Corrigendum to "Job Ladders by Firm Wage and Productivity" [Review of Economic Dynamics 58C (2025) 101307]

Layer 1: Overview

Research question and motivation. On-the-job search models typically organize firms along a “job ladder” — a common ranking by workers of available jobs — but they disagree on whether the rung is best captured by a firm’s average wage or its productivity, and empirical guidance has been scarce. Bertheau and Vejlin ask: (i) Is average wage or productivity the better empirical measure of a firm’s location on the job ladder? (ii) How does job creation across these ladders vary in the cross-section and over the business cycle? (iii) Do recessions slow reallocation into better firms (a “sullying” effect) or speed it up (a “cleansing” effect)? This matters for models of aggregate labor-market fluctuations and any imperfect-labor-market model that assumes some jobs are more desirable than others.

Data and strategy. The authors build matched employer-employee data from Danish administrative registers covering all employment relationships at DAILY frequency from 1992 to 2013, merged with firm financial-accounting data (sales, value added, capital stock, FTE employment, workforce composition). The sample is restricted to manufacturing, services, and trade (industries present from 1992); aggregate unemployment ranges from 3% to 10% over the period, spanning several recessions. Daily timing removes the time-aggregation bias of quarterly data (Bertheau and Vejlin 2022 show quarterly data overstate the EE transition rate by ~30%). Firms are ranked within industry-year cells by (a) residualized average hourly wage and (b) total factor productivity (TFP) estimated via the Olley-Pakes (1996) control-function approach (investment data available from 1999). Following Haltiwanger et al. (2018b), “low” firms are the bottom employment-weighted quintile and “high” firms the top two quintiles. Net employment change is decomposed into a net poaching (employer-to-employer/EE) channel and a net nonemployment channel; EE transitions are direct moves with under seven days of nonemployment. Taber and Vejlin (2020) find 80% of EE transitions are voluntary, so poaching flows reveal worker preferences. Cyclical indicators are the change in the unemployment rate (first difference) and the level (HP-filtered deviation from trend).

Main findings (magnitudes). (1) Productivity is the better job-ladder measure. Residualized wage and TFP are only weakly correlated (Spearman 0.32). Cross-sectionally, the high-vs-low gap in net job creation is far larger for TFP (0.52% vs -0.39%) than for wages (0.26% vs 0.22%), and the net-poaching differential is larger for productivity (0.75%) than wages (0.61%), since workers move up the productivity ladder faster than the wage ladder. (2) Cyclicality differs by ladder. A one-percentage-point rise in the CHANGE in unemployment raises the high-low differential job-creation rate by 0.30 pp for TFP — about 32% of the average TFP differential — driven entirely by the nonemployment channel (0.38 pp), while the poaching channel pulls the opposite way (-0.08 pp). This is a cleansing effect: low-productivity firms both fire more workers to nonemployment AND stop hiring from nonemployment in recessions. For the WAGE ladder the total differential instead contracts by 0.08 pp, because high-wage firms stop poaching (-0.21 pp) — the wage ladder breaks down (a sullying effect). (3) Measurement matters. Using sales per worker instead of TFP yields 0.12 pp on the change-in-unemployment indicator (~40% smaller than TFP’s 0.30), and with the LEVEL of unemployment the sign flips: TFP gives +0.11 pp but sales per worker gives -0.08 pp — matching Haltiwanger et al. (2021) on US LEHD data, implying their result reflects sales-per-worker proxying, not a US-Denmark difference.

Implications. Productivity (not the spot wage) is what workers climb toward, consistent with sequential-auction/outside-option models (Postel-Vinay and Robin 2002). Business-cycle labor models need endogenous hiring rates, since firms shut down hiring rather than only firing in recessions.

Layer 2: Deep Dive

What is the empirical strategy for ranking firms, and what are the main threats to it?

Firms are ranked within 2-digit NACE industry-year cells (68 industries) on two dimensions: (a) residualized average hourly wage (regressing firm average wage on workforce tenure, education, age, gender, plus year FE) and (b) TFP from an Olley-Pakes (1996) control-function production function using value added, capital stock, FTE employment, and workforce composition, estimated separately by industry. Quintiles are employment-weighted, so results are interpreted as effects on the average worker. To avoid reclassification bias, firms are ranked on year t-1 measures for flows in year t. Threats: (i) Olley-Pakes uses investment as the productivity proxy but investment data exist only from 1999, so coefficients are estimated post-1999 and back-applied, assuming production technology did not change materially over 1992-2013 — an explicit assumption. (ii) They cannot use Ackerberg-Caves-Frazer (2015) or Levinsohn-Petrin (2003) because detailed intermediate-input data are missing for most firms/years. (iii) AKM firm fixed effects are avoided because the large share of small firms induces limited-mobility bias; residualized average wages are used instead (Haltiwanger et al. 2021 find no difference between AKM FE and average wages). Results are robust to an unresidualized wage measure.

What are the two channels and how are they distinguished empirically?

Net job creation is decomposed as Net Job Creation = Net Poaching (EE hires minus EE separations) + Net Nonemployment (hires from minus separations to nonemployment). EE/poaching transitions are direct employer changes with fewer than seven days of nonemployment between jobs (threshold varied, results similar). Poaching flows are treated as primarily voluntary (80% per Taber and Vejlin 2020), so they reveal the job ladder; nonemployment flows capture involuntary separations and hiring from the jobless pool. The daily data are essential to cleanly separate EE moves from moves through a nonemployment spell.

What heterogeneity across firm types and channels is documented?

Cross-section: high-wage firms grow mainly via net poaching (0.21%) plus a little net nonemployment (0.06%); low-wage firms LOSE workers to poaching (-0.40%) but GAIN strongly via nonemployment (0.62%), so they still grow (0.22%). Low-productivity firms also lose via poaching (-0.47%) but, unlike low-wage firms, grow only marginally via nonemployment (0.08%), so they shrink overall (-0.39%). Low-type firms (both rankings) have more churn (higher hires and separations) than high-type firms. Over the cycle (Table 3, change in unemployment): when unemployment rises, low-productivity firms contract more (-1.02 pp) than high (-0.71 pp), driven by the nonemployment margin (-1.05 vs -0.67 pp) and by hiring from nonemployment rather than separations (hiring is more cyclically sensitive, consistent with Shimer 2012). High-wage firms contract more than low-wage firms; for high-wage firms separations to nonemployment rise sharply (0.26 pp vs 0.04 pp for low-wage), consistent with Mueller (2017) and Zullig (2022) that high residual-wage workers are more cyclically sensitive. Low-wage firms net-gain through poaching in recessions (0.08 pp) because poaching separations fall more than poaching hires.

What are the cyclicality regression estimates in detail?

Regressions of differential (high-minus-low) flow rates on a cyclical indicator (times 100), with seasonal dummies and a time trend, 82 quarterly observations. Change-in-unemployment, TFP: Total 0.30 pp (SE 0.10, ***), Poaching -0.08 (0.04, *), Nonemployment 0.38 (0.09, ***). Level-of-unemployment, TFP: Total 0.11 (0.05, **), Nonemployment 0.13 (0.04, ***), Poaching -0.02 (ns). Change-in-unemployment, Wage: Total -0.08 (0.06, ns), Poaching -0.21 (0.08, ***), Nonemployment 0.13 (0.06, **). Level-of-unemployment, Wage: Total -0.17 (0.03, ***), Poaching -0.15 (0.03, **), Nonemployment -0.02 (ns). The authors note that a 2-pp rise in unemployment (typical in a recession) raises the TFP differential job-creation rate by ~66% (20.30/0.91) of its mean.

How robust are the results to alternative measures and classifications?

Cross-sectional results are similar across TFP, value added per worker, and sales per worker, and across three high/low cutoffs (baseline top-2/bottom-1 quintiles; Haltiwanger 2021 top-2/bottom-3; Haltiwanger 2015 top-1/bottom-1). TFP consistently yields the largest net-poaching differential, so it is argued superior, though cross-sectional differences are minor. The key DIVERGENCE is in business-cycle estimates: sales per worker underestimates cyclicality (0.12 vs 0.30 pp on change-in-unemployment) and FLIPS sign on the level indicator (-0.08 vs +0.11 pp), a pattern confirmed across all three classifications. Value added per worker and an alternative OLS-based TFP measure both track baseline TFP closely and, crucially, do NOT produce the sign switch on the level indicator — isolating sales per worker as the outlier. Ranking on profits or employment growth (unreported) gives qualitatively similar results to TFP.

How does this paper relate to and differ from the closest prior work?

Closest empirical work is Haltiwanger et al. (2018a, 2021) on US LEHD data: 2018a concludes firm wage beats firm size as a job-ladder proxy and that high-wage firms are more cyclically sensitive; 2021 finds whether recessions cleanse depends on the cyclical indicator, using sales per worker as a productivity proxy. This paper adds direct TFP (LEHD lacks it), uses daily rather than quarterly data (removing time-aggregation bias, ~30% on EE rates), and shows the wage-ranking results replicate Haltiwanger qualitatively while TFP gives different and stronger conclusions. The wage-vs-sales sign discrepancy is shown to be a measurement artifact, not a US-Denmark institutional difference. Theoretically it is closest to Audoly (2020) and Moscarini and Postel-Vinay (2013), in which better (high-type) firms are more cyclically sensitive because they poach more in expansions when the unemployed pool is small; the paper finds support for this poaching margin using TFP but, being empirical, focuses on which firm characteristic best measures the ladder. It differs from Sorkin (2018), which identifies good firms via revealed preference but does not link them to productivity, and complements Lochner and Schulz (forthcoming) on sorting.

What are the theoretical/policy implications and their scope conditions?

Recessions speed productivity-enhancing reallocation (cleansing via the nonemployment channel) but impede progression up the wage ladder (sullying via the poaching channel). A central modeling implication: the cleansing effect is driven only PARTLY by the classical Mortensen-Pissarides (1994) channel of firing unproductive workers; equally important, low-productivity firms STOP HIRING from nonemployment in recessions. Models with exogenous arrival rates cannot fit this (more jobs should be created from nonemployment when unemployment is high); endogenous hiring decisions are needed (e.g., Lise and Robin 2017, where low aggregate states shift the vacancy distribution toward high types). Scope conditions: estimates come from Denmark’s flexicurity labor market (low firing/hiring regulation, decentralized firm-level wage bargaining, mobility closer to the US than to France/Italy — a Dane is ~2x more likely than a French/Italian worker to make a voluntary EE move, a US worker 2.5x), 1992-2013, manufacturing/services/trade only; means-tested social assistance prevents separating active from inactive nonemployment. Magnitudes are conditional on the chosen productivity measure — using sales per worker would understate or reverse the cleansing finding.

What is the nature of this record (corrigendum)?

The DOI 10.1016/j.red.2025.101320 is a corrigendum to the original RED article 101307 (2025). The full-text file provided is the underlying working paper (IZA Discussion Paper No. 15872, January 2023), itself a heavily revised version of an earlier IZA paper, ‘Employment Reallocation over the Business Cycle: Evidence from Danish Data,’ a chapter of Bertheau’s PhD dissertation. The summary reflects the substantive paper content; the corrigendum itself (corrections to the published version) is not detailed in the provided text.

Key Concepts

Job ladder: A common ranking by workers of available jobs from less to more desirable; the paper tests whether the rung is best indexed by a firm’s average wage or its TFP, treating the measure that best predicts voluntary (poaching) moves up as the true ladder.

Net poaching channel: Net employer-to-employer (EE) flows — hires poached from other firms minus separations to other firms (direct moves with under seven days of nonemployment). Treated as primarily voluntary (80% per Taber and Vejlin 2020) and thus revealing of the job ladder.

Net nonemployment channel: Net flows between a firm and the nonemployment pool — hires from nonemployment minus separations to nonemployment; not distinguished by type of nonemployment because Danish means-tested assistance prevents separating active from inactive jobseekers.

Cleansing effect: In this paper’s sense, recessions direct/retain employment in more productive firms: the high-low productivity gap in job creation WIDENS in recessions, as low-productivity firms both separate more workers to nonemployment and stop hiring from it.

Sullying effect: Workers are matched to better firms at a lower rate in bad times: the differential net POACHING rate between high and low firms shrinks in recessions, so the (especially wage) job ladder breaks down and workers get stuck in low-rung firms.

TFP (Olley-Pakes control function): Revenue-based total factor productivity estimated via the Olley-Pakes (1996) two-step method, using firm investment as a proxy for unobserved productivity; preferred over labor productivity/sales per worker because it nets out capital intensity and better predicts employment growth and net poaching.

Time-aggregation bias: The distortion in measured EE transitions when employment is observed only at low (e.g., quarterly) frequency, which conflates EE moves with moves through short nonemployment spells; daily Danish data avoid it (quarterly data overstate EE rates by ~30%, Bertheau and Vejlin 2022).