We explore inference on regression coefficients in semiparametric multinomial response models. We consider cross-sectional, and both static and dynamic panel settings where we focus throughout on inference under sufficient conditions for point identification. The approach to identification uses a matching insight throughout all three models coupled with variation in regressors: with cross-section data, we match across individuals while with panel data, we match within individuals over time. Across models, we relax the Indpendence of Irrelevant Alternatives (or IIA assumption, see McFadden (1974)) and allow for arbitrary correlation in the unobservables that determine utility of various alternatives. For the cross-sectional model, estimation is based on a localized rank objective function, analogous to that used in Abrevaya, Hausman, and Khan (2010), and presents a generalization of existing approaches. In panel data settings, rates of convergence are shown to exhibit a curse of dimensionality in the number of alternatives. The results for the dynamic panel data model generalize the work of Honoré and Kyriazidou (2000) to cover the semiparametric multinomial case. A simulation study establishes adequate finite sample properties of our new procedures. We apply our estimators to a scanner panel data set.

中文翻译：

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半参数多项式响应模型的推断

我们探索了对半参数多项式响应模型中回归系数的推断。我们考虑横截面以及静态和动态面板设置，在这些设置中，我们始终专注于在点识别的充分条件下进行推理。识别方法在所有三个模型中使用匹配洞察力以及回归变量的变化：对于横截面数据，我们在个体之间进行匹配，而对于面板数据，我们随着时间的推移在个体内部进行匹配。在所有模型中，我们放宽了无关替代方案的独立性（或 IIA 假设，参见 McFadden (1974)），并允许在确定各种替代方案效用的不可观察量中存在任意相关性。对于横截面模型，估计基于局部秩目标函数，类似于 Abrevaya、Hausman、和 Khan (2010)，并介绍了现有方法的概括。在面板数据设置中，收敛率显示出在备选方案数量上出现维数灾难。动态面板数据模型的结果概括了 Honoré 和 Kyriazidou (2000) 的工作以涵盖半参数多项式情况。模拟研究为我们的新程序建立了足够的有限样本属性。我们将估算器应用于扫描仪面板数据集。模拟研究为我们的新程序建立了足够的有限样本属性。我们将估算器应用于扫描仪面板数据集。模拟研究为我们的新程序建立了足够的有限样本属性。我们将估算器应用于扫描仪面板数据集。