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On Least Squares Estimation when the Dependent Variable is Grouped

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Author Info
Stewart, Mark B (Department of Economics, University of Warwick)

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Abstract

Models estimated from censored samples are now familar in the econometrics literature. For many cases Least Squares approximations to the Maximum Likelihood estimators are now well established. This paper is concerned with a more general problem ; that of estimating an equation on the basis of data in which the dependent variably is only observed to fall in a certain range on a continuous scale, its actual value remaining unobserved. The date are also censored in the usual sense in that both end ranges are assumed to be open-ended. A number of Least Square approximations to the Maximum Likelihood estimator are derived and compared. The results of Greene (1981) on the asymptotic bias of OLS are extended to this case. The question of information loss as a result of the grouping is also considered.

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Publisher Info
Paper provided by University of Warwick, Department of Economics in its series The Warwick Economics Research Paper Series (TWERPS) with number 207.

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Length: 41 pages
Date of creation: 1982
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Handle: RePEc:wrk:warwec:207

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Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Greene, William H, 1981. "On the Asymptotic Bias of the Ordinary Least Squares Estimator of the Tobit Model," Econometrica, Econometric Society, vol. 49(2), pages 505-13, March. [Downloadable!] (restricted)
  2. Heckman, James J, 1979. "Sample Selection Bias as a Specification Error," Econometrica, Econometric Society, vol. 47(1), pages 153-61, January. [Downloadable!] (restricted)
  3. Fair, Ray C, 1977. "A Note on the Computation of the Tobit Estimator," Econometrica, Econometric Society, vol. 45(7), pages 1723-27, October. [Downloadable!] (restricted)
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