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Inferential Theory for Granular Instrumental Variables in High Dimensions

Author

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  • Saman Banafti
  • Tae-Hwy Lee
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.

Suggested Citation

  • Saman Banafti & Tae-Hwy Lee, 2022. "Inferential Theory for Granular Instrumental Variables in High Dimensions," Papers 2201.06605, arXiv.org, revised Sep 2023.
    • Handle: RePEc:arx:papers:2201.06605
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    Cited by:

    1. Eric Qian, 2023. "Heterogeneity-robust granular instruments," Papers 2304.01273, arXiv.org, revised Jun 2024.

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    More about this item

    JEL classification:

    • C26 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Instrumental Variables (IV) Estimation
    • C36 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Instrumental Variables (IV) Estimation
    • C38 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Classification Methdos; Cluster Analysis; Principal Components; Factor Analysis

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