arXiv 23 Feb 2022 · Econometrics · publishedJournal of Econometrics (2024) · 1 citations (OpenAlex)
arXiv:2202.11671 · PDF · DOI · OpenAlex · Extracted main text
In the context of treatment effect estimation, this paper proposes a new methodology to recover the counterfactual distribution when there is a single (or a few) treated unit and possibly a high-dimensional number of potential controls observed in a panel structure. The methodology accommodates, albeit does not require, the number of units to be larger than the number of time periods (high-dimensional setup). As opposed to modeling only the conditional mean, we propose to model the entire conditional quantile function (CQF) without intervention and estimate it using the pre-intervention period by a l1-penalized regression. We derive non-asymptotic bounds for the estimated CQF valid uniformly over the quantiles. The bounds are explicit in terms of the number of time periods, the number of control units, the weak dependence coefficient (beta-mixing), and the tail decay of the random variables. The results allow practitioners to re-construct the entire counterfactual distribution. Moreover, we bound the probability coverage of this estimated CQF, which can be used to construct valid confidence intervals for the (possibly random) treatment effect for every post-intervention period. We also propose a new hypothesis test for the sharp null of no-effect based on the Lp norm of deviation of the estimated CQF to the population one. Interestingly, the null distribution is quasi-pivotal in the sense that it only depends on the estimated CQF, Lp norm, and the number of post-intervention periods, but not on the size of the post-intervention period. For that reason, critical values can then be easily simulated. We illustrate the methodology by revisiting the empirical study in Acemoglu, Johnson, Kermani, Kwak and Mitton (2016).
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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 | Belloni and Chernozhukov (2011) l1-penalized quantile regression in high-dimensional sparse models | 0.874 | 7 | 2 | 100% |
| 2 | Hsiao, Ching and Wan (2012) A panel data approach for program evaluation: measuring the benefits of political and economic integration of Hong Kong with mai… | 0.737 | 3 | 2 | 100% |
| 3 | Bühlmann and van de Geer (2011) Statistics for High-Dimensional Data: Methods, Theory and Applications | 0.644 | 3 | 2 | 67% |
| 4 | Acemoglu, Johnson, Kermani, Kwak and Mitton (2016) The value of connections in turbulent times: Evidence from the United States | 0.644 | 2 | 2 | 100% |
| 5 | Carvalho, Masini and Medeiros (2018) ArCo: An artificial counterfactual approach for high-dimensional panel time-series data | 0.644 | 2 | 2 | 100% |
| 6 | Doukhan, Massart and Rio (1995) Invariance principles for absolutely regular empirical processes | 0.511 | 3 | 2 | 33% |
| 7 | Chernozhukov, Fernández-Val and Galichon (2010) Quantile and probability curves without crossing | 0.511 | 2 | 2 | 50% |
| 8 | Doukhan (1994) Mixing | 0.511 | 2 | 1 | 100% |
| 9 | Gunsilius (2021) Distributional synthetic controls | 0.511 | 2 | 1 | 100% |
| 10 | Zheng, Peng and He (2015) Globally Adaptive Quantile Regression with ultra-high Dimensional Data | 0.511 | 2 | 1 | 100% |
Showing the top 10 of 24 scored citations.
arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.
| Citing paper | Intensity | Mentions | Sections | |
|---|---|---|---|---|
| 1 | Bayesian State-Space Modeling and Model-Based Counterfactual Analysis of Dynamic Income Distributions from Grouped Data | 0.405 | 1 | 1 |