A1892
Title: The blessing of overfitting in instrumental variables: Inference with non-sparse high-dimensional signals
Authors: Ruei-Chi Lee - Rutgers (United States) [presenting]
Abstract: The Factor IV model is revisited in the context of high-dimensional IV regression from a new perspective, providing theoretical justification for recent empirical findings that the first stage signal is dense. Moreover, the implied first stage coefficients shrink toward zero as the number of instruments diverges, exhibiting local-to-zero behavior commonly used to describe settings with many weak instruments. Building on this characterization, an IV estimator is proposed based on pseudo-inverse OLS (ridgeless regression) combined with sample splitting. This procedure remains well defined when the number of first-stage regressors exceeds the sample size. The asymptotic distribution of the resulting sample-splitting IV estimator is derived under regimes with very many weak instruments, and it is shown that, when the number of first-stage regressors is sufficiently large, its asymptotic variance coincides with that of an oracle Factor IV estimator that directly observes the latent factors. The analysis also provides practical guidance on constructing many regressors from control variables and on deliberately adding noise instruments.
