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Left-Censoring in Duration Data: Theory and Applications


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  • Anna Christina D'Addio
  • Michael Rosholm

    (Department of Economics, University of Aarhus, Denmark)


In this paper, we discuss how to best exploit the information contained in spells that are in progress when an observation period begins, that is, left-censored and left-truncated duration data. We provide a survey of censoring and truncation mechanisms in event history models. We describe some approaches that have been suggested in the literature to deal with left-censoring. Our contribution is the description of ways to use additional information to obtain more efficient parameter estimates using the left-censored informations, and particularly, the derivation of the associated likelihood expressions. In order to use the information efficiently, we often resort to the stationarity assumption. Hence, we provide a Hausman test for this assumption. The second part of the paper briefly presents some empirical examples which demonstrates the efficiency gains associated with the use of the information contained in the left-censored observations. In particular, we show how the use of some additional pieces of information allows us to obtain more efficient estimates of the parameters of interest. In doing this, we use the information reported in the waves 1990-1992 of the French Labour Force Surveys on young French individuals.

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Paper provided by School of Economics and Management, University of Aarhus in its series Economics Working Papers with number 2002-5.

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Length: 36
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Handle: RePEc:aah:aarhec:2002-5

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Related research

Keywords: left-censoring; left-truncation; conditional likelihood; hazard rate; stationarity;

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Cited by:
  1. Roberto IMPICCIATORE & Francesco C. BILLARI, 2010. "MAPLES: a general method for the estimation of age profiles from standard demographic surveys (with an application to fertility)," Departmental Working Papers 2010-40, Department of Economics, Management and Quantitative Methods at Università degli Studi di Milano.
  2. Sunder, Marco, 2005. "Toward generation XL: Anthropometrics of longevity in late 20th-century United States," Economics & Human Biology, Elsevier, vol. 3(2), pages 271-295, July.
  3. Georges Dionne & Benoit Dostie, 2007. "Estimating the effect of a change in insurance pricing regime on accidents with endogenous mobility," Cahiers de recherche 07-11, HEC Montréal, Institut d'économie appliquée.
  4. Ana Flávia Machado & Rafael Perez Ribas, 2008. "Do Changes in the Labour Market Take Families out of Poverty? Determinants of Exiting Poverty in Brazilian Metropolitan Regions," Working Papers 44, International Policy Centre for Inclusive Growth.
  5. Gielen, Anne C. & van Ours, Jan C., 2012. "Unhappiness and Job Finding," IZA Discussion Papers 6320, Institute for the Study of Labor (IZA).
  6. Brenton, Paul & Saborowski, Christian & von Uexkull, Erik, 2009. "What explains the low survival rate of developing country export flows ?," Policy Research Working Paper Series 4951, The World Bank.
  7. Niedergesäss, Markus, 2012. "Duration dependence, lagged duration dependence, and occurrence dependence in individual employment histories," University of Tuebingen Working Papers in Economics and Finance 26, University of Tuebingen, Faculty of Economics and Social Sciences.
  8. Doiron, Denise & Gørgens, Tue, 2008. "State dependence in youth labor market experiences, and the evaluation of policy interventions," Journal of Econometrics, Elsevier, vol. 145(1-2), pages 81-97, July.
  9. Anna Cristina D'Addio & Bo E. Honoré, 2002. "Duration dependence and time varying variables in discrete time duration models," 10th International Conference on Panel Data, Berlin, July 5-6, 2002 D6-3, International Conferences on Panel Data.
  10. Jakobsen, Vibeke & Rosholm, Michael, 2003. "Dropping out of School? A Competing Risks Analysis of Young Immigrants’ Progress in the Educational System," IZA Discussion Papers 918, Institute for the Study of Labor (IZA).
  11. Bruno, Giovanni S. F. & Caroleo, Floro Ernesto & Dessy, Orietta, 2012. "Stepping Stones versus Dead End Jobs: Exits from Temporary Contracts in Italy after the 2003 Reform," IZA Discussion Papers 6746, Institute for the Study of Labor (IZA).


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