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The Duration of Trade Revisited. Continuous-Time vs. Discrete-Time Hazards

The recent literature on the duration of trade has predominantly analyzed the determinants of trade flow durations using Cox proportional hazards models. The purpose of this paper is to show why it is inappropriate to analyze the duration of trade with continuous-time models such as the Cox model, and to propose alternative discrete-time models which are more suitable for estimation. Briefly, the Cox model has three major drawbacks when applied to large trade data sets. First, it faces problems in the presence of many tied duration times, leading to biased coefficient estimates and standard errors. Second, it is difficult to properly control for unobserved heterogeneity, which can result in spurious duration dependence and parameter bias. Third, the Cox model imposes the restrictive and empirically questionable assumption of proportional hazards. By contrast, with discrete-time models there is no problem handling ties; unobserved heterogeneity can be controlled for without difficulty; and the restrictive proportional hazards assumption can easily be bypassed. By replicating an influential study by Besedeš and Prusa from 2006, but employing discrete-time models as well as the original Cox model, we find empirical support for each of these arguments against the Cox model. Moreover, when comparing estimation results obtained from a Cox model and our preferred discrete-time specification, we find significant differences in both the predicted hazard rates and the estimated effects of explanatory variables on the hazard. In other words, the choice between models affects the conclusions that can be drawn.

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Paper provided by Lund University, Department of Economics in its series Working Papers with number 2010:1.

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Length: 27 pages
Date of creation: 19 Feb 2010
Date of revision:
Publication status: Forthcoming as Hess, Wolfgang and Maria Persson, 'The Duration of Trade Revisited. Continuous-Time vs. Discrete-Time Hazards' in Empirical Economics.
Handle: RePEc:hhs:lunewp:2010_001
Contact details of provider: Postal: Department of Economics, School of Economics and Management, Lund University, Box 7082, S-220 07 Lund,Sweden
Phone: +46 +46 222 0000
Fax: +46 +46 2224613
Web page: http://www.nek.lu.se/en

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  1. Paul Brenton & Christian Saborowski & Erik von Uexkull, 2010. "What Explains the Low Survival Rate of Developing Country Export Flows?," World Bank Economic Review, World Bank Group, vol. 24(3), pages 474-499, December.
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  4. Lancaster, Tony, 1979. "Econometric Methods for the Duration of Unemployment," Econometrica, Econometric Society, vol. 47(4), pages 939-56, July.
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  6. Thomas A. Mroz & Yaraslau V. Zayats, 2008. "Arbitrarily Normalized Coefficients, Information Sets, and False Reports of "Biases" in Binary Outcome Models," The Review of Economics and Statistics, MIT Press, vol. 90(3), pages 406-413, August.
  7. Nicoletti, Cheti & Rondinelli, Concetta, 2010. "The (mis)specification of discrete duration models with unobserved heterogeneity: A Monte Carlo study," Journal of Econometrics, Elsevier, vol. 159(1), pages 1-13, November.
  8. Bruce D. Meyer, 1988. "Unemployment Insurance And Unemployment Spells," NBER Working Papers 2546, National Bureau of Economic Research, Inc.
  9. Richard Newfarmer & William Shaw & Peter Walkenhorst, 2009. "Breaking Into New Markets," World Bank Publications, The World Bank, number 2616, June.
  10. Besedes, Tibor & Prusa, Thomas J., 2011. "The role of extensive and intensive margins and export growth," Journal of Development Economics, Elsevier, vol. 96(2), pages 371-379, November.
  11. Butler, J S & Moffitt, Robert, 1982. "A Computationally Efficient Quadrature Procedure for the One-Factor Multinomial Probit Model," Econometrica, Econometric Society, vol. 50(3), pages 761-64, May.
  12. Jaap H. Abbring & Gerard J. Van Den Berg, 2007. "The unobserved heterogeneity distribution in duration analysis," Biometrika, Biometrika Trust, vol. 94(1), pages 87-99.
  13. Volker Nitsch, 2007. "Die Another Day: Duration in German Import Trade," DEGIT Conference Papers c012_037, DEGIT, Dynamics, Economic Growth, and International Trade.
  14. Ana Cristina Molina and Marco Fugazza, 2009. "The determinants of trade survival," IHEID Working Papers 05-2009, Economics Section, The Graduate Institute of International Studies, revised Jun 2009.
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  16. McCall, Brian P, 1994. "Testing the Proportional Hazards Assumption in the Presence of Unmeasured Heterogeneity," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 9(3), pages 321-34, July-Sept.
  17. Heckman, James & Singer, Burton, 1984. "A Method for Minimizing the Impact of Distributional Assumptions in Econometric Models for Duration Data," Econometrica, Econometric Society, vol. 52(2), pages 271-320, March.
  18. Sueyoshi, Glenn T, 1995. "A Class of Binary Response Models for Grouped Duration Data," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 10(4), pages 411-31, Oct.-Dec..
  19. Tibor Besedeš, 2008. "A Search Cost Perspective on Formation and Duration of Trade," Review of International Economics, Wiley Blackwell, vol. 16(5), pages 835-849, November.
  20. Van den Berg, Gerard J., 2001. "Duration models: specification, identification and multiple durations," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 5, chapter 55, pages 3381-3460 Elsevier.
  21. Jenkins, Stephen P, 1995. "Easy Estimation Methods for Discrete-Time Duration Models," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 57(1), pages 129-38, February.
  22. Tibor Besedes & Thomas Prusa, 2006. "Ins, outs, and the duration of trade," Canadian Journal of Economics, Canadian Economics Association, vol. 39(1), pages 266-295, February.
  23. Hess, Wolfgang, 2009. "A Flexible Hazard Rate Model for Grouped Duration Data," Working Papers 2009:18, Lund University, Department of Economics.
  24. Besedes, Tibor & Prusa, Thomas J., 2006. "Product differentiation and duration of US import trade," Journal of International Economics, Elsevier, vol. 70(2), pages 339-358, December.
  25. Dolton, Peter J & van der Klaauw, Wilbert, 1995. "Leaving Teaching in the UK: A Duration Analysis," Economic Journal, Royal Economic Society, vol. 105(429), pages 431-44, March.
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