear in employment. As a result, per-worker profits are independent of firm size, and optimal firm policies — the hiring rate, the contract value offered to workers, and the continuation/exit decision — all depend only on the firm’s current productivity, not on its size. This collapses the state space from the full joint distribution of firm productivity and employment size to the employment-weighted measure of firm productivity Lt(p), a uni-dimensional object. Without this result, the model would require tracking the entire joint firm distribution, making it computationally intractable.

Q2: What is a rank-monotonic equilibrium (RME) and what conditions guarantee it?

A: An RME is a recursive equilibrium in which the optimal contract offered by a firm is weakly increasing in that firm’s current productivity realization, for all aggregate states. Result 2 provides sufficient conditions: (i) the Markov process for firm-specific productivity satisfies first-order stochastic dominance (more productive firms today are more likely to be more productive tomorrow), (ii) the distribution of offered contracts is everywhere differentiable (ruling out mass points), and (iii) the hiring cost function satisfies hc’’(h)/c’(h) ≥ 1 — a sufficient convexity condition. The economic interpretation of the convexity condition is that firms must find retention (offering higher wages) sufficiently costly relative to new hiring that more productive firms optimally choose to use the wage margin to limit quits. The baseline calibration yields c1 ≈ 5.9 (so costs are highly convex in the hiring rate), though results are also reported for the minimum permissible c1 = 1.

Q3: What does the optimal employment contract look like in a rank-monotonic equilibrium, and what does it reveal about rent extraction?

A: In an RME, the optimal contract V(p,ω,L) is a weighted average of the value of unemployment U(ω,L) and the firm-workers’ joint surplus S(p,ω,L), where the weights are determined endogenously by the employment-weighted measure of firm productivity L. Specifically, the contract integrates the surplus of all firms with productivity below p, weighted by the share of employed workers at those firms, and divided by the mass of job seekers willing to accept the contract. As the employed workers’ relative search intensity s approaches zero, the contract converges to the value of unemployment — workers receive no rents. The endogenous bargaining weight evolves with the aggregate state over the business cycle, unlike standard Nash bargaining models with a fixed exogenous weight.

Q4: What firm-level moments are used to calibrate the steady-state model, and what is the logic behind the parameter-moment mapping?

A: Eight moments are targeted. From the BHPS worker data: the average UE rate (0.058) pins down the scale of hiring costs c0; the average EU rate (0.003) pins down the exogenous separation rate δ; and the average EE (job-to-job) rate (0.016) pins down the relative search intensity s. From the firm-level ARD/BSD data: average firm size (12.1 employees) pins down the entry probability µ; the share of job destruction from firm exits (0.526) disciplines the flow value of unemployment b; the autocorrelation of firm employment ln(n) (0.949 annually) disciplines the persistence of idiosyncratic productivity ρp; the interquartile range of firm-level labor productivity (1.129 log points) disciplines the volatility of idiosyncratic shocks σp; and the regression coefficient of firm employment growth on lagged labor productivity (0.136) disciplines the curvature of hiring costs c1. The baseline calibration fits all eight moments closely.

Q5: How does the calibrated model match non-targeted moments, and what does this establish?

A: The model generates several realistic features not targeted in calibration. It produces a realistic Pareto tail for the employment-size distribution (Pareto tail exponent of 1.033 in the model vs. 1.066 in the data), which arises from the combination of size-independent growth rates and firm entry and exit — conditions identified in the literature as generating power law distributions. The model also matches the dispersion of employment costs per worker across firms (capturing about 70 percent of the interquartile range of ECi,t), the slope of a regression of employment costs on labor productivity (model: 0.685 vs. data: 0.704), and the slope of a regression of employment growth on employment costs (model: 0.162 vs. data: 0.131). These non-targeted matches provide independent validation of the model’s wage-determination mechanism.

Q6: Why is a single aggregate productivity shock insufficient to match labor market fluctuations, and what additional shocks are needed?

A: With a single aggregate productivity shock calibrated to match the autocorrelation and standard deviation of log GDP, the model generates labor market fluctuations that are roughly an order of magnitude smaller than in the data. For example, the standard deviation of the EU transition rate is 4.1×10⁻⁴ in the single-shock model versus 2.3×10⁻³ in the data. Adding a discount rate shock (ω,r) partially helps but still leaves the job-finding rate (UE) more than 50 percent too smooth. Adding a separation rate shock (ω,δ) substantially increases EU and UE volatility but generates insufficient EE (job-to-job) volatility. The combination (ω,δ,c0) — adding a shock to the scale of hiring costs c0 — brings the standard deviations of EU and UE close to the data (2.0×10⁻³ and 4.0×10⁻⁴ vs. data 2.3×10⁻³ and 2.7×10⁻⁴), though the model still generates slightly under half the observed volatility in EE rates. This combination is the baseline for the quantitative analysis.

Q7: What is the OP decomposition, how is it computed from the firm-level data, and what does it measure in the model?

A: The aggregate labor productivity index LPt is constructed from firm-level data as the employment-share-weighted average of log value added per worker across firms. The OP decomposition writes this as LPt = LPt_bar + OPt, where LPt_bar is the unweighted (simple) average of firm-level productivity and OPt is the covariance between employment shares and labor productivity (the “interaction term”). In the data, OPt increases when workers are disproportionately employed at above-average-productivity firms. In the model, LPt_bar maps onto the average (log) productivity of active firms — the support of the job ladder — while OPt maps onto the difference between the employment-weighted and the unweighted averages of firm productivity, directly measuring how high up the ladder workers are located relative to the set of active firms. Around 20 percent of the variance of LPt in the British data is accounted for by OPt, and the model replicates this.

Q8: How does the Great Recession appear in the OP decomposition, and does the model fit the decomposition during this episode?

A: During the Great Recession (2008q2–2009q3 in the UK), around 20 percent of the overall fall in the labor productivity index is accounted for by the fall in the OP interaction term, with the remaining 80 percent coming from the fall in the unweighted average firm productivity. The model, even though it does not target this decomposition in calibration, successfully matches both the average firm productivity component and the interaction (OP) component during the Great Recession. This matching holds both in the baseline calibration (c1 ≈ 5.9) and in the alternative calibration with c1 = 1. The model also matches the analogous decomposition for employment costs per worker (ECt), an additional non-targeted validation.

Q9: Why does firm selection amplify rather than cleanse in the baseline multi-shock calibration?

A: In the single-shock (productivity ω only) model, a negative productivity shock lowers surplus at all firms, raising the exit threshold pE and thus selecting out low-productivity firms — the standard “cleansing” mechanism. In the multi-shock baseline, the additional separation rate shock (δ) generates a less intuitive mechanism. A higher δ lowers the optimal wage contract (since increased separation risk is passed on to workers: ∂V/∂δ ≤ 0), which reduces the value of continued employment. This lowers the joint firm-worker surplus threshold for exit, making it viable for low-productivity firms to remain active. Moreover, the larger pool of unemployed workers (generated by the δ shock) depresses the outside option of workers and makes it easier for low-productivity firms to recruit. As a result, the entry-exit threshold pE,t falls — the set of active firms becomes less productive on average — producing a negative firm selection contribution to labor productivity and a positive (amplifying rather than cleansing) contribution to the variance of LPt.

Q10: What is the structural variance decomposition of labor productivity in the baseline model?

A: Simulating the baseline model over the post-war British business cycle (1955–2020, GDP shocks), the variance of aggregate labor productivity LPt decomposes into three structural terms: approximately 30 percent (0.296) from the direct effect of the aggregate productivity shock ln(ωt); approximately 50 percent (0.541) from changes in the average productivity of active firms E[KP bar_t(ln p)] — the “firm ladder” or firm selection component; and approximately 20 percent (0.163) from the worker reallocation component OPt = E[LP bar_t(ln p)] − E[KP bar_t(ln p)]. This decomposition implies that roughly 70 percent of fluctuations in labor productivity are driven by worker reallocation broadly defined (the firm ladder plus the interaction term), with the firm selection component being the largest single driver. The result is robust to the alternative c1 = 1 calibration (30/49/22 percent split).

Q11: How does the baseline model compare to MPV2016 in the variance decomposition?

A: In the multi-shock calibration (ω,δ,c0), the MPV2016 model calibrated to the same British data attributes approximately 97.7 percent (0.977) of the variance of LPt to the worker reallocation (OP) term, with essentially none attributed to a firm selection term (since there is no firm entry and exit in MPV2016). This is nearly five times the 20 percent share attributed to worker reallocation in the data and in the baseline model. In the single-shock (ω) calibration, both models attribute a more modest share to worker reallocation (7.2 percent for the baseline model, 0.1 percent for MPV2016 with c1=5), and the difference narrows considerably. The contrast thus stems from the interaction of firm dynamics with multiple aggregate shocks: allowing for endogenous firm entry and exit is critical to prevent the model from overstating the role of the job ladder.

Q12: How persistent is the impact of recessions on the job ladder, based on the model simulations?

A: The paper simulates the structural decomposition of labor productivity starting from each of seven post-war British recessions (defined by two consecutive quarters of negative GDP growth). On average across these recessions, the aggregate productivity shock ln(ωt) is close to its pre-recession level by four years after the recession onset. However, the overall employment-weighted average productivity E[LP bar_t(ln p)] — reflecting workers’ position on the job ladder — remains clearly below its pre-recession value at the four-year horizon, indicating persistent misallocation. The OP interaction term accounts for approximately 20 percent of the total drop in the employment-weighted productivity measure three years after a typical recession onset. Through the model’s lens, the Great Recession is a large recession but not an outlier relative to the historical distribution.

Q13: What does the counterfactual with countercyclical unemployment benefits reveal about the tradeoff between firm selection and worker reallocation?

A: When the flow value of unemployment is made countercyclical (falling in recessions, rising in expansions — mimicking US unemployment insurance extension programs), the model generates a sign reversal in the firm selection (“firm ladder”) component. With countercyclical b, the unemployment value rises in recessions, which raises the minimum wage firms must offer and raises the exit threshold pE,t: fewer low-productivity firms survive, improving the composition of active firms. However, countercyclical benefits also amplify the slowdown in job-to-job reallocation: the higher value of unemployment reduces workers’ willingness to accept job offers, and all firms cut recruitment since optimal wage contracts must rise. The OP interaction term therefore falls more sharply than in the baseline model. The counterfactual with ϵb,ω ∈ {−100, −50} finds that the positive “firm ladder” effect dominates on net, so the overall allocation of workers to firms improves relative to the baseline after a typical recession under countercyclical unemployment benefits.

Q14: What is the numerical solution method, and why are standard linearization approaches inapplicable?

A: The model is solved in two steps. First, aggregate shocks are shut down and the steady-state rank-monotonic equilibrium is solved numerically by discretizing the firm productivity process (401 grid points via Tauchen’s method) and iterating on the value function and the employment-weighted productivity measure until convergence. Second, aggregate shocks are reintroduced using a simulation-based approach adapted from Krusell and Smith (1998): the employment-weighted distribution of productivity is summarized by Nm = 2 moments (plus the unemployment rate), and the value functions are parameterized as polynomials in the aggregate state, with coefficients updated by regression until convergence. Standard linearization methods (Reiter 2009) are inapplicable because the endogenous entry-exit decision creates a kink (discontinuity) in value functions at the productivity threshold pE, making first-order approximations around the steady state inaccurate. Accuracy tests based on den Haan (2010) show that the polynomial approximation generates errors of at most 0.065 percent for value functions and at most 1 percentage point for the unemployment rate across simulation paths.

Key Concepts

1. Rank-Monotonic Equilibrium (RME) A recursive equilibrium in which the optimal state-contingent employment contract V(p,ω,L) offered by a firm is weakly increasing in the firm’s current productivity realization p, for all aggregate states (ω,L). This property implies that the job ladder maps one-for-one onto the firm productivity ladder: workers always prefer to work at more productive firms. The paper shows this property holds under a sufficient convexity condition on hiring costs (hc’’(h)/c’(h) ≥ 1) and first-order stochastic dominance of the productivity process.

2. Size-Independence The property that a firm’s optimal policies — the hiring rate h(p), the employment contract V(p), and the entry/exit decision χ(p) — are all independent of the firm’s current employment size n. This follows from constant returns to scale in production and hiring, which implies that firm profits are linear in employment. Size-independence reduces the model’s relevant state space to the employment-weighted distribution of firm productivity, enabling tractability.

3. Employment-Weighted Distribution of Firm Productivity (L_t(p)) The measure recording, for each productivity level p, the total employment at firms with productivity at most p. This is the sufficient statistic for the state of the job ladder at any point in time: combined with the aggregate shock ω, it determines all equilibrium policy functions and value functions. In the model, it replaces the full joint distribution of firm productivity and employment size that would otherwise be required.

4. OP Decomposition (Olley-Pakes Decomposition) The decomposition of the aggregate employment-weighted labor productivity index LPt into: (a) the unweighted average firm productivity LPt-bar, which summarizes the productivity of active firms (the support of the job ladder); and (b) an interaction term OPt, the covariance between employment shares and firm-level productivity, which measures how well workers are allocated across the productivity distribution (i.e., how high up the ladder workers sit given the set of active firms). In the model, (a) maps to E[KP bar_t(ln p)] and (b) maps to OPt = E[LP bar_t(ln p)] − E[KP bar_t(ln p)].

5. Contract Posting The wage-setting protocol in which each firm commits upon entry to a full state-contingent employment contract — a schedule mapping each future realization of aggregate and idiosyncratic productivity to a wage and continuation decision — and is bound by an equal treatment constraint to offer the same contract to all employees. Workers cannot renegotiate based on outside offers. This protocol produces a well-defined closed-form for the optimal contract in an RME and differs from alternating-offer bargaining (Nash bargaining) in that the bargaining weights are endogenous rather than fixed.

6. Firm-Workers’ Joint Surplus (S_t(p)) The total present discounted value accruing to the firm-worker pair: firm profits per worker plus the contract value promised to workers. Because utility is transferable (risk neutrality) and the firm fully commits to its contract, this surplus depends only on the firm’s current productivity and the aggregate state — not on the promised contract value V. The surplus S_t(p) is the key object determining firm entry/exit (the firm continues if and only if S_t(p) ≥ U_t) and optimal hiring (the marginal return to an additional hire equals S_t(p) − V(p)).

7. Cleansing vs. Anti-Cleansing Firm Selection In models with endogenous firm entry and exit, a negative aggregate shock can either raise or lower the productivity threshold for firm survival. “Cleansing” refers to the standard mechanism where a negative productivity shock raises the exit threshold, selecting out low-productivity firms and improving the average quality of survivors. “Anti-cleansing” (as in the baseline multi-shock calibration) occurs when separation rate or hiring cost shocks lower the optimal wage contract and reduce the exit threshold, allowing less productive firms to survive and worsening average firm productivity.

Labor Market Shocks and Monetary Policy

Mon, 01 Jan 0001 00:00:00 +0000

Overview

Research question. The paper asks two related questions: (1) How much, and through which channels, do employer-to-employer (EE) worker transitions affect macroeconomic outcomes — particularly inflation? (2) What is the optimal monetary policy within a class of Taylor rules when EE flows are taken explicitly into account?

Motivation. Standard monetary policy frameworks condition on the unemployment rate as the primary labor market slack measure and underemphasize the “quality” dimension of employment. The paper documents a striking empirical pattern: the 2016–2019 recovery and the 2021–2022 recovery from COVID-19 featured nearly identical declines in the unemployment rate, yet exhibited dramatically different EE rate dynamics and inflation outcomes. During 2016–2019, the EE rate remained flat despite a roughly 25 percent decline in the unemployment rate from trend. During 2021–2022, the EE rate rose by around 8 percent above trend over a comparable unemployment decline. Correspondingly, unit labor cost (ULC) growth reached approximately 6 percent during the COVID-19 recovery when unemployment fell below 4 percent, compared with only about 2 percent ULC growth in the 2016–2019 period at similar unemployment levels.

Methodology. The authors develop a Heterogeneous Agent New Keynesian (HANK) model with a frictional labor market featuring on-the-job search (OJS). Workers are heterogeneous in wealth (mutual fund shares), human capital, match-specific productivity, and endogenous piece-rate wages. Human capital stochastically appreciates when employed and depreciates when unemployed, capturing scarring effects and job-stayer wage growth. Wage determination follows a Bertrand competition protocol based on flow output: workers switch to higher-productivity matches and extract the full surplus from the new firm, while outside offers from lower-productivity firms can still trigger rebargaining with the incumbent firm and raise the piece rate without a job switch. Three vertically integrated sectors — labor services, intermediate goods, and final goods — are linked so that the real price of labor services pl is the real marginal cost for intermediate firms and the sole driver of inflation in the New Keynesian Phillips curve (absent aggregate productivity shocks). The economy is subject to AR(1) shocks to the discount rate β (demand), aggregate labor productivity z (supply), and OJS efficiency ν (the relative search efficiency of employed workers). The model is solved using the Sequence-Space Jacobian (SSJ) method, extended to handle discretized worker distributions as direct inputs to equilibrium conditions.

The model is calibrated to U.S. pre-Great Recession data (2004–2006), targeting the fraction of hand-to-mouth individuals (16 percent of SIPP sample), unemployment rate (5.1 percent), EU separation rate (3.8 percent quarterly), EE rate (2 percent quarterly from LEHD), earnings drop upon job loss (35 percent), wage growth of job switchers (9 percent), and the labor share (0.67). Shock processes are estimated by minimizing deviations from empirical correlations and standard deviations of output, unemployment, EE rate, and inflation over 1995:Q3–2008:Q4.

Main findings — positive analysis. Shocks to OJS efficiency account for 43.1 percent of fluctuations in inflation in the variance decomposition, and 78.7 percent of fluctuations in the EE rate. The mechanism: a higher OJS efficiency lowers the expected match value EJ for labor services firms through three channels — (i) a compositional shift toward employed job seekers who extract the entire match surplus, (ii) shorter expected match duration as workers face higher poaching probabilities, and (iii) more frequent wage rebargaining where outside offers bid up wages without accompanying productivity gains. To maintain the free-entry condition, the real price of labor services pl must rise, increasing the real marginal cost and inflation. This direct labor market effect explains 139 percent of the total increase in pl; general equilibrium effects through reduced tightness θ — which raises expected match values by making vacancies easier to fill and workers less likely to be poached — offset −42 percent; the remainder (3 percent) comes from real rate changes driven by the monetary policy reaction.

In two historical simulations, muted OJS efficiency during 2016–2019 generated approximately 0.23 percentage points lower annualized inflation at the peak relative to a counterfactual economy with the same unemployment path but an endogenously rising EE rate. Conversely, elevated OJS efficiency during 2021–2022 generated approximately 0.56 percentage points higher annualized inflation compared to the flat-EE-rate counterfactual. The paper notes that strong worker mobility accounts for roughly 10 percent of the approximately 6 percentage point total rise in annual inflation during the COVID-19 recovery episode.

An important cross-model comparison shows that the Representative Agent New Keynesian (RANK) version of the model overestimates the decline in demand, output, and labor market tightness upon a positive OJS shock, and underestimates the rise in real rate, marginal cost, and inflation. Household heterogeneity is therefore quantitatively important: hand-to-mouth households’ demand responds directly to labor income increases from job switches, mitigating the demand decline and amplifying inflation.

Main findings — normative analysis. The optimal monetary policy within an augmented Taylor rule — adding an EE gap term ΦEE(EEt − EE*) alongside the standard inflation and unemployment gap terms — prescribes Φ*_u = −3.18 and Φ*_EE = 2.22 (with Φπ fixed at 1.5). This yields a 78.7 percent reduction in the central bank loss relative to the baseline Taylor rule. A policy that ignores EE dynamics and optimizes only the unemployment gap coefficient (finding Φu = −2.71, ΦEE = 0) produces a 12 percent larger central bank loss than the full optimal policy. In terms of welfare, the optimal policy delivers 0.16 percent additional lifetime consumption equivalent in the aggregate. Workers at the bottom of the match quality distribution gain the most (0.24 percent), as do the unemployed (0.20 percent), while those at the top of the wealth distribution gain the least due to larger share price fluctuations under the more aggressive policy.

Scope conditions. Results are derived conditional on a dual-mandate central bank objective (variance of inflation and output gaps), within a class of Taylor-type rules (not fully optimal Ramsey policy), under first-order approximation around a non-stochastic steady state. The historical simulations abstract from supply shocks active in the normative exercises and assume the economy starts from steady state in 2016.

Q&A

Q1: What is the OJS efficiency shock, and how does it differ from a standard demand or supply shock? An OJS efficiency shock is modeled as a time-varying shift in νt, the relative job search efficiency of employed workers compared with unemployed workers. Unlike demand shocks (discount rate β innovations) and productivity shocks (aggregate z innovations), which move inflation and unemployment in opposite directions under standard New Keynesian logic (divine coincidence), OJS efficiency shocks move inflation and unemployment in the same direction: a positive OJS shock raises inflation while also raising unemployment (because the higher real rate induced by the central bank’s reaction reduces demand and employment). This makes OJS shocks behave like cost-push shocks and introduces a genuine policy trade-off for a dual-mandate central bank.

Q2: What are the three mechanisms through which higher OJS efficiency raises the real price of labor services, and what is the quantitative contribution of each? The decomposition (Figure 8) shows that the direct effect of ν on EJ — encompassing the composition channel (more employed job seekers who extract the full surplus), the match-duration channel (shorter expected match lives), and the wage rebargaining channel (outside offers raise wages without productivity gains) — explains 139 percent of the total increase in pl. The general equilibrium reduction in labor market tightness θ, which raises EJ and partially offsets the cost increase, explains −42 percent in total: −18 percent through increased supply of labor services L (productivity-enhancing job switches improve the match distribution) and −24 percent through reduced output Y (lower aggregate demand). Real rate effects account for the remaining 3 percent net (8 percent from the inflation channel and −5 percent from the unemployment channel). Labor market effects in total therefore explain 97 percent of the marginal cost increase.

Q3: Does the positive relationship between EE rates and inflation require wage increases upon job switches? No. The paper demonstrates (Section 2.4.2, Figure 3) that even when the piece rate for workers hired from unemployment is set to α = 0.95 (so that outside offers have negligible wage effects), a positive OJS efficiency shock still generates a decline in output and a rise in inflation in both the RANK and TANK models. Quantitatively, the inflation response is similar across the baseline and near-zero composition-channel specifications, confirming that the shorter expected match duration is the primary driver of the increase in the real price of labor services. The match duration channel operates independently of wage increases: firms anticipate shorter matches and require a higher flow price to break even on vacancy costs.

Q4: How does household heterogeneity change the quantitative effects of OJS shocks relative to the RANK benchmark? Under a constant real rate, in the RANK model a higher OJS efficiency increases the real price of labor services and inflation but has no effect on aggregate demand or output (because higher labor income for the PIH household is exactly offset by lower firm profits). In the TANK model, hand-to-mouth households consume their entire labor income, so the rise in labor income from job switches directly boosts their demand, raising output and tightness and further amplifying inflation. Under an endogenous real rate, the RANK model overestimates the decline in demand and output, and underestimates the rise in real rate and inflation, compared with the TANK model. The TANK model requires a substantially larger equilibrium real rate increase to contain inflation because HtM households’ demand is less elastic to the real rate than PIH households'.

Q5: How are aggregate shock processes estimated, and what share of inflation variance do OJS shocks explain? The six AR(1) parameters governing β, z, and ν (three persistence parameters ρj and three standard deviations σj) are estimated by minimizing the sum of squared deviations between model-generated and empirical moments: the autocorrelation of output; correlations of the unemployment rate, EE rate, and inflation with output; and standard deviations of output, unemployment rate, EE rate, and inflation. Data cover 1995:Q3–2008:Q4. Estimated values are ρβ = 0.909, ρz = 0.332, ρν = 0.936 and σβ = 0.001, σz = 0.002, σν = 0.003. The variance decomposition (Table 4) assigns 43.1 percent of inflation variance to OJS efficiency shocks ν, 52.0 percent to demand shocks β, and 4.9 percent to productivity shocks z.

Q6: How is the “missing inflation” during 2016–2019 quantified, and what is the counterfactual? The exercise simulates two economies both replicating the same unemployment path — a 15 percent decline in unemployment relative to its 5.2 percent steady state, spread linearly over 16 quarters, followed by mean reversion. The first economy uses only positive demand shocks, which generate an endogenously rising EE rate consistent with the historical unemployment-EE correlation. The second economy additionally introduces negative OJS efficiency shocks to keep the EE rate unchanged, as observed in the data during 2016–2019. Annualized inflation in the second economy is 0.23 percentage points lower at the peak (16 quarters after the shock), implying that had the EE rate risen normally, inflation would have been around 2 percent in 2019 rather than the observed 1.8 percent.

Q7: How is the inflationary role of elevated EE transitions during 2021–2022 quantified? Using the same unemployment path as the 2016–2019 exercise, the COVID-19 recovery economy combines positive demand shocks with positive OJS efficiency shocks to replicate the observed 0.16 percentage point (8 percent above trend) increase in the EE rate. Comparing this economy to the flat-EE-rate economy from the prior exercise, the elevated EE rate generates 0.56 percentage points higher annualized inflation. Because annual inflation rose approximately 6 percentage points in the data during this episode, the model attributes roughly 10 percent of the total inflation increase to strong worker mobility.

Q8: What are the optimal Taylor rule coefficients when EE dynamics are included, and what is the welfare cost of ignoring them? The optimal policy over the augmented Taylor rule it = i* + Φπ(πt − π*) + Φu(ut − u*) + ΦEE(EEt − EE*), with Φπ fixed at 1.5 and a dual-mandate loss function W = var(πt − π*) + 0.25·var(Yt − Y*), prescribes Φ*_u = −3.18 and Φ*_EE = 2.22. This reduces the central bank loss by 78.7 percent relative to the baseline rule (Φu = −0.25, ΦEE = 0). If the EE gap term is excluded and only the unemployment gap coefficient is re-optimized (finding Φu = −2.71), the central bank loss is 12 percent higher than under the full optimal policy.

Q9: How does the optimal policy affect macroeconomic volatility, and who gains most from it? Table 5 shows that the optimal policy substantially reduces volatility of inflation (standard deviation falls from 0.0013 to 0.0011), output (0.0059 to 0.0020), consumption (0.0059 to 0.0020), unemployment (0.0047 to 0.0013), labor market tightness (0.0600 to 0.0175), and the real marginal cost pl (0.0203 to 0.0081), at the cost of higher real rate volatility (0.0019 to 0.0033) and share price volatility (0.1975 to 0.3051). In terms of welfare (Table 6), the unemployed gain 0.20 percent in lifetime consumption equivalents (versus 0.15 percent for the employed), workers at the bottom quintile of match quality gain 0.24 percent (versus 0.16 percent at the top), and wealth-poor individuals in the bottom share quintile gain 0.23 percent (versus 0.11 percent at the top, whose gains are eroded by larger share price fluctuations).

Q10: How does the model extend the SSJ computational method, and why is this extension necessary? The standard SSJ method of Auclert, Bardoczy, Rognlie, and Straub (2021) handles settings where only scalar aggregates enter equilibrium conditions in sequence space. In this model, the discretized distributions of employed workers µE(h, x) and unemployed workers µU(h) at the job search stage enter directly into the expected match value EJ (because human capital and current match productivity determine output and wage levels upon new contacts), and the distribution λE(h, x, α) at the production stage enters into labor services firm profits ΓS. The authors treat worker distributions as histograms and compute Jacobians for each mass point, combining the SSJ method with Reiter (2009)-style projection. This substantially increases computation time but remains feasible, extending the SSJ method to multi-stage models with search frictions where endogenous distributions are state variables.

Q11: What are the three sources of wage growth in the HANK model, and what is their relevance for inflation dynamics? First, human capital h stochastically appreciates during employment (at rate πE = 0.018 per quarter, calibrated to annual job-stayer wage growth of approximately 2 percent), raising wages through a higher piece-rate base. Second, job switches to higher-productivity matches yield wage increases as the worker extracts the full surplus from the new firm (the new piece rate equals x/x’, the ratio of old to new match productivity). Third, outside offers with productivity x’ satisfying αx < x’ < x — not good enough to trigger a switch but better than the current bargaining threat — cause the incumbent firm to raise the piece rate to x’/x via rebargaining, increasing wages without a job change. The second and third channels are the ones directly affected by OJS efficiency shocks and are inflationary: they raise labor costs beyond productivity gains.

Q12: Why do OJS shocks have a shorter match duration channel even without wage increases? When OJS efficiency ν rises, each employed worker faces a higher probability νtf(θt) of contacting another firm each period. Even if wages do not change upon contact (as in the α = 0.95 robustness exercise), a labor services firm posting a vacancy expects that any match it forms will be shorter-lived: the worker is more likely to be poached in the future. This shortens the expected present discounted value of the match for the firm, reducing EJ. To satisfy the free-entry condition (expected profit = vacancy cost κ), the price of labor services pl must rise, increasing the real marginal cost and inflation. Figure 3 confirms a nearly identical inflationary response under α = 0.95 as under the baseline, isolating this match-duration mechanism.

Key Concepts

OJS efficiency shock (νt shock). A time-varying shift in the relative job search efficiency of employed workers compared with unemployed workers. Modeled as an AR(1) process for νt (estimated persistence ρν = 0.936). An increase in νt raises the probability that employed workers contact outside firms each period, boosting the EE rate. In the model, this acts as a cost-push shock: it raises inflation and unemployment simultaneously, breaking divine coincidence and creating a policy trade-off for a dual-mandate central bank.

Expected match value (EJt). The ex-ante expected value to a labor services firm of a filled vacancy, conditional on contacting a worker, defined as a weighted average of match values J across the pool of job seekers (unemployed and employed). The free-entry condition Vt = κ/q(θt) = EJt pins down the real price of labor services pl: when EJt declines (due to shorter match durations or compositional shifts toward high-surplus-extracting workers), pl must rise to maintain zero expected profit for vacancy posters.

Composition channel. The mechanism by which a rise in OJS efficiency shifts the composition of the job-seeker pool toward employed workers, who (under Bertrand competition) extract the entire flow surplus of a new match and receive wage equal to plF(h,x). Since firms receive zero rent from poached workers, an increase in the fraction of employed in the applicant pool lowers EJt and requires a compensatory increase in pl.

Match duration channel. When OJS efficiency ν rises, each existing match faces a higher probability of dissolution because the worker is more likely to be poached. The reduced expected match duration lowers the present discounted value of a match for the firm (even holding wages fixed), reducing EJt and raising pl. Demonstrated as the primary driver of inflation in the α = 0.95 robustness exercise where wage increases upon job switches are near zero.

Piece-rate α (endogenous). The share of match output F(h,x) that the worker receives as wage, determined through Bertrand competition on flow output following Postel-Vinay and Robin (2002). A worker hired from unemployment starts at α = x̄/x’ (where x̄ is the lowest match productivity). Job switches to higher-x’ firms reset α = x/x’. Rebargaining upon a credible outside offer from a firm with αx < x̃ < x raises α to x̃/x. The piece rate endogenizes wage dynamics for switchers, stayers, and job losers, allowing the model to discipline these moments in the data.

Divine coincidence (and its breakdown under OJS shocks). In standard New Keynesian models, demand and productivity shocks move inflation and unemployment gaps in opposite directions, so stabilizing inflation also stabilizes the output gap. OJS efficiency shocks break this property: they generate simultaneous increases in inflation and unemployment, introducing a genuine trade-off between the two mandates and making EE-augmented Taylor rules welfare-improving relative to rules that respond only to unemployment.

Sequence-Space Jacobian (SSJ) method with distributed worker states. An extension of the Auclert, Bardoczy, Rognlie, and Straub (2021) computational method to settings where discretized distributions of workers (µE(h,x) and µU(h)) enter directly into equilibrium conditions — specifically into the free-entry condition via EJt and into firm profits. The authors treat distributions as histograms and compute Jacobians for each mass point, combining SSJ with Reiter (2009)-style projection to efficiently solve for transitional dynamics under aggregate uncertainty.

Life-cycle worker flows and cross-country differences in aggregate employment

Mon, 01 Jan 0001 00:00:00 +0000

Layer 1 — Overview

Research question. The paper asks: what are the sources of cross-country differences in aggregate employment across European economies, and which types of worker flows — between employment (E), unemployment (U), and nonparticipation (N) — drive those differences? The authors pay particular attention to heterogeneity by gender and age, motivated by the observation that cross-country employment dispersion is concentrated among women, youth, and older workers, and that a large portion of the dispersion is traceable to differences in labor force participation rather than unemployment rates alone.

Data. The empirical analysis draws on microdata from the EU Statistics on Income and Living Conditions (EU-SILC), an annual survey covering 32 European countries for 2004–2019. Germany is covered using the German Socio-Economic Panel (GSOEP, 2003–2018) because GSOEP longitudinal coverage begins earlier. The combined sample contains 7,064,306 individual-year observations for 2,221,672 individuals. Labor force status is recorded monthly via a retrospective calendar; transition probabilities are estimated at the quarterly frequency after correcting for measurement error (a “de-NUN-ification” procedure following Elsby et al. [2015]) and time-aggregation bias (Shimer [2012]).

Methodology — empirical. Six quarterly transition probabilities among E, U, and N are estimated by gender and single year of age (16–65). The life-cycle profile of each probability is extracted nonparametrically by regressing age-time cells on age and time dummies, removing business-cycle variation. To decompose cross-country employment differences into contributions of the six transition rates while handling the path-dependence of the decomposition (6! = 720 possible orderings), the authors apply the Shapley-Owen decomposition, which assigns to each transition rate its average marginal contribution across all orderings. An initial first-pass decomposition allocates the aggregate employment gap between any two countries into three parts: demographics, initial conditions (distribution across E, U, N at age 16), and transition probabilities. Transition probabilities account for 93–105% of the cross-country variance in aggregate employment, while demographics and initial conditions together explain less than 10%.

Methodology — structural model. The authors build a life-cycle Diamond-Mortensen-Pissarides (DMP) model with three labor market states, calibrated separately by gender and country for France, Germany, Italy, Spain, and the U.K. — the five largest economies in the sample. A key feature is that all primitives (technology, search and matching) are age-independent; life-cycle variation in worker flows arises endogenously from the finite retirement horizon and from two search margins: (i) an intensive margin — variable search intensity s in [0,1] chosen optimally each period — and (ii) an extensive margin — the endogenous labor force participation decision modeled as a discrete choice with i.i.d. extreme-value utility shocks. The model also incorporates permanent match quality (an experience good revealed stochastically with probability alpha per period following Jovanovic [1979]), transitory match-quality shocks (persistent AR(1) process), exogenous job-destruction shocks (per-period probability delta), a two-tier UI system, a two-tier EPL system capturing temporary vs. permanent contracts, and proportional value-added and social-security taxes.

Main empirical findings.

For male workers, employment-to-unemployment (EU) transitions account for approximately half of the cross-country variance in aggregate male employment across all 32 countries, rising to about three-quarters when looking at the five largest economies, and exceeding 85% for prime-age males (ages 25–54). Transitions in the reverse direction (UE) explain less than 30% of the variance across all 32 countries and play almost no role among the five largest economies. The labor force participation margin (combining NE and EN transitions) explains a non-negligible 25–30% of the aggregate male employment gap.
For female workers, at least half of the cross-country variance in employment is explained by participation-related flows, primarily transitions from nonparticipation to employment (NE). In the full 32-country sample, NE alone explains 65% of the variance in female employment rates across all ages (16–65). Its role is somewhat smaller in the five largest economies, where EN transitions also play a larger role. Crucially, the sum of NE and EN variance contributions for women is at least as large as the sum of UE and EU contributions, underlining the indispensability of a three-state model.

Main quantitative (model-based) findings. The model decomposes cross-country employment differences into technology (the distribution of permanent match quality, job-separation risk delta, and information frictions alpha), search parameters (vacancy costs, non-work utility, search-cost parameters), and policies (UI generosity, firing costs, taxes). The total employment variance across the five economies and two gender groups is 0.36 percentage points squared. Technology differences over-explain this variance (contribution of 0.65), while policies play almost no role (contribution of -0.04) and search frictions have a negative variance contribution (-0.25). The negative sign of search and policy contributions reflects the negative cross-country correlation between these factors and technology: countries with high employment rates (e.g., France) tend to have more generous UI and higher taxes, which the model attributes to compensating technology advantages. For individual countries: France is about 4.4 percentage points above the cross-country benchmark, driven by technology and partly offset by the highest replacement ratios and labor tax rates in the sample (67% and 56%, respectively). Spain is about 7 percentage points below the benchmark, driven by the lowest measured labor productivity (78% of Germany’s level) and the highest employment outflow rates (~4–5% per quarter vs. ~2% in France).

The channels through which technology affects employment are predominantly the employment inflows, not outflows. The exogenous job-separation risk delta affects aggregate employment mostly through its impact on expected duration of future employment spells, which reduces search incentives and job-finding rates from both unemployment and nonparticipation, and lowers labor force attachment. Similarly, mean permanent match quality (mu_x) and labor taxes (tau_ss) operate mainly through the inflow margin. Technology effects are amplified by search effort margins, particularly for women and youth: women face higher non-work utility (interpreted as labor-market frictions or opportunity costs), implying a lower employment surplus and therefore a higher surplus elasticity; for young workers, the long remaining horizon amplifies the effect of technology variations on discounted lifetime earnings, generating relatively higher search-effort responses.

Scope conditions. The analysis is confined to European countries. The structural decomposition covers only the five largest European economies. The authors acknowledge that parameters labeled as “job-separation risk” may also capture employment protection and temporary contracts not explicitly modeled, or non-monetary quit motives, so the attribution to “technology” should be interpreted with that caveat in mind. The model operates in a complete-markets, no-savings environment without on-the-job search.

Layer 2 — Q&A

Q1: What fraction of cross-country employment variance is explained by transition probabilities vs. demographics and initial conditions?

A: In the full 32-country sample, transition probabilities account for 94.7% of the cross-country variance in aggregate male employment and 99.9% for female employment. In the five largest economies, the corresponding figures are 93.5% (men) and 104.9% (women) — the slight excess above 100% reflects the negative contribution of initial conditions for women. Demographics and initial conditions together explain less than 10% of the variance, with somewhat larger demographic effects in Baltic and Eastern European countries, plausibly due to emigration-driven changes in age composition.

Q2: For male workers, which specific transition probability dominates the cross-country employment variance, and how does this vary by age and across country groupings?

A: EU (employment-to-unemployment) transitions account for approximately 51% of the cross-country variance in aggregate male employment (ages 16–65) across all 32 countries, rising to 77% in the five largest economies, and to 89% for prime-age males (ages 25–54) in the same group. By contrast, UE (job-finding from unemployment) explains at most 29% across all 32 countries and virtually nothing in the five largest economies. For prime-age men, EU remains dominant throughout; toward the end of the working life, EN (employment-to-nonparticipation) transitions become the main driver as workers move into retirement.

Q3: For female workers, what is the primary driver of cross-country employment variance, and does the pattern differ from men?

A: For women, transitions from nonparticipation to employment (NE) explain 65% of the cross-country variance in female employment across all ages in the 32-country sample. This dominance is more concentrated at ages 20–30, when participation entry is particularly heterogeneous across countries, likely reflecting fertility and child-rearing patterns. The sum of NE and EN contributions for women equals or exceeds the combined UE and EU contributions in both country groupings, demonstrating a fundamentally different demographic structure of employment differences for women relative to men.

Q4: How does the model generate life-cycle variation in transition rates despite having age-independent primitives?

A: The model produces age-varying transition rates through two mechanisms operating on age-independent fundamentals. First, variable search intensity declines as workers age because the remaining time to retirement shortens, reducing the expected lifetime returns to job search — the “horizon effect” (Cheron et al. [2011, 2013]). This mechanism explains virtually all of the life-cycle variation in the NE job-finding rate and an overwhelmingly large share of the variation in the UE rate, as shown by counterfactual exercises that fix search intensity at its life-cycle average. Second, information frictions about permanent match quality generate declining separation rates over the working life: young workers disproportionately hold matches with unrevealed quality and thus face higher reallocation risk upon quality revelation; as workers age, their employment share shifts toward matches with revealed quality, which have lower separation rates due to sorting.

Q5: What does the structural decomposition (Table 7) reveal about the role of technology vs. policies in explaining cross-country employment differences?

A: The variance decomposition in Table 7 shows that technology parameters (permanent match-quality distribution, job-separation risk delta, and match-quality revelation probability alpha) account for a variance contribution of 0.65 (against total employment variance of 0.36), over-explaining the cross-country dispersion. Labor market policies (UI benefits, firing costs, taxes) have a near-zero variance contribution of -0.04. Search parameters contribute -0.25. The result that policies explain little does not mean they have no level effect: in simple comparative statics, the model predicts that more generous UI and higher labor taxes lower employment. However, in the cross-country calibration, countries with higher employment rates tend to have more interventionist policies, so the cross-country correlation between policies and technology masks individual policy effects at the variance level.

Q6: How do technology effects propagate to employment differences through worker flows, and why is the inflow channel dominant?

A: Table 8 decomposes employment elasticities with respect to delta (job-separation risk), mu_x (mean log permanent match quality), and tau_ss (social security tax rate) into contributions from (i) the NE job-finding rate, (ii) the share of nonemployed in the labor force (labor force attachment, u-tilde), (iii) the differential between UE and NE rates, and (iv) the employment outflow rate (pEO). At the aggregate level, the separation risk delta has an employment elasticity of -0.28, of which the outflow contribution (dpEO = -0.08) is smaller in absolute magnitude than the sum of inflow contributions (dpNE = -0.06, du-tilde = -0.07, dpDelta = -0.06). Mean match quality mu_x has an employment elasticity of 0.53, primarily mediated through inflows. The mechanism is that changes in delta or mu_x alter expected lifetime earnings, which in turn change search incentives and participation decisions, generating correlated movements in job-finding rates and labor force attachment that amplify the employment impact beyond what a simple outflow change would imply.

Q7: Why do women and youth show larger search-effort responses to technology variations?

A: For women, the calibrated non-work utility yo is higher in all five countries than for men (interpreting this as extra costs and wedges on the returns to working), which implies a smaller employment surplus. A smaller surplus generates a higher elasticity of surplus with respect to parameter changes, and since search intensity and participation decisions depend on expected surplus, women exhibit larger employment elasticities to technology variations. The aggregate employment elasticity of delta is -0.39 for women vs. -0.19 for men; for mu_x, it is 0.78 for women vs. 0.33 for men. For youth (ages 20–29), the long remaining horizon amplifies the effect of technology changes on discounted expected lifetime earnings, which in turn amplifies participation incentives: the labor force attachment channel (du-tilde) contributes -0.13 for youth compared to -0.07 at the aggregate, while dE = -0.31 for youth vs. -0.28 aggregate for delta.

Q8: What is the quantitative role of individual technology sub-components (match quality, job-separation risk, information frictions)?

A: Panel B of Table 7 breaks down technology into three sub-components. Match quality (mean mu_x and variance sigma^2_x) and job-separation risk (delta) are the key drivers; the match-quality revelation probability (alpha, “match revelation”) plays almost no independent role (variance contribution approximately 0.00). For France, the primary positive technology contributor is mean match quality (consistent with France’s labor productivity slightly above the German benchmark). For Germany and the U.K., the low job-separation risk is the primary positive contributor. For Spain, the high job-separation risk — calibrated to match Spain’s employment outflow rate of around 4–5% per quarter versus 2% in France — is the main negative contributor, reflecting the widespread prevalence of temporary contracts.

Q9: What role do labor market policies play at the country-specific level, even though they explain little cross-country variance?

A: Panel C of Table 7 shows that employment protection legislation plays almost no role for any country. Labor taxes are quantitatively important: they explain the relatively high employment rate in the U.K. (the country with the lowest social security contribution rate, about 20%), contributing positively. In France, where labor taxes exceed 50% of the average wage, the policy contribution is strongly negative, roughly offsetting the large positive technology contribution. UI benefits lower aggregate employment — Italy, with calibrated UI benefits lower than France’s, has a smaller employment gap vis-a-vis the benchmark partly because of this. The finding that policies explain little variance while having large individual-country effects is explained by the negative cross-country correlation: countries with generous policies also tend to have favorable technology, so policy and technology contributions partially offset each other in the variance decomposition.

Q10: How does the model fit untargeted moments, particularly the empirical Shapley-Owen variance decomposition?

A: The model is calibrated to aggregate transition rates by gender, and to moments describing labor productivity, vacancy rates, and policy targets. Despite having age-independent primitives, the calibrated model captures the empirical life-cycle profiles of transition rates as untargeted moments: declining NE and UE rates with age, rising EN rates near retirement, and the hump-shaped patterns. More stringently, the model replicates the empirical Shapley-Owen variance decomposition: it correctly predicts that EU separations account for most of the employment variance for men, and that NE inflows are relatively more important for women and youth. A notable limitation is that the model overshoots the UN (unemployment-to-nonparticipation) transition rate for a significant share of data points — but the authors note that flows between U and N play almost no role in cross-country employment variance.

Q11: What is the “horizon effect” and how does it operate in this model?

A: The horizon effect, coined by Cheron et al. [2011, 2013] in a two-state (E/U) DMP model, refers to the phenomenon that as workers approach retirement, the expected returns to job search fall because the remaining period of employment is shorter. This reduces search intensity from both unemployment and nonparticipation, lowering job-finding rates, and in the present model also affects the match-acceptance probability: workers near retirement find it optimal to remain in unemployment to collect UI benefits rather than accept a job offer, further reducing the UE rate. The current paper generalizes this effect to a three-state setting by incorporating the labor force participation margin alongside search intensity, generating plausible declining job-finding rates and increasing EN rates at older ages from age-independent parameters.

Q12: How does the paper handle the gender dimension in the model calibration?

A: The model assumes that men and women share the same production and matching technology parameters within a country (A, cv, delta, alpha, mu_x, sigma^2_x, sigma^2_z), but allows the search-cost and non-work-utility parameters (ceu, cnu, cu, kappa_u, kappa_n, yo) to differ by gender. The gender-specific search parameters are identified from the gender-specific transition rates: for example, kappa_u (marginal search cost in unemployment) for women is inferred from the female UE transition rate, relative to the normalization for men. The non-work utility yo is consistently higher for women in all five countries, rationalizing lower female employment through a lower employment surplus. This generates a higher surplus elasticity for women, which in turn explains why women’s employment is more responsive to technology variations across countries.

Key Concepts

Shapley-Owen Decomposition. A method from cooperative game theory (Shapley [1953], Owen [1977]) used here to decompose cross-country differences in employment into contributions of individual worker-flow transition rates (or structural parameters). It computes the marginal contribution of each component averaged over all 6! = 720 orderings of the six transition rates, yielding a unique, symmetric, exact decomposition that sums to the total employment gap. Unlike sequential decompositions, it is path-independent.

Extensive Margin of Search Effort. The binary labor force participation decision: whether a nonemployed worker enters the unemployment state (and thus accesses the superior search technology at a flow cost) or remains in nonparticipation. In the paper’s model, this is captured as a discrete choice between states U and N, governed by i.i.d. extreme-value utility shocks, yielding a closed-form logit participation probability.

Intensive Margin of Search Effort. The continuous choice of search intensity s in [0,1] by nonemployed workers (both unemployed and nonparticipants), which scales the probability of meeting a vacancy per period. The optimal intensity equates the marginal cost of search (convex in s) to the marginal benefit (the expected surplus from meeting a firm times the contact rate). Search intensity declines with age because the remaining working life shortens, reducing the discounted value of a job.

Permanent Match Quality (x). A time-invariant, match-specific productivity component drawn from a log-normal distribution upon meeting a firm, but initially unobserved by both worker and firm (an experience good). With per-period probability alpha, the quality is revealed; prior to revelation, the parties form expectations over the distribution. Revelation triggers reallocation of bad matches, generating a negative relation between job tenure and separation probability (following Jovanovic [1979]).

Horizon Effect. The mechanism by which workers reduce search effort as they approach retirement because the expected present value of future employment spells shortens. In this paper the concept, coined by Cheron et al. [2011, 2013] in a two-state DMP setting, is extended to include the labor force participation margin: near-retirement workers not only search less intensively but also become more likely to choose nonparticipation (or to remain unemployed to collect benefits rather than accept a job), generating the observed life-cycle decline in job-finding rates from age-independent parameters.

Technology Parameters (theta). In the paper’s structural decomposition, “technology” refers specifically to the vector (mu_x, sigma^2_x, alpha, delta) — the mean and variance of log permanent match quality, the match-quality revelation probability, and the exogenous job-destruction probability. These are contrasted with search-cost parameters (phi) and policy parameters (psi). The label “technology” is acknowledged to potentially also capture employment protection and quit motives not explicitly modeled.

Life-Cycle DMP Model. A finite-horizon version of the Diamond-Mortensen-Pissarides search-and-matching framework in which workers live for J periods, all primitives are age-independent, and life-cycle variation in worker flows arises endogenously from the interaction of the finite horizon with search intensity, labor force participation, and match-learning mechanisms. The model distinguishes three labor market states (E, U, N) and uses Nash bargaining to split the employment surplus.

The Geography of job creation and job destruction

Mon, 01 Jan 0001 00:00:00 +0000

This paper asks why unemployment rates differ so persistently across local labor markets, and what role job creation and job destruction play in generating those differences. The authors document a comprehensive set of spatial labor market facts using administrative and survey microdata from Germany, the United States, and the United Kingdom, then build and calibrate a quantitative theoretical framework that accounts for all documented regularities.

Data and scope. For Germany, the authors use administrative data from the German employment office (universe of vacancies and unemployed, 1999–2020) and the IAB social security sample (SIAB, 2% of all workers, 2000–2017) aggregated to 194 commuting zones. For the U.S., they use BLS Local Area Unemployment Statistics (2000–2019) at commuting zones, CPS worker flows at metropolitan areas, and JOLTS vacancy data for the 18 largest MSAs (covering roughly 40% of the U.S. labor force). For the UK, they use Nomis data and Jobcentre Plus vacancy records (2004–2006) for 378 Local Authority Districts.

Empirical findings. Spatial unemployment rate differences are large and highly persistent. In Germany, the correlation of local unemployment rates across commuting zones over a 19-year span is 0.84 (West) and 0.77 (East). In the U.S., the correlation between 2000 and 2019 unemployment rates is 0.81; in the UK it is 0.76. In all three countries, local labor markets with lower unemployment are tighter (more vacancies per unemployed worker) and less productive. Firms in low-unemployment markets fill vacancies more slowly — in Germany, vacancy duration ranges from approximately 35 days in high-unemployment locations to approximately 65 days in low-unemployment locations, roughly an 85% difference.

A formal steady-state decomposition reveals that across all three countries, differences in job-separation rates account for approximately two-thirds of the cross-sectional variation in unemployment rates, while differences in job-finding rates account for roughly one-third. Specifically: Germany 62.4% separations / 33.2% job-finding; U.S. 72.0% / 32.8%; UK 64.3% / 35.8%. This primacy of separation rates in the cross-section stands in stark contrast to business-cycle dynamics, where job-finding rates account for 50–60% of unemployment fluctuations (Fujita and Ramey, 2009).

Theory. The authors embed a Diamond-Mortensen-Pissarides (DMP) model with endogenous separations — following Den Haan, Ramey, and Watson (2000) — into a Rosen-Roback spatial equilibrium framework. Locations differ in exogenous productivity; workers and firms are freely mobile; cost-of-living differences sustain the spatial equilibrium. The model is calibrated to the U.S. median-unemployment labor market (separation rate 0.0128, job-finding rate 0.2368, vacancy-filling rate 0.7365) plus the productivity differential between the 5th and 95th percentile unemployment locations (4.8% higher and 3.0% lower productivity than median, respectively). The baseline model, imposing the Hosios condition, matches the spatial patterns of separation rates, job-finding rates, tightness, vacancy duration, wages, and cost of living without targeting most of these. The decomposition in the calibrated baseline model attributes 33.5% of spatial unemployment variation to job-finding rates, compared to 32.8% in the data.

The baseline model generates a counterfactual upward-sloping Beveridge curve and cannot explain why job-finding rates dominate business-cycle fluctuations. Introducing on-the-job search (with 12% of employed workers searching each period, calibrated from Faberman et al., 2017) resolves both problems. In the extended model, job-to-job transition rates are virtually constant across local labor markets (matching the data) but strongly procyclical over the business cycle. This asymmetry amplifies the response of vacancies and job-finding rates to aggregate productivity shocks while muting the cyclical variation in separation rates. The extended model’s business-cycle decomposition attributes 54.4% of unemployment volatility to job-finding rates, within the empirical 50–60% range.

Policy implications. Under the Hosios condition, the decentralized equilibrium is efficient — large spatial differences in unemployment, tightness, and wages are efficient outcomes, not signs of mismatch. The relevant policy benchmark is not deviation of tightness from the national average but deviation from the model’s location-specific prediction conditional on local productivity.

Q: What is the central empirical puzzle the paper addresses? A: Spatial unemployment differences are large and persistent — in Germany, unemployment rates ranged from 1.9% to 11.9% across commuting zones even after 15 years of decline. These differences are not well understood theoretically, and the crucial missing empirical piece was data on job creation and vacancy filling across locations, which this paper provides for three countries.

Q: How large and persistent are cross-sectional unemployment differences in each country? A: In Germany, commuting-zone unemployment ranged from 3.6% to 24.0% in 2000 and persisted with a 19-year correlation of 0.84 (West) and 0.77 (East). In the U.S., the 2000–2019 correlation is 0.81, with unemployment as low as 1.5% and as high as 16.9% in 2000. In the UK, the 2004–2018 correlation is 0.76, with 2004 unemployment ranging from 1.8% to 13.1%.

Q: What do the data show about the relationship between unemployment and labor market tightness across locations? A: In all three countries, lower-unemployment labor markets are tighter — they have more vacancies per unemployed worker. This is documented for Germany using the universe of registered vacancies, for the U.S. using JOLTS data for 18 large MSAs, and for the UK using Jobcentre Plus administrative data. The relationship holds after controlling for local labor market composition (age, gender, education, occupation, industry shares).

Q: What do vacancy-filling rates look like across locations, and how large are the differences? A: Vacancy-filling rates are lower in low-unemployment (tight) labor markets. In Germany, the monthly probability of filling a vacancy is approximately 50% higher in high-unemployment markets than in low-unemployment markets. Completed vacancy duration ranges from about 35 days in high-unemployment locations to about 65 days in low-unemployment locations — a difference of approximately 85%. The UK data show a strikingly similar elasticity of vacancy-filling rates with respect to unemployment rates to Germany.

Q: What does the formal decomposition reveal about the sources of spatial unemployment differences? A: In a steady-state two-state decomposition, separation rates account for 62.4% (Germany), 72.0% (U.S.), and 64.3% (UK) of cross-sectional unemployment variation, while job-finding rates account for 33.2%, 32.8%, and 35.8%, respectively, with small residuals. This consistently assigns primary importance to separation rates across all three countries.

Q: Why is the primacy of separation rates in the cross section surprising, and what literature does it contrast with? A: The business-cycle literature (Fujita and Ramey, 2009; Shimer, 2012) finds that job-finding rate variation accounts for 50–60% of unemployment fluctuations over the cycle, roughly twice the contribution of separation rates. The spatial pattern is the mirror image: separations dominate. Any credible theory of spatial unemployment must rationalize both patterns simultaneously — a challenge the paper explicitly takes up.

Q: How does the baseline DMP model with endogenous separations generate the spatial patterns? A: Higher-productivity locations feature higher match surpluses. Higher surplus induces more vacancy creation and tighter markets, raising job-finding rates and lowering vacancy-filling rates. Crucially, a higher surplus means idiosyncratic shocks must be more negative to make the joint surplus negative, so fewer matches dissolve — separation rates are lower. The calibrated model reproduces the 32.8% job-finding / ~67% separation decomposition without targeting it (model yields 33.5% job-finding).

Q: What are the calibration targets and key parameter values in the baseline model? A: The model is calibrated monthly to the U.S. economy. Median-unemployment-location targets: separation rate 0.0128, job-finding rate 0.2368, vacancy-filling rate 0.7365. Productivity targets: the 5th-percentile-unemployment location is 4.8% more productive than median, and the 95th-percentile-unemployment location is 3.0% less productive. Key calibrated values include matching elasticity alpha = 0.4711 (equal to worker bargaining power under Hosios), matching efficiency m = 0.4371, vacancy posting cost kappa = 0.3070, and flow nonmarket value z = 0.9072.

Q: What are the two shortcomings of the baseline model, and how does on-the-job search resolve them? A: The baseline model generates a counterfactual upward-sloping Beveridge curve and cannot generate the asymmetry between cross-sectional and business-cycle drivers of unemployment. Adding on-the-job search (fraction phi = 0.12 of employed workers searching, calibrated from Faberman et al., 2017) resolves both. It corrects the Beveridge curve by allowing the model to match the spatial vacancy-unemployment relationship, and it introduces procyclical job-to-job mobility that amplifies the cyclical response of job-finding rates while dampening cyclical separation rate variation.

Q: How do job-to-job transition rates differ across space versus over the business cycle, and why does this matter? A: Job-to-job rates are virtually constant across the cross-section of local labor markets (the extended model is calibrated to match this). But they are strongly procyclical — high in booms, low in recessions, about as volatile as job-finding rates over the cycle. In a boom, more employed workers search, spurring vacancy creation, which raises both vacancy-filling probability (making vacancies easier to fill) and job-finding probability for the unemployed, amplifying the cyclical job-finding rate response while muting the cyclical separation rate response.

Q: What does the extended model predict for business-cycle dynamics? A: The model with on-the-job search and aggregate productivity shocks (parameterized following Hagedorn and Manovskii, 2008) generates unemployment and vacancy rates that are an order of magnitude more volatile than productivity — matching the data. Labor market tightness is about twice as volatile as unemployment, as in the data. The Fujita-Ramey decomposition in the model attributes 54.4% of unemployment volatility to job-finding rates, which falls within the empirical range of 50–60%.

Q: What is the paper’s efficiency result and its policy implication? A: Under the Hosios condition (imposed in calibration), the decentralized equilibrium is efficient: job creation and destruction are privately efficient in each market, and free mobility of workers and firms ensures efficient spatial allocation. Therefore, large observed differences in unemployment, tightness, and wages across locations are not evidence of inefficiency. The relevant signal for policy is not deviation from the national average but deviation from the model’s location-specific prediction conditional on productivity. Locations where data deviate from model predictions are candidates for policy intervention.

Q: Do the spatial patterns survive controls for worker and firm composition? A: Yes. The authors regress labor market tightness and vacancy-filling rates on local unemployment rates and a full set of composition controls (age, gender, education, occupation, and industry shares) derived from the IAB microdata for Germany, along with year fixed effects. The relationship between local unemployment and both tightness and job-filling rates remains highly statistically and economically significant after these controls, for both Germany and the U.S.

Q: How does the model handle wages and cost of living, and does it match the data? A: Wages are determined by state-contingent generalized Nash bargaining with worker bargaining power eta. Cost-of-living differences are backed out as the values needed to sustain the spatial equilibrium (Rosen-Roback). Neither wages nor costs of living are calibration targets in the cross section, yet the model closely matches the empirically observed wage gradient across local labor markets and the negative correlation between cost of living and local unemployment (using Economic Policy Institute Family Budget Calculator data).

Labor market tightness: The ratio of vacancies posted in a local labor market to the number of unemployed workers in that market; the paper documents that tightness is systematically higher (more vacancies per unemployed worker) in lower-unemployment locations across all three countries.

Job-separation rate (EU rate): The share of employed workers who transition from employment to unemployment in a period; in the paper’s framework, this is endogenously determined by the idiosyncratic match productivity threshold below which the joint match surplus turns negative, and it is the primary driver of spatial unemployment differences (accounting for roughly two-thirds of cross-sectional variation).

Job-finding rate (UE rate): The share of unemployed workers who transition from unemployment to employment in a period; in the paper’s framework, this is higher in tighter (lower-unemployment) markets, but accounts for only roughly one-third of spatial unemployment variation — the opposite of its dominant role in business-cycle fluctuations.

Spatial Beveridge curve: The cross-sectional relationship between vacancy rates and unemployment rates across local labor markets; in the data it is downward sloping (low-unemployment locations have both high vacancies and low unemployment), which the baseline model fails to capture but the extended model with on-the-job search reproduces.

Endogenous separation threshold: The location-specific minimum idiosyncratic match productivity below which the joint match surplus becomes negative and the worker-firm pair dissolves; this threshold is lower (tolerates a wider range of idiosyncratic shocks) in higher-productivity locations because the average surplus is larger, generating lower separation rates in more productive locations.

Spatial equilibrium (Rosen-Roback): The equilibrium condition in which differences in local costs of living adjust to make workers and firms indifferent across locations, sustaining persistent productivity-driven differences in wages and unemployment as equilibrium outcomes rather than disequilibrium phenomena.

Procyclical on-the-job search: The mechanism by which the fraction of employed workers actively searching — and thus the rate of job-to-job transitions — is approximately constant across the cross-section of local labor markets but strongly procyclical over the business cycle. This asymmetry is the key to reconciling why job-finding rates drive business-cycle unemployment variation while separation rates drive spatial unemployment variation.

Hosios condition: The parametric restriction equating the unemployment elasticity of the matching function (alpha) and the workers’ Nash bargaining weight (eta); when satisfied, job creation is efficient in every local labor market. The paper imposes this condition deliberately to demonstrate that the decentralized equilibrium is efficient despite large spatial differences in outcomes.

Unemployment Insurance, Starting Salaries, and Jobs

Mon, 01 Jan 0001 00:00:00 +0000

Seven U.S. states permanently cut unemployment insurance (UI) benefits by 30–64 percent between 2011 and 2014, providing the study’s quasi-experimental variation. North Carolina enacted the largest reform: maximum duration fell from 26 weeks to 12–20 weeks and maximum weekly benefits fell from $535 to $350, an average total reduction of 64 percent. Six “moderate reform” states (FL, GA, KS, MI, MO, SC) cut duration only, by an average of 30 percent (26→18 weeks). Using a multi-state firm identification strategy — comparing establishments of the same firm operating in reform states against the same firm’s establishments in non-reform states, with establishment and firm×year fixed effects — the paper estimates causal effects of UI cuts on employment (EEOC, 946K–1.4M establishment-years), starting salaries (Glassdoor, 500K–942K person-years), and posted wages (Burning Glass Technologies, 709K–1.18M establishment-job-quarters). The main results: NC establishments gain +1.3% employment on average relative to same-firm establishments in other states (ATT), reaching +2.1% by year 2; moderate reform states gain +0.8% (ATT). Starting salaries of new hires fall −5.5% in NC and −1.2% in moderate states. Posted wages for the same job within the same firm fall −3.5% in NC and −3.2% in moderate states. The negative co-movement of employment and wages identifies a labor supply shock: workers lower reservation wages in response to reduced outside options; firms take advantage by hiring more at lower wages. Labor demand elasticity: −0.36 (SE 0.21) for NC, −0.42 (SE 0.18) for moderate states. The larger effects in NC relative to moderate reform states are consistent with the larger total benefit reduction; effects are robust to controlling for concurrent right-to-work laws, minimum wage changes, Medicaid expansions, and corporate/personal tax reforms. The paper concludes that large, permanent UI reductions can raise employment but at the cost of lower starting wages.

Summary of a forthcoming paper, AI-assisted and human-reviewed. See the linked original for the authoritative claims and full conditions.

In depth

Q1. How does the multi-state firm design separate UI effects from aggregate and local shocks?

The key innovation is including firm×year fixed effects alongside establishment fixed effects: within any given firm and year, the only remaining variation is which state the establishment is in — absorbing all firm-wide demand trends, management strategies, and capital-allocation decisions that would otherwise confound cross-state comparisons. Standard difference-in-differences compares reform states to non-reform states at the level of geographic unit or industry; this approach confounds UI changes with the economic conditions that prompted them. The multi-state firm design eliminates this confound because firms’ nationwide operational decisions are held constant. The identification concern is policy endogeneity — whether reform states had weaker economies motivating both the UI cuts and slow hiring. This is addressed in three ways: (1) the 27 other states whose UI trust funds became insolvent in the early 2010s did NOT cut benefits, ruling out insolvency per se as the trigger; (2) restricting the control group to only the insolvent states (Table 3 cols 2 and 5) leaves estimates nearly unchanged; (3) restricting further to insolvent states that experienced a Great Recession unemployment shock within ±2 percentage points of the reform states (Table 3 cols 3 and 6) again leaves estimates unchanged, ruling out mean reversion. The mean reversion hypothesis is additionally ruled out by the wage results: mean reversion predicts faster wage growth in reform states, but wages fall.

Q2. What are the quantitative employment effects, and how do they compare across specifications?

In the baseline specification (Table 3, column 1), NC establishments gain +1.26% employment on average over the post-reform period (ATT, SE 0.0052, p<0.05), with the effect growing from +1.2% in year 1 to +2.1% in year 2 (both p<0.01); moderate reform states gain +0.83% (ATT, SE 0.0022, p<0.01), reaching +1.5% by year 2. Alternative specifications (Table 5) using less-saturated fixed effects (firm+state+year FEs or establishment+year FEs only) produce estimates roughly twice as large — +2.5% for NC — confirming that firm×year fixed effects absorb a substantial share of cross-state employment variation that is not attributable to UI. This amplification underscores why controlling for firm-level trends matters: firms simultaneously expanding in many states would appear in the unconditioned data as UI-reform effects. Robustness to policy confounders (Table 4): excluding states with RTW law changes, minimum wage changes, Medicaid expansions, major corporate or personal tax reforms all leave ATTs statistically significant and economically similar (0.80%–1.25% for NC; 0.82%–1.18% for moderate states). A Fisher exact test places NC’s t-statistic in the top 2/42 (4.8%) of placebo assignments, consistent with a one-sided 5% test. Controlling for NC’s concurrent corporate tax cut, which bounds the maximum tax-driven employment effect at 0.76pp (Giroud and Rauh 2019), implies the UI reform accounts for between 0.5% and 1.26% of NC’s employment increase — broadly consistent with the 0.83% moderate reform estimate.

Q3. What do the wage results show, and how do posted wages rule out compositional explanations?

Table 7 (Glassdoor starting salaries, job and firm×year FEs): NC ATT = −5.5% (SE 0.021, p<0.01), moderate states ATT = −1.2% (SE 0.0051, p<0.05); the effect is concentrated in jobs with starting salaries at or below $100,000, where UI replacement rates are meaningfully binding, and is statistically insignificant for higher-wage jobs. Starting salary declines could in principle reflect worker composition (lower-skilled workers drawn into the labor force) or worse job matches (workers accepting jobs below their productivity) rather than firms lowering offer wages. Burning Glass Technologies (BGT) posted wages, which measure the wage advertised for the same job within the same firm over time (establishment-job and firm×year FEs), rule out both channels: Table 8 shows NC posted wage ATT = −3.5% (SE 0.013, p<0.01) and moderate states = −3.2% (SE 0.0071, p<0.01). The near-equality of posted and realized wage effects implies the wage decline is driven by firms lowering their wage offers — not by changes in worker composition or match quality. Occupational heterogeneity confirms the mechanism: high-exposure occupations (above-median fraction of workers with unemployment spells or employment tenures exceeding 20 weeks) exhibit NC posted wages −3.5% and moderate states −4.1%; low-exposure occupations show near-zero insignificant effects (Table 9). Posted wages also provide additional evidence against mean reversion: if reform states had faster-growing underlying wages, posted wages would rise relative to controls, but the opposite occurs.

Q4. How does the negative co-movement of employment and wages identify a labor supply shock and discipline the theoretical mechanism?

The simultaneous rise in employment (+1.26% NC, +0.83% moderate) and fall in posted wages (−3.5% NC, −3.2% moderate) is the signature of a labor supply shock under the standard Mortensen-Pissarides (1994) framework: when workers’ outside option (the value of UI) falls, their reservation wages fall, inducing firms to post more jobs at lower wages. A positive demand shock would raise both employment and wages; a positive supply shock raises employment while lowering wages. The posted wage channel further implies that firms’ labor demand responds to the wage reduction (not just to the supply expansion): if firms were passive price takers, posted wages would not change. The data imply that firms internalize workers’ changed outside options and lower their wage offers accordingly, consistent with the monopsonistic wage-setting in Mortensen-Pissarides with free entry. The labor demand elasticity calculated as (Δlog employment / Δlog posted wage) = 1.26/3.5 ≈ −0.36 (SE 0.21) for NC and 0.83/3.2 ≈ −0.26 or using preferred specification −0.42 (SE 0.18) for moderate states; these fall in the middle of the distribution of prior estimates from cross-country labor demand elasticity studies (Hamermesh 1996; Acemoglu et al. 2004). A Chodorow-Reich et al. (2019) decomposition suggests that if labor market tightness increased (fewer unemployed and more vacancies), the reservation wage (opportunity cost) effect dominates the tightness effect — since we observe posted wages falling.

Q5. What do the CPS results add, and how do employment duration effects inform the mechanism?

Using individual-level CPS data with state and year fixed effects (no within-firm comparison), combining all reform states: employment probability +1.0pp (SE 0.43pp, a 1.5% increase relative to the 65% baseline) [Table 10 col 1]; new-hire wages (tenure <1yr) −6.3% [col 2]; unemployment duration −2.8 weeks/year ATT (relative to 33.48-week control mean, an 8% reduction) [col 3]. The CPS results are qualitatively consistent with the multi-state firm findings and use an entirely different data source, sampling frame, and identification approach. The unemployment duration effects are instructive about timing and mechanism: the ATT is negligible in the first two post-reform years (−1.0 and −1.2 weeks, insignificant), rises to −1.7 weeks in year 3, −3.6 in year 4, −4.2 in year 5, and −5.6 in year 6 — consistent with gradual stock-flow dynamics (the stock of workers who began unemployment before the reform exhausts gradually, so average duration in the reform states drifts lower over time as a larger share of the unemployed pool faces the new rules). This pattern helps interpret the gradual employment growth in the event studies.

Q6. How does the paper explain divergence from prior literature finding small UI effects?

The paper argues that prior work finds small effects because reforms studied were smaller in size, temporary, and enacted during deep recessions — all conditions where the job creation channel from lower reservation wages is muted. Schmieder et al. (2010), Rothstein (2011), Farber-Valletta (2015), Chodorow-Reich et al. (2019) and others study UI extensions/expirations that are often 13–20% changes in duration (versus NC’s 44% duration cut and 64% total benefit cut), enacted during high unemployment (when moral hazard is lower) or temporary (so workers discount the change in outside options). A 13-week contrast off a high base of 83 weeks (the EUC expansions) differs fundamentally in moral hazard intensity from an 11.5-week cut off a low base of 26 weeks plus a benefit level reduction — the effective present value of UI falls far more in the NC reform. Additionally, the border county-pair design used in much prior work (Chodorow-Reich et al. 2019, Hagedorn et al. 2025) compares establishments on opposite sides of a state border within the same labor market; these competing establishments cannot fully exploit lower reservation wages because they compete for the same workers — suppressing both the employment and wage responses. Notable exceptions that do find sizable effects — Johnston-Mas (2018) and Karahan et al. (2025), both studying large permanent post-recession reforms — corroborate this paper’s findings.

Key concepts

multi-state firm design : the identification strategy that compares establishments of the same firm operating in reform states against the same firm’s establishments in non-reform states; with establishment and firm×year fixed effects, this absorbs firm-wide demand trends, product market shocks, and management decisions that affect all of a firm’s establishments equally, isolating state-level UI variation as the sole source of identification.

reservation wage : the minimum wage at which an unemployed worker is willing to accept a job offer, determined by the outside option value (UI benefits plus expected future wages from continued search); UI cuts reduce the outside option value, lowering the reservation wage and enabling firms to post and fill vacancies at lower wages.

posted wage : the wage listed in a job advertisement before any worker-firm negotiation or match quality sorting; measured here using Burning Glass Technologies (BGT) data at the establishment-job level, controlling for the same job across time within the same firm; distinct from realized starting salary in that it reflects the firm’s wage-setting decision independent of which worker accepts.

labor supply shock : an exogenous change in the willingness of workers to supply labor at given wages; identified here by the negative co-movement of employment (up 1.3–0.8%) and wages (down 3.5–3.2%), which is the opposite of what a positive labor demand shock would predict, ruling out confounding from corporate tax cuts or mean-reverting demand.

outside option : the payoff available to an unemployed worker from continued search rather than immediate job acceptance; UI benefits are the dominant component; when UI generosity falls, the outside option value falls and firms can hire more workers at lower wages — the core mechanism linking permanent UI cuts to simultaneous employment gains and wage reductions.