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Multiplicative Measurement Error and the Simulation Extrapolation Method

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Abstract

Whereas the literature on additive measurement error has known a considerable treatment, less work has been done for multiplicative noise. In this paper we concentrate on multiplicative measurement error in the covariates, which contrary to additive error not only modi es proportionally the original value, but also conserves the structural zeros. This paper compares three variants to specify the multiplicative measurement error model in the simulation step of the Simulation-Extrapolation (SIMEX) method originally proposed by Cook and Stefanski (1994): i) as an additive one without using a logarithmic transformation, ii) as the well-known logarithmic transformation of the multiplicative error model, and iii) as an approach using the multiplicative measurement error model as such. The aim of the paper is to analyze how well these three approaches reduce the bias caused by the multiplicative measurement error. We apply three variants to the case of data masking by multiplicative measurement error, in order to obtain parameter estimates of the true data generating process. We produce Monte Carlo evidence on how the reduction of data quality can be minimized.

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  • Elena Biewen & Sandra Nolte & Martin Rosemann, 2008. "Multiplicative Measurement Error and the Simulation Extrapolation Method," IAW Discussion Papers 39, Institut für Angewandte Wirtschaftsforschung (IAW).
    • Handle: RePEc:iaw:iawdip:39
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    References listed on IDEAS

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    1. Friedrich Schneider & Robert Klinglmair, 2004. "Shadow economies around the world: what do we know?," Economics working papers 2004-03, Department of Economics, Johannes Kepler University Linz, Austria.
    2. Lin, An-loh, 1989. "Estimation of multiplicative measurement-error models and some simulation results," Economics Letters, Elsevier, vol. 31(1), pages 13-20.
    3. Stephen J. Iturria & Raymond J. Carroll & David Firth, 1999. "Polynomial Regression and Estimating Functions in the Presence of Multiplicative Measurement Error," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(3), pages 547-561.
    4. Peter Gottfried & Hannes Schellhorn, 2004. "Empirical Evidence on the Effects of Marginal Tax Rates on Income – The German Case," IAW Discussion Papers 15, Institut für Angewandte Wirtschaftsforschung (IAW).
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    More about this item

    Keywords

    Errors-in-variables in nonlinear models; disclosure limitation methods; multiplicative error;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models

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