Nonstandard Errors in AI Agents
Organizations: Naveen Jindal School of Management, University of Texas at Dallas
Abstract
We study whether state-of-the-art AI coding agents, given the same data and research question, produce the same empirical results. Deploying 150 autonomous Claude Code agents to independently test six hypotheses about market quality trends in NYSE TAQ data for SPY (2015--2024), we find that AI agents exhibit sizable nonstandard errors (NSEs), that is, uncertainty from agent-to-agent variation in analytical choices, analogous to those documented among human researchers. AI agents diverge substantially on measure choice (e.g., autocorrelation vs.\ variance ratio, dollar vs.\ share volume). Different model families (Sonnet 4.6 vs.\ Opus 4.6) exhibit stable ``empirical styles,'' reflecting systematic differences in methodological preferences. In a three-stage feedback protocol, AI peer review (written critiques) has minimal effect on dispersion, whereas exposure to top-rated exemplar papers reduces the interquartile range of estimates by 80--99% within converging measure families. Convergence occurs both through within-family estimation tightening and through agents switching measure families entirely, but convergence reflects imitation rather than understanding. These findings have implications for the growing use of AI in automated policy evaluation and empirical research.
Figures & tables
| Hyp | Q10 | Q25 | Median | Q75 | Q90 | IQR | IDR | |
|---|---|---|---|---|---|---|---|---|
| H1 | 150 | 1.65 | 0.74 | 0.06 | 1.70 | 2.86 | 2.43 | 4.51 |
| H2 | 150 | 6.74 | 6.63 | 6.21 | 6.21 | 6.19 | 0.43 | 0.55 |
| H3 | 150 | 1.17 | 2.33 | 4.75 | 7.61 | 9.21 | 5.28 | 8.05 |
| H4 | 150 | 4.71 | 4.60 | 5.84 | 6.09 | 6.09 | 10.69 | 10.80 |
| H5 | 150 | 2.98 | 3.00 | 3.08 | 3.54 | 3.67 | 0.54 | 0.69 |
| H6 | 150 | 14.97 | 13.23 | 10.31 | 2.89 | 1.35 | 10.34 | 13.62 |
| Hypothesis | Median | IQR | IDR | |
|---|---|---|---|---|
| H1:autocorrelation | 87 | 0.33 | 2.73 | 7.40 |
| H1:variance_ratio | 63 | 0.05 | 1.45 | 2.70 |
| H2 (all) | 150 | 6.21 | 0.43 | 0.55 |
| H3 (all) | 150 | 4.75 | 5.28 | 8.05 |
| H4:dollar_volume | 90 | 6.09 | 0.25 | 0.82 |
| H4:share_volume | 60 | 4.60 | 0.11 | 0.55 |
| Hyp | Overall IQR | Dominant source | Within-source IQR |
|---|---|---|---|
| H1 | 2.43 | Hypothesis abstraction (AC vs VR) + sub-forks (abs/signed, 1min/5min) | AC: 2.74, VR: 1.45. Within AC sub-cells: 0.02–0.34. |
| H2 | 0.43 | Specification (log vs level OLS) | Level: 0.003. Log: 0.11 |
| H3 | 5.28 | Specification (trade weighting) | Equal-wtd: 3.26. Vol-wtd: 2.04. Dollar-wtd: 1.26 |
| H4 | 10.69 | Hypothesis abstraction (dollar vs share volume) | Dollar: 0.25. Share: 0.11 |
| H5 | 0.54 | Specification (log vs level OLS) | Level: 0.005. Log: 0.12 |
| H6 | 10.34 | Hypothesis abstraction (price impact vs Amihud vs Kyle ) | Price impact: 2.59. Amihud: 1.35 |
| Hypothesis | Fork | Sonnet 4.6 ( =100) | Opus 4.6 ( =50) | Test |
| H1 | Autocorrelation | 87% | 0% | 10.97*** |
| Variance ratio | 13% | 100% | ||
| Level OLS | 96% | 36% | ||
| Log OLS | 4% | 64% | ||
| H2 | Level OLS | 90% | 14% | 37.64*** |
| Log OLS | 10% | 86% |
| Hyp | S1 IQR | S2 IQR | S3 IQR | S1 S2 | S2 S3 | S1 S3 |
|---|---|---|---|---|---|---|
| H1 | 2.43 | 2.69 | 5.68 | 10.7% | 111.1% | 133.6% |
| H2 | 0.43 | 0.43 | 0.01 | 0.2% | 98.1% | 98.1% |
| H3 | 5.28 | 5.56 | 3.01 | 5.4% | 46.0% | 43.0% |
| H4 | 10.69 | 10.69 | 10.69 | 0.0% | 0.0% | 0.0% |
| H5 | 0.54 | 0.54 | 0.96 | 0.2% | 78.1% | 78.4% |
| H6 | 10.34 | 10.44 | 2.09 | 1.0% | 80.0% | 79.8% |
| Family | S1 IQR | S3 IQR | IQR | -value | ||
| Panel A: All agents (S1 and S3 populations may differ) | ||||||
| H1:autocorrelation | 87 | 25 | 2.74 | 0.13 | 95.4% | |
| H1:variance_ratio | 63 | 125 | 1.45 | 5.51 | 281.5% | |
| H4:dollar_volume | 90 | 45 | 0.25 | 0.007 | 97.0% | |
| H4:share_volume | 60 | 88 | 0.11 | 0.001 | 99.3% | |
| Panel B: Stayers only (same agents in S1 and S3) and unstratified | ||||||
| Category | Fork | Distribution |
|---|---|---|
| Measure | H1 measure family | autocorrelation 58%, variance ratio 42% |
| H1 abs vs. signed | absolute 73%, signed 27% | |
| H4 measure family | dollar volume 60%, share volume 40% | |
| H6 measure type | price impact 56%, Amihud 40%, Kyle 4% | |
| Estimation | Functional form | level OLS 56%, log OLS 44% |
| SE correction | HAC 59%, NW 21%, robust/HC3 11%, none 9% |
| Hypothesis | Fork | -stat | Sig. | |
| H1: Efficiency | abs_or_signed | 0.165 | 29.3 | |
| measure_family | 0.165 | 29.1 | ||
| llm (Sonnet/Opus) | 0.132 | 22.5 | ||
| scale (log/level) | 0.085 | 4.5 | ||
| H2: Quoted Spread | scale (log/level) | 0.882 | 1110.8 | |
| llm (Sonnet/Opus) | 0.446 | 119.0 |
| Property | Human ( Menkveld et al., 2024 ) | AI (this paper) |
|---|---|---|
| Paradigm diversity | High (linear trend 35%, relative changes 58%, log-diff 6%) | Low (level regression 56%, log regression 44%; no relative changes) |
| Measure diversity | Moderate | High (model-dependent) |
| Jensen’s inequality | Major source of outliers | Absent |
| Feedback response | Gradual, each stage contributes | Binary: exemplars work, critiques do not |
| PE quality NSE | Higher quality 33% IQR | Mixed (Appendix B ): significant for H4, H6; not for H1, H2, H5 |
| Convergence S1 S3/S4 | 47% IQR (4 stages) | 80% to 99% stratified (3 stages) |
Appendix figures & tables2 assets
Supplementary material from the paper’s appendix.
Appendix
| Mean | Median | Min | Max | ||
| API cost ($ per agent-stage) | |||||
| Sonnet S1 | 3.54 | 2.85 | 1.30 | 14.03 | |
| Sonnet S2 | 2.13 | 1.58 | 0.69 | 13.63 | |
| Sonnet S3 | 3.12 | 2.56 | 1.27 | 10.52 | |
| Opus S1 | 5.59 | 4.19 | 1.83 | 18.70 | |
| Opus S2 | 3.21 | 2.57 | 1.31 | 19.05 | |
| Hyp | Spearman | -value | Low-rated IQR | Mid-rated IQR | High-rated IQR |
|---|---|---|---|---|---|
| H1 | 0.040 | 0.628 | 2.45 | 2.31 | 1.09 |
| H2 | 0.125 | 0.127 | 0.06 | 0.53 | 0.38 |
| H3 | 0.189 | 0.021** | 5.83 | 3.81 | 3.18 |
| H4 | 0.325 | 0.001*** | 10.60 | 10.70 | 0.82 |
| H5 | 0.099 | 0.229 | 0.54 | 0.54 | 0.48 |
| H6 | 0.601 | 0.001*** | 5.77 | 11.88 | 2.44 |
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