Federico Crudu, Giovanni Mellace, Zsolt Sándor
arXiv 16 Apr 2026 · Econometrics
arXiv:2604.15437 · PDF · DOI · OpenAlex · Extracted main text
This paper introduces a class of jackknife-based test statistics for linear regression models with endogeneity and heteroskedasticity in the presence of many potentially weak instrumental variables. The tests may be used when considering hypotheses on the full parameter vector or hypotheses defined as linear restrictions. We show that in the limit and under the null the proposed statistics are distributed as a combination of chi squares but by modifying the objective function we derive more familiar chi square limits. An extensive simulation study shows the competitive finite sample properties of the proposed tests in particular against Anderson-Rubin-type of statistics. Finally, we provide an empirical illustration that applies the proposed tests to study the effect of alcohol consumption on body mass index using genetic variants as instrumental variables using the UK Biobank.
appendix boundary found by appendix_command · 39% of the source is main text. Read the extracted text to check this.
The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Hausman, J. A. and Newey, W. K. and Woutersen, T. and Chao, J. C. an… (2012) Instrumental variable estimation with heteroskedasticity and many instruments | 1.000 | 10 | 4 | 100% |
| 2 | Matsushita, Yukitoshi and Otsu, Taisuke (2024) A jackknife Lagrange multiplier test with many weak instruments | 1.000 | 5 | 4 | 100% |
| 3 | Crudu, Federico and Mellace, Giovanni and Sándor, Zsolt (2021) Inference in instrumental variable models with heteroskedasticity and many instruments self | 0.933 | 16 | 5 | 81% |
| 4 | Bekker, P. A. and Crudu, F (2015) Jackknife Instrumental Variable Estimation with Heteroskedasticity self | 0.928 | 15 | 5 | 80% |
| 5 | Mikusheva, Anna and Sun, Liyang (2022) Inference with many weak instruments | 0.874 | 10 | 2 | 100% |
| 6 | Kleibergen, F (2002) Pivotal Statistics for Testing Structural Parameters in Instrumental Variables Regression | 0.811 | 4 | 2 | 100% |
| 7 | Angrist, Joshua D and Imbens, Guido W and Krueger, Alan B (1999) Jackknife instrumental variables estimation | 0.737 | 3 | 2 | 100% |
| 8 | Staiger, D. and Stock, J. H (1997) Instrumental Variables Regression with Weak Instruments | 0.737 | 3 | 2 | 100% |
| 9 | Bekker, P. A (1994) Alternative approximations to the distributions of instrumental variable estimators | 0.644 | 2 | 2 | 100% |
| 10 | Chao, J. C. and Hausman, J. A. and Newey, W. K. and Swanson, N. R. a… (2014) Testing Overidentifying Restrictions with Many Instruments and Heteroskedasticity | 0.644 | 2 | 2 | 100% |
Showing the top 10 of 58 scored citations.