Post-Selection and Post-Regularization Inference in Linear Models with Many Controls and Instruments

By Victor Chernozhukov, Christian Hansen, Martin Spindler. 2015

208 citations recorded by the source corpus.

In this note, we offer an approach to estimating structural parameters in the presence of many instruments and controls based on methods for estimating sparse high-dimensional models. We use these high-dimensional methods to select both which instruments and which control variables to use. The approach we take extends Belloni et al. (2012), which covers selection of instruments for IV models with a small number of controls, and extends Belloni, Chernozhukov and Hansen (2014), which covers selection of controls in models where the variable of interest is exogenous conditional on observables, to accommodate both a large number of controls and a large number of instruments. We illustrate the approach with a simulation and an empirical example. Technical supporting material is available in a supplementary appendix here.

Subfields: Economics and Econometrics, Marketing

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Economics and Econometrics

In Marketing

Citations in the corpus

The Econometrics of Randomized Experiments (2016, methodology): “…of interest have low dimension (that is, a small number of covariates have important interactions with the treatment), valid confidence intervals can be derived (without using sample splitting as described above); see, e.g., Chernozhukov, Hansen, and Spindler (2015) and references therein.”
Double/Debiased Machine Learning for Treatment and Causal Parameters (2016, methodology): “ C()-statistic, or the orthogonal score statistic, has been explicitly used for testing and estimation in highdimensional sparse models in [11]. The discussion of Neyman’s construction here draws on [30]. DOUBLE MACHINE LEARNING 15 where the nuisance parameter is = (0;vec()0)02TDˆ Rp; p= p 0 + dp 0;”
Program evaluation with high-dimensional data (2013, methodology): “…estimates of the eligibility effect from the linear model without selection and with selection using the approach of Belloni et al. (2014a) and estimates of the participation effect from linear instrumental variables estimation without selection and with selection as in Chernozhukov et al. (2015).”
Sparse Signals in the Cross‐Section of Returns (2018, unknown): “Belloni et al. (2012, 2014) and Chernozhukov et al. (2015) apply the LASSO to estimate treatment effects in settings where there are a large number of (potentially weak) instruments.”
Program evaluation and causal inference with high-dimensional data (2013, methodology): “For example, Chernozhukov et al. (2015a) 5 provide estimates of parameters characterizing a simple structural demand model based loosely on the analysis in Berry et al. (1995) using the framework developed here; see also Chernozhukov et al. (2015b).”
Double machine learning for treatment and causal parameters (2016, background): “The discussion of Neyman’s construction here draws on [28].”
Double/debiased machine learning for treatment and structural parameters (2017, unknown): “The discussion of Neyman’s construction here draws on Chernozhukov et al. (2015a).”