Choosing the Dictionary and Penalty for IV-LASSO
Abstract
Estimating an instrumental variables (IV) first stage with the least absolute shrinkage and selection operator (LASSO) requires choosing a dictionary and penalty. Existing rules target first-stage objectives, although these choices affect structural estimation. We derive a feasible approximate mean squared error (AMSE) criterion for full-sample IV-LASSO with one endogenous regressor and homoskedastic Gaussian errors. For a prespecified list of dictionary-penalty pairs, the criterion trades off approximation of the optimal instrument against a complexity cost that depends on the first two moments of the LASSO effective dimension and on the degree of endogeneity. The selected pair attains the smallest candidate-specific AMSE component up to vanishing relative error. In simulations calibrated to Paravisini et al. (2015), the criterion improves substantially on the plug-in rule at low endogeneity and on cross-validation at high endogeneity, with nearly identical results under non-Gaussian errors. A supplementary appendix formally extends analysis to a class of non-Gaussian errors.
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BibTeX
@misc{ma2026choosing,
title = {{Choosing the Dictionary and Penalty for IV-LASSO}},
author = {Yukun Ma and Manu Navjeevan and Bogdan Salahub},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.07033},
eprint = {2609.07033},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.07033},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Choosing the Dictionary and Penalty for IV-LASSO
AU - Yukun Ma
AU - Manu Navjeevan
AU - Bogdan Salahub
PY - 2026
DA - 2026/10/27
PB - arXiv
DO - 10.48550/arxiv.2609.07033
UR - https://arxiv.org/abs/2609.07033
AB - Estimating an instrumental variables (IV) first stage with the least absolute shrinkage and selection operator (LASSO) requires choosing a dictionary and penalty. Existing rules target first-stage objectives, although these choices affect structural estimation. We derive a feasible approximate mean squared error (AMSE) criterion for full-sample IV-LASSO with one endogenous regressor and homoskedastic Gaussian errors. For a prespecified list of dictionary-penalty pairs, the criterion trades off approximation of the optimal instrument against a complexity cost that depends on the first two moments of the LASSO effective dimension and on the degree of endogeneity. The selected pair attains the smallest candidate-specific AMSE component up to vanishing relative error. In simulations calibrated to Paravisini et al. (2015), the criterion improves substantially on the plug-in rule at low endogeneity and on cross-validation at high endogeneity, with nearly identical results under non-Gaussian errors. A supplementary appendix formally extends analysis to a class of non-Gaussian errors.
ER -