Machine Learning for Instrumental Variables Estimation – MLIVE

Regressions with Instrumental Variables (IVs) play a central role in applied econometrics. They are employed to recover causal effects and to estimate structural models obtained from economic theory.

However, the reliability of estimates from IV regressions is often limited by the strong parametric restrictions imposed on the functions of interest, e.g. linearity assumptions. While these restrictions simplify the estimation procedure, they can rarely be justified from an economic perspective. Hence, they bring along the risk of misspecification: when the true regression function of interest does not follow the parametric model, the estimates are biased and the counterfactual analysis obtained from such models is misleading.

More flexible (nonparametric) estimation method for IV regressions have been proposed in the literature, but they are often difficult to implement, as they require running multiple nonparametric regressions and selecting multiple regularization parameters. Furthermore, they are computationally prohibitive in the presence of large datasets. In an era of big data, it is of utmost importance to rely on easy-to-implement econometric tools which are designed to handle large datasets while coming with strong theoretical guarantees.

In this project, we rely on the theory of Reproducing Kernel Hilbert Spaces, popular in machine learning, to develop estimation techniques for IV nonparametric regressions that (i) are easy to implement and compute, (ii) do not require selecting multiple regularization parameters, and (iii) avoid running multiple nonparametric regressions.

We have three specific objectives. The first is to derive the rates of convergence of the proposed estimators. Our second aim is to develop valid inference procedures for both the nonparametric regression function or some of its functional of interest. Finally, we want to develop R packages implementing our proposed techniques to facilitate their use in empirical research.