CoChat
Sign Up
Cited by 601Advanced Causal Inference TechniquesStatistical Methods and InferenceSpatial and Panel Data Analysis

Inference on Counterfactual Distributions

Open access
Victor Chernozhukov, Iván Fernández‐Val, Blaise Melly·2013·Econometrica
DOI 10.3982/ecta10582
Open this paper in CoChat — free accountOpen PDF

Abstract

Counterfactual distributions are important ingredients for policy analysis and decomposition analysis in empirical economics. In this article, we develop modeling and inference tools for counterfactual distributions based on regression methods. The counterfactual scenarios that we consider consist of ceteris paribus changes in either the distribution of covariates related to the outcome of interest or the conditional distribution of the outcome given covariates. For either of these scenarios, we derive joint functional central limit theorems and bootstrap validity results for regression-based estimators of the status quo and counterfactual outcome distributions. These results allow us to construct simultaneous confidence sets for function-valued effects of the counterfactual changes, including the effects on the entire distribution and quantile functions of the outcome as well as on related functionals. These confidence sets can be used to test functional hypotheses such as no-effect, positive effect, or stochastic dominance. Our theory applies to general counterfactual changes and covers the main regression methods including classical, quantile, duration, and distribution regressions. We illustrate the results with an empirical application to wage decompositions using data for the United States. As a part of developing the main results, we introduce distribution regression as a comprehensive and flexible tool for modeling and estimating the entire conditional distribution. We show that distribution regression encompasses the Cox duration regression and represents a useful alternative to quantile regression. We establish functional central limit theorems and bootstrap validity results for the empirical distribution regression process and various related functionals.

The claims and statistics of this paper haven’t been checked yet.

Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.

A few free checks a day · papers already verified open instantly · results are public

Integrity signals

Registry

Crossref · 10.3982/ecta10582

Cites

105 of 105 references verified0 citation errors · 0 not checkable

Statistics

Claims the paper makes

The claims and statistics of this paper haven’t been checked yet.

Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.

A few free checks a day · papers already verified open instantly · results are public

Claims other papers make about this one

Each is checked against this paper’s own text: does it say what the citing paper says it does?

  • Counterfactual inference techniques explicitly assume that there are no unmeasured confounders (unobservable variables Z) that could affect the outcome Y.

    “However, counterfactual inference techniques explicitly assume that there are no unmeasured confounders (that is, no unobservable variables Z) that could affect the outcome Y.”

    From The Selective Labels Problem (2017) · cites this paper as [9]

    Section 2.1 (page unavailable) represents the outcome as a function of observed covariates and a disturbance U, so the paper does not rule out unobserved factors affecting Y. Its stated assumption is instead that the conditional distribution of Y given the covariates remains unchanged by the intervention (Section 2.1, page unavailable). The disturbance is independent of the covariates in this representation; the passage does not identify it as a confounder. (LLM, conf=0.82)

    Checked by a reasoning model — may be wrong.

    Experimental — accuracy not yet measured

Self-check

Percentages, sums and reported differences re-computed from the paper’s own numbers.

The self-check needs the paper’s full text.

Cites

Flagged first, then by citations

Research works printed but not linked: 13

  1. Billingsley, P. (1968): Convergence of Probability Measures. Wiley. New York.
  2. DeJong, R.M., and J. Davidson (2000): The functional Central Limit Theorem And Weak Conver- gence To Stochastic Integrals I: Weakly Dependent Processes, Econometric Theory 16, pp. 621-642.
  3. Engel, E. (1857), "Die Produktions und Konsumptionsverhaltnisse des Konigreichs Sachsen," Zeitschnft des Statistischen Bureaus des Koniglich Sdchsischen Misistenums des Innerrn, 8, pp. 1-54.
  4. Fernholz, L.T. (1983): von Mises Calculus for Statistical Functionals, Lecture Notes in Statistics 19, Springer. New York. ' •
  5. Goldie, C. M. (1977): "Covergence Theorems for Empirical Lorenz Curves and their Inverses," Advances in Applied Probability 9, pp. 765-791.
  6. Gutenbrunner, C, and J. Jureckova (1992): "Regression Quantile and Regression Rank Score Process in the Linear Model and Derived Statistics," Annals of Statistics 20, pp. 305-330.
  7. Koenker, R. (2005), Quantile Regression. Econometric Society Monograph Series 38, Cambridge University Press.
  8. Koenker R. and G. Bassett (1978): "Regression Quantiles," Econometrica 46, pp. 33-50.
  9. Lancaster, T. (1990): The Econometric Analysis of Transition Data, An Econometric Society Mono- graph, Cambridge University Press.
  10. Perthel, D. (1975), "Engel's Law Revisited," International Statistical Review 43 , no. 2, 211-218.
  11. Resnick, S. I. (1987), Extreme values, regular variation, and point processes, Applied Probability. A Series of the Applied Probability Trust, 4. Springer-Verlag, New York.
  12. Stocks, J.H. (1991): "Nonparametric Pohcy Analysis: An Application to Estimating Hazardous Waste Cleanup Benefits," in Nonparametric and Semiparametric Methods m Econometrics and Sta- ' tistics, eds. W. Barnett, J. Powell, and G. Tauchen, Cambridge, U.K.: Cambridge University Press.
  13. White, H. (2001): Asymptotic Theory for Econometricians: Revised Edition, Acaudemic Press.

Cited by

Sorted by citations

Related

Authors
Chernozhukov, V., Fernández‐Val, I., & Melly, B.
Affiliations
  • Massachusetts Institute of Technology (US)
  • Boston University (US)
  • University of Bern (CH)
ORCID
Venue
Econometrica
Publisher
The Econometric Society
Published
2013
Volume
81
Issue
6
Pages
2205-2268
ISSN
0012-9682 (ISSN-L)
DOI
10.3982/ecta10582
OpenAlex
W2951225967
Cited by
601
References
105
Citations by year
2026: 37 · 2025: 54 · 2024: 66 · 2023: 59 · 2022: 61 · 2021: 60 · 2020: 52 · 2019: 45 · 2018: 57 · 2017: 36 · 2016: 26 · 2015: 27 · 2014: 11 · 2013: 6
FWCI
21.18
Type
journal article
Language
en
Open access
Licence
doi.wiley.com/10.1002/tdm_license_1.1 (tdm, 973 d)
Locations
Econometrica (publishedVersion)
Funders
  • National Science Foundation
  • Alfred P. Sloan Foundation
Topics
  • Physical Sciences › Mathematics › Statistics and Probability › Advanced Causal Inference Techniques
  • Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Inference
  • Social Sciences › Economics, Econometrics and Finance › Economics and Econometrics › Spatial and Panel Data Analysis
Keywords
counterfactual distributions, distribution regression, invariance principle, bootstrap validity, stochastic dominance, quantile function, wage decomposition, distributional effects, quantile regression

About these checks

Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.

Statistics and arithmetic are recomputed, not judged.

Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.

What counts as a claim ›How we measure confidence ›How we check this ›

Are you an author, or do you see a problem with this page? Request a review