US labor market conditions and migration: a reassessment of Bahar (2025)

Francisco Rodriguez; Giancarlo Bravo

arxiv: 2512.21429 · v2 · pith:2DTBARR7new · submitted 2025-12-24 · 💰 econ.EM

US labor market conditions and migration: a reassessment of Bahar (2025)

Francisco Rodriguez , Giancarlo Bravo This is my paper

Pith reviewed 2026-05-25 07:20 UTC · model grok-4.3

classification 💰 econ.EM

keywords cointegrationEngle-Granger testUS labor marketmigrationborder crossingstime seriesreplication

0 comments

The pith

Correct application of the Engle-Granger test to levels eliminates evidence of cointegration between US job vacancies and southwest border crossings.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

Bahar (2025) claims a long-term cointegrating relationship exists between US job vacancies and southwest border crossings. The reassessment shows this rests on applying the Engle-Granger test to first differences instead of the levels of the series. When the test is run properly on the levels, the evidence for cointegration disappears. Without cointegration, the error-correction model used to separate short-run and long-run elasticities cannot be justified. The original results therefore provide no reliable information on how US labor market conditions relate to migration flows.

Core claim

Bahar (2025) concludes there is a cointegrating relationship between US job vacancies and southwest border crossings based on an Engle-Granger test. However, that test was applied to first differences rather than the levels of the variables. When the Engle-Granger test is applied correctly to the levels, there is no evidence of cointegration. Consequently, the error-correction model used to estimate short- and long-run elasticities is invalid, and the results do not inform the relationship between labor market conditions and migration.

What carries the argument

The Engle-Granger cointegration test applied to the levels of the time series for US job vacancies and southwest border crossings, which fails to reject the null of no cointegration.

If this is right

The short-run and long-run elasticity estimates in Bahar (2025) cannot be interpreted as coming from a valid error-correction model.
No long-run equilibrium relationship between US job vacancies and southwest border crossings is supported by the data under the corrected specification.
Analyses of migration that rely on the cointegration finding from Bahar (2025) lose their statistical foundation.
Alternative time-series methods that do not presuppose cointegration are required to study links between labor market tightness and border crossings.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

Studies of economic drivers of migration that use similar cointegration tests on other variables may require the same level-versus-difference check.
Policy discussions that cite a stable long-run link between job openings and migration flows should note the absence of supporting evidence once the test specification is corrected.
Future work could examine whether other common cointegration procedures, such as Johansen tests, also fail to find a relationship in these series.

Load-bearing premise

The reassessment depends on the premise that Bahar (2025) applied the Engle-Granger test to first differences rather than to the levels of the series and that this choice constitutes a misspecification that removes support for cointegration.

What would settle it

Re-running the Engle-Granger test on the original levels of the US job vacancies and southwest border crossings series and obtaining a test statistic that rejects the null of no cointegration at conventional significance levels would falsify the central claim.

Figures

Figures reproduced from arXiv: 2512.21429 by Francisco Rodriguez, Giancarlo Bravo.

read the original abstract

Bahar (2025) argues that there is a long-term cointegrating relationship between US job vacancies and southwest border crossings. We show that this conclusion is based on a misspecified Engle-Granger test applied to first differences. Once the Engle-Granger test is correctly applied to levels, evidence for a cointegrating relationship vanishes, invalidating the paper's approach to estimating short- and long-run elasticities. Bahar's approach is therefore uninformative about the relationship between US labor market conditions and migration.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper shows that running Engle-Granger on levels instead of differences removes evidence of cointegration between vacancies and border crossings, but the whole argument depends on proving Bahar actually used differences.

read the letter

The main point is that this comment re-applies the Engle-Granger test the standard way on the levels of the series and finds no cointegrating relationship between US job vacancies and southwest border crossings. That undercuts Bahar's estimates of short- and long-run elasticities and leaves the original approach uninformative about labor market conditions and migration. The paper does the straightforward thing of correcting the test specification and reporting the changed result. It uses an established procedure without new data or techniques, which is fine for a targeted correction if the premise holds. The logic follows directly from how the test is meant to work on non-stationary levels. The soft spot is the missing step of showing that Bahar actually ran the test on first differences. The abstract states the misspecification but does not quote the original regression, residual series, or variable transformation. Without that documentation the central claim stays an assertion rather than a demonstrated fact. The no-cointegration result on levels only matters once the original error is established. If the full manuscript supplies the specific evidence from Bahar, the case is stronger; if not, the critique does not fully land. This note is for readers already working on migration time series or cointegration applications who want a direct check on one published claim. It is narrow but the method is transparent and the question is factual. I would send it to peer review because the test is reproducible and referees can judge whether the misspecification is properly shown.

Referee Report

2 major / 0 minor

Summary. The manuscript claims that Bahar (2025) reached an erroneous conclusion of a cointegrating relationship between US job vacancies and southwest border crossings because the Engle-Granger test was misspecified by application to first-differenced series rather than levels; when the test is correctly run on levels, the cointegration evidence disappears, rendering Bahar's short- and long-run elasticity estimates uninformative.

Significance. If the premise that Bahar applied Engle-Granger to first differences is substantiated by direct evidence from the original paper and the re-test on levels is shown to produce no cointegration, the reassessment would be significant for highlighting the sensitivity of migration-labor market inferences to correct implementation of cointegration procedures. The current manuscript, however, provides no replication details, test statistics, or quotations, limiting its ability to alter the evidentiary record.

major comments (2)

[Abstract] Abstract: the central claim that Bahar (2025) 'applied the Engle-Granger test to first differences' is asserted without quoting or citing the specific regression equation, residual series, or variable transformation used in the original paper. This premise is load-bearing for the subsequent invalidation of cointegration and elasticity estimates.
[Abstract] Abstract: the statement that 'evidence for a cointegrating relationship vanishes' when the test is applied to levels is presented without any reported test statistic, lag selection, critical values, sample period, or variable definitions (e.g., exact vacancy or crossing series). Full verification of the no-cointegration result therefore cannot be performed from the provided text.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for these comments on the abstract. We agree that both the claim about Bahar (2025)'s specification and the no-cointegration result require explicit documentation to be verifiable. We will revise the manuscript to add the requested details.

read point-by-point responses

Referee: [Abstract] Abstract: the central claim that Bahar (2025) 'applied the Engle-Granger test to first differences' is asserted without quoting or citing the specific regression equation, residual series, or variable transformation used in the original paper. This premise is load-bearing for the subsequent invalidation of cointegration and elasticity estimates.

Authors: We accept the point. The abstract as currently written does not quote or cite the specific equation from Bahar (2025). In the revision we will insert direct quotations from Bahar (2025) that describe the Engle-Granger procedure, the exact regression equation estimated on first-differenced series, and the variable transformations applied. revision: yes
Referee: [Abstract] Abstract: the statement that 'evidence for a cointegrating relationship vanishes' when the test is applied to levels is presented without any reported test statistic, lag selection, critical values, sample period, or variable definitions (e.g., exact vacancy or crossing series). Full verification of the no-cointegration result therefore cannot be performed from the provided text.

Authors: We accept the point. The abstract does not report the test statistics or supporting details. The revised manuscript will include the Engle-Granger test statistic on levels, the lag-selection method and chosen lag, critical values, the precise sample period, and the exact definitions of the vacancy and border-crossings series. revision: yes

Circularity Check

0 steps flagged

No circularity; relies on standard Engle-Granger application independent of target paper

full rationale

The paper's derivation applies the standard definition of the Engle-Granger test (residual unit root test after levels regression) to reassess cointegration between vacancies and crossings. This is an external econometric procedure whose validity does not reduce to any fitted values, self-citation chain, or definitional loop within the present manuscript. The claim that Bahar (2025) used first differences is an empirical assertion about another work, not a self-referential reduction; even if disputed, it does not create circularity under the enumerated patterns. No equations equate a prediction to its own input by construction, and the central result (vanishing cointegration on levels) follows from re-application of the test rather than from any ansatz or renaming internal to this paper.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Based on abstract only; no free parameters, axioms, or invented entities are described.

pith-pipeline@v0.9.0 · 5604 in / 982 out tokens · 37342 ms · 2026-05-25T07:20:36.215673+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

3 extracted references · 3 canonical work pages

[1]

Not a border crisis, but a labor market crisis: The o ften overlooked “pull

https://doi.org/10.1111/pam.22665/suppl file/pam22665-sup-0001-onlineappendix.pdf . 2025a. “Not a border crisis, but a labor market crisis: The o ften overlooked “pull” factor of U.S. border crossings.” Journal of Policy Analysis and Management 44, no. 2 (April): 674–680. https://doi.org/10.1002/pam.22665. . 2025b. “Correction to ”Not a border crisis, but...

work page doi:10.1111/pam.22665/suppl
[2]

6 Greene, William H

http://www.jstor.org/stable/1913236. 6 Greene, William H

work page arXiv
[3]

Princeton University Press

Time Series Analysis. Princeton University Press. isbn: 9780691042893. https://press.princeton.edu/books/hardcover/9780691042893/time-series-analysis . Rodr ´ ıguez, Francisco, and Giancarlo Bravo. 2025.Why Bahar and Hausmann Tell Us Nothing About Venezuelan Migration Flows to the United States. https://cepr.net/publications/why-bahar-and-hausman n- Cente...

work page arXiv 2025

[1] [1]

Not a border crisis, but a labor market crisis: The o ften overlooked “pull

https://doi.org/10.1111/pam.22665/suppl file/pam22665-sup-0001-onlineappendix.pdf . 2025a. “Not a border crisis, but a labor market crisis: The o ften overlooked “pull” factor of U.S. border crossings.” Journal of Policy Analysis and Management 44, no. 2 (April): 674–680. https://doi.org/10.1002/pam.22665. . 2025b. “Correction to ”Not a border crisis, but...

work page doi:10.1111/pam.22665/suppl

[2] [2]

6 Greene, William H

http://www.jstor.org/stable/1913236. 6 Greene, William H

work page arXiv

[3] [3]

Princeton University Press

Time Series Analysis. Princeton University Press. isbn: 9780691042893. https://press.princeton.edu/books/hardcover/9780691042893/time-series-analysis . Rodr ´ ıguez, Francisco, and Giancarlo Bravo. 2025.Why Bahar and Hausmann Tell Us Nothing About Venezuelan Migration Flows to the United States. https://cepr.net/publications/why-bahar-and-hausman n- Cente...

work page arXiv 2025