Two-Step Estimation and Inference with Possibly Many Included Covariates

By M. D. Cattaneo, Michael Jansson, Xinwei Ma. 2018

69 citations recorded by the source corpus.

We study the implications of including many covariates in a first-step estimate entering a two-step estimation procedure. We find that a first-order bias emerges when the number of included covariates is “large” relative to the square-root of sample size, rendering standard inference procedures invalid. We show that the jackknife is able to estimate this “many covariates” bias consistently, thereby delivering a new automatic bias-corrected two-step point estimator. The jackknife also consistently estimates the standard error of the original two-step point estimator. For inference, we develop a valid post-bias-correction bootstrap approximation that accounts for the additional variability introduced by the jackknife bias-correction. We find that the jackknife bias-corrected point estimator and the bootstrap post-bias-correction inference perform excellent in simulations, offering important improvements over conventional two-step point estimators and inference procedures, which are not robust to including many covariates. We apply our results to an array of distinct treatment effect, policy evaluation, and other applied microeconomics settings. In particular, we discuss production function and marginal treatment effect estimation in detail.

Subfields: Statistics and Probability

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Citations in the corpus

Deep Neural Networks for Estimation and Inference: Application to Causal Effects and Other Semiparametric Estimands (2018, background): “Weaker variance-related assumptions, or “overﬁtting” robustness (Cattaneo, Jansson, and Ma (2019)), may also be possible following deep learning, but are less automatic at present.”
Cross-fitting and fast remainder rates for semiparametric estimation (2017, unknown): “Also, Cattaneo, Jansson, and Ma (2017) show that the jackknife can be used to reduce bias of plug-in series estimators.”
High-dimensional econometrics and regularized GMM (2018, background): “Within the same framework, [38] extend this work to address inference about parameters estimated using two-step procedures where the first step is a linear regression with many variables.”
Econometric Methods for Program Evaluation (2018, methodology): “The most popular approaches for validating RD designs in practice include: (i) testing for balance on pre-intervention covariates among units near the cutoff (Lee, 2008), (ii) testing for continuity of the score’s density function near the cutoff (McCrary, 2008; Cattaneo et al., 2017c), and (iii) gr”
Estimation and Inference about Heterogeneous Treatment Effects in High-Dimensional Dynamic Panels. (2017, background): “ctional (Andrews (1994), Newey (1994), van der Vaart (1998), Robinson (1988), Ai and Chen (2003), Robins and Rotnitzky (1995), Belloni et al. (2015), Chen and Christensen (2018), Kline et al. (2018), Cattaneo et al. (2019)), dependent (Chen and Christensen (2015), Li and Liao (2020)) and panel data ”
Double Debiased Machine Learning Nonparametric Inference with Continuous Treatments (2019, unknown): “Alternative estimators for estimating the GPS can be the kernel density estimator, the artificial neural networks in Chen and White (1999), the Lasso methods in Su et al.”
Targeted Undersmoothing. (2017, methodology): “This behavior can be viewed as a failure of the delta-method in moderate or high-dimensional models; see [20].”