arXiv 15 Dec 2025 · Econometrics
arXiv:2512.13645 · PDF · DOI · OpenAlex · Extracted main text
The interpretation of coefficients from multivariate linear regression relies on the assumption that the conditional expectation function is linear in the variables. However, in many cases the underlying data generating process is nonlinear. This paper examines how to interpret regression coefficients under nonlinearity. We show that if the relationships between the variable of interest and other covariates are linear, then the coefficient on the variable of interest represents a weighted average of the derivatives of the outcome conditional expectation function with respect to the variable of interest. If these relationships are nonlinear, the regression coefficient becomes biased relative to this weighted average. We show that this bias is interpretable, analogous to the biases from measurement error and omitted variable bias under the standard linear model.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Shlomo Yitzhaki (1996) On using linear regressions in welfare economics | 0.811 | 4 | 2 | 100% |
| 2 | Joshua D. Angrist and Alan B. Krueger (1999) Empirical strategies in labor economics | 0.644 | 2 | 2 | 100% |
| 3 | Joshua D. Angrist and Jörn-Steffen Pischke (2009) Mostly Harmless Econometrics: An Empiricist's Companion | 0.644 | 2 | 2 | 100% |
| 4 | Christine Blandhol, John Bonney, Magne Mogstad, and Alexander Torgov… (2022) When is tsls actually late? | 0.644 | 2 | 2 | 100% |
| 5 | Jeffrey M. Wooldridge (2015) Introductory Econometrics: A Modern Approach | 0.644 | 2 | 2 | 100% |
| 6 | Edward H. Kennedy (2024) Semiparametric doubly robust targeted double machine learning: A review | 0.511 | 2 | 2 | 50% |
| 7 | Whitney K. Newey and Thomas M. Stoker (1993) Efficiency of weighted average derivative estimators and index models | 0.511 | 2 | 2 | 50% |
| 8 | Aad W. van der Vaart (1998) Asymptotic Statistics, volume 3 of Cambridge Series in Statistical and Probabilistic Mathematics | 0.511 | 2 | 2 | 50% |
| 9 | Scott Cunningham (2021) Causal Inference: The Mixtape | 0.511 | 2 | 1 | 100% |
| 10 | Shoya Ishimaru (2024) Empirical decomposition of the iv-ols gap with heterogeneous and nonlinear effects | 0.511 | 2 | 1 | 100% |
Showing the top 10 of 25 scored citations.