We study identification in a binary choice panel data model with a single \emph{predetermined} binary covariate (i.e., a covariate sequentially exogenous conditional on lagged outcomes and covariates). The choice model is indexed by a scalar parameter $\theta$, whereas the distribution of unit-specific heterogeneity, as well as the feedback process that maps lagged outcomes into future covariate realizations, are left unrestricted. We provide a simple condition under which $\theta$ is never point-identified, no matter the number of time periods available. This condition is satisfied in most models, including the logit one. We also characterize the identified set of $\theta$ and show how to compute it using linear programming techniques. While $\theta$ is not generally point-identified, its identified set is informative in the examples we analyze numerically, suggesting that meaningful learning about $\theta$ may be possible even in short panels with feedback. As a complement, we report calculations of identified sets for an average partial effect, and find informative sets in this case as well.

翻译：本文研究具有单个二元预定协变量（即协变量在给定滞后结果和协变量条件下满足序列外生性）的二元选择面板数据模型的识别问题。该选择模型由标量参数θ索引，而个体异质性的分布以及将滞后结果映射至未来协变量实现的反馈过程均未设具体形式。我们给出一个简单条件，证明无论可用的时间期数有多少，参数θ均无法实现点识别。该条件适用于包括Logit模型在内的大多数模型。同时，我们刻画了θ的识别集，并展示如何通过线性规划方法对其进行计算。尽管θ通常无法点识别，但数值示例分析表明其识别集具有信息量，这意味着即使在包含反馈的短面板中也可能实现对θ的有意义推断。作为补充，我们计算了平均部分效应的识别集，并发现该情形下同样存在信息丰富的识别集。