Skip to main content

A Note on the Topology of the First Stage of 2SLS with Many Instruments

Tchuente, Guy (2021) A Note on the Topology of the First Stage of 2SLS with Many Instruments. Working paper. arXiv (Submitted) (KAR id:98820)

PDF Pre-print
Language: English

Download (172kB)
[thumbnail of 2106.15003.pdf]
This file may not be suitable for users of assistive technology.
Request an accessible format
Official URL:


The finite sample properties of estimators are usually understood or approximated using asymptotic theories. Two main asymptotic constructions have been used to characterize the presence of many instruments. The first assumes that the number of instruments increases with the sample size. I demonstrate that in this case, one of the key assumptions used in the asymptotic construction may imply that the number of ``effective" instruments should be finite, resulting in an internal contradiction. The second asymptotic representation considers that the number of instrumental variables (IVs) may be finite, infinite, or even a continuum. The number does not change with the sample size. In this scenario, the regularized estimator obtained depends on the topology imposed on the set of instruments as well as on a regularization parameter. These restrictions may induce a bias or restrict the set of admissible instruments. However, the assumptions are internally coherent. The limitations of many IVs asymptotic assumptions provide support for finite sample distributional studies to better understand the behavior of many IV estimators.

Item Type: Monograph (Working paper)
Subjects: H Social Sciences
H Social Sciences > HA Statistics
Divisions: Divisions > Division of Human and Social Sciences > School of Economics
Depositing User: Guy Tchuente Nguembu
Date Deposited: 06 Dec 2022 22:47 UTC
Last Modified: 09 Dec 2022 10:37 UTC
Resource URI: (The current URI for this page, for reference purposes)
Tchuente, Guy:
  • Depositors only (login required):


Downloads per month over past year