Present Value Functions and Recursions

Using a Markov-induced decomposition of time in the labor force, the authors compute means, standard deviations, and other distributional characteristics of the present value of years of labor force activity. They also provide bootstrap estimates of the mean present value and the corresponding standard deviations of sample means. This paper combines years of future labor force activity, decomposed with a Markov process, with discounting that activity to the present, whereas previous literature has analyzed only undiscounted years of activity. It is well known that a person's worklife expectancy does not provide enough information to accurately compute the associated present value, since worklife will on average be allocated over future years in a particular pattern dictated by the underlying Markov model. The authors conclude with a brief discussion of the possible uses of expected present values and probability mass functions of present value random variables.