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On the Treatment of Interrupted Spells and Initial Conditions in Event History Analysis

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  • ALFRED HAMERLE

    (University of Konstanz)

Abstract

This article deals with some problems of event history analysis that arise in special types of sampling plans where spells in progress at time t 0 , the start date of the observation period, are sampled. Then, the available data are random samples of interrupted spells, or else may be spells that begin after the start date of the sample. For the interrupted spells, all relevant probability distributions of the elapsed duration until t 0 and the duration of the spell after t 0 have to account for the condition that the individual is in the state y 0 in question at time t 0 . Relying on results of Ridder (1984) and Heckman and Singer (1986), we discuss the distribution of the “sampled†spells (i.e., conditional on the presence of the individual in state y 0 at time t 0 ), in particular the joint distribution of pre-interview and post-interview durations. In general, this distribution depends on the entry rate into the state y 0 . The distribution of the sampled spells for the special sampling plans differs from the corresponding duration distributions in the population. We then show that, sampling spells in progress, the distribution of the explanatory variables in the sample becomes informative for the parameters of interest. Next, we investigate the distribution of the sampled spells of individuals who enter or leave the state in question. This referred to as “sampling the flow.†We then discuss the special case of a time invariant entry rate. Appropriate likelihood contributions are given depending on which pre-interview, post-interview, and completed durations are observable. We also discuss a conditional likelihood approach due to Lancaster (1979) that does not require any assumptions on the entry rate. Next we derive the appropriate likelihood contributions of right censored observations and both left and right censored observations for the specific sampling plans considered here. Finally, we present the results of some simulation studies that show the usefulness of taking into account the observable part of spells with unknown origin in the estimation procedure.

Suggested Citation

  • Alfred Hamerle, 1991. "On the Treatment of Interrupted Spells and Initial Conditions in Event History Analysis," Sociological Methods & Research, , vol. 19(3), pages 388-414, February.
  • Handle: RePEc:sae:somere:v:19:y:1991:i:3:p:388-414
    DOI: 10.1177/0049124191019003005
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    References listed on IDEAS

    as
    1. Alfred Hamerle, 1989. "Multiple‐Spell Regression Models for Duration Data," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 38(1), pages 127-138, March.
    2. Heckman, James J. & Singer, Burton, 1986. "Econometric analysis of longitudinal data," Handbook of Econometrics, in: Z. Griliches† & M. D. Intriligator (ed.), Handbook of Econometrics, edition 1, volume 3, chapter 29, pages 1689-1763, Elsevier.
    3. Andrew Chesher & Tony Lancaster, 1983. "The Estimation of Models of Labour Market Behaviour," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 50(4), pages 609-624.
    4. Christopher J. Flinn & James J. Heckman, 1982. "Models for the Analysis of Labor Force Dynamics," NBER Working Papers 0857, National Bureau of Economic Research, Inc.
    5. Lancaster, Tony, 1985. "Generalised residuals and heterogeneous duration models : With applications to the Weilbull model," Journal of Econometrics, Elsevier, vol. 28(1), pages 155-169, April.
    6. Burdett, Kenneth & Kiefer, Nicholas M. & Sharma, Sunil, 1985. "Layoffs and duration dependence in a model of turnover," Journal of Econometrics, Elsevier, vol. 28(1), pages 51-69, April.
    7. Nickell, Stephen J, 1979. "Estimating the Probability of Leaving Unemployment," Econometrica, Econometric Society, vol. 47(5), pages 1249-1266, September.
    8. Kiefer, Nicholas M, 1988. "Economic Duration Data and Hazard Functions," Journal of Economic Literature, American Economic Association, vol. 26(2), pages 646-679, June.
    9. Hans-Peter Blossfeld & Alfred Hamerle, 1989. "Unobserved heterogeneity in hazard rate models: a test and an illustration from a study of career mobility," Quality & Quantity: International Journal of Methodology, Springer, vol. 23(2), pages 129-141, June.
    10. Lancaster, Tony, 1979. "Econometric Methods for the Duration of Unemployment," Econometrica, Econometric Society, vol. 47(4), pages 939-956, July.
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