Ellen Munroe, Alexander Newton, Meet Shah
arXiv 13 Mar 2026 · Econometrics
arXiv:2603.12536 · PDF · DOI · OpenAlex · Extracted main text
Economists often interpret estimates from linear regressions with log dependent variables as elasticities. However, the coefficients from log-log regressions estimate the elasticity of the geometric mean of $y_i|x_i$, not the arithmetic mean. The unbounded difference between the two is known as retransformation bias and can take either sign. We develop a specification-robust debiased estimator of the average arithmetic elasticity and re-estimate 50 results from top 5 papers published in 2020. We find that 19 are significantly different, with the median absolute difference being 65% of the OLS elasticity estimate. Furthermore, we show standard instrumental variables assumptions with log dependent variables do not identify the elasticity. We specify a control function approach and re-estimate papers that use 2SLS with log dependent variables. We find that 13 of 19 results from top 5 papers are significantly different between the two approaches. Retransformation bias arises as a result of heterogeneous responses. The geometric mean elasticity corresponds to the average response. Arithmetic and geometric means are elements of the power mean family. We show power mean elasticities are sufficient statistics for a common class of decision problems.
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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 | Manning (1998) The Logged Dependent Variable, Heteroscedasticity, and the Retransformation Problem | 0.843 | 4 | 4 | 75% |
| 2 | Chernozhukov, Chetverikov, Demirer, Duflo, Hansen, Newey and Robins (2018) Double/Debiased Machine Learning for Treatment and Structural Parameters | 0.737 | 3 | 2 | 100% |
| 3 | Chernozhukov, Escanciano, Ichimura, Newey and Robins (2022) Locally Robust Semiparametric Estimation | 0.737 | 3 | 2 | 100% |
| 4 | Ai and Norton (2008) A Semiparametric Derivative Estimator in Log Transformation Models | 0.644 | 2 | 2 | 100% |
| 5 | Hyvärinen (2005) Estimation of Non-Normalized Statistical Models by Score Matching | 0.644 | 2 | 2 | 100% |
| 6 | Duan (1983) Smearing Estimate: A Nonparametric Retransformation Method | 0.585 | 3 | 1 | 100% |
| 7 | Chernozhukov, Newey and Singh (2022) Automatic Debiased Machine Learning of Causal and Structural Effects | 0.511 | 2 | 1 | 100% |
| 8 | Goldberger (1968) The Interpretation and Estimation of Cobb-Douglas Functions | 0.511 | 2 | 1 | 100% |
| 9 | Santos Silva and Tenreyro (2006) The Log of Gravity | 0.511 | 2 | 1 | 100% |
| 10 | Bellemare and Wichman (2020) Elasticities and the Inverse Hyperbolic Sine Transformation | 0.405 | 1 | 1 | 100% |
Showing the top 10 of 25 scored citations.