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Using Heteroscedasticity to Identify and Estimate Mismeasured and Endogenous Regressor Models

Arthur LEWBEL

Department of Economics, Boston College, 140 Commonwealth Avenue, Chestnut Hill, MA 02467

(lewbel@bc.edu)

This article proposes a new method of obtaining identification inmismeasured regressormodels, triangular systems, and simultaneous equation systems. The method may be used in applications where other sources of identification, such as instrumental variables or repeated measurements, are not available. Associated estimators take the form of two-stage least squares or generalized method of moments. Identification comes from a heteroscedastic covariance restriction that is shown to be a feature of many models of endogeneity or mismeasurement. Identification is also obtained for semiparametric partly linear models, and associated

estimators are provided. Set identification bounds are derived for cases where point-identifying assumptions fail to hold. An empirical application estimating Engel curves is provided.

KEY WORDS: Endogeneity; Heteroscedastic errors; Identification; Measurement error; Partly linear model; Simultaneous system.

本文提出了一种获得非测回归模型、三角系统和联立方程系统的辨识方法。该方法可用于没有其它鉴别来源的应用，如工具变量或重复测量。关联估计量采用两阶段最小二乘或广义矩法的形式。认同来自于异方差协方差限制，这被证明是许多内生性或错误测量模型的特征。并对半参数部分线性模型进行了辨识，估计被提供。针对点识别假设不成立的情况，导出了设定识别边界。给出了一个估计恩格尔曲线的经验应用。

Instrumental variables estimation using heteroskedas

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