Economic growth driven by imperfect instruments

Invalid Instruments? How to Navigate Economic Research Like a Pro

Mira Elwood in Business & Economy August 2025 • 4 min read.

"Unlock new identification strategies in economic modeling, even when your instrumental variables aren't perfect."

In the world of economics, researchers often grapple with the challenge of determining cause-and-effect relationships. For example, does more education (the treatment variable) directly lead to higher earnings (the outcome variable)? Ideally, we'd love a clean, straightforward answer. But in real-world data, things get messy. Factors like innate ability or socioeconomic background (unobserved heterogeneity) can influence both education levels and earnings, making it difficult to isolate the true impact of schooling.

One common approach to tackle this endogeneity problem is using instrumental variables (IVs). A valid IV acts like a proxy, strongly related to the treatment but affecting the outcome only through that treatment. Think of it as a lever that moves the treatment variable without directly interfering with the outcome. However, finding these 'perfect' IVs is like searching for a unicorn. Real-world instruments often fall short, being either weakly related to the treatment (weak relevance) or having some sneaky direct influence on the outcome (failure of exclusion restriction).

But what if we could still get reliable results even with these imperfect instruments? This article explores how a novel approach using 'quasi-instrumental variables' (quasi-IVs) can provide robust identification, even when traditional IV assumptions are not fully met. Let's dive into how this strategy works, its potential applications, and what it means for economic research.

What are Quasi-Instrumental Variables and Why Should You Care?

Economic growth driven by imperfect instruments

The heart of this method lies in using quasi-IVs. A quasi-IV is a variable that, while related to the treatment, might not be perfectly 'valid' in the traditional sense. It could be endogenous (influenced by the same unobserved factors as the treatment) or not strictly excluded (having a potential direct effect on the outcome).

The trick is to combine two complementary quasi-IVs:

An excluded quasi-IV: This is relevant to the treatment but might be endogenous. Think of a proxy variable strongly associated with the unobserved factors that also drive the treatment decision.
An exogenous quasi-IV: This is exogenous conditional on the excluded quasi-IV. This variable is conditionally independent of the unobservables, relevant to the treatment, but possibly included.

Rank Invariance: Used in quantile models, this assumes that the relative ranking of individuals remains consistent across different potential outcomes.
Additive Models: Suitable when treatment effects are homogenous, simplifying the analysis.
Local Average Treatment Effect (LATE) Models: Useful for understanding treatment effects within specific subpopulations.

To be valid, Complementary validity requires that these two quasi-IVs are jointly relevant for the selection into treatment. Joint relevance means that W and Z also have a "jointly relevant" nonseparable effect on the selection into treatment.

The Future of Economic Research: Embracing Imperfection

The use of quasi-IVs represents a pragmatic step forward in economic research. It acknowledges the limitations of real-world data and offers a pathway to derive meaningful insights even when ideal instruments are elusive. As researchers continue to refine these methods and explore new applications, we can expect a more nuanced and robust understanding of complex economic phenomena. This approach empowers analysts to tackle previously intractable questions and make more informed decisions in a world of inherent uncertainty.

About this Article -

This article was crafted using a human-AI hybrid and collaborative approach. AI assisted our team with initial drafting, research insights, identifying key questions, and image generation. Our human editors guided topic selection, defined the angle, structured the content, ensured factual accuracy and relevance, refined the tone, and conducted thorough editing to deliver helpful, high-quality information.See our About page for more information.

This article is based on research published under:

DOI-LINK: https://doi.org/10.48550/arXiv.2401.0399,

Title: Identification With Possibly Invalid Ivs

Subject: econ.em

Authors: Christophe Bruneel-Zupanc, Jad Beyhum

Published: 08-01-2024

Everything You Need To Know

What are instrumental variables (IVs) and why are they important in economic research?

Instrumental variables (IVs) are used to determine cause-and-effect relationships, such as how education affects earnings, by acting as a proxy strongly related to the treatment variable (e.g., education) but only affecting the outcome (e.g., earnings) through that treatment. They help address the endogeneity problem that occurs when factors like ability or socioeconomic background influence both the treatment and outcome, making it difficult to isolate the true impact. Finding 'perfect' IVs is challenging because real-world instruments are often weakly related to the treatment or directly influence the outcome.

What are quasi-instrumental variables (quasi-IVs), and how do they differ from traditional instrumental variables?

Quasi-instrumental variables (quasi-IVs) are variables related to the treatment but may not be perfectly 'valid' in the traditional sense, as they may be endogenous or not strictly excluded. Unlike traditional instrumental variables, quasi-IVs don't need to meet the strict criteria of relevance and exclusion restriction. Instead, they are used in combination to achieve robust identification. This involves using an *excluded quasi-IV* (relevant to the treatment but potentially endogenous) and an *exogenous quasi-IV* (exogenous conditional on the excluded quasi-IV).

What is 'complementary validity' in the context of quasi-instrumental variables, and why is it important?

Complementary validity, within the context of quasi-instrumental variables, requires that the two quasi-IVs (the excluded and exogenous quasi-IVs) are jointly relevant for the selection into treatment. Joint relevance means that they have a "jointly relevant" nonseparable effect on the selection into treatment. This is crucial because the combination of these variables helps to identify the causal effect of the treatment even when individual instruments might be imperfect, thus providing a more robust estimation.

In what types of economic models can quasi-instrumental variables be effectively applied?

Quasi-instrumental variables can be effectively applied in several types of economic models, including: *Rank Invariance* in quantile models, which assumes the ranking of individuals remains consistent across potential outcomes; *Additive Models*, which are suitable when treatment effects are homogenous; and *Local Average Treatment Effect (LATE) Models*, which are useful for understanding treatment effects within specific subpopulations. The choice of model depends on the specific assumptions one is willing to make about the treatment effects and the structure of the data.

What are the implications of using quasi-instrumental variables for the future of economic research?

The use of quasi-instrumental variables represents a pragmatic advancement in economic research by acknowledging the limitations of real-world data. This approach allows researchers to derive meaningful insights even when ideal instruments are unattainable. As these methods are refined, a more nuanced understanding of complex economic phenomena can be achieved. Analysts are empowered to tackle previously intractable questions, making informed decisions in uncertain environments. This suggests a move towards more flexible and robust methodologies, ultimately enhancing the reliability and applicability of economic research.