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Research Publications

Working papers

Working papers from the Federal Reserve Bank of Dallas are preliminary drafts circulated for professional comment.

2026

No. 2603

Mean Group and Pooled Mixed-Frequency Estimators of Responses of Low-Frequency Variables to High-Frequency Shocks

Alexander Chudik and Lutz Kilian

Abstract: This paper proposes mean group and pooled estimators of impulse responses based on mixed-frequency auxiliary distributed lag (DL), autoregressive distributed lag (ARDL) or vector autoregressive distributed lag (VARDL) estimating equations. Our setup assumes that the data are generated by a high-frequency VAR process. While the shock of interest is directly observed at high frequency, the outcome variable is only observed as a temporally aggregated variable at a lower frequency. We derive the asymptotic distributions of the six proposed estimators. Monte Carlo experiments show that pooled estimators generally perform better than the corresponding mean group estimators for relevant sample sizes. An empirical illustration to the pass-through from daily wholesale gasoline price shocks to monthly consumer price inflation illustrates the usefulness of the proposed methods.

DOI: https://doi.org/10.24149/wp2603

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No. 2602

Disparate Impacts of Teacher Certification Exams

Christa Deneault, Evan Riehl and Jian Zou

Abstract: We use Texas administrative data to assess the long-standing claim that teacher certification exams discriminate against underrepresented minority (URM) candidates. In a regression discontinuity design, we find that failing a certification exam delays entry into teaching and costs the average candidate $10,000 in forgone earnings. These costs fall disproportionately on URM candidates both because they are more likely to fail and because their earnings losses from failing are 50 percent larger on average. To examine whether these disparities are justified by racial/ethnic differences in teaching quality, we develop a new measure of disparate impact and estimate it using a policy change that increased the difficulty of Texas’ elementary certification exam. The harder exam reduced the URM share of new teachers but had no significant benefits for teaching quality or student achievement. Taken together, our findings show that certification exams have a disparate impact in the sense that they impose much larger economic costs on URM teaching candidates than on white candidates with similar potential teaching quality.

DOI: https://doi.org/10.24149/wp2602

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No. 2601

Weak Instrument Bias in Impulse Response Estimators

Daniel J. Lewis and Karel Mertens

Abstract: We approximate the finite-sample distribution of impulse response function (IRF) estimators that are just-identified with a weak instrument using the conventional local-to-zero asymptotic framework. Since the distribution lacks a mean, we assess bias using the mode and conclude that researchers prioritizing robustness against weak instrument bias should favor vector autoregressions (VARs) over local projections (LPs). Existing testing procedures are ill-suited for assessing weak instrument bias in IRF estimates, and we propose a novel simple test based on the usual first-stage F-statistic. We investigate instrument strength in several applications from the literature, and discuss to what extent structural parameters must be restricted ex-ante to reject meaningful bias due to weak identification.

DOI: https://doi.org/10.24149/wp2601

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