Before revision:  Lastly, we demonstrate the discontinuity in the asymptotic distribution for extreme cases of identification failures where we observe a degenerate U-statistics asymptotics .
After revision:  Nonidentification has important implications for the large sample distribution of the Tikhonov-regularized estimator, and we document the transition between the Gaussian and the weighted chi-squared limits. The theoretical results are illustrated for the nonparametric IV and the functional linear IV regressions and are further supported by the Monte Carlo experiments .