arXiv 8 Aug 2021 · Econometrics · 12 citations (OpenAlex)
arXiv:2108.03726 · PDF · DOI · OpenAlex · Extracted main text
Instrumental variables (IV) regression is widely used to estimate causal treatment effects in settings where receipt of treatment is not fully random, but there exists an instrument that generates exogenous variation in treatment exposure. While IV can recover consistent treatment effect estimates, they are often noisy. Building upon earlier work in biostatistics (Joffe and Brensinger, 2003) and relating to an evolving literature in econometrics (including Abadie et al., 2019; Huntington-Klein, 2020; Borusyak and Hull, 2020), we study how to improve the efficiency of IV estimates by exploiting the predictable variation in the strength of the instrument. In the case where both the treatment and instrument are binary and the instrument is independent of baseline covariates, we study weighting each observation according to its estimated compliance (that is, its conditional probability of being affected by the instrument), which we motivate from a (constrained) solution of the first-stage prediction problem implicit to IV. The resulting estimator can leverage machine learning to estimate compliance as a function of baseline covariates. We derive the large-sample properties of a specific implementation of a weighted IV estimator in the potential outcomes and local average treatment effect (LATE) frameworks, and provide tools for inference that remain valid even when the weights are estimated nonparametrically. With both theoretical results and a simulation study, we demonstrate that compliance weighting meaningfully reduces the variance of IV estimates when first-stage heterogeneity is present, and that this improvement often outweighs any difference between the compliance-weighted and unweighted IV estimands. These results suggest that in a variety of applied settings, the precision of IV estimates can be substantially improved by incorporating compliance estimation.
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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 | Huntington-Klein, N (2020) Instruments with Heterogeneous Effects: Bias, Monotonicity, and Localness | 1.000 | 14 | 5 | 100% |
| 2 | Joffe, M. M. and Brensinger, C (2003) Weighting in instrumental variables and G-estimation | 1.000 | 9 | 4 | 100% |
| 3 | Borusyak, K. and Hull, P (2020) Non-Random Exposure to Exogenous Shocks: Theory and Applications | 1.000 | 7 | 4 | 100% |
| 4 | Abadie, A., Gu, J., and Shen, S (2019) Instrumental variable estimation with first stage heterogeneity | 1.000 | 7 | 4 | 100% |
| 5 | Wager, S. and Athey, S (2018) Estimation and inference of heterogeneous treatment effects using random forests | 0.843 | 3 | 3 | 100% |
| 6 | Chen, J., Chen, D. L., and Lewis, G (2020) Mostly Harmless Machine Learning: Learning Optimal Instruments in Linear IV Models | 0.811 | 4 | 2 | 100% |
| 7 | Bond, S. J., White, I. R., and Sarah Walker, A (2007) Instrumental variables and interactions in the causal analysis of a complex clinical trial | 0.737 | 3 | 2 | 100% |
| 8 | Chamberlain, G (1987) Asymptotic efficiency in estimation with conditional moment restrictions | 0.737 | 3 | 2 | 100% |
| 9 | Belloni, A., Chen, D., Chernozhukov, V., and Hansen, C (2012) Sparse Models and Methods for Optimal Instruments With an Application to Eminent Domain | 0.644 | 2 | 2 | 100% |
| 10 | Hansen, C. and Kozbur, D (2014) Instrumental variables estimation with many weak instruments using regularized JIVE | 0.644 | 2 | 2 | 100% |
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