A maze of econometric equations leads to a clear destination, symbolizing bias reduction in economic modeling.

Navigating Economic Models: A Practical Guide to Handling Bias in Overidentified Data

Samir D’Costa in Business & Economy August 2025 • 4 min read.

"Uncover strategies for mitigating bias in overidentified linear models and learn how new estimators like UOJIVE1 and UOJIVE2 can enhance your economic analysis."

In the realm of economic research, overidentified two-stage least squares (TSLS) models have become increasingly common. Mogstad et al. (2021) noted that numerous papers from top economic journals utilized overidentified TSLS. However, a significant problem arises: overidentification introduces bias, distorting results and complicating analysis. This bias can be particularly severe, undermining the reliability of findings derived from these models.

The challenge lies in the inherent complexity of evaluating the bias in TSLS. Estimating the exact bias requires comprehensive knowledge of the distributions of both observable and unobservable variables—a condition that is rarely met in practice. Traditional methods often rely on strong assumptions, such as jointly normal error terms, which may not hold true for many economic scenarios. These assumptions, while enabling finite sample distribution evaluations, can be overly restrictive and impractical for economists.

To overcome these limitations, econometricians often turn to the concept of 'approximate bias.' This approach involves dividing the difference between an estimator and the target parameter into parts, focusing on the lower stochastic order component. While widely used, the existing definitions of approximate bias have limitations. The definition proposed by Nagar (1959) is confined to k-class estimators, while the definition used by Angrist et al. (1999) and Ackerberg and Devereux (2009) applies to a broader but still limited class of estimators. This paper addresses these gaps by formalizing a more generalized definition of approximate bias and expanding its applicability.

Tackling Bias: Introducing Approximately Unbiased Estimators

A maze of econometric equations leads to a clear destination, symbolizing bias reduction in economic modeling.

The challenge of overidentification bias in economic models has spurred the development of new estimators aimed at mitigating this issue. This paper introduces innovative estimators, UOJIVE1 and UOJIVE2, designed to be approximately unbiased, thereby enhancing the accuracy and reliability of economic analyses.

UOJIVE1 and UOJIVE2 represent significant advancements in addressing bias, each with unique characteristics and strengths. UOJIVE1 can be seen as a generalization of the existing estimator UIJIVE1. Crucially, both UOJIVE1 and UOJIVE2 have been proven to be consistent and asymptotically normal under a fixed number of instruments and controls as the sample size increases. These properties ensure that as more data becomes available, the estimators converge to the true parameter values, providing confidence in their results.

UOJIVE1: Building on UIJIVE1, UOJIVE1 offers refined bias reduction but relies on the absence of high leverage points in the data, making it sensitive to outliers.
UOJIVE2: In contrast, UOJIVE2 does not require this assumption, providing more robustness in the presence of high leverage points. Moreover, UOJIVE2 is consistent under many-instrument asymptotics, making it suitable for complex models with numerous instruments.

The properties of UOJIVE1 and UOJIVE2 make them valuable tools for economists, and their approximate bias are asymptotically vanishing which has been proved with provided formulations and derivations.

Moving Forward: Implications for Economic Research

The introduction of UOJIVE1 and UOJIVE2 offers a significant step forward in addressing the challenges posed by overidentification bias. These estimators provide economists with robust tools for analyzing complex models, offering consistency and asymptotic normality. The research highlights the importance of selecting the appropriate estimator based on the characteristics of the data, particularly regarding the presence of high leverage points and potential outliers. By leveraging these advancements, economists can achieve more accurate and reliable insights, enhancing the validity and applicability of their research findings.

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This article is based on research published under:

DOI-LINK: https://doi.org/10.48550/arXiv.2305.17615,

Title: Estimating Overidentified Linear Models With Heteroskedasticity And Outliers

Subject: econ.em

Authors: Lei Bill Wang

Published: 27-05-2023

Everything You Need To Know

What is overidentification bias, and why is it a problem in economic models?

Overidentification bias arises in overidentified two-stage least squares (TSLS) models, which are frequently used in economic research. This bias distorts results and complicates analysis, undermining the reliability of findings. The severity of the bias is a significant concern because it can lead to inaccurate conclusions and flawed policy recommendations. The difficulty lies in accurately estimating the bias, as it requires extensive knowledge of both observable and unobservable variable distributions, which is rarely available in real-world scenarios.

How do traditional methods attempt to address bias in economic models, and what are their limitations?

Traditional methods often rely on strong assumptions, like jointly normal error terms, to evaluate bias. However, these assumptions may not hold true in many economic scenarios, limiting their practicality. Estimating the exact bias is complex, requiring comprehensive information on variable distributions. Researchers often use 'approximate bias' which focuses on lower stochastic order components. Definitions like those by Nagar (1959) are limited to k-class estimators, while others like Angrist et al. (1999) and Ackerberg and Devereux (2009) have broader but still restricted applications.

What are UOJIVE1 and UOJIVE2, and how do they improve economic analysis?

UOJIVE1 and UOJIVE2 are innovative estimators designed to mitigate overidentification bias, enhancing the accuracy and reliability of economic analyses. UOJIVE1 builds on the existing UIJIVE1, offering refined bias reduction but is sensitive to high leverage points. UOJIVE2, on the other hand, provides more robustness in the presence of high leverage points and is consistent under many-instrument asymptotics. Both estimators are consistent and asymptotically normal as the sample size increases, ensuring they converge to true parameter values with more data. This means economists can have more confidence in the results from models that use them.

What are the key differences between UOJIVE1 and UOJIVE2, and when should each be used?

The primary difference lies in their robustness to high leverage points. UOJIVE1 offers refined bias reduction but is sensitive to outliers and high leverage points in the data. If the data contains high leverage points, UOJIVE1 may produce unreliable results. UOJIVE2 is more robust and does not require the assumption of the absence of high leverage points, making it suitable for a broader range of datasets. UOJIVE2's consistency under many-instrument asymptotics further extends its applicability to complex models with numerous instruments.

What are the broader implications of using UOJIVE1 and UOJIVE2 for economic research?

The introduction of UOJIVE1 and UOJIVE2 represents a significant step forward in tackling overidentification bias in economic research. By providing estimators with desirable properties such as consistency and asymptotic normality, these tools empower economists to analyze complex models more effectively. The ability to select the appropriate estimator based on data characteristics, especially regarding high leverage points, allows for more accurate and reliable insights. This leads to more valid and applicable research findings, ultimately enhancing the quality of economic analysis and the decisions informed by it.