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IV regression with distribution-valued outcomes

David Van Dijcke, Kaspar Wüthrich

arXiv 27 May 2026 · Econometrics

arXiv:2605.28749 · PDF · DOI · OpenAlex · Extracted main text

Abstract

We develop IV Fréchet regression (IVFR), an instrumental-variable (IV) method for settings where the outcome is an entire distribution. Framing the problem as an IV regression in 2-Wasserstein space, IVFR extends global Fréchet regression to the case with endogenous covariates. IVFR projects IV-weighted quantile curves onto the space of valid distributions and then recovers the corresponding regression coefficient functions. The projection provably reduces the estimation error in finite samples and guarantees valid fitted distributions. We show that the IVFR estimator converges weakly to a mean-zero Gaussian process and establish the validity of a multiplier bootstrap procedure for uniform inference. In simulations, the projection reduces the integrated mean squared error (IMSE) by up to 63% relative to existing methods. Revisiting the effects of Chinese import competition on the wage distribution within commuting zones, the proposed method produces 9-10% narrower confidence bands than existing methods. Using our novel uniform confidence bands, we find no evidence that import competition reduced wages at the very bottom of the distribution, but only between the 10th and 35th quantile. We also revisit the effect of county food stamp programs on the county's birth weight distribution and find no significant effects.

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65
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Most heavily cited references

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.

ReferenceIntensityMentionsSectionsMain text
1Autor, D. H., Dorn, D., and Hanson, G. H (2013) The China Syndrome: Local Labor Market Effects of Import Competition in the United States0.87452100%
2Petersen, A. and Müller, H.-G (2019) Fréchet regression for random objects with Euclidean predictors0.81142100%
3Petersen, A., Liu, X., and Divani, A. A (2021) Wasserstein F-tests and confidence bands for the Fréchet regression of density response curves0.7374450%
4Melly, B. and Pons, M (2025) Minimum distance estimation of quantile panel data models0.73732100%
5Van Dijcke, D (2025) Regression discontinuity design with distribution-valued outcomes0.71411336%
6Almond, D., Hoynes, H. W., and Schanzenbach, D. W (2011) Inside the war on poverty: The impact of food stamps on birth outcomes0.64441100%
7Frölich, M. and Melly, B (2013) Unconditional quantile treatment effects under endogeneity0.64422100%
8van der Vaart, A. W. and Wellner, J. A (1996) Weak Convergence and Empirical Processes: With Applications to Statistics0.61313323%
9Ayer, M., Brunk, H. D., Ewing, G. M., Reid, W. T., and Silverman, E (1955) An empirical distribution function for sampling with incomplete information0.5112250%
10Kruskal, J. B (1964) Nonmetric multidimensional scaling: a numerical method0.5112250%

Showing the top 10 of 65 scored citations.