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# Three essays on the cross-sectional distribution of completed lifetimes

 Tian, Maoshan 2019. Three essays on the cross-sectional distribution of completed lifetimes. PhD Thesis, Cardiff University. Item availability restricted.

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## Abstract

The Distribution of completed lifetimes (DCL) is a new estimator defined and derived by Dixon (2012) in the context of the general Taylor price model (GTE). If we have panel data, the DCL is an estimator of the cross-sectional distribution of completed lifetimes. It is a new statistic to describe the data alongside the more familiar survival function and hazard function. Chapter 1 focuses on the cross-sectional distribution in relation to survival analysis. The delta method is applied to derive the variance of the of three distribution functions: the distribution of the duration, the cross-sectional distribution of age and the distribution of completed lifetimes. The Monte Carlo method is applied to evaluate the performances of those formulas. The simulation results show that the asymptotic variance formula of the DCL, age distribution and distribution of durations perform well when the sample size is above 50. With larger sample sizes, the bias of the variance is reduced. In chapter 2, the pairs bootstrap method is applied to calculate the variance of the age distribution and the distribution of completed lifetimes (DCL). These results are compared with the asymptotic expansion of the variance. The Monte Carlo simulation is applied to investigate and evaluate the properties. In addition, the traditional Fieller’s method and the delta method are applied to construct the confidence intervals for the DCL. The pairs bootstrap is applied to calculate the bootstrapped version of the variance of DCL and the construct the percentile confidence interval. In addition, the bootstrapped Fieller’s method and delta method are also shown in this chapter. The numerical methods show that all methods provide the accurate confidence intervals for the DCL when the sample size above vi 200. But Fieller’s method and the delta method are superior to the remaining methods when the sample size is below 50. In chapter 3, we look at the CPI micro data. The CPI micro data are dealt by with different methods. We calculate the frequency and size of the price change. In addition, both the parametric and non-parametric methods are applied. We focus on comparing the survival function and the hazard function to determine whether they follow the same distribution. The null hypothesis is that both the survival function and the hazard function follow the same distribution between different groups. We show that there exist significant differences between the hazard functions and the survival functions before and after the financial crisis. The Cox model and the accelerated failure time model show that the frequency of price change after financial crisis is higher than the frequency of price change before financial crisis.

Item Type: Thesis (PhD) Acceptance Unpublished Business (Including Economics) survival analysis, delta method, completed lifetimes, paris bootstrap, Fieller's theorem, confidence interval, CPI micro data, cox model, cross-sectional distribution 19 August 2019 August 2019 19 Aug 2019 12:37 http://orca.cf.ac.uk/id/eprint/124788

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