The Falsification Adaptive Set in Linear Models with Instrumental Variables that Violate the Exogeneity or Exclusion Restriction

12/09/2022
by   Nicolas Apfel, et al.
0

For the classical linear model with an endogenous variable estimated by the method of instrumental variables (IVs) with multiple instruments, Masten and Poirier (2021) introduced the falsification adaptive set (FAS). When a model is falsified, the FAS reflects the model uncertainty that arises from falsification of the baseline model. It is the set of just-identified IV estimands, where each relevant instrument is considered as the just-identifying instrument in turn, whilst all other instruments are included as controls. It therefore applies to the case where the exogeneity assumption holds and invalid instruments violate the exclusion assumption only. We propose a generalized FAS that reflects the model uncertainty when some instruments violate the exogeneity assumption and/or some instruments violate the exclusion assumption. This FAS is the set of all possible just-identified IV estimands where the just-identifying instrument is relevant. There are a maximum of k_z2^k_z-1 such estimands, where k_z is the number of instruments. If there is at least one relevant instrument that is valid in the sense that it satisfies the exogeneity and exclusion assumptions, then this generalized FAS is guaranteed to contain β and therefore to be the identified set for β.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
10/20/2021

One Instrument to Rule Them All: The Bias and Coverage of Just-ID IV

Two-stage least squares estimates in heavily over-identified instrumenta...
research
12/30/2018

Salvaging Falsified Instrumental Variable Models

What should researchers do when their baseline model is refuted? We prov...
research
07/10/2022

Detecting Grouped Local Average Treatment Effects and Selecting True Instruments

In the context of an endogenous binary treatment with heterogeneous effe...
research
11/12/2020

Mostly Harmless Machine Learning: Learning Optimal Instruments in Linear IV Models

We provide some simple theoretical results that justify incorporating ma...
research
09/25/2020

Parameter Restrictions for the Sake of Identification: Is there Utility in Asserting that Perhaps a Restriction Holds?

Statistical modeling can involve a tension between assumptions and stati...
research
02/13/2016

Designing Intelligent Instruments

Remote science operations require automated systems that can both act an...
research
05/22/2022

Fast Instrument Learning with Faster Rates

We investigate nonlinear instrumental variable (IV) regression given hig...

Please sign up or login with your details

Forgot password? Click here to reset