Journal Of The Econometric Society

An International Society for the Advancement of Economic
Theory in its Relation to Statistics and Mathematics

Edited by: Guido W. Imbens • Print ISSN: 0012-9682 • Online ISSN: 1468-0262

Econometrica: May, 1984, Volume 52, Issue 3

Censored Normal Regression with Measurement Error on the Dependent Variable<737:CNRWME>2.0.CO;2-X
p. 737-760

David C. Stapleton, Douglas J. Young

When zero mean measurement error is added to the dependent variable for the nonlimit observations of the censored normal regression model, the conventional maximum likelihood estimator (Tobit) is inconsistent. "Correct" maximum likelihood estimation appears to be computationally difficult under various specifications for the distribution of the measurement error. Estimators based on either the expectation function or the conditional expectation function for uncensored observations remain consistent in the presence of measurement error. Eight such estimators are examined. The results of a numerical experiment suggest that several of these estimators are substantially more efficient than the conventional maximum likelihood estimator when measurement error exists and that they also will do reasonably well when it does not.

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