Distributional Treatment Effect with Latent Rank Invariance
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866916952410161152 |
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| author | Shin, Myungkou |
| author_facet | Shin, Myungkou |
| contents | Treatment effect heterogeneity is of a great concern when evaluating policy impact: "is the treatment Pareto-improving?", "what is the proportion of people who are better off under the treatment?", etc. However, even in the simple case of a binary random treatment, existing analysis has been mostly limited to an average treatment effect or a quantile treatment effect, due to the fundamental limitation that we cannot simultaneously observe both treated potential outcome and untreated potential outcome for a given unit. This paper assumes a conditional independence assumption that the two potential outcomes are independent of each other given a scalar latent variable. With a specific example of strictly increasing conditional expectation, I label the latent variable as 'latent rank' and motivate the identifying assumption as 'latent rank invariance.' In implementation, I assume a finite support on the latent variable and propose an estimation strategy based on a nonnegative matrix factorization. A limiting distribution is derived for the distributional treatment effect estimator, using Neyman orthogonality. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_18503 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Distributional Treatment Effect with Latent Rank Invariance Shin, Myungkou Econometrics Treatment effect heterogeneity is of a great concern when evaluating policy impact: "is the treatment Pareto-improving?", "what is the proportion of people who are better off under the treatment?", etc. However, even in the simple case of a binary random treatment, existing analysis has been mostly limited to an average treatment effect or a quantile treatment effect, due to the fundamental limitation that we cannot simultaneously observe both treated potential outcome and untreated potential outcome for a given unit. This paper assumes a conditional independence assumption that the two potential outcomes are independent of each other given a scalar latent variable. With a specific example of strictly increasing conditional expectation, I label the latent variable as 'latent rank' and motivate the identifying assumption as 'latent rank invariance.' In implementation, I assume a finite support on the latent variable and propose an estimation strategy based on a nonnegative matrix factorization. A limiting distribution is derived for the distributional treatment effect estimator, using Neyman orthogonality. |
| title | Distributional Treatment Effect with Latent Rank Invariance |
| topic | Econometrics |
| url | https://arxiv.org/abs/2403.18503 |