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A Dual Least-Squares Estimator of the Errors-In-Variables Model Using Only First And Second Moments

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  • Paris, Quirino

Abstract

The paper presents an estimator of the errors-in-variables in multiple regressions using only first and second-order moments. The consistency property of the estimator is explored by Monte Carlo experiments. Based on these results, we conjecture that the estimator is consistent. The proof of consistency, to be dealt in another paper, is based upon the assumptions of Kiefer and Wolfowitz (1956). The novel treatment of the errors-in-variables model relies crucially upon a neutral parameterization of the error terms of the dependent and the explanatory variables. The estimator does not have a closed form solution. It requires the maximization of a dual least-squares objective function that guarantees a global optimum. This estimator, therefore, includes the naïve least-squares method (when only the dependent variable is measured with error) as a special case.

Suggested Citation

  • Paris, Quirino, 2014. "A Dual Least-Squares Estimator of the Errors-In-Variables Model Using Only First And Second Moments," Working Papers 181288, University of California, Davis, Department of Agricultural and Resource Economics.
    • Handle: RePEc:ags:ucdavw:181288
    DOI: 10.22004/ag.econ.181288
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    References listed on IDEAS

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    1. Delaigle, Aurore & Meister, Alexander, 2007. "Nonparametric Regression Estimation in the Heteroscedastic Errors-in-Variables Problem," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 1416-1426, December.
    2. Paris,Quirino, 2011. "Economic Foundations of Symmetric Programming," Cambridge Books, Cambridge University Press, number 9780521123020, September.
    3. K. van Montfort & A. Mooijaart & J. de Leeuw, 1987. "Regression with errors in variables: estimators based on third order moments," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 41(4), pages 223-238, December.
    4. Dagenais, Marcel G. & Dagenais, Denyse L., 1997. "Higher moment estimators for linear regression models with errors in the variables," Journal of Econometrics, Elsevier, vol. 76(1-2), pages 193-221.
    5. Pal, Manoranjan, 1980. "Consistent moment estimators of regression coefficients in the presence of errors in variables," Journal of Econometrics, Elsevier, vol. 14(3), pages 349-364, December.
    6. Paris,Quirino, 2011. "Economic Foundations of Symmetric Programming," Cambridge Books, Cambridge University Press, number 9780521194723, September.
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