Instrumental Variable Treatment of Nonclassical Measurement Error Models
证明，在非经典测量误差模型中，利用工具变量可以识别一大类连续变量非线性模型，并提出基于特征分解的筛估计方法，通过蒙特卡洛模拟验证了其有限样本表现。
While the literature on nonclassical measurement error traditionally relies on the availability of an auxiliary data set containing correctly measured observations, we establish that the availability of instruments enables the identification of a large class of nonclassical nonlinear errors-in-variables models with continuously distributed variables. Our main identifying assumption is that, conditional on the value of the true regressors, some “measure of location” of the distribution of the measurement error (e.g., its mean, mode, or median) is equal to zero. The proposed approach relies on the eigenvalue–eigenfunction decomposition of an integral operator associated with specific joint probability densities. The main identifying assumption is used to “index” the eigenfunctions so that the decomposition is unique. We propose a convenient sieve-based estimator, derive its asymptotic properties, and investigate its finite-sample behavior through Monte Carlo simulations.