Measuring and explaining the effects of mortality changes on life expectancy has been discussed for the past three decades. Different approaches have been proposed using discrete or continuous methods. Two basic ideas underlie these approaches. The first compares two different mortality schedules and quantifies the contribution of each age group to the increase in life expectancy. The second analyzes how the progress in the mortality schedule translates into progress in life expectancy. This

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... er discusses and compares the approaches proposed by the United Nations 1982), Arriaga (1984) , Pollard (1982 and 1988 , identifying their problems, advantages, and the types of situations where each one can best be applied. * I thank the valuable comments and suggestions of Noreen Goldman, German Rodriguez, Burt Singer and James Trussell. This is a modified version of the paper Changes in life expectancy in Brazil: 1940Brazil: /1990: methodological issues, which was awarded the Charles Westoff Prize in Demography in 2000. perfectly, it is necessary to understand how changes in mortality affect life expectancy, and to devise a method that allows the decomposition of changes in life expectancy by age groups. Although some methods have been proposed, it is necessary to compare them and identify the types of situations where each one is best recommended. In 1982, three different authors dealt with this issue. A United Nations (1982) study proposed a method to decompose the change in life expectancy at birth in three major age ranges (0 to 29 years, 30 to 64 years and 65 years and over), based on Kitagawa's (1955) technique to compute the differences between two sets of specific rates. Arriaga (1982) introduced the notion of temporary life expectancy, and suggested an index to measure, by each age group, the annual relative change in the years to be lived. Finally, Pollard (1982) proposed a continuous method that compares the difference between two different mortality schedules, and quantifies the contribution of each age group to the increase in life expectancy at birth. Two years later, Arriaga (1984) developed a technique to measure and explain the changes in life expectancy, considering the changes in the age-specific mortality rates. It was a discrete method constructed on the basis of life table functions. Later, Vaupel (1986) extended Keyfitz's work (Keyfitz and Golini, 1975 and Keyfitz, 1977) and proposed a continuous method to analyze how the progress in the mortality schedule would translate into progress in life expectancy at birth. Finally, Pollard (1988) revisited the method he first proposed in 1982, showing its similarity with Arriaga's discrete approach. The purpose of this paper is to compare the different methods proposed, using Brazilian data for the period between 1940 and 1990, pointing out the strengths,