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No standard errors are shown because the outputs are numerical.\",\"units_stated_in_notes\":true,\"standard_errors_description\":\"none\"},\"figures\":{\"uncertainty_shown\":\"no\"},\"conclusion\":{\"bounded_claims\":true,\"policy_implications\":false,\"open_questions\":false,\"restates_contribution\":true},\"hedging\":{\"level\":\"low\",\"typical_devices\":[\"modal 'can' for error magnitudes\",\"conditioning on high persistence or parameter regions\",\"noting that lower-persistence models have small errors\"]},\"claim_evidence\":[{\"claim\":\"Log-linearization overstates the equity premium by about 100 bps and return predictability by roughly a factor of two in the Bansal-Kiku-Yaron calibration.\",\"evidence_type\":\"table\",\"evidence_ref\":\"Table V, Table VI\"},{\"claim\":\"Approximation errors in moments can exceed 70% at the high-persistence (95% quantile) estimates of Schorfheide-Song-Yaron.\",\"evidence_type\":\"table\",\"evidence_ref\":\"Appendix table of annualized moments and errors for Schorfheide, Song, and Yaron (2018); Figure E3\"},{\"claim\":\"Nonlinearities stem from highly persistent state processes and their interaction with stochastic volatility.\",\"evidence_type\":\"figure\",\"evidence_ref\":\"Figures 1, 2, 6, 7; Table I\"},{\"claim\":\"Errors grow with persistence and risk aversion across parameter choices.\",\"evidence_type\":\"figure\",\"evidence_ref\":\"Figures 4, 5\"},{\"claim\":\"Log-linearization can invert the slope of the nominal yield curve in bond models.\",\"evidence_type\":\"figure\",\"evidence_ref\":\"Figures 8, 9\"},{\"claim\":\"The projection benchmark is highly accurate, with Euler errors below 4e-9.\",\"evidence_type\":\"table\",\"evidence_ref\":\"Table II; Appendix B\"}],\"structural_summary\":\"The paper opens from a landmark model and the standard approximation technique, then asks whether neglected higher-order terms matter. It previews large errors with concrete magnitudes across six published models, closing the introduction with a usage recommendation and a roadmap. A model-framework section is followed by an analysis isolating the sources of nonlinearity (persistence, volatility interaction, the unitary-EIS special case). A model-by-model comparison of moments, predictability and yield curves comes next. The conclusion restates the findings with bounds, noting small errors for low-persistence models. 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