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Estimation of the Probit Model from Anonymized Micro Data

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  • Gerd Ronning
  • Martin Rosemann

Abstract

The demand of scientists for confidential micro data from official sources has created discussion of how to anonymize these data in such a way that they can be given to the scientific community. We report results from a German project which exploits various options of anonymization for producing such ”scientific-use- files”. The main concern in the project however is whether estimation of stochastic models from these perturbed data is possible and – more importantly – leads to reliable results. In this paper we concentrate on estimation of the probit model under the assumption that only anonymized data are available. In particular we assume that the binary dependent variable has undergone post-randomization (PRAM) and that the set of explanatory variables has been perturbed by addition of noise. We employ a maximum likelihood estimator which is consistent if only the dependent variable has been anonymized by PRAM. The errors-in-variables structure of the regressors then is handled by the simulation extrapolation (SIMEX) estimation procedure where we compare performance of quadratic and nonlinear (rational) extrapolation.

Suggested Citation

  • Gerd Ronning & Martin Rosemann, 2006. "Estimation of the Probit Model from Anonymized Micro Data," IAW Discussion Papers 25, Institut für Angewandte Wirtschaftsforschung (IAW).
    • Handle: RePEc:iaw:iawdip:25
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    References listed on IDEAS

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    1. Hausman, J. A. & Abrevaya, Jason & Scott-Morton, F. M., 1998. "Misclassification of the dependent variable in a discrete-response setting," Journal of Econometrics, Elsevier, vol. 87(2), pages 239-269, September.
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    3. Lechner Sandra & Pohlmeier Winfried, 2005. "Data Masking by Noise Addition and the Estimation of Nonparametric Regression Models," Journal of Economics and Statistics (Jahrbuecher fuer Nationaloekonomie und Statistik), De Gruyter, vol. 225(5), pages 517-528, October.
    4. Frazis, Harley & Loewenstein, Mark A., 2003. "Estimating linear regressions with mismeasured, possibly endogenous, binary explanatory variables," Journal of Econometrics, Elsevier, vol. 117(1), pages 151-178, November.
    5. Pohlmeier, Winfried & Lechner, Sandra, 2003. "Schätzung ökonometrischer Modelle auf der Grundlage anonymisierter Daten," CoFE Discussion Papers 03/04, University of Konstanz, Center of Finance and Econometrics (CoFE).
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