Demography and the statistics of lifetime economic transfers under individual stochasticity

Abstract

Background: As individuals progress through the life cycle, they receive income and consume goods and services. The age schedules of labor income, consumption, and life cycle deficit reflect the economic roles played at different ages. Lifetime accumulation of economic variables has been less well studied, and our goal here is to rectify that. Objective: To derive and apply a method to compute the lifetime accumulated labor income, consumption, and life cycle deficit, and to go beyond the calculation of mean lifetime accumulation to calculate statistics of variability among individuals in lifetime accumulation. Methods: To quantify variation among individuals, we calculate the mean, standard deviation, coefficient of variation, and skewness of lifetime accumulated transfers, using the theory of Markov chains with rewards (Caswell 2011), applied to National Transfer Account data for Germany of 1978, and 2003. Results: The age patterns of lifetime accumulated labor income are relatively stable over time. Both the mean and the standard deviation of remaining lifetime labor income decline with age; the coefficient of variation, measuring variation relative to the mean, increases dramatically with age. The skewness becomes large and positive at older ages. Education level affects all the statistics. About 30% of the variance in lifetime income is due to variance in age-specific income, and about 70% is contributed by the mortality schedule. Lifetime consumption is less variable (as measured by the CV) than lifetime labor income. Conclusions: We conclude that demographic Markov chains with rewards can add a potentially valuable perspective to studies of the economic lifecycle. The variation among individuals in lifetime accumulations in our results reflects individual stochasticity, not heterogeneity among individuals. Incorporating heterogeneity remains an important problem.