arXiv 7 Jul 2024 · Econometrics
arXiv:2407.05372 · PDF · DOI · OpenAlex · Extracted main text
We introduce a new convexified matching method for missing value imputation and individualized inference inspired by computational optimal transport. Our method integrates favorable features from mainstream imputation approaches: optimal matching, regression imputation, and synthetic control. We impute counterfactual outcomes based on convex combinations of observed outcomes, defined based on an optimal coupling between the treated and control data sets. The optimal coupling problem is considered a convex relaxation to the combinatorial optimal matching problem. We estimate granular-level individual treatment effects while maintaining a desirable aggregate-level summary by properly constraining the coupling. We construct transparent, individual confidence intervals for the estimated counterfactual outcomes. We devise fast iterative entropic-regularized algorithms to solve the optimal coupling problem that scales favorably when the number of units to match is large. Entropic regularization plays a crucial role in both inference and computation; it helps control the width of the individual confidence intervals and design fast optimization algorithms.
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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 | Sinkhorn, Richard (1967) Diagonal equivalence to matrices with prescribed row and column sums | 1.000 | 5 | 3 | 100% |
| 2 | Cuturi, Marco (2013) Sinkhorn distances: lightspeed computation of optimal transport | 0.928 | 4 | 3 | 100% |
| 3 | Hirano, Keisuke, Imbens, Guido W (2001) Estimation of causal effects using propensity score weighting: An application to data on right heart catheterization | 0.811 | 4 | 2 | 100% |
| 4 | LaLonde, Robert J (1986) Evaluating the econometric evaluations of training programs with experimental data | 0.811 | 4 | 2 | 100% |
| 5 | Rosenbaum, Paul R, Rubin, Donald B (1983) The central role of the propensity score in observational studies for causal effects | 0.737 | 3 | 2 | 100% |
| 6 | Villani, Cédric (2003) Topics in Optimal Transportation | 0.644 | 2 | 2 | 100% |
| 7 | Dehejia, Rajeev H, Wahba, Sadek (1999) Causal effects in nonexperimental studies: Reevaluating the evaluation of training programs | 0.585 | 3 | 1 | 100% |
| 8 | Hirano, Keisuke, Imbens, Guido W, Ridder, Geert (2003) Efficient estimation of average treatment effects using the estimated propensity score | 0.585 | 3 | 1 | 100% |
| 9 | Rosenbaum, Paul R (1987) Model-based direct adjustment | 0.585 | 3 | 1 | 100% |
| 10 | Farrell, Max H (2015) Robust inference on average treatment effects with possibly more covariates than observations | 0.511 | 2 | 1 | 100% |
Showing the top 10 of 43 scored citations.