There are many environments in econometrics which require nonseparable modeling of a structural disturbance. In a nonseparable model with endogenous regressors, key conditions are validity of instrumental variables and monotonicity of the model in a scalar unobservable variable. Under these conditions the nonseparable model is equivalent to an instrumental quantile regression model. A failure of the key conditions, however, makes instrumental quantile regression potentially inconsistent. This article develops a methodology for testing the hypothesis whether the instrumental quantile regression model is correctly specified. Our test statistic is asymptotically normally distributed under correct specification and consistent against any alternative model. In addition, test statistics to justify the model simplification are established. Finite sample properties are examined in a Monte Carlo study and an empirical illustration is provided.

中文翻译：

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非参数仪器分位数回归中的规范测试

计量经济学中有许多环境需要对结构扰动进行不可分离的建模。在具有内生回归变量的不可分模型中，关键条件是工具变量的有效性和模型在标量不可观察变量中的单调性。在这些条件下，不可分模型等效于工具分位数回归模型。然而，关键条件的失败会使工具分位数回归可能不一致。本文开发了一种方法来检验工具分位数回归模型是否正确指定的假设。我们的测试统计量在正确的规范下是渐近正态分布的，并且与任何替代模型一致。此外，建立了证明模型简化的检验统计量。