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Locally Robust Semiparametric Estimation

Journal: Econometrica

Date: 20220701

Author: Chernozhukov, Victor; Escanciano, Juan Carlos; Ichimura, Hidehiko; Newey, Whitney K.; Robins, James M.

Abstract:
Many economic and causal parameters depend on nonparametric or high dimensional first steps. We give a general construction of locally robust/orthogonal moment functions for GMM, where first steps have no effect, locally, on average moment functions. Using these orthogonal moments reduces model selection and regularization bias, as is important in many applications, especially for machine learning first steps. Also, associated standard errors are robust to misspecification when there is the same number of moment functions as parameters of interest. We use these orthogonal moments and cross-fitting to construct debiased machine learning estimators of functions of high dimensional conditional quantiles and of dynamic discrete choice parameters with high dimensional state variables. We show that additional first steps needed for the orthogonal moment functions have no effect, globally, on average orthogonal moment functions. We give a general approach to estimating those additional first steps. We characterize double robustness and give a variety of new doubly robust moment functions. We give general and simple regularity conditions for asymptotic theory.

Link: Google Scholar

Key Findings

Debiased GMM Reduces Selection Bias

The debiased Generalized Method of Moments (GMM) estimator significantly reduces model selection and regularization bias compared to plug-in GMM, leading to more reliable statistical inference.

Improved Standard Errors

When using the same number of moment functions as parameters, standard errors are robust to misspecification, providing more reliable confidence intervals.

Double Robustness

The orthogonal moment functions exhibit double robustness - estimation remains consistent if either the first step or the adjustment term is correctly specified.

Performance Comparison: Linear Model Results

  • Debiased GMM shows consistently lower bias compared to plug-in GMM across sample sizes
  • Coverage probabilities for debiased GMM remain closer to nominal 95% level
  • Standard deviation remains stable even with increasing sample size

Coverage Probabilities Across Methods

  • Debiased GMM maintains coverage probabilities close to 95% nominal level
  • Plug-in GMM shows significant deterioration in coverage with larger samples
  • Results demonstrate superior inference properties of debiased approach

Monte Carlo Simulation Results

  • Standard errors remain stable across sample sizes for debiased GMM
  • Median standard errors align well with actual standard deviations
  • Results demonstrate reliability of asymptotic approximations

Contribution and Implications

  • Provides a general framework for constructing debiased estimators that are robust to first-step estimation error
  • Enables reliable statistical inference even with machine learning methods in first-step estimation
  • Demonstrates practical improvements in finite sample performance compared to traditional methods
  • Offers new tools for empirical researchers working with high-dimensional data and complex models

Data Sources

  • Bias comparison chart constructed using data from Table I, showing linear specification results
  • Coverage probability chart based on coverage results from Table I for different sample sizes
  • Standard error comparison uses Median SE and DB SD columns from Table I