Inferential Theory for Granular Instrumental Variables in High Dimensions

• URL: http://arxiv.org/abs/2201.06605v2
• Date: Mon, 25 Sep 2023 16:56:07 GMT
• Title: Inferential Theory for Granular Instrumental Variables in High Dimensions
• Authors: Saman Banafti and Tae-Hwy Lee
• Abstract summary: Granular Instrumental Variables (GIV) methodology exploits panels with factor error structures to construct instruments to estimate structural time series models. We show that the sampling error in the estimated instrument and factors is negligible when considering the limiting distribution of the structural parameters. Monte Carlo evidence is presented to support our theory and application to the global crude oil market leads to new results.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The Granular Instrumental Variables (GIV) methodology exploits panels with factor error structures to construct instruments to estimate structural time series models with endogeneity even after controlling for latent factors. We extend the GIV methodology in several dimensions. First, we extend the identification procedure to a large $N$ and large $T$ framework, which depends on the asymptotic Herfindahl index of the size distribution of $N$ cross-sectional units. Second, we treat both the factors and loadings as unknown and show that the sampling error in the estimated instrument and factors is negligible when considering the limiting distribution of the structural parameters. Third, we show that the sampling error in the high-dimensional precision matrix is negligible in our estimation algorithm. Fourth, we overidentify the structural parameters with additional constructed instruments, which leads to efficiency gains. Monte Carlo evidence is presented to support our asymptotic theory and application to the global crude oil market leads to new results.

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