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Response error in a transformation model with an application to earnings-equation estimation*


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    Seminar participants at Harvard, MIT, University College London, and Statistics Canada provided valuable feedback. Comments by Pravin Trivedi and two anonymous referees greatly improved this paper. Mark Rainey provided excellent research assistance.


Summary  This paper considers estimation of a transformation model in which the transformed dependent variable is subject to classical measurement error. We consider cases in which the transformation function is known and unspecified. In special cases (e.g. log and square-root transformations), least-squares or non-linear least-squares estimators are applicable. A flexible approximation approach (based on Taylor expansion) is proposed for a parametrized transformation function (like the Box–Cox model), and a semi-parametric approach (combining a semi-parametric linear-index estimator and non-parametric regression) is proposed for the case of an unspecified transformation function. The methods are applied to the estimation of earnings equations, using wage data from the Current Population Survey (CPS).