Alexandre Belloni, Victor Chernozhukov, Christian Hansen, Damian Kozbur
arXiv 24 Nov 2014 · Statistics — Methodology · publishedJournal of Business and Economic Statistics (2015) · 183 citations (OpenAlex)
arXiv:1411.6507 · PDF · DOI · OpenAlex · Extracted main text
We consider estimation and inference in panel data models with additive unobserved individual specific heterogeneity in a high dimensional setting. The setting allows the number of time varying regressors to be larger than the sample size. To make informative estimation and inference feasible, we require that the overall contribution of the time varying variables after eliminating the individual specific heterogeneity can be captured by a relatively small number of the available variables whose identities are unknown. This restriction allows the problem of estimation to proceed as a variable selection problem. Importantly, we treat the individual specific heterogeneity as fixed effects which allows this heterogeneity to be related to the observed time varying variables in an unspecified way and allows that this heterogeneity may be non-zero for all individuals. Within this framework, we provide procedures that give uniformly valid inference over a fixed subset of parameters in the canonical linear fixed effects model and over coefficients on a fixed vector of endogenous variables in panel data instrumental variables models with fixed effects and many instruments. An input to developing the properties of our proposed procedures is the use of a variant of the Lasso estimator that allows for a grouped data structure where data across groups are independent and dependence within groups is unrestricted. We provide formal conditions within this structure under which the proposed Lasso variant selects a sparse model with good approximation properties. We present simulation results in support of the theoretical developments and illustrate the use of the methods in an application aimed at estimating the effect of gun prevalence on crime rates.
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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 | Cook and Ludwig (2006) The social costs of gun ownership | 1.000 | 27 | 3 | 100% |
| 2 | Belloni and Chernozhukov (2013) Least Squares After Model Selection in High-dimensional Sparse Models | 0.928 | 4 | 3 | 100% |
| 3 | Belloni, Chernozhukov, and Hansen (2014) Inference on Treatment Effects After Selection Amongst High-Dimensional Controls self | 0.916 | 13 | 6 | 77% |
| 4 | Belloni, Chen, Chernozhukov, and Hansen (2012) Sparse Models and Methods for Optimal Instruments with an Application to Eminent Domain | 0.909 | 16 | 6 | 75% |
| 5 | Bickel, Ritov, and Tsybakov (2009) Simultaneous analysis of Lasso and Dantzig selector | 0.737 | 3 | 2 | 100% |
| 6 | Arellano (1987) Computing Robust Standard Errors for Within-Groups Estimators | 0.737 | 3 | 2 | 100% |
| 7 | Leeb and Pötscher (2008) Can one estimate the unconditional distribution of post-model-selection estimators? | 0.737 | 3 | 2 | 100% |
| 8 | Jing, Shao, and Wang (2003) Self-normalized Cramr-type large deviations for independent random variables | 0.644 | 3 | 2 | 67% |
| 9 | Belloni, Chernozhukov, and Hansen (2010) LASSO Methods for Gaussian Instrumental Variables Models self | 0.644 | 2 | 2 | 100% |
| 10 | Bertrand, Duflo, and Mullainathan (2004) How Much Should We Trust Differences-in-Differences Estimates? | 0.644 | 2 | 2 | 100% |
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