arXiv 28 Nov 2023 · Econometrics · 2 citations (OpenAlex)
arXiv:2311.17021 · PDF · DOI · OpenAlex · Extracted main text
This paper discusses estimation with a categorical instrumental variable in settings with potentially few observations per category. The proposed categorical instrumental variable estimator (CIV) leverages a regularization assumption that implies existence of a latent categorical variable with fixed finite support achieving the same first stage fit as the observed instrument. In asymptotic regimes that allow the number of observations per category to grow at arbitrary small polynomial rate with the sample size, I show that when the cardinality of the support of the optimal instrument is known, CIV is root-n asymptotically normal, achieves the same asymptotic variance as the oracle IV estimator that presumes knowledge of the optimal instrument, and is semiparametrically efficient under homoskedasticity. Under-specifying the number of support points reduces efficiency but maintains asymptotic normality. In an application that leverages judge fixed effects as instruments, CIV compares favorably to commonly used jackknife-based instrumental variable estimators.
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| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Chyn, E., Frandsen, B., and Leslie, E. C (2024) Examiner and judge designs in economics: A practitioner's guide | 1.000 | 11 | 4 | 100% |
| 2 | Dobbie, W., Goldin, J., and Yang, C. S (2018) The effects of pre-trial detention on conviction, future crime, and employment: Evidence from randomly assigned judges | 1.000 | 7 | 3 | 100% |
| 3 | Kolesár, M (2013) Estimation in an instrumental variables model with treatment effect heterogeneity | 0.935 | 11 | 6 | 82% |
| 4 | Belloni, A., Chen, D., Chernozhukov, V., and Hansen, C (2012) Sparse models and methods for optimal instruments with an application to eminent domain | 0.916 | 13 | 6 | 77% |
| 5 | Angrist, J. D. and Frandsen, B (2022) Machine labor | 0.894 | 7 | 5 | 71% |
| 6 | Angrist, J. D., Imbens, G. W., and Krueger, A. B (1999) Jackknife instrumental variables estimation | 0.894 | 7 | 4 | 71% |
| 7 | Donald, S. G. and Newey, W. K (2001) Choosing the number of instruments | 0.874 | 6 | 3 | 67% |
| 8 | Blandhol, C., Bonney, J., Mogstad, M., and Torgovitsky, A (2022) When is TSLS actually LATE? | 0.843 | 4 | 4 | 75% |
| 9 | Bonhomme, S. and Manresa, E (2015) Grouped patterns of heterogeneity in panel data | 0.817 | 11 | 4 | 55% |
| 10 | Chao, J. C., Swanson, N. R., Hausman, J. A., Newey, W. K., and Woute… (2012) Asymptotic distribution of JIVE in a heteroskedastic iv regression with many instruments | 0.811 | 4 | 2 | 100% |
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