  In this paper, I study the nonparametric identification and estimation of the
marginal effect of an endogenous variable $X$ on the outcome variable $Y$,
given a potentially mismeasured instrument variable $W^*$, without assuming
linearity or separability of the functions governing the relationship between
observables and unobservables. To address the challenges arising from the
co-existence of measurement error and nonseparability, I first employ the
deconvolution technique from the measurement error literature to identify the
joint distribution of $Y, X, W^*$ using two error-laden measurements of $W^*$.
I then recover the structural derivative of the function of interest and the
"Local Average Response" (LAR) from the joint distribution via the "unobserved
instrument" approach in Matzkin (2016). I also propose nonparametric estimators
for these parameters and derive their uniform rates of convergence. Monte Carlo
exercises show evidence that the estimators I propose have good finite sample
performance.
