Inference for Regression with Variables Generated by AI or Machine Learning (2402.15585v5)

Abstract: Researchers now routinely use AI or other machine learning methods to estimate latent variables of economic interest, then plug-in the estimates as covariates in a regression. We show both theoretically and empirically that naively treating AI/ML-generated variables as "data" leads to biased estimates and invalid inference. To restore valid inference, we propose two methods: (1) an explicit bias correction with bias-corrected confidence intervals, and (2) joint estimation of the regression parameters and latent variables. We illustrate these ideas through applications involving label imputation, dimensionality reduction, and index construction via classification and aggregation.

• The paper demonstrates that the traditional two-step approach leads to biased regression estimates due to measurement error in AI-generated variables.
• It employs Hamiltonian Monte Carlo to efficiently perform high-dimensional integration and jointly estimate both information retrieval and econometric models.
• Empirical tests on CEO behavior confirm that the one-step strategy produces less biased coefficient estimates even with limited unstructured data.

Addressing Bias in Analyzing Unstructured Data with a One-Step Inference Strategy

Analyzing unstructured data, such as text, images, and audio recordings, is becoming increasingly important in empirical research, particularly in economics. Typically, this analysis involves a two-step strategy: first, deriving quantitative representations from unstructured data using information retrieval models; and second, treating these representations as data in downstream econometric models for further analysis. While pragmatic, this approach is fraught with challenges, notably measurement error, which this paper rigorously examines. It posits that the conventional two-step strategy leads to biased inference on downstream regression coefficients due to this measurement error. Moreover, the magnitude of this bias is contingent on the relative sizes of measurement error and sampling error, potentially leading to incorrect empirical conclusions under certain conditions.

Theoretical Insights and Practical Solutions

Through a detailed examination, the paper provides a comprehensive theoretical framework that illustrates why and how the two-step strategy can lead to biased inference. This issue arises because the estimated latent variables inherent in the representations of unstructured data are treated as observed variables in subsequent econometric analysis, overlooking the measurement error introduced in the first step. As an alternative, the paper proposes a robust one-step strategy for valid inference that jointly estimates both the information retrieval and econometric models, thereby accommodating the measurement error directly.

Computational Methodology: A Novel Inference Approach

Implementing the one-step strategy poses significant computational challenges, particularly due to the necessity of high-dimensional numerical integration. This paper navigates these challenges by employing Hamiltonian Monte Carlo (HMC), a Markov Chain Monte Carlo algorithm that is well-suited for sampling from complex, high-dimensional distributions. Leveraged in conjunction with modern probabilistic programming languages, HMC facilitates scalable and efficient inference across large datasets. The practicality of this approach is underscored through comprehensive simulation exercises and an empirical application analyzing CEO behavior, demonstrating its superiority over the conventional two-step method.

Empirical Validation and Insights

The empirical analysis revisits a paper of CEO time use, contrasting findings from the one-step and two-step strategies. Notably, when the amount of unstructured data per observation is limited, the one-step strategy yields considerably less biased estimates of regression coefficients related to CEO behavior and firm performance. These outcomes are consistent across various simulation settings and empirical applications, underscoring the importance of the proposed methodology in addressing measurement error.

Towards Robust Analysis of Unstructured Data

This research marks a significant advance in the empirical analysis of unstructured data, providing a rigorous methodological foundation to combat the pervasive issue of measurement error. By integrating the information retrieval and econometric models, the one-step strategy offers a more accurate and theoretically sound approach to analyzing unstructured data. As the volume of such data continues to grow, this methodology will undoubtedly become a critical tool for researchers seeking to harness its full potential in empirical analysis.

Future Directions and Scalability

Looking ahead, the paper acknowledges the scalability limitations of HMC and suggests that alternative methods, such as variational inference, may offer viable solutions for analyzing massive datasets. The paper's insights and methodologies not only have immediate practical applications but also open avenues for future research in developing scalable and statistically robust tools for analyzing unstructured data.

In conclusion, this paper makes a pivotal contribution to the literature, challenging the prevailing two-step strategy and providing a compelling alternative that mitigates bias through a sophisticated computational approach. Its ramifications extend beyond economics, offering a valuable framework for any field grappling with the analysis of unstructured data.