notes Population Projections-the Lee-Carter Model

notes Population Projections-the Lee-Carter Model - Eco 572...

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Unformatted text preview: Eco 572: Research methods in Demography The Lee-Carter Model In this unit we will examine some features of the Lee-Carter approach to forecasting U.S. mortality. The Mortality Surface The basic model seeks to summarize an age-period surface of log-rates in terms of vectors a and b along the age dimension and k along the time dimension so that log m x t = a x + b x k t + e x t with restrictions such that the b's are normalized to sum to unity and the k's sum to zero, so the a's are average log-rates. The vector a can be interpreted as an average age-profile, the vector k tracks changes over time, and the vector b determines how much each age group changes when k changes. When k is linear on time each age group changes at its own exponential rate, but this is not a requirement of the model. The error term reflects age-period effects not captured by the model. Lee and Carter estimated the a's, b's and k's with U.S. mortality data for 1933 to 1987 using a singular value decomposition that will be illustrated below. In a second step they re-estimate k so it predicts the correct total number of deaths each year. (This essentially changes the weight of each age group.) Estimates of k are obtained for each year from 1900 to 1989 (and then forecast into the future). The basic data used in the original paper consisted of rates up to ages 80-84 and 85+. Because a large fraction of the population survives to age 80 (30% in 1987) they extended the model to older ages on the basis of work by Coale and Kisker and Coale and Guo showing that after age 80 mortality increases at a linearly declining rate, rather than a constant rate as implied in a Gompertz model. The Singular Value Decomposition The Human Mortality Database (HMD) has U.S. mortality rates for five-year age groups (0,1-4,5-9,...,105-109,110+) and single calendar years for 1933 to 2001. We will use these data to examine the model. The file usm3301.dat has rates for both sexes combined for each year. Note that age is coded using the starting value to simplify numerical manipulation. We will reshape this file to a year by age matrix. . infile year age m using /// >, clear (1656 observations read) . reshape wide m, i(year) j(age) (note: j = 0 1 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110) Data long -> wide----------------------------------------------------------------------------- Number of obs. 1656 -> 69 Number of variables 3 -> 25 j variable (24 values) age -> (dropped) xij variables: m -> m0 m1 ... m110----------------------------------------------------------------------------- The next step is to move the data to Mata, compute logs, and get the mean of each rate over the period 1933-1987....
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notes Population Projections-the Lee-Carter Model - Eco 572...

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