An individual’s earnings ability is an exogenous function of her age, her type, and the level of labor-augmenting technical progress, which grows at a constant rate A. We concentrate all skill differences by age and type in an efficiency parameter б/. Thus, the wage rate for an agent of type j and age s is wj = ej w0 where wt is the growth-adjusted real wage at time t. ej increases with age to reflect not only the accumulation of human capital, but also technical progress.
To permit balanced growth for our specifications of preferences given the restriction on leisure shown in equation (2), we assume that technical progress also causes the time endowment of each successive generation to grow at rate A3 Thus, if EJ is the endowment of type j at age s and time t, then EJ = (1+A) ESJ, for all s, t, and j. Notice that the endowment depends only on an agent’s year of birth. Because E grows at rate A from one cohort to the next, there will be no underlying trend in wt. The growth-adjusted earnings ability profiles take the form
Values of the a coefficients for j-type groups 1 through 12—in ascending order of lifetime income—are based on regressions fitted to the University of Michigan’s Panel Study of Income Dynamics and are taken from Altig, Auerbach, Kotlikoff, Smetters and Walliser (1997). Groups 1 and 12 comprise the bottom and top 2 percent of lifetime wage income earners, and groups 2 and 11 the remaining 8 percent of the top and bottom deciles. All other groups constitute 10 percent of the population.
For example, group 3 is the second decile of lifetime-wage income, group four the third decile, and so on up to group 10. The estimated eamings-ability profiles, scaled to include the effects of technical progress. Given our benchmark parameterization, peak hourly wages valued in 1996 dollars are $4.00, $14.70, and $79.50 for individuals in classes 1, 6, and 12, respectively. More generally, steady-state annual labor incomes derived from the model’s assumptions and the endogenous labor supply choices range from $9,000 to $130,000. These calculations do yet include labor compensation in the form of fringe benefits (discussed below).
Transfers are received by children, with interest, at the beginning of the period after they are made by their parents. We restrict all parental transfers to bequests, so that bj = 0, for s * 75, and gj = О, for s * 56. In the steady state, therefore, gf = У, for all j (where we have dropped the age subscripts for convenience). The parameters \x! are derived endogenously for the initial steady state such that the ratio of the bequest to economy-wide mean income corresponds to the ratio originally estimated by Menchik and David (1982) and updated by Fullerton and Rogers (1993). Bequests range from $4,800 to $450,000 for the lowest and highest lifetime earnings classes, respectively.
Choices for the remaining technology, preference, and demographic parameters are summarized in Table 1. The benchmark values for 6, y, p, and n are those in Auerbach and Kotlikoff (1987). The parameter a is chosen so that agents devote, on average, about 40 percent of their available time endowment (of 16 hours per day) to labor during their prime working years (real-life ages of roughly 21-55). cheapest payday loans