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Economics

Heterogeneous Effects of the German Minimum Wage on Working Hours and Minijobs

A retrospective quasi-experimental analysis of Germany’s 2015 national minimum wage, using the Structure of Earnings Survey across three waves to estimate effects on hours, minijobs, and wage inequality. The minijob institutional angle is a real contribution; magnitudes do not yet reconcile across sections and the identification package is asked to carry too much interpretive weight for a Labour Economics submission.

Abstract

In 2015, Germany introduced a national minimum wage. While the literature agrees on at most limited negative effects on the overall employment level, we go into detail and analyze the impact on the working hours dimension and on the subset of minijobs. Using data from the German Structure of Earnings Survey in 2010, 2014, and 2018, we find empirical evidence that the minimum wage significantly reduces inequality in hourly and monthly wages. While various theoretical mechanisms suggest a reduction in working hours, these remain unchanged on average. However, minijobbers experience a notable reduction in working hours which can be linked to the specific institutional framework. Regarding employment, the results show no effects for regular jobs, but there is a noteworthy decline in minijobs, driven by transitions to regular employment and non-employment. The transitions in non-employment imply a wage elasticity of employment of −0.1 for minijobs.

1. Introduction

The introduction of a national minimum wage in Germany on 1 January 2015 — set initially at €8.50 per hour — is one of the largest labour-market interventions in the post-reunification era. Existing studies have found at most modest aggregate employment effects, but the policy introduced an institutional setting that creates heterogeneous incentives across job types: in particular, the German minijob category (jobs paying up to €450/month, exempt from social security contributions on the worker side) creates a kink in the effective wage that interacts with a binding hourly minimum.

Workers below the threshold prior to the reform were paid an average of 26 percent below the minimum wage threshold in 2014. Minijobs made up as much as 21 percent of all jobs in 2014. In absolute terms, 104,000 minijobs vanished due to the minimum wage; we find that 54,000 minijobbers entered non-employment, while the other half was upgraded to regular employment.

2. Data

We use three waves of the German Structure of Earnings Survey (SES) — 2010, 2014, and 2018 — supplemented with the Establishment History Panel (BHP) and Integrated Employment Biographies (IEB). The SES covers establishments with at least 10 employees subject to social security (regular employees) and excludes agriculture, the public sector, apprentices, and a small set of further restricted categories. Sample sizes are large (typical analytic N in the millions of worker-year observations); the sample size of the SES varies materially between 2010 and 2014/2018 due to wave-to-wave panel-design changes.

Table 1 reports descriptive statistics. In our main SES sample of establishments with at least 10 regular employees, the minijob share is 16.4% — distinct from the 21% headline figure in the introduction, which is taken over the full German employment population. Mean nominal hourly wages are reported in current euros; for the cross-wave wage-distribution comparisons in Section 4 we deflate to 2014 €.

3. Identification strategy

We exploit county-level variation in the bite of the minimum wage. The county bite Biter​ is the share of workers in county r earning below €8.50 in 2014. The reduced-form specification regresses an outcome Yirt​ on a treatment-period interaction:

Yirt​=α+δBiter​⋅1[t=2018]+βXirt​+γr​+γt​+εirt​.

We use one pre-period (2010 → 2014) for placebo testing and inspect the implied parallel-trends pattern visually. Distributional effects on the wage are estimated via Recentered Influence Function (RIF) regressions following Firpo–Fortin–Lemieux. For the small-establishment subsample (Sec. 5.5) we use the IEB-augmented sample and identical bite-interaction specification.

4. Wage and inequality results

Table 2 reports a county-bite coefficient of 0.456 on the log hourly wage for the affected segment. If we extrapolate and compare the average hourly wage effect of 45.6 percent (for affected workers) with the average initial wage gap of affected workers of 26 percent, the implied increase exceeds the gap — consistent with spillovers above the minimum threshold.

The RIF estimates show that the lower tail of the hourly wage distribution compresses sharply between 2014 and 2018; the upper tail moves little. Monthly wage inequality (measured by the Gini and the 50/10 ratio) falls correspondingly. Figure 1 shows the real hourly wage distributions for 2014 and 2018, deflated to 2014 €; the distributional shift is visible at the new statutory minimum.

5. Employment, hours, and minijobs

Average working hours show no statistically significant response. Conditional on the minijob status, however, hours decline materially: minijobbers above the implicit hourly cap (working more than 50 hours per month at the new floor would breach the €450 monthly threshold) bunch downward.

Section 5.3 reports the institutional adjustment. About 600,000 minijobbers with hours beyond 50 per month are no longer observed in 2018. Of these, 200,000 jobs may have been downgraded to 45–49 hours. Consequently, the other 400,000 jobs must have been either terminated or upgraded to regular jobs. The implied causal minijob loss is on the order of 104,000 net positions, with 54,000 transitions into non-employment (implying a wage elasticity of employment of −0.1 for minijobs).

For regular jobs, the bite-interaction coefficient is statistically indistinguishable from zero across both panels of Table 5 (large vs small plants). Section 5.4 presents the small-plant analysis using the IEB sample and a bite-specific trend Biter​⋅Yeart​ to control for differential pre-2015 employment trends, following Ahlfeldt, Roth, and Seidel (2018) and Bossler and

References

  1. [1] D. Card and A. B. Krueger, Am. Econ. Rev. 84, 772 (1994).

  2. [2] D. Cengiz, A. Dube, A. Lindner, B. Zipperer, Q. J. Econ. 134, 1405 (2019).

  3. [3] C. Dustmann, A. Lindner, U. Schönberg, M. Umkehrer, P. vom Berge, Q. J. Econ. 137, 267 (2022).

  4. [4] M. Caliendo, A. Fedorets, M. Preuß, C. Schröder, L. Wittbrodt, Eur. Econ. Rev. 117, 36 (2019).

  5. [5] M. Bossler and H.-D. Gerner, ILR Rev. 73, 1070 (2020).

  6. [6] M. Bossler and T. Schank, J. Labor Econ. 41, 813 (2023).

  7. [7] G. M. Ahlfeldt, D. Roth, T. Seidel, J. Public Econ. 162, 1 (2018).

  8. [8] M. Biewen, B. Fitzenberger, M. Rümmele, J. Labor Econ. 41, 235 (2023).

  9. [9] B. T. Hirsch, B. E. Kaufman, T. Zelenska, ILR Rev. 70, 1124 (2017).

  10. [10] J. Manning, Monopsony in Motion (Princeton University Press, 2003).

  11. [11] A. Manning, J. Hum. Resour. 56, 3 (2021).

  12. [12] G. Burauel, M. Caliendo, M. Grabka, C. Obst, M. Preuß, C. Schröder, J. Labor Econ. 38, 1011 (2020).

  13. [13] H. Bonin et al., German Minimum Wage Commission Report (2018).

  14. [14] S. Firpo, N. M. Fortin, T. Lemieux, Econometrica 77, 953 (2009).

  15. [15] S. Athey and G. W. Imbens, Annu. Rev. Econ. 9, 685 (2017).

  16. [16] M. Bossler, N. Gerner, German Statistical Society proceedings (2019).

  17. [17] A. Garloff, IAB-Kurzbericht 14/2019.

  18. [18] B. Caliendo, F. Wittbrodt, IZA Discussion Paper No. 12200 (2019).

  19. [19] M. Bachmann, R. Bauer, IAB Forschungsbericht 4/2020.

  20. [20] H. Bachmann, J. Frings, B. Stops, J. Tauchmann, Labour Econ. 78, 102217 (2022).

Distilled from the public preprint at arXiv:2403.17206 · econ.GN — applied microeconomics

This is a Manusights review of a publicly-available preprint. The preprint authors are not affiliated with Manusights and have not endorsed this review. Reproduced for illustrative purposes; full text remains at the source.

Overall Feedback

Substantial revisions required first — magnitudes do not reconcile, ID strategy needs strengthening

Likely outcome if submitted today: desk-reject if the file ends mid-sentence in Section 5.4 as the supplied version does (Labour Economics will not review an incomplete manuscript); major revision at best if the missing back half exists but the current framing and inconsistencies remain.

The institutional-minijob angle is a real contribution to the German-minimum-wage literature, and the SES + IEB combination is the right empirical platform. The single most important fix this week is a coordinated "estimand and magnitudes reconciliation" pass — one table that reconciles every minijob quantity in the paper (total minijobs in 2014/2018, high-hours minijobs above the 50.9-hour threshold, net causal employment effect, gross descriptive bin changes, transitions to regular employment, transitions to non-employment, and the implied elasticity), with each number labeled as descriptive, reduced-form causal, transition-based, or back-of-envelope elasticity. Then rewrite the abstract, introduction, and Section 5 so each number sits inside its appropriate estimand.

Recommended target: Labour Economics remains plausible after revision; the minijob institutional contribution is real. Cascade fallback: LABOUR: Review of Labour Economics and Industrial Relations or Journal for Labour Market Research if the identification package cannot be strengthened. Time to submission readiness: 3–5 weeks if all analyses already exist; 6–8 weeks if new pre-trend / robustness work must be produced.

Detailed Feedback

  • High severity.
    #1MethodologySec. 3; Sec. 5.4

    The causal identification package is asked to carry more weight than one pre-period and county-bite variation can support

    The identification strategy rests on county-level variation in the minimum-wage bite, with a single pre-period (2010 → 2014) used as a placebo. Three problems compound: (a) one pre-period is the minimum acceptable parallel-trends evidence at top labour journals, where two or three pre-periods are now the bar; (b) the small-establishment Sec. 5.5 results are presented without explicit pre-trend evidence at all; (c) the RIF distributional estimates inherit identification from the same bite-variation source but are presented as if independently informative.

    For Labour Economics, this combination is currently asked to carry too much interpretive weight. The reviewer most likely to handle the paper (Bossler, Caliendo, or Dustmann's circle) will press on each of the three. The fix is not to abandon the bite-variation strategy — it is the right strategy — but to put bounds on its identification, e.g. by showing the 2010-2014 pre-trend explicitly for each of the main outcomes used in Sec. 5, and by reporting an event-study version with at least 2 pre-periods if the data permit.

    Suggested fix

    Add a pre-trend figure (2010 vs 2014, by bite quartile) for each main outcome — wages, hours, minijob share, regular-employment share. If a 2008 SES wave is accessible, add it as a second pre-period and present an event study. For the small-establishment subsample, replicate the same pre-trend evidence; if pre-trends are differential, downgrade those results to "suggestive" in the abstract and conclusion.

  • High severity.
    #2MethodologySec. 4; Table 2

    The 45.6% "for affected workers" interpretation conflates a regional reduced-form coefficient with an individual treatment-on-the-treated estimate

    Section 4 reports: "If we extrapolate and compare the average hourly wage effect of 45.6 percent (for affected workers) with the average initial wage gap of affected workers of 26 percent…" Table 2 reports a coefficient of 0.456 on the county-bite × post-2014 interaction. That coefficient is the effect of moving from a zero-bite county to a full-bite county on the log hourly wage of a representative worker — it is not directly an estimate of the wage gain experienced by initially-subminimum workers.

    The current language reads as if individual affected workers' wages are estimated to have risen by 45.6%. The clean interpretation is: the regional reduced-form coefficient is 0.456; if the effect is concentrated only among initially subminimum workers (who are roughly 14–18% of the workforce in the highest-bite counties), the implied per-affected-worker increase is mechanically larger than 26% and the gap reflects spillovers above the threshold. That is consistent with the data and with the literature, but it should be stated, not implied.

    Suggested fix

    Rewrite the relevant paragraph: "Scaling the regional reduced-form coefficient (0.456 in Table 2) by the affected share (≈X%) suggests that, if effects were concentrated only among initially subminimum workers, the implied increase would exceed the average initial wage gap of 26%; this is consistent with positive spillovers above the threshold, and is qualitatively in line with [Cengiz et al. 2019] and [Dustmann et al. 2022]." Add a footnote stating the affected-share figure used in the scaling.

  • High severity.
    #3MethodologyAbstract; Sec. 1; Sec. 5.3

    Magnitudes do not yet cohere: 104k vs 54k vs 600k vs 400k vs 200k minijob figures use different estimands without saying so

    The Introduction says "104,000 minijobs vanished due to the minimum wage" and "54,000 minijobbers entered non-employment, while the other half was upgraded to regular employment." Section 5.3 says "about 600,000 minijobbers with hours beyond 50 per month are no longer observed in 2018. Of these, 200,000 jobs may have been downgraded to 45–49 hours. Consequently, the other 400,000 jobs must have been either terminated or upgraded to regular jobs."

    These can all be true only if they refer to different estimands: 104k is a net causal employment effect; 600k is a descriptive gross disappearance from a high-hours bin (which includes substitution within minijobs and movement to regular jobs); 400k is a within-bin transition count; 54k is an individual-level transition into non-employment. The paper currently does not say this. A reviewer will ask: if 400,000 high-hours minijobs were terminated/upgraded, why is the causal minijob loss only 104,000 and the non-employment transition only 54,000?

    The mechanical answer is that most of the 400,000 are within-minijob hours adjustment or upgrades to regular employment, which net out in the 104,000 figure. But the prose currently leaves the reader to reconstruct that themselves, which is not a defensible posture for a Labour Economics submission.

    Suggested fix

    Add a "minijob mass-balance table" at the start of Sec. 5.3. Rows: (i) total minijobs 2014; (ii) total minijobs 2018; (iii) gross disappearance from the >50-hours bin; (iv) within-minijob downgrade to ≤50 hours; (v) upgrade to regular job; (vi) transition to non-employment; (vii) net causal effect. Each row labeled "descriptive," "transition-based," or "reduced-form causal." The 104k / 54k / 400k / 600k figures all come from rows of this table, and the reader can see where each one sits.

  • High severity.
    #6Internal consistencyEnd of Sec. 5.4

    The submitted PDF ends mid-sentence in Section 5.4 — file-integrity blocker

    The supplied text stops at: "Following the literature on employment effects of the German minimum wage, the model includes a bite-specific trend Bite_r * Year_t which controls for employment trends that were present already before the minimum wage was introduced (Ahlfeldt, Roth, and Seidel, 2018; Bossler and Ger…" The submission file is missing the rest of Sec. 5.4, all employment tables, the conclusion, references, and any appendix or supplementary material. Labour Economics will not review an incomplete manuscript.

    Suggested fix

    Verify the submission PDF compiles end-to-end. The missing material — Sec. 5.4 conclusion, tables, references, declarations — must all be present before submission. If this was a truncation in the arXiv version only, no action is needed; if it reflects the actual submission file, this is a desk-reject blocker.

  • High severity.
    #11Reporting guidelineEnd matter

    Data availability statement is missing — required by Labour Economics

    The manuscript identifies the SES, BHP, and IEB as data sources, but does not include a data availability statement. The SES is German Federal Statistical Office data with a controlled-access route through the FDZ research data centers; the BHP and IEB are administrative microdata from the IAB with similar restrictions. None of these can be released as supplementary data files, but each has a defined access procedure (FDZ remote-execution, on-site visits at IAB Nuremberg) that the data-availability statement should name explicitly.

    Suggested fix

    Add a Data Availability section: "Analysis uses three administrative datasets accessed via Germany's research-data-center system. The Structure of Earnings Survey (SES) is available via FDZ-Bund (https://www.forschungsdatenzentrum.de) under controlled-access procedures. The Establishment History Panel (BHP) and Integrated Employment Biographies (IEB) are available via the IAB-FDZ (https://fdz.iab.de) under on-site or remote-execution procedures. Replication code is available at [repository]; the underlying microdata cannot be redistributed but can be reproduced by qualified researchers under the same access procedures."

  • High severity.
    #12Reporting guidelineEnd matter

    Code availability is not stated — required for empirical economics submissions

    The study relies on survey weighting, difference-in-differences estimation, RIF distributional regressions, and combinations across multiple administrative datasets. None of this is reproducible without analysis code. The submission has no code availability statement and no software/version information. Labour Economics, like most economics journals, increasingly expects the analysis code (Stata or R scripts) deposited at a public repository with a DOI, with restricted-data fields removed or replaced with synthetic equivalents.

    Suggested fix

    Deposit analysis code on GitHub or the AEA Data and Code Repository, with a Zenodo DOI for the submitted version. Add a Code Availability statement: "Replication code is available at github.com/<repo>, archived at Zenodo doi:10.5281/zenodo.<id>. Analyses run on Stata 17 / R 4.3; full dependency list in environment.yml." This is no longer optional at top labour journals.

  • Medium severity.
    #4MethodologySec. 4 (RIF subsection)

    Distributional RIF estimates are presented as independently informative but inherit identification from the same bite-variation source

    The Recentered Influence Function (Firpo–Fortin–Lemieux) estimates of distributional effects on the wage distribution are presented in their own subsection and discussed as if they were independent evidence. They are not — RIF regressions estimated on the same SES sample with the same bite-interaction instrument inherit all the identification assumptions of the mean-difference specification. If the parallel-trends assumption is questionable for the mean, it is also questionable for the quantiles.

    The RIF results are still useful — they characterize the shape of the wage-distribution shift, which the mean estimate alone does not — but they should be framed as quantile-by-quantile reductions in conditional inequality under the same identifying assumptions, not as cross-validating evidence. Right now they are doing rhetorical work the framing does not justify.

    Suggested fix

    Add a one-paragraph framing to the RIF subsection: "The RIF estimates are identified under the same assumptions as the mean specification; they characterize the distributional shape of the policy effect rather than cross-validating it. Robustness of the parallel-trends assumption is therefore a joint robustness check across both specifications."

  • Medium severity.
    #5Novelty assessmentSec. 1

    Positioning vs Bossler-Gerner, Dustmann-Lindner, and Cengiz-Dube-Lindner-Zipperer is left implicit

    The minimum-wage literature has three loud recent contributions on the German setting: Bossler-Gerner (ILR Review 2020) on heterogeneous wage effects; Dustmann-Lindner-Schönberg-Umkehrer-vom Berge (QJE 2022) on within-firm spillovers; Caliendo et al. (Eur Econ Rev 2019) on aggregate employment. The minijob institutional angle is genuinely novel relative to these — minijob hours are not the central object in any of them — but the introduction does not explicitly position the present paper against this triangle.

    A reviewer at Labour Economics handling this manuscript will know all three works. The standard expected paragraph is: "Bossler-Gerner show heterogeneous wage effects but do not separate minijobs; Dustmann et al. focus on regular-employment spillovers; Caliendo et al. estimate aggregate employment. The present paper extends this literature by separately analyzing the minijob institutional kink, which generates predictable hours adjustment that none of the prior three identify." Three sentences; without them the contribution is asserted, not positioned.

    Suggested fix

    Add a "Related literature" paragraph at the end of Sec. 1 explicitly distinguishing this paper's contribution from Bossler-Gerner 2020, Dustmann et al. 2022, and Caliendo et al. 2019. Frame the minijob institutional channel as the specific contribution. This is two paragraphs of writing, no new analysis required.

  • Medium severity.
    #7Internal consistencyIntroduction; Table 1

    Minijob shares use different denominators (16.4% vs 21%) without warning the reader

    The Introduction says minijobs were "21 percent of all jobs in 2014." Table 1 reports the minijob share as 0.164 in 2014. These are not contradictory — Table 1 restricts to establishments with ≥10 regular employees and excludes agriculture, public sector, and apprentices, while the 21% headline is over the full German employment population — but the reader is not warned at the point where 21% appears. A careful referee will catch this and ask whether the rest of the paper's magnitudes are over the full population or the SES sample.

    Suggested fix

    Add a footnote at the 21% mention: "In the full German employment population, minijobs accounted for 21%; in our main SES sample of establishments with at least 10 regular employees, the corresponding share is 16.4% (Table 1)." Either footnote or one inline parenthesis works.

  • Medium severity.
    #8Internal consistencySec. 2; Table 1; Table 5

    "At least 10 employees" vs "at least 10 regular employees" used inconsistently across prose, tables, and panel headings

    The sample restriction is described as "establishments with less than ten employees subject to social security (regular employees)" in the data section. Table 1 says "establishments with at least 10 regular employees." The prose says "the weighted number of employees in plants with at least 10 employees grew." Table 5 panel B is labeled "Small plants (<10 employees)." These are not the same sample — minijobs are excluded from "regular employees" but central to the paper, so "<10 regular employees" and "<10 employees" allow or exclude different establishments depending on minijob composition.

    Suggested fix

    Use one term throughout: "establishments with at least 10 regular employees subject to social security contributions." Update Table 5 panel B title to "Small plants (<10 regular employees)" if that is the actual sample definition. Run a global find-and-replace pass on "10 employees" to confirm no other instances.

  • Medium severity.
    #9Internal consistencySec. 1; Table 1

    Wage-gap denominator: "26% below the threshold" vs Table 1's (MW − wage)/wage are different concepts

    The Introduction says affected workers were "paid an average of 26 percent below the minimum wage threshold." Table 1 defines the relative gap as (8.50 − nominal gross hourly wage) / nominal gross hourly wage. These compute different quantities: "26% below the threshold" naturally reads as (MW−wage)/MW; the Table 1 definition is the percentage wage increase required to reach the threshold, (MW−wage)/wage. If the table mean is 0.256, the average wage is about €6.77 and the shortfall relative to the minimum wage is about 20.4%, not 25.6%.

    Suggested fix

    Either change the Introduction prose to "required an average wage increase of 26% to reach the minimum wage" — keeping the Table 1 definition — or report the shortfall relative to the minimum wage threshold (≈20.4%) in the Introduction. Consistency between prose and table is the goal; either choice works.

  • Medium severity.
    #10Reporting guidelineSec. 2; Sec. 5.5

    Sample-size and power justification are weak for a quasi-experimental study with multiple subgroup analyses

    The manuscript reports very large analytic sample sizes and discusses survey weighting for representativeness, but does not provide an a priori power calculation or a principled minimum-detectable-effect rationale. For a quasi-experimental study with multiple subgroup analyses (regular vs minijob, large vs small plants, age × bite, hours bins), pre-specifying minimum detectable effects per subgroup is the standard expectation at top labour journals — it disciplines post-hoc subgroup-mining concerns.

    Suggested fix

    Add a short Methods subsection: "Power and minimum detectable effects." For each main outcome and the principal subgroup splits (regular vs minijob, large vs small plants), report the MDE under standard parallel-trends assumptions. Even a back-of-envelope calculation is sufficient — the goal is to establish that the small-plant null result in Sec. 5.5 is not just a power problem.

  • Medium severity.
    #13Internal consistencyEnd matter

    References are cited inline but the supplied bibliography is truncated

    The manuscript cites Card, Cengiz et al., Dustmann et al., Biewen et al., Bossler and Schank, the German Minimum Wage Commission report, Ahlfeldt-Roth-Seidel, and others, but the supplied file contains no bibliography section. As with the truncation finding above, this may be a side-effect of the supplied PDF being incomplete — but it must be verified before submission.

    Suggested fix

    Verify the bibliography compiles in the submission PDF. Run the build locally with bibtex twice (or biber if using biblatex) to confirm no unresolved keys. Check that all inline citations appear in the bibliography and vice versa.

  • Medium severity.
    #14Editorial framingAbstract; Sec. 5; Conclusion

    Worker-level language is sometimes stronger than the reduced-form, repeated-cross-section design can support

    Phrases such as "for affected workers," "significant spillovers," "non-compliance," and "minijobs disappeared" appear in the abstract and Section 5. The estimates are reduced-form bite-county-by-period interactions on a repeated cross-section; they identify regional intensity effects under parallel-trends assumptions, not individual worker-level outcomes. Spillovers and non-compliance are interpretations of the regional patterns, not directly estimated quantities.

    A reviewer with the literature in front of them will read each of these phrases as overclaiming. The fix is not to remove the interpretations — they are well-supported as interpretations — but to qualify the language: "consistent with worker-level spillovers above the threshold," "suggestive of non-compliance," "regional minijob declines that translate to an estimated 104k net positions" rather than "minijobs disappeared."

    Suggested fix

    Run a global pass through the abstract, Sec. 5, and conclusion. Replace each instance of strong worker-level language with the qualified interpretive language above. The substantive results survive intact; the framing becomes defensible.

  • Medium severity.
    #15Submission readinessSubmission package

    Elsevier-required statements (declarations of interest, funding, author contributions) are missing

    Labour Economics is an Elsevier journal. Elsevier requires each submission to include: (a) declarations of interest, (b) funding statement, (c) author contributions per CRediT, (d) data and code availability statements (covered separately above), (e) signed Elsevier copyright/licensing agreement at acceptance. None of (a)-(c) are in the supplied file. (e) is post-acceptance; (a)-(c) must be in the submission.

    Suggested fix

    Add a "Declarations" end-matter block with: "Declaration of competing interest: The authors declare no competing interests." "Funding: [grant numbers, or 'No external funding received.']" "CRediT author statement: <author 1> Conceptualization, Methodology, Writing — original draft. <author 2> Data curation, Formal analysis, Writing — review & editing." Use the actual contributions; the format is Elsevier-required.

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