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Estimation with inequality constraints on the parameters: dealing with truncation of the sampling distribution

Author

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  • Barnett, William A.
  • Seck, Ousmane

Abstract

Theoretical constraints on economic-model parameters often are in the form of inequality restrictions. For example, many theoretical results are in the form of monotonicity or nonnegativity restrictions. Inequality constraints can truncate sampling distributions of parameter estimators, so that asymptotic normality no longer is possible. Sampling theoretic asymptotic inference is thereby greatly complicated or compromised. We use numerical methods to investigate the resulting sampling properties of inequality constrained estimators produced by popular methods of imposing inequality constraints. In particular, we investigate the possible bias in the asymptotic standard errors of estimators of inequality constrained estimators, when the constraint is imposed by the popular method of squaring. That approach is known to violate a regularity condition in the available asymptotic proofs regarding the unconstrained estimator, since the sign of the unconstrained estimator, prior to squaring, is nonidentified.

Suggested Citation

  • Barnett, William A. & Seck, Ousmane, 2008. "Estimation with inequality constraints on the parameters: dealing with truncation of the sampling distribution," MPRA Paper 12500, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:12500
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    File URL: https://mpra.ub.uni-muenchen.de/14987/2/MPRA_paper_14987.pdf
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    References listed on IDEAS

    as
    1. William A. Barnett, 2000. "Economic Monetary Aggregates: An Application of Index Number and Aggregation Theory," Contributions to Economic Analysis, in: The Theory of Monetary Aggregation, pages 11-48, Emerald Group Publishing Limited.
    2. Barnett, William A, 1977. "Recursive Subaggregation and a Generalized Hypocycloidal Demand Model," Econometrica, Econometric Society, vol. 45(5), pages 1117-1136, July.
    3. William A. Barnett, 2000. "The User Cost of Money," Contributions to Economic Analysis, in: The Theory of Monetary Aggregation, pages 6-10, Emerald Group Publishing Limited.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    inequality constraints; truncation of sampling distribution; asymptotics; constrained estimation;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C16 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Econometric and Statistical Methods; Specific Distributions
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General

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