Infant mortality rates: time trends and fractional integration

Abstract

This paper examines the existence of time trends in the infant mortality rates in a number of countries in the twentieth century. We test for the presence of deterministic trends by adopting a linear model for the log-transformed data. Instead of assuming that the error term is a stationary I(0), or alternatively, a non-stationary I(1) process, we allow for the possibility of fractional integration and hence for a much greater degree of flexibility in the dynamic specification of the series. Indeed, once the linear trend is removed, all series appear to be I(d) with 0<d<1, implying long-range dependence. As expected, the time trend coefficients are significantly negative, although of a different magnitude from those obtained assuming integer orders of differentiation.

Keywords:

• infant mortality rates
• time trends
• fractional integration

JEL Classification::

• C22
• I12

Notes

1. Note that in Equations (2) and (3) can be more general than a white noise process and it can be specified in terms of a general stationary linear process.

2. See Robinson [31], Doukham et al. [9] and Gil-Alana and Hualde [15] for recent reviews of I(d) models.

3. The Whittle function is an approximation of the likelihood function.

4. Demetrescu et al. [5] use a similar version of the LM test of Robinson [30]’ although specified in the time domain.

5. Other parametric estimation approaches [2,32] were also employed for the empirical analysis producing very similar results to those obtained using the method of Robinson [30].