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Models of Truncation, Sample Selection, and Limited Dependent Variables: Suggestions for a Common Language

Author

Listed:
  • Biørn, Erik

    () (Dept. of Economics, University of Oslo)

  • R. Wangen, Knut

    () (Department of Health Management and Health Economics, University of Oslo)

Abstract

The aim of this paper is two-fold: (a) to establish a ‘map’ for describing the wide class of Limited Dependent Variables (LDV) univariate and multivariate models in the econometric literature and (b) to localize typical models in this tradition within the structure, extending typologies of Heckman (1976) and Amemiya (1984). The classification system, or language, proposed, is given at different level of detail. Its scope is (1) that the latent variables can have any parametric distribution, (2) that a set of observation rules which include the observed, censored, missing status, is imposed, (3) that it should be possible to write a model combining (1) and (2) by means of a computer algorithm, also potentially applicable for generating samples and (4) that the models belonging to the system should have names to facilitate communication among researchers. The likelihood functions corresponding to the models’ observed endogenous variables are discussed, but the paper is not concerned with describing the application of these functions for inference.

Suggested Citation

  • Biørn, Erik & R. Wangen, Knut, 2011. "Models of Truncation, Sample Selection, and Limited Dependent Variables: Suggestions for a Common Language," Memorandum 18/2011, Oslo University, Department of Economics.
  • Handle: RePEc:hhs:osloec:2011_018
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    File URL: https://www.sv.uio.no/econ/english/research/unpublished-works/working-papers/pdf-files/2011/Memo-18-2011.pdf
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    References listed on IDEAS

    as
    1. James J. Heckman, 1976. "The Common Structure of Statistical Models of Truncation, Sample Selection and Limited Dependent Variables and a Simple Estimator for Such Models," NBER Chapters,in: Annals of Economic and Social Measurement, Volume 5, number 4, pages 475-492 National Bureau of Economic Research, Inc.
    2. Amemiya, Takeshi, 1984. "Tobit models: A survey," Journal of Econometrics, Elsevier, vol. 24(1-2), pages 3-61.
    3. Dagenais, Marcel G, 1975. "Application of a Threshold Regression Model to Household Purchases of Automobiles," The Review of Economics and Statistics, MIT Press, vol. 57(3), pages 275-285, August.
    4. Nelson, Forrest D., 1977. "Censored regression models with unobserved, stochastic censoring thresholds," Journal of Econometrics, Elsevier, vol. 6(3), pages 309-327, November.
    Full references (including those not matched with items on IDEAS)

    More about this item

    Keywords

    Micro-econometrics; Limited dependent variables; Latent variables; Discrete choice; Censoring; Truncation; Missing observations;

    JEL classification:

    • C16 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Econometric and Statistical Methods; Specific Distributions
    • C24 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Truncated and Censored Models; Switching Regression Models; Threshold Regression Models
    • C25 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions; Probabilities
    • C34 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Truncated and Censored Models; Switching Regression Models
    • C35 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation

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