On Least Squares Estimation When the Dependent Variable is Grouped
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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|Date of creation:||Nov 1982|
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