Testing Sign Congruence Between Two Parameters
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866912760431902720 |
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| author | Miller, Douglas L. Molinari, Francesca Stoye, Jörg |
| author_facet | Miller, Douglas L. Molinari, Francesca Stoye, Jörg |
| contents | We test the null hypothesis that two parameters $(μ_1,μ_2)$ have the same sign, assuming that (asymptotically) normal estimators $(\hatμ_1,\hatμ_2)$ are available. Examples of this problem include the analysis of heterogeneous treatment effects, causal interpretation of reduced-form estimands, meta-studies, and mediation analysis. A number of tests were recently proposed. We recommend a test that is simple and rejects more often than many of these recent proposals. Like all other tests in the literature, it is conservative if the truth is near $(0,0)$ and therefore also biased. To clarify whether these features are avoidable, we also provide a test that is unbiased and has exact size control on the boundary of the null hypothesis, but which has counterintuitive properties and hence we do not recommend. We use the test to improve p-values in Kowalski (2022) from information contained in that paper's main text and to establish statistical significance of some key estimates in Dippel et al. (2021). |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2405_11759 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Testing Sign Congruence Between Two Parameters Miller, Douglas L. Molinari, Francesca Stoye, Jörg Econometrics We test the null hypothesis that two parameters $(μ_1,μ_2)$ have the same sign, assuming that (asymptotically) normal estimators $(\hatμ_1,\hatμ_2)$ are available. Examples of this problem include the analysis of heterogeneous treatment effects, causal interpretation of reduced-form estimands, meta-studies, and mediation analysis. A number of tests were recently proposed. We recommend a test that is simple and rejects more often than many of these recent proposals. Like all other tests in the literature, it is conservative if the truth is near $(0,0)$ and therefore also biased. To clarify whether these features are avoidable, we also provide a test that is unbiased and has exact size control on the boundary of the null hypothesis, but which has counterintuitive properties and hence we do not recommend. We use the test to improve p-values in Kowalski (2022) from information contained in that paper's main text and to establish statistical significance of some key estimates in Dippel et al. (2021). |
| title | Testing Sign Congruence Between Two Parameters |
| topic | Econometrics |
| url | https://arxiv.org/abs/2405.11759 |