Abstract

This paper provides a test for completeness in a class of nonparametric specification with an additive and independent error term. It is known that such a nonparametric location family of functions is complete if and only if the characteristic function of the error term has no zeros on the real line. Because a zero of the error characteristic function implies that of an observed marginal distribution, we propose a simple test for zeros of characteristic function of the observed distribution, in which rejection of the null hypothesis implies the completeness. This test is applicable to many popular settings, such as nonparametric regression models with instrumental variables, and nonclassical measurement error models. We describe the asymptotic behavior of the tests under the null and alternative hypotheses and investigate the finite sample properties of the proposed test through a Monte Carlo study. We illustrate our method empirically by estimating a measurement error model using the CPS/SSR 1978 exact match file.

摘要

本文提供了对具有附加和独立误差项的一类非参数规范的完整性测试。众所周知，当且仅当误差项的特征函数在实线上没有零点时，这样的非参数位置函数族是完整的。因为误差特征函数的零点意味着观察到的边缘分布的零点，所以我们提出了一个简单的测试来检验观察到的分布的特征函数的零点，其中拒绝原假设意味着完整性。该检验适用于许多流行的设置，例如具有工具变量的非参数回归模型和非经典测量误差模型。我们描述了在零假设和替代假设下测试的渐近行为，并通过蒙特卡洛研究研究了所提议测试的有限样本特性。我们通过使用 CPS/SSR 1978 精确匹配文件估计测量误差模型来凭经验说明我们的方法。