A compass pointing in multiple, conflicting directions on a broken economic graph symbolizes economic model misspecification.

Is Your Economic Model Leading You Astray? How to Navigate the Pitfalls of Misspecification

Samir D’Costa in Business & Economy August 2025 • 5 min read.

"Uncover hidden flaws and safeguard your economic analysis from misleading conclusions. Learn to build robust models that stand up to scrutiny."

Economic models are essential for understanding and predicting complex systems, from financial markets to consumer behavior. However, constructing a perfect model is often impossible. Economists frequently rely on simplified versions that capture the main dynamics but inevitably introduce some degree of misspecification. The key challenge is understanding and mitigating the impact of these imperfections.

A common approach to dealing with model uncertainty is to use 'outer sets,' which are broader ranges of possible outcomes that contain the 'identified set'—the most precise characterization of what the model predicts. The idea is that even if the model isn't perfect, the true outcome should still fall within the outer set. However, a recent study reveals a surprising twist: when models are flawed, different outer sets can sometimes point to completely contradictory conclusions. This phenomenon, termed 'discordancy,' highlights a critical risk in economic analysis.

This article delves into the concept of discordant models and provides insights from the paper 'Discordant Relaxations of Misspecified Models'. We'll explore why these discrepancies arise, how to detect them, and what strategies can be used to ensure your economic analysis remains robust, even when your initial model isn't perfect. Understanding these issues is crucial for anyone who relies on economic models for decision-making, policy recommendations, or forecasting.

Why Outer Sets Can Lead You Down the Wrong Path

A compass pointing in multiple, conflicting directions on a broken economic graph symbolizes economic model misspecification.

In set-identified models, pinpointing an exact characterization of the identified set can be quite challenging. Consequently, researchers often employ non-sharp identification conditions, leading to empirical results grounded in an outer set of the identified set. This approach is conventionally seen as a valid and conservative strategy since an outer set encompasses the identified set. However, this seemingly safe practice can become problematic when the assumed model is not a perfect reflection of reality.

The study "Discordant Relaxations of Misspecified Models" illuminates that when a model is refuted by data, the application of multiple non-sharp identification conditions stemming from the same model can result in disjointed outer sets. This discordancy leads to conflicting empirical outcomes, undermining the reliability of the analysis. In simpler terms, imagine you're trying to estimate a range for a key economic parameter, like the unemployment rate. Using one set of assumptions might suggest a range of 4-6%, while another, equally plausible set of assumptions suggests 8-10%. Which range is correct? If the model is misspecified, neither might be, and relying on either could lead to poor decisions.

Conditional Moment Inequalities: These models involve constraints on the expected values of certain variables, given specific conditions. Misspecification here can lead to outer sets that conflict depending on which conditions are emphasized.
Artstein Inequalities: Used in various contexts including game theory, these inequalities provide bounds on probabilities. When a model using these inequalities is misspecified, different selections of these inequalities can produce irreconcilable outer sets.

The lesson here is that blindly trusting outer sets without considering the possibility of model misspecification can be dangerous. While outer sets are meant to provide a conservative estimate, they can be highly sensitive to the specific assumptions and conditions used to derive them.

The Path Forward: Toward More Robust Economic Analysis

The existence of discordant submodels poses a significant challenge to economic analysis. However, by understanding the potential for these issues, researchers and practitioners can take steps to mitigate the risks and build more robust and reliable models. The key is to move beyond a naive reliance on outer sets and embrace a more critical and nuanced approach to model validation. By adopting these strategies, we can ensure that economic models remain a valuable tool for understanding and shaping the world around us.

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This article is based on research published under:

DOI-LINK: https://doi.org/10.48550/arXiv.2012.11679,

Title: Discordant Relaxations Of Misspecified Models

Subject: econ.em

Authors: Lixiong Li, Désiré Kédagni, Ismaël Mourifié

Published: 21-12-2020

Everything You Need To Know

What is misspecification in economic models and why is it a problem?

Misspecification in economic models refers to the situation where a model does not perfectly reflect the real-world system it attempts to represent. This is often unavoidable because economic models are simplifications. The problem arises because misspecified models can lead to inaccurate predictions, misleading conclusions, and poor decision-making. The core issue is that the results derived from a misspecified model may not be reliable, potentially leading to incorrect policy recommendations or flawed business strategies.

How do 'outer sets' relate to model uncertainty, and what's the risk associated with them?

Outer sets are used to address model uncertainty by providing a broader range of possible outcomes that contain the 'identified set,' which represents the most precise predictions of a model. The intention is to provide a conservative estimate, ensuring that the true outcome falls within the outer set. However, the risk lies in the phenomenon of 'discordancy.' When models are flawed (misspecified), different outer sets, derived from the same model using different assumptions or conditions, can yield contradictory conclusions. This undermines the reliability of the analysis, as it's unclear which outer set, if any, reflects reality.

Can you explain 'discordancy' in the context of economic models, and how does it occur?

Discordancy describes the situation where, due to model misspecification, different outer sets derived from the same model lead to conflicting empirical outcomes. This occurs when researchers use non-sharp identification conditions to construct outer sets. The study "Discordant Relaxations of Misspecified Models" highlights that if the model is refuted by data, applying various non-sharp identification conditions from the same model can create disjointed outer sets. For instance, using different sets of assumptions within a misspecified model to estimate a range for a key economic parameter (like the unemployment rate) can result in completely different ranges, making it difficult to draw accurate conclusions.

What are 'Conditional Moment Inequalities' and 'Artstein Inequalities,' and how do they contribute to discordancy?

Conditional Moment Inequalities involve constraints on the expected values of certain variables under specific conditions. When a model using these inequalities is misspecified, the outer sets can conflict depending on which conditions are emphasized. Artstein Inequalities, used in contexts like game theory, provide bounds on probabilities. If a model using these inequalities is misspecified, different selections of these inequalities can produce irreconcilable outer sets. Both contribute to discordancy by allowing for the creation of conflicting empirical results when the underlying model is flawed.

What steps can be taken to ensure economic analysis remains robust in the face of model misspecification?

To build more robust economic analysis, it's crucial to move beyond a naive reliance on outer sets and embrace a more critical approach to model validation. This includes understanding the potential for discordancy and being aware of the sensitivity of outer sets to specific assumptions and conditions. Researchers and practitioners should carefully evaluate the assumptions underlying their models, test models against data, and consider multiple perspectives. By acknowledging the potential for model misspecification and the possibility of discordant results, we can improve the reliability and trustworthiness of economic analysis.