Econometrics and Applied Micro Seminar

This paper contributes to the literature on the important yet difficult nonparametric instrumental variables (NPIV) regression as follows. First, we derive the minimax optimal sup-norm (uniform) convergence rates in nonparametric estimation of the structural function and its derivatives. Second, we show that the computationally simple spline and wavelet sieve NPIV estimators can attain the optimal sup-norm rates. Third, we introduce a novel data-driven procedure for choosing the sieve dimension. We show that the procedure is sup-norm rate-adaptive in estimating the structural function and its derivatives, without knowing the smoothness of the structural function and the degree of ill-posedess of the operator. Fourth, we use our sup- norm rates together with exponential inequalities for random matrices to establish pointwise and uniform limit theories of sieve t-statistics for possibly nonlinear functionals of the NPIV. The validity of a sieve score bootstrap for constructing asymptotically exact uniform confidence bands of the NPIV function is a special case of this analysis. Finally, as an application, we establish the asymptotic normality of sieve t-statistics for exact consumer surplus and deadweight loss functionals in nonparametric demand estimation allowing prices, and possibly incomes, to be endogenous.