Quality & Quantity 35: 203–230, 2001.
© 2001 Kluwer Academic Publishers. Printed in the Netherlands.
Unemployment Duration: An Analysis of
Incomplete, Completed, and Multiple Spells in
and FRANCESCO PATTARIN
Università di Modena e Reggio Emilia, Dipartimento di Economia Politica, Via Jacopo
Berengario 51, 41100 Modena – Italy. Tel. ++39 059 2056846; e-mail: firstname.lastname@example.org
Università di Roma ‘La Sapienza’, Dipartimento di Economia Pubblica. Tel. ++39 059 2056830;
Abstract. Sets of incomplete and completed spells of unemployment were obtained from the Italian
Quarterly Labour Force Survey, carried out by ISTAT in Emilia-Romagna (1993:1–1995:1). The
data were analysed through a proportional hazards model with a Weibull speciﬁcation of the baseline
hazard, including both unobserved heterogeneity applied to the scale parameter of the duration dis-
tribution, and telescoping effect to account for spikes in the distribution of unemployment spells.
They were compared formally also with a non-proportional hazard model based on a log-logistic
distribution of duration. The estimation of the parameters was carried out separately on both com-
pleted spells and quarterly incomplete spells to ascertain differences and to envisage the potential
seasonal effect. The results showed that the shape parameters changed over time. The parameters of
each covariate proved to be statistically stable over time and were also equal to the parameters of the
completed spells model. Therefore, the analysis of incomplete spells is fairly feasible when an even
(closed form) baseline hazard function is suitable for data.
Key words: Emilia-Romagna, unemployment spells, hazard function, parameter estimation
Italian Labour Force data are gathered by ISTAT through a quarterly rotating cur-
rent population survey, in which the sampling units are the families and the rotation
scheme is 2-2-2. Each rotation group is included for two consecutive quarters,
drops out for two subsequent quarters, and then returns for two successive quarters.
However, the surveys are conducted at a given point in time and they measure the
lengths of on-going spells of unemployment (or employment) for sample subjects
who are currently unemployed (employed) and whose position is also referred
to as state. Therefore, durations are right-censored and termed incomplete spells
because the end of unemployment (or employment) spells are not known as of the
survey date. Nevertheless, through the rotation scheme, it is possible to obtain a
The study was developed for the National Research Project “Lavoro e disoccupazione: ques-
tioni di misura e di analisi”, coordinated by Ugo Trivellato and ﬁnanced by MURST (Ministry of
University Education and Scientiﬁc and Technological Research).