Automatic Locally Robust GMM with Machine-Learning-Generated Regressors
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866914396461072384 |
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| author | Escanciano, Juan Carlos Pérez-Izquierdo, Telmo |
| author_facet | Escanciano, Juan Carlos Pérez-Izquierdo, Telmo |
| contents | Machine-learning (ML) methods now routinely generate regressors used in subsequent econometric analyses, for example, estimated propensity scores, control-function residuals, imputed covariates, learned proxies, or low-dimensional embeddings of high-dimensional data. As these ML-generated regressors become ubiquitous, the lack of general inference methods for models that use them has become a critical limitation. Standard plug-in and Double ML procedures ignore how generated regressors enter later stages, leading to large biases and invalid inference. We develop a three-step locally robust GMM framework for inference with ML generated regressors. A key new insight is downstream local robustness: by a functional chain rule, moment functions that are constructed to be orthogonal to the second step eliminate the complicated indirect (conditioning) effects from the ML-generated regressors. We show how to implement this automatically by estimating the associated Riesz representers through cross-fitted auxiliary regressions, allowing for generic non-Donsker ML in both early steps. In leading treatment-effect and counterfactual settings, simulations demonstrate severe bias in existing methods and reductions of 85-95% using our procedures. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2301_10643 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Automatic Locally Robust GMM with Machine-Learning-Generated Regressors Escanciano, Juan Carlos Pérez-Izquierdo, Telmo Econometrics Machine-learning (ML) methods now routinely generate regressors used in subsequent econometric analyses, for example, estimated propensity scores, control-function residuals, imputed covariates, learned proxies, or low-dimensional embeddings of high-dimensional data. As these ML-generated regressors become ubiquitous, the lack of general inference methods for models that use them has become a critical limitation. Standard plug-in and Double ML procedures ignore how generated regressors enter later stages, leading to large biases and invalid inference. We develop a three-step locally robust GMM framework for inference with ML generated regressors. A key new insight is downstream local robustness: by a functional chain rule, moment functions that are constructed to be orthogonal to the second step eliminate the complicated indirect (conditioning) effects from the ML-generated regressors. We show how to implement this automatically by estimating the associated Riesz representers through cross-fitted auxiliary regressions, allowing for generic non-Donsker ML in both early steps. In leading treatment-effect and counterfactual settings, simulations demonstrate severe bias in existing methods and reductions of 85-95% using our procedures. |
| title | Automatic Locally Robust GMM with Machine-Learning-Generated Regressors |
| topic | Econometrics |
| url | https://arxiv.org/abs/2301.10643 |