Identification and Estimation of Nonseparable Triangular Equations with Mismeasured Instruments

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.