Data panel transforming into an unbiased graph using forward orthogonal deviations.

Decoding GMM: How to Avoid Bias in Your Panel Data Analysis

Beau Callahan in Business & Economy December 2025 • 4 min read.

"A simplified guide to using Forward Orthogonal Deviations to enhance the accuracy of your economic models."

Panel data analysis is a powerful tool for economists and researchers, allowing them to study trends and relationships over time across different entities. A cornerstone of this analysis is the Generalized Method of Moments (GMM), a statistical technique used to estimate parameters in models where theoretical equations provide moment conditions about the data.

However, GMM estimators are not without their challenges. One significant issue is the potential for bias, especially when dealing with dynamic panel data regressions. This bias can arise when the number of time periods in your dataset is substantial relative to the number of cross-sectional units, leading to skewed results and unreliable conclusions.

This article provides a simplified guide to understanding and mitigating bias in GMM estimators, focusing on the use of Forward Orthogonal Deviations (FOD). We'll explore how FOD transformations can help ensure the accuracy and reliability of your panel data analysis, making it more robust and trustworthy.

What are Forward Orthogonal Deviations (FOD)?

Data panel transforming into an unbiased graph using forward orthogonal deviations.

Forward Orthogonal Deviations (FOD) are a transformation technique used to remove fixed effects in panel data. Fixed effects represent time-invariant characteristics of individual entities (like companies or countries) that can confound your analysis if not properly addressed. FOD eliminates these effects by subtracting the average of future values from each observation.

Imagine you are tracking the performance of several companies over a decade. Each company has unique, unchanging attributes (e.g., founding principles, location) that influence its performance. FOD helps you isolate the impact of time-varying factors (e.g., market conditions, policy changes) by removing these constant, company-specific influences.

Fixed Effects Removal: FOD gets rid of time-invariant characteristics.
Future Data Averaging: It subtracts the average of future values from each data point.
Bias Reduction: This process helps minimize bias in GMM estimators, leading to more accurate results.
Transformation: FOD transforms data for dynamic panel analysis.

By applying FOD, you ensure that your GMM estimators are less susceptible to the bias caused by the correlation between the regressors and the fixed effects. This leads to more reliable and accurate estimates of the parameters you are interested in.

Making Sense of Your Data

By understanding and applying techniques like Forward Orthogonal Deviations, you can significantly improve the accuracy and reliability of your panel data analysis. This ensures that your insights are robust, trustworthy, and provide a solid foundation for informed decision-making. Embracing these methods not only enhances the quality of your research but also empowers you to uncover meaningful patterns and relationships within your data.

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.2212.14075,

Title: Forward Orthogonal Deviations Gmm And The Absence Of Large Sample Bias

Subject: econ.em

Authors: Robert F. Phillips

Published: 28-12-2022

Everything You Need To Know

What is the main challenge addressed when using Generalized Method of Moments (GMM) in panel data analysis?

The primary challenge when employing the Generalized Method of Moments (GMM) in panel data analysis is the potential for bias. This bias is especially concerning in dynamic panel data regressions. It occurs when the number of time periods is large relative to the cross-sectional units, which can lead to skewed results and unreliable conclusions. The goal is to mitigate this bias to ensure the accuracy and reliability of the analysis.

How does Forward Orthogonal Deviations (FOD) help improve the accuracy of panel data analysis using GMM?

Forward Orthogonal Deviations (FOD) enhance the accuracy of panel data analysis by addressing fixed effects, which are time-invariant characteristics specific to each entity. FOD removes these fixed effects, such as founding principles or location of a company, by subtracting the average of future values from each data point. This transformation helps to minimize bias in Generalized Method of Moments (GMM) estimators, providing more reliable and accurate estimates of the parameters being studied. Consequently, the insights drawn from the analysis become more robust and trustworthy.

Can you explain the concept of fixed effects in panel data analysis and why it's important to address them?

In panel data analysis, fixed effects represent time-invariant characteristics that are unique to individual entities, such as companies or countries. These characteristics remain constant over time and can significantly influence the outcomes of the analysis. Failing to address fixed effects can lead to biased results, as the effects of these unchanging attributes can confound the analysis. Addressing fixed effects is crucial for isolating the impact of time-varying factors and ensuring the accuracy and reliability of the conclusions drawn from the data. Forward Orthogonal Deviations (FOD) is one method used to eliminate these effects.

What specific steps does Forward Orthogonal Deviations (FOD) take to transform the data in panel data analysis, and how does this lead to bias reduction?

Forward Orthogonal Deviations (FOD) transform the data in panel data analysis by subtracting the average of future values from each observation. This process eliminates fixed effects, which represent time-invariant characteristics of the individual entities. By removing these fixed effects, FOD ensures that the Generalized Method of Moments (GMM) estimators are less susceptible to the bias caused by the correlation between regressors and these fixed effects. This transformation leads to more reliable and accurate estimates, as the analysis can then focus on the impact of time-varying factors rather than being skewed by constant, entity-specific attributes.

In practical terms, how does the application of Forward Orthogonal Deviations (FOD) impact the decision-making process based on panel data analysis results?

The application of Forward Orthogonal Deviations (FOD) significantly enhances the decision-making process by improving the accuracy and reliability of panel data analysis results. By mitigating the bias inherent in Generalized Method of Moments (GMM) estimators, FOD allows researchers and economists to draw more trustworthy conclusions from their data. This translates into more robust insights and a solid foundation for informed decision-making. With more reliable results, decision-makers can have greater confidence in the patterns and relationships they identify within the data, leading to better-informed strategies and more effective outcomes.