We simulate the consumption and savings decisions made by households in response to changing economic and demographic conditions. Household heads are motivated by a desire to smooth consumption over their lifetime.
Representative households: We do not simulate all the households that comprise an economy. Instead, we simulate one household for each possible age of household head -- 90 households (ages 21 to 110). This means we assume that all households headed by 45 year olds can be represented by a single household headed by a 45 year old, with the average income of 45 year olds, one-half of the average number of children of 45 year olds, and the average demographic and economic prospects of 45 year olds.
Unisex individuals: These households are comprised of unisex individuals. The economic profiles are based on the average wages and labor force participation rates of men and women combined. The mortality rates are based on the average mortality rates of men and women combined. The fertility rates are based on the the fertility rates of women divided by 2. There is no marriage, and households are comprised of 1 adult household head and her co-residing descendants. The population is forecast based on these fertility and mortality rates. There is no immigration.
Household formation: At the age of economic independence, the individual leaves her parental household with her children (if any) and becomes the head of her own household with zero wealth. At her death, her household is dissolved. There is lateral inheritance of both orphaned children and wealth. That is, we distribute the children and wealth of deceased household heads to other households with the same age head. The lateral inheritance of wealth is equivalent to assuming that all savings are held as annuities.
Some childbearing may take place before the age of economic independence, so that households formed at the age of economic independence may be comprised of a little more than 1.0 persons. Household members are added via childbearing and adoption (of orphaned children). Household members are removed through death; upon reaching the age of economic independence; and, in the case of very young children living in their grandparent's home, upon their parent reaching the age of economic independence.
Households make one decision: At the start of each year, households make a single decision: how much to consume during the coming year. They base this decision on their expectations about lifetime wealth and their current consumption needs relative to future needs. The greater their expectations of lifetime wealth, the greater their consumption. The greater their current consumption needs relative to future needs, the greater their consumption.
Lifetime wealth is the sum of current wealth, expected future earnings, and expected lateral inheritance. Future earnings reflect both expectations about future characteristics of the household (such as the number and age of members) and expectations about future characteristics of the economy (such as the wage rate and the interest rate). Expected lateral inheritance is based on expectations about future mortality rates. As noted earlier, including expectations about lateral inheritance in lifetime wealth is equivalent to assuming all savings are held as annuitites. In making their annual consumption decision, households make no distinction between the wealth they currently hold and their future income from earnings or lateral inheritance. They make their consumption decision based on lifetime wealth. They expect to spend this entire sum during their lifetime and so leave no inheritance to their children.
To decide how much of their lifetime wealth to consume in a given year, households must weigh their current consumption needs against future needs. These needs are measured in units of equivalent adult consumers with 1 unit assigned to each adult and fractional units (0.2, 0.4, 0.6, and 0.8) assigned to children depending on their age. Thus, the needs of the household in any future year y are based simply on the expected number and age of household members in year y. By some algorithm, the household must combine the needs of all future years to arrive at a single value representing future needs. The ratio of current needs to future needs determines the share of lifetime wealth that is consumed this year.
In our simulation model, this algorithm for weighting future needs is based on expectations about the future economy (the interest rate, r), the intertemporal elasticity of substitution (1/g), and the rate of time preference (p). This derives from a generalization of a household utility function used by Tobin (1967) -- in essence, utility is derived from both the number of household members and the consumption per member. Note that while household size enters the utility function, we assume that the household head makes no decisions about future household size (for example, fertility). Households make only one decision: how much of their lifetime wealth to consume during the coming year. Under this utility specification, households maximize their utility when consumption per equivalent adult consumer rise over their life cyle at the rate: (r-p)/g. A higher interest rate (r) increases the importance of future consumption needs relative to the present. A higher rate of time preference (p) decreases the importance of future consumption needs relative to the present. The higher the elasticity of intertemporal substitution the greater the responsiveness of households to changes in these two rates. In most models, we assume that the rate of time preference is zero -- households value utility in the future as much as utility in the present. In addition, the intertemporal rate of subsitution is set at 0.64. Hence, households maximize utility by smoothing their consumption so that consumption per equivalent adult consumer rises over their life cycle at an annual rate of 0.64 times the interest rate.
Percent of the current US population which is descended from immigrants who arrived ...
| Before 1800 | 33% | 1800-1849 | 12% | 1850-1899 | 26% | 1900-1949 | 12% | 1950-1999 | 17% |