Technical Overview

The microsimulation models the economy as consisting of a large number of individuals each with several individual-level attributes that may or may not change over time. In additions, individuals may undergo particular events appropriate for their particular life-cycle stage. These attributes and events include, for example, items such as:

  • Fertility
  • Immigration
  • Mortality
  • Education
  • Marriage and Divorce
  • Disability
  • Labor-force participation and earnings
  • Employment status changes (into and out of self-employment)
  • Unemployment spells
  • Retirement
  • Tax payments and transfer receipts from welfare programs

Individual attributes evolve according to the Markov process which may or may not be stationary, as appropriate, based on micro-data survey information. The empirical attribute distributions are calibrated to the distributions observed for the U.S. economy, and changes in those distributions over time. For example, the likelihood of a female marrying a wealthy male is conditioned on the distribution of wealth among eligible males in the economy. The wealth distribution itself depends on a wide variety of demographic factors, including the composition of marriage and divorce in the previous period. In this way, the microsimulation model captures a rich variety of feedback effects and interactions between different demographic attributes.

Example: Years of Education

To illustrate, we present two simple examples, the first of a simple binary Markov process (education), and the second of a simple marriage process.

In the microsimulation model, education attainment is modeled as a variable which can take one of two values “education advances by one year” or “education remains the same as last year.” In the full model, the education advancement process is allowed to depend on the current year, the gender of the individual, their race, age, and total number of years of education already received. In the microsimulation, the estimates of these values are derived from the CPS.

Figure 1: Education levels in the CPS (left), and the microsimulation (right), simulated from 1996 - 2070.

Figure 1: Education levels in the CPS (left), and the microsimulation (right), simulated from 1996 - 2070.

Probability of Gaining A Year of Education, by Age

Then, imagine, a 7-year old has a 9% chance of gaining a year of education, and a 21-year old has a 27% chance of gaining a year of education. Levels of education in the economy can then be predicted using simulation or transition rules. If, for example, there are 100,000 7-year olds in the economy in 1995, all of whom have no education, then in 1996 there will be 9,000 8-year olds with one year of education, and 91,000 8-year olds with no education. In reality, the probability of receiving a year of education depends on many other factors, and the conditioning set is allowed to be much wider. The predicted levels of education are then compared to the CPS. Charts showing the comparison of CPS and microsimulation predictions are included in this document, both for education, and for other demographic variables.

Many of the demographic attributes of individuals in the microsimulation model evolve in a way similar to that of education acquisition. Some, however, are modeled as dependent on (the distributions of) other individual characteristics. We now consider an example:

Figure 2: Disability levels in the CPS (left), and the microsimulation (right), simulated from 1996 - 2070.

Figure 2: Disability levels in the CPS (left), and the microsimulation (right), simulated from 1996 - 2070.

Figure 3: Race composition in the CPS (left), and the microsimulation (right), simulated from 1996 - 2070.

Figure 3: Race composition in the CPS (left), and the microsimulation (right), simulated from 1996 - 2070.

Figure 4: Wage income deciles in the CPS (left), and the microsimulation (right), simulated from 1996 - 2070.

Figure 4: Wage income deciles in the CPS (left), and the microsimulation (right), simulated from 1996 - 2070.

Many of the demographic attributes in the microsimulation model evolve in a way similar to that of education. Some, however, are allowed to evolve in a way dependent on the distribution of other characteristics in the population. We now consider an example of this.

Example: Marriage

For each attribute, the controlling Markov process is calibrated to the distribution of individuals’ attributes in the U.S. economy. Consider the marriage market: marriage events are simulated according to the following simplified sequences of search and matching in the marriage market. In each period, eligible (single) men and women search for other eligible individuals of the opposite sex. For example, a woman draws (or “meets”) men from the pool of male eligibles. These draws are calibrated in a specific way by individuals’ ethnic affiliations: One-half of each woman’s draws are from the pool of eligible partners of her own race and the remaining one-half are purely random draws across men of all ethnicities. Given a meeting, “acceptance” rates, that control whether a marriage pairing will occur, are conditioned on the both partners’ ages, ethnicities, and educational attainments.

In this setting, marriage rates can change if population distributions of race, education and age change. For example, if people obtain more education over time, overall marriage rates would increase. This is because acceptance rates for pairings (calibrated to U.S. micro-data information) where both potential partners are highly educated are higher than if the partners have different education levels. The same reasoning applies to ethnicity: If the population share of a particular ethnicity increases, marriage events involving that race will also increase. However, within-ethnicity marriages for the growing ethnic group will increase by more because inter-ethnicity meetings occur at a lower frequency.

Figure 5: Race levels of marriage in the CPS (left), and the microsimulation (right), simulated from 1996 - 2070.

Figure 5: Race levels of marriage in the CPS (left), and the microsimulation (right), simulated from 1996 - 2070.

Figure 6: Whether a spouse has the same race in the CPS (left), and the microsimulation (right), simulated from 1996 - 2070.

Figure 6: Whether a spouse has the same race in the CPS (left), and the microsimulation (right), simulated from 1996 - 2070.

Figure 7: Composition of family types to which individuals belong in the CPS (left), and the microsimulation (right), simulated from 1996 - 2070.

Figure 7: Composition of family types to which individuals belong in the CPS (left), and the microsimulation (right), simulated from 1996 - 2070.

Mortality

Individuals may also suffer mortality shocks. If either the man or the woman suffers a mortality shock, then the family becomes one with a single head. If both heads of the family suffer mortality shocks, then the family is not dissolved. Instead, any children become orphans, and exit the family as they would normally at age 18. If all the members of the family die, then the family is dissolved.

Income and Employment

The microsimulation models income and employment path histories for individuals, including non-wage income and income from government programs. Income histories are of direct policy relevance in quantifying the fiscal impact of government programs which depend both on income levels as well as the lifecycle of income.

Transitions to and from employment, unemployment, and the labor force are estimated using data from the CPS. The income process itself is predicted with an auto-regression model conditioning on a variety of individual attributes as well as income in the previous year.

Figure 8: Income distribution in the CPS (left), and the microsimulation (right), simulated from 1996 - 2070. Deciles are defined as deciles of wage income in the microsimulation model for the year of interest.

Figure 8: Income distribution in the CPS (left), and the microsimulation (right), simulated from 1996 - 2070. Deciles are defined as deciles of wage income in the microsimulation model for the year of interest.