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Under-5 Mortality Rates in G7 Countries: Analysis of Fractional Persistence, Structural Breaks and Nonlinear Time Trends

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Abstract

This paper deals with the analysis of the under-5 mortality rate series in the G7 countries by using fractional integration techniques, including structural breaks and potential nonlinearities in the data. Several features were detected in the results: Firstly, we observed that for the neonatal data, the order of integration is equal to or higher than one in all cases, contrary to what happens for the remaining cases (< 1– < 5 years) where mean reversion is found in many cases, especially as we increase the age of death. Thus, shocks affecting the neonatal (< 1 month from delivery) mortality rates will have permanent effects requiring special attention to recover the original trends. As expected, all the time trend coefficients were significantly negative and the highest reduction in the mortality rates was obtained in Japan, which might be related with the 17-year increase in life expectancy for the country. Due to the sensitivity of the methodological approaches, the use of robust time series approaches when analyzing child mortality rates is highly recommended.

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Notes

  1. The model is \(\ln \left( {{}_{n}q_{{_{0} }} } \right)_{i} = b_{0} + b_{1} \left( {\text{date}} \right) + b_{2} \left( {{\text{postk}}1} \right) + b_{3} \left( {{\text{postk}}2} \right) + b_{4} \left( {{\text{postk}}3} \right) + \cdots + {\text{e}}_{i}\) where “date” is the calendar year; postk1 is date minus the date of the earliest defined knot if positive, or zero otherwise, and picks up any change in trend after the first knot (note that the knots are defined from the present backwards into the past, but the earliest knot is defined to ensure at least five observations between it and the start of the series); postk2 is date minus the date of the second defined knot if positive, or zero otherwise, and picks up any change in trend after the second knot; and so on.

  2. Conley and Springer (2001), Silva (2007) and Siah and Lee (2015) have considered modeling mortality time series using models that allows for the inclusion of structural breaks.

  3. This model has been widely applied in many disciplines because of its relationship to the first-order stochastic differential equation.

  4. Such a feature (mean-reversion) is considered by some authors as a misnomer given the nonstationary nature of the series (Phillips and Xiao 1999).

  5. In other standard large sample testing procedures, Wald and Likelihood Ratio (LR) test statistics against fractional alternatives have the same null and limit theory as the LM test of Robinson (1994). See Velasco and Lobato (2007).

  6. Given that the residuals of the auxiliary regression are I(0) stationary by assumption, t-statistics are valid to test for the significance of the nonlinear trends. This solves the problem of choosing the order of the Chebyshev polynomials, which was not clearly defined by Bierens (1997) for the unit root case.

  7. A similar approach was conducted by Gil-Alana (2008) for the fractional case. Very similar results in terms of the break dates were obtained to the Bai and Perron’s (2003) approach.

  8. Due to unavailability of longtime series for the case of Germany, we have taken the averages of longtime series for West and East Germany and these are considered as proxies for the German mortality rates.

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Acknowledgements

Comments from the Editor and two anonymous reviewers are gratefully acknowledged.

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Authors and Affiliations

  1. School of Research and Post-Graduate Studies, Faculty of Human and Social Sciences, North West University (Mafikeng Campus), Mmabatho, South Africa

    OlaOluwa S. Yaya & Acheampong Y. Amoateng

  2. Department of Statistics, University of Ibadan, Ibadan, Nigeria

    OlaOluwa S. Yaya

  3. Faculty of Economics and ICS (NCID), University of Navarra, Pamplona, Spain

    Luis A. Gil-Alana

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  1. OlaOluwa S. Yaya
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  2. Luis A. Gil-Alana
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  3. Acheampong Y. Amoateng
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Correspondence to OlaOluwa S. Yaya.

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Yaya, O.S., Gil-Alana, L.A. & Amoateng, A.Y. Under-5 Mortality Rates in G7 Countries: Analysis of Fractional Persistence, Structural Breaks and Nonlinear Time Trends. Eur J Population 35, 675–694 (2019). https://doi.org/10.1007/s10680-018-9499-8

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