US labor market conditions and migration: a reassessment of Bahar (2025)
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.
Summary
This paper by Rodriguez and Bravo (2025) critically reassesses the findings of Bahar (2025), which claimed a long-term cointegrating relationship between US job vacancies and southwest border crossings, suggesting a significant "pull" factor driving migration. Rodriguez and Bravo demonstrate that Bahar's conclusion is based on a misspecified Engle-Granger cointegration test. Specifically, Bahar applied the test to first differences of the time series data instead of the levels, which is incorrect for I(1) variables. When the Engle-Granger test is correctly applied to the levels of the variables, the evidence for cointegration disappears. The authors meticulously examine Bahar's methodology, including his replication code and related work with Hausmann. They found inconsistencies and coding errors beyond the misspecified cointegration test. They demonstrate that correcting these errors significantly alters the estimated elasticities and casts doubt on the validity of Bahar's conclusions regarding the relationship between US labor market conditions and migration. The paper argues that because Bahar's empirical strategy relies heavily on the existence of a cointegrating relationship, the failure to establish this relationship undermines his entire analysis, rendering his findings uninformative about the true drivers of migration.
Key Insights
- •Bahar's (2025) conclusion of a long-term cointegrating relationship between US job vacancies and southwest border crossings is invalidated by a misspecified Engle-Granger test applied to first differences instead of levels.
- •Applying the Engle-Granger test to first differences of I(1) variables inherently yields spurious evidence of cointegration because linear combinations of stationary (first-differenced I(1)) variables are stationary. Monte Carlo simulations showed a 100% false positive rate when applying this test to first differences of non-cointegrated unit root series.
- •When the Engle-Granger test is correctly applied to the levels of the variables, Rodriguez and Bravo find little evidence of cointegration. Only one out of twelve specifications rejected the null hypothesis of no cointegration at the 5% significance level, a stark contrast to Bahar's reported results. The range of test statistics obtained from the corrected estimates spanned from -1.851 to -4.061, with a median value of -2.914, far from Bahar's reported -18.829.
- •The paper identifies additional coding errors and misrepresentations in Bahar's work, including miscoded equation specifications leading to the inclusion of incorrect control variables. For example, they found the true estimated elasticity during the Bush administration was 1.01, not the 0.50 displayed in Figure 3(a) of Bahar's paper due to the inclusion of incorrect controls.
- •Bahar incorrectly used the `D12` command in Stata to calculate year-over-year differences instead of the `S12` command, a mistake appearing in 23 lines of code. This significantly altered the corrected year-over-year differences, as shown in Figure 2.
- •The replication code provided by Bahar is incomplete, missing crucial `.do` files required to reproduce Appendices D and F.
Practical Implications
- •This research highlights the importance of rigorous econometric methodology and careful code verification in empirical studies, particularly when analyzing complex macroeconomic relationships. Researchers should be cautious about applying cointegration tests to differenced data without proper justification.
- •Policymakers and analysts relying on Bahar's (2025) findings should be aware that the claimed relationship between US labor market conditions and border crossings is likely spurious and should not be used as a basis for policy decisions.
- •This paper opens avenues for future research to explore the true drivers of migration to the US, using sound econometric techniques and carefully considering potential confounding factors. It encourages a re-evaluation of the "pull" versus "push" factors debate, free from the biases introduced by misspecified models.
- •Future research should focus on identifying appropriate control variables and exploring alternative econometric techniques to accurately model the complex dynamics of migration flows.