IDEAS home Printed from
   My bibliography  Save this paper

Estimating Systematic Continuous-time Trends in Recidivism using a Non-Gaussian Panel Data Model


  • Siem Jan Koopman

    () (Vrije Universiteit Amsterdam)

  • André Lucas

    () (Vrije Universiteit Amsterdam)

  • Marius Ooms

    () (Vrije Universiteit Amsterdam)

  • Kees van Montfort

    () (Vrije Universiteit Amsterdam)

  • Victor van der Geest

    (Netherlands Institute for the Study of Crime and Law Enforcement (NCSR), Leiden)


This discussion paper led to an article in the Statistica Neerlandica (2008). Vol. 62, issue 1, pages 104-130. We model panel data of crime careers of juveniles from a Dutch Judicial Juvenile Institution. The data are decomposed into a systematic and an individual-specific component, of which the systematic component reflects the general time-varying conditions including the criminological climate. Within a model-based analysis, we treat (1) shared effects of each group with the same systematic conditions, (2) strongly non-Gaussian features of the individual time series, (3) unobserved common systematic conditions, (4) changing recidivism probabilities in continuous time, (5) missing observations. We adopt a non-Gaussian multivariate state space model that deals with all of these issues simultaneously. The parameters of the model are estimated by Monte Carlo maximum likelihood methods. This paper illustrates the methods empirically. We compare continuous-time trends and standard discrete-time stochastic trend specifications. We find interesting common time-variation in the recidivism behavior of the juveniles during a period of 13 years, while taking account of significant heterogeneity determined by personality characteristics and initial crime records.

Suggested Citation

  • Siem Jan Koopman & André Lucas & Marius Ooms & Kees van Montfort & Victor van der Geest, 2007. "Estimating Systematic Continuous-time Trends in Recidivism using a Non-Gaussian Panel Data Model," Tinbergen Institute Discussion Papers 07-027/4, Tinbergen Institute.
  • Handle: RePEc:tin:wpaper:20070027

    Download full text from publisher

    File URL:
    Download Restriction: no

    Other versions of this item:

    References listed on IDEAS

    1. Geweke, John, 1989. "Bayesian Inference in Econometric Models Using Monte Carlo Integration," Econometrica, Econometric Society, vol. 57(6), pages 1317-1339, November.
    2. Gary S. Becker, 1974. "Crime and Punishment: An Economic Approach," NBER Chapters,in: Essays in the Economics of Crime and Punishment, pages 1-54 National Bureau of Economic Research, Inc.
    3. Bergstrom, A.R., 1984. "Continuous time stochastic models and issues of aggregation over time," Handbook of Econometrics,in: Z. Griliches† & M. D. Intriligator (ed.), Handbook of Econometrics, edition 1, volume 2, chapter 20, pages 1145-1212 Elsevier.
    4. Koopman, Siem Jan & Lucas, André, 2008. "A Non-Gaussian Panel Time Series Model for Estimating and Decomposing Default Risk," Journal of Business & Economic Statistics, American Statistical Association, vol. 26, pages 510-525.
    5. Joon Y. Park & Peter C. B. Phillips, 2000. "Nonstationary Binary Choice," Econometrica, Econometric Society, vol. 68(5), pages 1249-1280, September.
    6. Durbin, James & Koopman, Siem Jan, 2012. "Time Series Analysis by State Space Methods," OUP Catalogue, Oxford University Press, edition 2, number 9780199641178, June.
    7. Schmidt, Peter & Witte, Ann Dryden, 1989. "Predicting criminal recidivism using 'split population' survival time models," Journal of Econometrics, Elsevier, vol. 40(1), pages 141-159, January.
    8. Jukka Nyblom & Andrew Harvey, 2001. "Testing against smooth stochastic trends," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 16(3), pages 415-429.
    9. Johan Oud & Robert Jansen, 2000. "Continuous time state space modeling of panel data by means of sem," Psychometrika, Springer;The Psychometric Society, vol. 65(2), pages 199-215, June.
    10. Siem Jan Koopman & Neil Shephard & Jurgen A. Doornik, 1999. "Statistical algorithms for models in state space using SsfPack 2.2," Econometrics Journal, Royal Economic Society, vol. 2(1), pages 107-160.
    11. J. Durbin, 2002. "A simple and efficient simulation smoother for state space time series analysis," Biometrika, Biometrika Trust, vol. 89(3), pages 603-616, August.
    12. Francesco Bartolucci & Fulvia Pennoni & Brian Francis, 2007. "A latent Markov model for detecting patterns of criminal activity," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 170(1), pages 115-132.
    13. Levitt, Steven D, 1997. "Using Electoral Cycles in Police Hiring to Estimate the Effect of Police on Crime," American Economic Review, American Economic Association, vol. 87(3), pages 270-290, June.
    14. Catrien C.J.H. Bijleveld & Ab Mooijaart, 2003. "Latent Markov Modelling of Recidivism Data," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 57(3), pages 305-320.
    15. Andrews, Donald W K, 2001. "Testing When a Parameter Is on the Boundary of the Maintained Hypothesis," Econometrica, Econometric Society, vol. 69(3), pages 683-734, May.
    16. Cornwell, Christopher & Trumbull, William N, 1994. "Estimating the Economic Model of Crime with Panel Data," The Review of Economics and Statistics, MIT Press, vol. 76(2), pages 360-366, May.
    Full references (including those not matched with items on IDEAS)


    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.

    Cited by:

    1. Mesters, G. & Koopman, S.J., 2014. "Generalized dynamic panel data models with random effects for cross-section and time," Journal of Econometrics, Elsevier, vol. 180(2), pages 127-140.
    2. Suncica Vujic & Jacques Commandeur & Siem Jan Koopman, 2012. "Structural Intervention Time Series Analysis of Crime Rates: The Impact of Sentence Reform in Virginia," Tinbergen Institute Discussion Papers 12-007/4, Tinbergen Institute.
    3. Vujić Sunčica & Koopman Siem Jan & Commandeur J.F., 2012. "Economic Trends and Cycles in Crime: A Study for England and Wales," Journal of Economics and Statistics (Jahrbuecher fuer Nationaloekonomie und Statistik), De Gruyter, vol. 232(6), pages 652-677, December.
    4. Vujić, Sunčica & Commandeur, Jacques J.F. & Koopman, Siem Jan, 2016. "Intervention time series analysis of crime rates: The case of sentence reform in Virginia," Economic Modelling, Elsevier, vol. 57(C), pages 311-323.

    More about this item


    non-Gaussian state space modeling; nonlinear panel data model; binomial time series; recidivism behavior; continuous time modelling;

    JEL classification:

    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C33 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Models with Panel Data; Spatio-temporal Models
    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement

    NEP fields

    This paper has been announced in the following NEP Reports:


    Access and download statistics


    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:tin:wpaper:20070027. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Tinbergen Office +31 (0)10-4088900). General contact details of provider: .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.