We study a semi-/nonparametric regression model with a general form of nonclassical measurement error in the outcome variable. We show equivalence of this model to a generalized regression model. Our main identifying assumptions are a special regressor type restriction and monotonicity in the nonlinear relationship between the observed and unobserved true outcome. Nonparametric identification is then obtained under a normalization of the unknown link function, which is a natural extension of the classical measurement error case. We propose a novel sieve rank estimator for the regression function and establish its rate of convergence. In Monte Carlo simulations, we find that our estimator corrects for biases induced by nonclassical measurement error and provides numerically stable results. We apply our method to analyze belief formation of stock market expectations with survey data from the German Socio-Economic Panel (SOEP) and find evidence for nonclassical measurement error in subjective belief data.
翻译:我们研究的是半/非参数回归模型,其结果变量中一般形式的非古典测量错误。我们显示了该模型与普遍回归模型的等同性。我们的主要识别假设是观测到和未观测到的真实结果之间非线性关系中一种特殊的递减型限制和单一性。然后在未知联系功能的正常化下获得非对称识别,这是古典测量错误案例的自然延伸。我们建议为回归函数提供一个新型的筛选等级估计器,并确立其趋同率。在蒙特卡洛模拟中,我们发现我们的估计器纠正了非古典测量错误引起的偏差,并提供了数字稳定的结果。我们用德国社会经济小组(SOEP)的调查数据来分析股票市场预期的信念形成,并在主观信仰数据中找到非古典测量错误的证据。