# When Predictions Become Regressors: A Split-Sample Correction for Biases in Downstream Inference

arXiv: https://arxiv.org/abs/2608.02909 · HTML: https://mlsanity.com/paper/2608.02909/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 30 references that are in the map.
- First posted on arXiv 3 Aug 2026.

## Builds on (most cited first, 9 of 9)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Prediction-Powered Inference](https://mlsanity.com/paper/2301.09633/) (2023)
- [Using Imperfect Surrogates for Downstream Inference: Design-based Supervised Learning for Social Science Applications of Large Language Models](https://mlsanity.com/paper/2306.04746/) (2023)
- [Large Language Models: An Applied Econometric Framework](https://mlsanity.com/paper/2412.07031/) (2024)
- [Political-LLM: Large Language Models in Political Science](https://mlsanity.com/paper/2412.06864/) (2024)
- [Inference for Regression with Variables Generated by AI or Machine Learning](https://mlsanity.com/paper/2402.15585/) (2024)
- [A Review of Multivariate Distributions for Count Data Derived from the Poisson Distribution](https://mlsanity.com/paper/1609.00066/) (2016)
- [Achieving Reliable Causal Inference with Data-Mined Variables: A Random Forest Approach to the Measurement Error Problem](https://mlsanity.com/paper/2012.10790/) (2020)
- [Improving Probabilistic Models in Text Classification via Active Learning](https://mlsanity.com/paper/2202.02629/) (2022)

## Abstract (arXiv)

Prediction-based methods, including Large Language Models (LLMs) and other machine learning techniques, are often used to construct measures of political phenomena that are difficult to quantify directly, such as policy positions in manifestos or emotions expressed on social media. In many applications, these prediction-generated measures are used as explanatory variables in regression models, even though they are measured with error. This leads to biased estimates. In this paper, we propose a simple solution to these biases: instrumental variables constructed from multiple measures created on independent splits of the original data. This approach is theoretically valid, easy to implement, and does not require new data. Through simulations, we show that this approach recovers estimates close to the true values, even in relatively small samples, while the standard approach can produce substantial bias in practice. We illustrate the method by revisiting two applications: whether gendered speech affects legislative outcomes in the German Parliament, and whether political risk influences poverty alleviation programs in China.