On the Testability of Identification in Some Nonparametric Models With Endogeneity

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The hardness of conditional independence testing and the generalised covariance measure (2018, background): “[11] shows that certain problems arising in the context of identification of some nonparametric models are not testable.”
Nonlinear Panel Data Estimation via Quantile Regressions (2015, methodology): “Similarly as completeness, injectivity is a high-level condition; see for example Canay et al. (2012) for results on the testability of completeness assumptions.”
Impossible inference in econometrics: Theory and applications (2016, unknown): “As noted by Canay et al. (2013), the topology induced by the LP metric is not ﬁne enough to guarantee convergence of integrals of any test function φ .”
Nonparametric Counterfactual Predictions in Neoclassical Models of International Trade (2017, background): “As noted by Chiappori and Ekeland (2009), such results are useful because they can help select the most adequate moment conditions, that is, the source of variation in the data directly related to the economic relation of interest.”
Nonparametric Instrumental Variable Estimation Under Monotonicity (2015, background): “In this paper, we show that restricting the problem to models with monotone regression functions and monotone instruments significantly weakens the ill-posedness of the problem.”