There are many economic parameters that depend on nonparametric first steps. Examples include games, dynamic discrete choice, average exact consumer surplus, and treatment effects. Often estimators of these parameters are asymptotically equivalent to a sample average of an object referred to as the influence function. The influence function is useful in local policy analysis, in evaluating local sensitivity of estimators, and constructing debiased machine learning estimators. We show that the influence function is a Gateaux derivative with respect to a smooth deviation evaluated at a point mass. This result generalizes the classic Von Mises (1947) and Hampel (1974) calculation to estimators that depend on smooth nonparametric first steps. We give explicit influence functions for first steps that satisfy exogenous or endogenous orthogonality conditions. We use these results to generalize the omitted variable bias formula for regression to policy analysis for and sensitivity to structural changes. We apply this analysis and find no sensitivity to endogeneity of average equivalent variation estimates in a gasoline demand application.
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Locally Robust Semiparametric Estimation
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.
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- Award ID(s):
- 1757140
- NSF-PAR ID:
- 10469095
- Editor(s):
- Imbens, G.
- Publisher / Repository:
- Econometric Society
- Date Published:
- Journal Name:
- Econometrica
- Volume:
- 90
- Issue:
- 4
- ISSN:
- 1468-0262
- Page Range / eLocation ID:
- https://doi.org/10.3982/ECTA16294
- Subject(s) / Keyword(s):
- Local robustness, orthogonal moments, double robustness, semiparametric estimation, bias, GMM.
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.3982/ECTA16294
