Low-Rank Approximations of Nonseparable Panel Models

Fernández‐Val, Iván; Freeman, Hugo; Weidner, Martin

doi:10.48550/arxiv.2010.12439

Cited by 3 publications

(3 citation statements)

References 24 publications

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“…In a panel data model, the analyst observes many units over time. Works in this literature posit a low rank [23,11,70,30,10] or approximately low rank [9,5] linear factor model for potential outcomes over units and times (and even interventions [4]). Observed outcomes are interpreted as corrupted potential outcomes with idiosyncratic noise.…”

Section: Treatment Effects With Corrupted Datamentioning

confidence: 99%

Causal Inference with Corrupted Data: Measurement Error, Missing Values, Discretization, and Differential Privacy

Agarwal¹,

Singh²

2021

Preprint

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Even the most carefully curated economic data sets have variables that are noisy, missing, discretized, or privatized. The standard workflow for empirical research involves data cleaning followed by data analysis that typically ignores the bias and variance consequences of data cleaning. We formulate a semiparametric model for causal inference with corrupted data to encompass both data cleaning and data analysis. We propose a new end-to-end procedure for data cleaning, estimation, and inference with data cleaning-adjusted confidence intervals. We prove √ n-consistency, Gaussian approximation, and semiparametric efficiency for our estimator of the causal parameter by finite sample arguments. Our key assumption is that the true covariates are approximately low rank. In our analysis, we provide nonasymptotic theoretical contributions to matrix completion, statistical learning, and semiparametric statistics. We verify the coverage of the data cleaning-adjusted confidence intervals in simulations.

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Section: Treatment Effects With Corrupted Datamentioning

confidence: 99%

Causal Inference with Corrupted Data: Measurement Error, Missing Values, Discretization, and Differential Privacy

Agarwal¹,

Singh²

2021

Preprint

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“…Another recent exciting line of work that we build upon is that of panel data and matrix completion, see Amjad et al (2018Amjad et al ( , 2019; Arkhangelsky et al (2019); Bai and Ng (2019); Fernández-Val et al (2020); Athey et al (2021); Agarwal et al (2021c,a,b); Agarwal and Singh (2021). Some of these works allow for MNAR data and entries of a matrix to be deterministically missing.…”

Section: Introductionmentioning

confidence: 99%

Causal Matrix Completion

Agarwal,

Dahleh,

Shah

et al. 2021

Preprint

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Matrix completion is the study of recovering an underlying matrix from a sparse subset of noisy observations. Traditionally, it is assumed that the entries of the matrix are "missing completely at random" (MCAR), i.e., each entry is revealed at random, independent of everything else, with uniform probability. This is likely unrealistic due to the presence of "latent confounders", i.e., unobserved factors that determine both the entries of the underlying matrix and the missingness pattern in the observed matrix. For example, in the context of movie recommender systems-a canonical application for matrix completion-a user who vehemently dislikes horror films is unlikely to ever watch horror films. In general, these confounders yield "missing not at random" (MNAR) data, which can severely impact any inference procedure that does not correct for this bias.We develop a formal causal model for matrix completion through the language of potential outcomes, and provide novel identification arguments for a variety of causal estimands of interest. We design a procedure, which we call "synthetic nearest neighbors" (SNN), to estimate these causal estimands. We prove finite-sample consistency and asymptotic normality of our estimator. Our analysis also leads to new theoretical results for the matrix completion literature. In particular, we establish entry-wise, i.e., max-norm, finite-sample consistency and asymptotic normality results for matrix completion with MNAR data. As a special case, this also provides entry-wise bounds for matrix completion with MCAR data. Across simulated and real data, we demonstrate the efficacy of our proposed estimator.

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“…There are also recent papers that use matrix completion methods for the purpose of treatment effect estimation in panel models with two-way heterogeneity, e.g. Athey, Bayati, Doudchenko, Imbens and Khosravi (2017) and Amjad, Shah and Shen (2018), Chernozhukov, Hansen, Liao and Zhu (2020), and Fernández-Val, Freeman and Weidner (2020. Those papers do not require the additive separability between the regressors and error term in (1), but as a result they also have to make stronger assumptions and employ more complicated estimation methods than we do here.…”

Section: Introductionmentioning

confidence: 99%

Linear Panel Regressions with Two-Way Unobserved Heterogeneity

Freeman¹,

Weidner²

2021

Preprint

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This paper studies linear panel regression models in which the unobserved error term is an unknown smooth function of two-way unobserved fixed effects. In standard additive or interactive fixed effect models the individual specific and time specific effects are assumed to enter with a known functional form (additive or multiplicative), while we allow for this functional form to be more general and unknown. We discuss two different estimation approaches that allow consistent estimation of the regression parameters in this setting as the number of individuals and the number of time periods grow to infinity. The first approach uses the interactive fixed effect estimator in Bai ( 2009), which is still applicable here, as long as the number of factors in the estimation grows asymptotically. The second approach first discretizes the two-way unobserved heterogeneity (similar to what Bonhomme, Lamadon and Manresa 2017 are doing for one-way heterogeneity) and then estimates a simple linear fixed effect model with additive two-way grouped fixed effects. For both estimation methods we obtain asymptotic convergence results, perform Monte Carlo simulations, and employ the estimators in an empirical application to UK house price data.

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Low-Rank Approximations of Nonseparable Panel Models

Cited by 3 publications

References 24 publications

Causal Inference with Corrupted Data: Measurement Error, Missing Values, Discretization, and Differential Privacy

Causal Inference with Corrupted Data: Measurement Error, Missing Values, Discretization, and Differential Privacy

Causal Matrix Completion

Linear Panel Regressions with Two-Way Unobserved Heterogeneity

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