Another Variation on the Lee-Carter Model

Douglas A. Wolf, Syracuse University

The Lee-Carter mortality model contains two equations. One represents the age pattern of death rates using age-specific constants and a period-specific constant. The other represents the sequence of period-specific constants as a random walk with drift. Lee and Carter estimated the model using the singular value decomposition along with time-series methods; least-squares and ML estimators have also been proposed. I reformulate Lee-Carter as a set of equations for year-to-year changes in log-rates, arranging the equations in the familiar seemingly-unrelated regressions setup. I show that Lee-Carter imposes very strong restrictions: using rates for 19 age groups, the Lee-Carter approach (in first-difference form) requires estimating 21 parameters, although there are 209 empirical means, variances, and covariances with which to identify parameters. I estimate the restricted and unrestricted versions of the model, along with models of intermediate complexity; test the identifying restrictions; and assess the projected values of life expectancy produced by each.