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| Format: | Preprint |
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2025
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| Online Access: | https://arxiv.org/abs/2510.11659 |
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| _version_ | 1866914337229111296 |
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| author | Boussim, Onil |
| author_facet | Boussim, Onil |
| contents | Many policy evaluations involve vectors of category-specific quantities, either categorical outcomes (e.g., employment type, major choice) or compositional measures (e.g., GDP by sector, votes by party, electricity generation by source). In these settings, both intensive margins (shares) and extensive margins (totals) can matter. However, existing Difference-in-Differences (DiD) strategies typically focus only on the shares and do not jointly identify treatment effects on totals. In addition, these approaches usually lack a clear economic interpretation. I develop Compositional Difference-in-Differences (CoDiD), a new framework that identifies treatment effects on both shares and totals in a coherent way. The key assumption is parallel growth: in the absence of treatment, the log-quantities of each category would have evolved in parallel for the treated and control groups. I show that, under a random-utility discrete-choice model, this condition is equivalent to parallel trends in expected utilities, meaning that the change in average latent attractiveness for each alternative is identical across groups. Furthermore, geometrically, the counterfactual distributions (shares) follow parallel trajectories in the probability simplex. In settings with multiple time periods, I introduce a relaxation that delivers bounds when parallel growth may not hold. I illustrate the empirical relevance of the method by examining how early voting reforms affected the 2008 U.S. election. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_11659 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Compositional difference-in-differences Boussim, Onil Econometrics Many policy evaluations involve vectors of category-specific quantities, either categorical outcomes (e.g., employment type, major choice) or compositional measures (e.g., GDP by sector, votes by party, electricity generation by source). In these settings, both intensive margins (shares) and extensive margins (totals) can matter. However, existing Difference-in-Differences (DiD) strategies typically focus only on the shares and do not jointly identify treatment effects on totals. In addition, these approaches usually lack a clear economic interpretation. I develop Compositional Difference-in-Differences (CoDiD), a new framework that identifies treatment effects on both shares and totals in a coherent way. The key assumption is parallel growth: in the absence of treatment, the log-quantities of each category would have evolved in parallel for the treated and control groups. I show that, under a random-utility discrete-choice model, this condition is equivalent to parallel trends in expected utilities, meaning that the change in average latent attractiveness for each alternative is identical across groups. Furthermore, geometrically, the counterfactual distributions (shares) follow parallel trajectories in the probability simplex. In settings with multiple time periods, I introduce a relaxation that delivers bounds when parallel growth may not hold. I illustrate the empirical relevance of the method by examining how early voting reforms affected the 2008 U.S. election. |
| title | Compositional difference-in-differences |
| topic | Econometrics |
| url | https://arxiv.org/abs/2510.11659 |