Testing a parametric model against a nonparametric alternative with identification through instrumental variables

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Optimal sup-norm rates and uniform inference on nonlinear functionals of nonparametric IV regression (2015, unknown): “We use the 2001 National Household Travel Survey gasoline demand data from Blundell, Horowitz, and Parey (2012, 2017).12 The main variables are annual household 11Endogeneity may also be an issue in the estimation of static models of labor supply, in which Qi represents hours worked, Pi is the wage,”
Applied Nonparametric Instrumental Variables Estimation (2011, methodology): “The n τ test of Horowitz (2006) that is described in Section 4.3 rejects the hypothesis that the Engel curve is a linear, quadratic, or cubic function ( 0.05 p in all cases).”
Inference in Nonparametric Instrumental Variables With Partial Identification (2012, background): “Horowitz (2006) derives a parametric specification test against nonparametric alternatives for model (1).”