Identification of Binary Response Models
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二元反应模型的识别
- 研究问题
- 在阈值穿越型二元反应模型中，对不可观测项施加不同条件分布限制时，系数能够被识别到什么程度？
- 方法与思路
- 作者在不可观测项条件分布连续且严格递增的前提下，比较均值独立、分位数独立、指标充分性及统计独立。
- 材料陈述的贡献
- 摘要称，均值独立没有识别力；其他限制结合相应支持条件可给出尺度或符号下的识别，已知分布时要求更弱。
- 阅读关注点
- 应核对丰富支持与满秩条件的精确定义、截距和斜率的区别，以及各限制如何影响尺度、符号和结构解释。
- 阅读边界
- 仅据版本未注明的 OpenAlex 摘要；丰富支持条件的细节及证明未提供，识别结论依赖所列维持假设，不能推断刊本变化。
原文摘要
This article studies identification of the threshold-crossing model of binary response. Most research on binary response has considered specific estimators and tests. The study of identification exposes the foundations of binary response analysis by making explicit the assumptions needed to justify different methods. It also clarifies the connections between reduced-form and structural analyses of binary response data. Assume that the binary outcome z is determined by an observable random vector x and by an unobservable scalar u through a model z = 1[xβ + u ≤ 0]. Also assume that Fu|x , the probability distribution of u conditional on x, is continuous and strictly increasing. Given these maintained assumptions, we investigate the identifiability of β given the following restrictions on the distributions (Fu|x, x ∈ X): mean independence, quantile independence, index sufficiency, statistical independence, and statistical independence with the distribution known. We find that mean independence has no identifying power. On the other hand, quantile independence implies that β is identified up to scale, provided that the distribution of x has sufficiently rich support. Index sufficiency can identify the slope components of β up to scale and sign, again provided that the distribution of x has a rich support. Statistical independence subsumes both quantile independence and index sufficiency and so implies all of the positive findings previously reported. If u is statistically independent of x with the distribution known, identification requires only that the distribution of x have full rank.