Achieving Semiparametric Efficiency Bounds in Left-Censored Duration Models

• Published in: Econometrica 1996-03, Vol.64 (2), p.439-442
• Main Author: Goto, Fumihiro
• Format: Article
• Language: English
• Subjects: Applications; Biology, psychology, social sciences; Econometrics; Economic models; Economic theory; Efficiency; Estimators; Exact sciences and technology; Insurance, economics, finance; Mathematics; Maximum likelihood estimation; Medical sciences; Notes and Comments; Probability and statistics; Random variables; Reliability, life testing, quality control; Sampling techniques; Sciences and techniques of general use; Statistical methods; Statistics; Studies; Unemployment
• ISSN: 0012-9682; 1468-0262
• DOI: 10.2307/2171791

The estimation of unemployment duration is considered for the case when the statistician samples individuals from the pool of unemployed persons and later interviews them and asks how long they had been unemployed. This incurs the problem of left-censoring; ignoring left-censoring overestimates the mean duration since longer spells tend to be observed more frequently than shorter spells. Lancaster (1979) gives a simple and convenient solution to the problem by introducing a conditional maximum likelihood estimator (MLE), i.e., analysis conditional on duration at the time of sampling. The question is whether or not such an approach is optimal in the sense that a semiparametric efficiency bound is achieved. A theorem is given that provides in a general framework a sufficient condition for a semiparametric estimator achieving the efficiency bound. The theorem is applied to single-state and 2-state left-censored duration models, showing that the condition MLE coincides with the semiparametric MLE and achieves the efficiency bound.