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The variances of non-parametric estimates of the cross-sectional distribution of durations

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  • Maoshan Tian
  • Huw Dixon

Abstract

This paper focuses on the link between non-parametric survival analysis and three distributions. The delta method is applied to derive the variances of the non-parametric estimators of three distributions: the distribution of durations (DD), the cross-sectional distribution of ages (CSA) and the cross-sectional distribution of (completed) durations (CSD). The non-parametric estimator of the the cross-sectional distribution of durations (CSD) has been defined and derived by Dixon (2012) and used in the generalized Taylor price model (GTE) by Dixon and Le Bihan (2012). The Monte Carlo method is applied to evaluate the variances of the estimators of DD and CSD and how their performance varies with sample size and the censoring of data. We apply those estimators to two data sets: the UK CPI micro-price data and waiting-time data from UK hospitals. Both the estimates of the distributions and their variances are calculated. Depending on the empirical results, the estimated variances indicate that the DD and CSD estimators are all significant.

Suggested Citation

  • Maoshan Tian & Huw Dixon, 2022. "The variances of non-parametric estimates of the cross-sectional distribution of durations," Econometric Reviews, Taylor & Francis Journals, vol. 41(10), pages 1243-1264, November.
    • Handle: RePEc:taf:emetrv:v:41:y:2022:i:10:p:1243-1264
    DOI: 10.1080/07474938.2022.2114623
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    References listed on IDEAS

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    1. Taylor, J.B., 2016. "The Staying Power of Staggered Wage and Price Setting Models in Macroeconomics," Handbook of Macroeconomics, in: J. B. Taylor & Harald Uhlig (ed.), Handbook of Macroeconomics, edition 1, volume 2, chapter 0, pages 2009-2042, Elsevier.
    2. Huw Dixon & Luigi Siciliani, 2009. "Waiting Time Targets in Healthcare Markets: How Long Are We Waiting?," Discussion Papers 09/05, Department of Economics, University of York.
    3. repec:ecj:econjl:v:122:y:2012:i::p:532-554 is not listed on IDEAS
    4. Coenen, Günter & Mohr, Matthias & Straub, Roland, 2008. "Fiscal consolidation in the euro area: Long-run benefits and short-run costs," Economic Modelling, Elsevier, vol. 25(5), pages 912-932, September.
    5. Huw David Dixon & Kun Tian, 2017. "What We can Learn About the Behaviour of Firms from the Average Monthly Frequency of Price-Changes: An Application to the UK CPI Data," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 79(6), pages 907-932, December.
    6. Kiviet, Jan F. & Phillips, Garry D.A., 2014. "Improved variance estimation of maximum likelihood estimators in stable first-order dynamic regression models," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 424-448.
    7. Dixon Huw, 2012. "A Unified Framework for Using Micro-Data to Compare Dynamic Time-Dependent Price-Setting Models," The B.E. Journal of Macroeconomics, De Gruyter, vol. 12(1), pages 1-45, July.
    8. Eyal Baharad & Benjamin Eden, 2004. "Price Rigidity and Price Dispersion: Evidence from Micro Data," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 7(3), pages 613-641, July.
    9. repec:nbr:nberre:0126 is not listed on IDEAS
    10. Huw Dixon & Hervé Le Bihan, 2012. "Generalised Taylor and Generalised Calvo Price and Wage Setting: Micro‐evidence with Macro Implications," Economic Journal, Royal Economic Society, vol. 122(560), pages 532-554, May.
    11. Taylor, John B, 1980. "Aggregate Dynamics and Staggered Contracts," Journal of Political Economy, University of Chicago Press, vol. 88(1), pages 1-23, February.
    12. Dixon, Huw & Siciliani, Luigi, 2009. "Waiting-time targets in the healthcare sector: How long are we waiting?," Journal of Health Economics, Elsevier, vol. 28(6), pages 1081-1098, December.
    13. Huw Dixon & Kul Luintel & Kun Tian, 2020. "The Impact of the 2008 Crisis on UK Prices: What We Can Learn from the CPI Microdata," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 82(6), pages 1322-1341, December.
    14. Dixon, Huw David & Tian, Maoshan, 2022. "The Confidence Interval of Cross-Sectional Distribution of Durations," Cardiff Economics Working Papers E2022/15, Cardiff University, Cardiff Business School, Economics Section.
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    Cited by:

    1. Dixon, Huw David & Tian, Maoshan, 2022. "The Confidence Interval of Cross-Sectional Distribution of Durations," Cardiff Economics Working Papers E2022/15, Cardiff University, Cardiff Business School, Economics Section.

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