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Weak instrumental variables due to nonlinearities in panel data: A Super Learner Control Function estimator

Monika Avila Marquez

arXiv 4 Apr 2025 · Econometrics

arXiv:2504.03228 · PDF · DOI · OpenAlex · Extracted main text

Abstract

A triangular structural panel data model with additive separable individual-specific effects is used to model the causal effect of a covariate on an outcome variable when there are unobservable confounders with some of them time-invariant. In this setup, a linear reduced-form equation might be problematic when the conditional mean of the endogenous covariate and the instrumental variables is nonlinear. The reason is that ignoring the nonlinearity could lead to weak instruments As a solution, we propose a triangular simultaneous equation model for panel data with additive separable individual-specific fixed effects composed of a linear structural equation with a nonlinear reduced form equation. The parameter of interest is the structural parameter of the endogenous variable. The identification of this parameter is obtained under the assumption of available exclusion restrictions and using a control function approach. Estimating the parameter of interest is done using an estimator that we call Super Learner Control Function estimator (SLCFE). The estimation procedure is composed of two main steps and sample splitting. We estimate the control function using a super learner using sample splitting. In the following step, we use the estimated control function to control for endogeneity in the structural equation. Sample splitting is done across the individual dimension. We perform a Monte Carlo simulation to test the performance of the estimators proposed. We conclude that the Super Learner Control Function Estimators significantly outperform Within 2SLS estimators.

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Most heavily cited references

The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.

ReferenceIntensityMentionsSectionsMain text
1Chernozhukov, V., D. Chetverikov, M. Demirer, E. Duflo, C. Hansen, W… (2018) Double/debiased machine learning for treatment and structural parameters0.84333100%
2Deryugina, T., G. Heutel, N. H. Miller, D. Molitor, and J. Reif (2019) The mortality and medical costs of air pollution: Evidence from changes in wind direction0.73732100%
3Guo, Z., M. Zheng, and P. Bühlmann (2022) Robustness against weak or invalid instruments: Exploring nonlinear treatment models with machine learning0.73732100%
4Van der Laan, M. J., E. C. Polley, and A. E. Hubbard (2007) Super learner0.73732100%
5Baltagi, B. H., D. Li, et al (2002) Series estimation of partially linear panel data models with fixed effects0.64422100%
6Robinson, P. M (1988) Root-n-consistent semiparametric regression0.64422100%
7Zabrocki, L., A. Alari, and T. Benmarhnia (2022) Improving the design stage of air pollution studies based on wind patterns0.64422100%
8Emmenegger, C. and P. Bühlmann (2023) Plug-in machine learning for partially linear mixed-effects models with repeated measurements0.6069322%
9Cai, Z., Y. Fang, and H. Li (2012) Weak instrumental variables models for longitudinal data0.51121100%
10Avila Márquez, M. and J. Kirshnakumar (2023, July) (2023) On the use of random forests to estimate triangular two-level panel data models with individual fixed effects0.40511100%

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Cited by, within the corpus

arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.

Citing paperIntensityMentionsSections
1Double Machine Learning for Static Panel Data with Instrumental Variables: New Method and Applications0.73732
2xtdml: Double Machine Learning Estimation to Static Panel Data Models with Fixed Effects in R0.40511