Fatima Kasenally, Ruoxi Guan, Frank Windmeijer
arXiv 18 Jun 2026 · Econometrics
arXiv:2606.20240 · PDF · DOI · OpenAlex · Extracted main text
Two-sample IV is a popular estimation method when the outcome and treatment variables are available in different samples, whereas instruments are available in both samples. The standard estimator is two-sample two-stage least squares estimator, which is efficient under homoskedasticity and homogeneity of the samples. We develop a robust two-step procedure for efficient estimation under general heteroskedasticity and heterogeneity of the samples, and propose a related two-sample Hansen overidentification test. A key feature of our approach is that only summary statistics from the linear regressions of the reduced form and first-stage in the two samples are needed. These are the six objects of the estimated coefficient vectors, and the homoskedastic and heteroskedasticity robust estimated variance matrices. We further show that the first-stage F-statistic in the treatment sample can be used as a test for weak instruments in the standard way under homoskedasticity and homogeneity, with the relative bias here a proportional bias. We propose an extension of the effective F-statistic of Montiel-Olea and Pflueger (2013) for the heteroskedastic case, following the generalization in Windmeijer (2025). We illustrate the estimators and tests in an application studying the effect of education on voting behavior from Marshall (2019), with cluster robust inference.
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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 | Marshall, John (2019) The anti-Democrat diploma: How high school education decreases support for the Democratic Party | 1.000 | 6 | 3 | 100% |
| 2 | Zhao, Qingyuan and Wang, Jingshu and Spiller, Wes and Bowden, Jack a… (2019) Two-Sample Instrumental Variable Analyses Using Heterogeneous Samples | 1.000 | 5 | 3 | 100% |
| 3 | Montiel Olea, José Luis and Pflueger, Carolin (2013) A Robust Test for Weak Instruments | 0.928 | 4 | 3 | 100% |
| 4 | Stock, James H. and Yogo, Motohiro (2005) Testing for Weak Instruments in Linear IV Regression | 0.874 | 5 | 2 | 100% |
| 5 | Pacini, David and Windmeijer, Frank (2016) Robust inference for the Two-Sample 2SLS estimator self | 0.843 | 3 | 3 | 100% |
| 6 | Windmeijer, Frank (2025) The robust F-statistic as a test for weak instruments self | 0.843 | 3 | 3 | 100% |
| 7 | Staiger, Douglas and Stock, James H (1997) Instrumental Variables Regression with Weak Instruments | 0.644 | 2 | 2 | 100% |
| 8 | N. Anders Klevmarken (1982) Missing Variables and Two-Stage Least Squares Estimation from More than One Data Set | 0.511 | 2 | 1 | 100% |
| 9 | Angrist, Joshua D. and Krueger, Alan B (1992) The Effect of Age at School Entry on Educational Attainment: An Application of Instrumental Variables with Moments from Two Samp… | 0.405 | 1 | 1 | 100% |
| 10 | Angrist, Joshua D. and Krueger, Alan B (1995) Split-Sample Instrumental Variables Estimates of the Return to Schooling | 0.405 | 1 | 1 | 100% |
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