arXiv 29 Mar 2026 · Econometrics
arXiv:2603.27762 · PDF · DOI · OpenAlex · Extracted main text
Normalization is ubiquitous in economics, and a growing literature shows that “normalizations” can matter for interpretation, counterfactual analysis, misspecification, and inference. This paper provides a general framework for these issues, based on the formalized notion of modeling equivalence that partitions the space of unknowns into equivalence classes, and defines normalization as a WLOG selection of one representative from each class. A counterfactual parameter is normalization-free if and only if it is constant on equivalence classes; otherwise any point identification is created by the normalization rather than by the model. Applications to discrete choice, demand estimation, and network formation illustrate the insights made explicit through this criterion. We then study two further sources of fragility: an extension trilemma establishes that fidelity, invariance, and regularity cannot simultaneously hold at a boundary singularity, while a normalization can itself introduce a coordinate singularity that distorts the topological and metric structures of the parameter space, with consequences for estimation and inference.
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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 | Freyberger, J (2025) Normalizations and Misspecification in Skill Formation Models | 1.000 | 8 | 5 | 100% |
| 2 | Gao, W. Y (2020) Nonparametric Identification in Index Models of Link Formation self | 1.000 | 7 | 3 | 100% |
| 3 | Agostinelli, F. and M. Wiswall (2025) Estimating the Technology of Children's Skill Formation | 1.000 | 5 | 5 | 100% |
| 4 | Hamilton, J. D., D. F. Waggoner, and T. Zha (2007) Normalization in Econometrics | 0.928 | 4 | 4 | 100% |
| 5 | Chen, J. and J. Roth (2024) Logs with Zeros? Some Problems and Solutions | 0.874 | 5 | 2 | 100% |
| 6 | Graham, B. S (2017) An econometric model of network formation with degree heterogeneity | 0.843 | 3 | 3 | 100% |
| 7 | Berry, S., J. Levinsohn, and A. Pakes (1995) Automobile Prices in Market Equilibrium | 0.644 | 2 | 2 | 100% |
| 8 | Manski, C. F (1975) Maximum score estimation of the stochastic utility model of choice | 0.511 | 2 | 1 | 100% |
| 9 | Agostinelli, F. and M. Wiswall (2016) Identification of Dynamic Latent Factor Models: The Implications of Re-Normalization in a Model of Child Development, Working Pa… | 0.405 | 1 | 1 | 100% |
| 10 | Berry, S. T. and P. A. Haile (2014) Identification in Differentiated Products Markets Using Market Level Data | 0.405 | 1 | 1 | 100% |
Showing the top 10 of 25 scored citations.