This paper provides a specification test for semiparametric models with nonparametrically generated regressors. Such variables are not observed by the researcher but are nonparametrically identified and estimable. Applications of the test include models with endogenous regressors identified by control functions, semiparametric sample selection models, or binary games with incomplete information. The statistic is built from the residuals of the semiparametric model. A novel wild bootstrap procedure is shown to provide valid critical values. We consider nonparametric estimators with an automatic bias correction that makes the test implementable without undersmoothing. In simulations the test exhibits good small sample performances, and an application to women's labor force participation decisions shows its implementation in a real data context.

翻译：本文针对含非参数生成回归量的半参数模型提出了一种设定检验。此类变量虽无法被研究者直接观测，但可通过非参数方法识别并估计。该检验的应用场景包括：由控制函数识别内生回归量的模型、半参数样本选择模型，以及不完全信息二元博弈。检验统计量基于半参数模型的残差构建，并采用一种新颖的野刀自举法提供有效临界值。我们考虑使用自动偏差校正的非参数估计量，使得检验可在无需欠光滑处理的情况下实施。模拟实验表明该检验在小样本下表现良好，而基于女性劳动参与决策的实证分析则展示了其在真实数据场景中的应用。