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Identification and Method of Moments Estimation in Polynomial Measurement Error Models

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Estimation of polynomial regression equations in one error-ridden variable and a number of error-free regressors, as well as an instrument set for the former is considered. Procedures for identification, operating on moments up to a certain order, are elaborated for single- and multi-equation models. Weak distributional assumptions are made for the error and the latent regressor. Simple order-conditions are derived, and procedures involving recursive identification of the moments of the regressor and its measurement errors together with the coefficients of the polynomials are considered. A Generalized Method of Moments (GMM) algorithm involving the instruments and proceeding stepwise from the identification procedures, is presented. An illustration for systems of linear, quadratic and cubic Engel functions, with household consumption and income data is given.

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  • Biørn, Erik, 2017. "Identification and Method of Moments Estimation in Polynomial Measurement Error Models," Memorandum 01/2017, Oslo University, Department of Economics.
    • Handle: RePEc:hhs:osloec:2017_001
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    More about this item

    Keywords

    Errors in variables; Polynomial regression; Error distribution; Identification; Instrumental variables; Method of Moments; Engel functions;
    All these keywords.

    JEL classification:

    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data; Spatio-temporal Models
    • C31 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models; Quantile Regressions; Social Interaction Models
    • C33 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Models with Panel Data; Spatio-temporal Models
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • E21 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - Consumption; Saving; Wealth

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