Transition Events in the Dynamics of Poverty

Chapter III:
Conceptual Framework

A Simple Model of Poverty
- Determinants of Poverty
- Events Hypothesized to Affect Poverty
Poverty Rate

III.1. A Simple Model of Poverty

Our conceptual model, which draws on human capital and other existing theories, motivates the variables included in our empirical model. Our model is based on the utility maximization framework where individuals choose the outcomes that are best for themselves and their families. Individuals choose, for example, how many goods to consume and how many children to have. In this model, individuals' choices are constrained by the resources available to them, such as their income. We briefly present the main features of the model, as they provide information about the factors that affect individuals' poverty statuses.

Choose Outcomes to Maximize Family Utility: In this model, a family’s level of well-being (i.e., utility) is based on several factors: (1) the amount of market purchased goods they jointly consume; (2) the number of children they have; (3) the amount of time spent on leisure (both the male and female); (4) the quality of their home life; and (4) preferences. Family members choose the outcomes that maximize their family's well-being, but these choices are constrained. Individuals face two constraints—a constraint on their time and a constraint on the amount of market goods they can purchase. Examining these constraints provides information about the trade-offs that individuals face when making decisions, for example about work versus leisure, which in turn have an impact on their poverty status.

Time Constraint: An individual’s time is constrained such that the amount of time spent (1) working in the wage labor market, (2) working on home production (where home production includes time caring for children, preparing meals, or other activities geared toward improving the quality of children and home life), and (3) leisure cannot exceed the amount of time available, where this maximum amount of time can be thought of as the number of hours in a week, month, or year. Each person in the family faces this constraint. This constraint tells us that a reduction in time spent working in the wage labor market does not necessarily imply an increase in the amount of leisure time. The trade-off may be between working in the wage labor market and working on home production. This trade-off may be particularly important for single-parent families as there is only one adult to perform these two work activities. The time constraint suggests that a family’s number of children and age of those children may affect hours worked, since the need for home production is higher both with more and younger children.

Consumption Constraint: What families consume in goods is restricted by family income. Family income is made up of both earned and unearned income. Unearned (or non-labor) income is comprised of government transfers, private transfers (e.g., money received from family members), and asset income. Family earned income is simply the product of hours spent in the wage labor market and the wages individuals in the family command.

Determinants of Poverty

This discussion of individuals' choices and the constraints that they face (i.e., our utility maximization framework) provides information on the factors that directly affect families' poverty statuses. They are:

family earned income,
family unearned income, and
family size.

These components are discussed in turn below.

1. Determinants of Family Earned Income

Family earned income is directly determined by the total number of hours family members worked in the wage labor market and the wage rate.

Determinants of hours worked in wage labor market: Total family hours worked in the wage labor are determined by:

wages,
unearned income,
number of adults in the family,
number of children in the family,
age of the children and adults in the family,
family members’ health or disability status,
state of the economy, and
family preferences.

Higher wages have two offsetting effects on hours worked. On the one hand, higher wages increase hours because the cost of leisure and home production increases.⁽¹²⁾ On the other hand, higher wages decrease hours worked because individuals do not need to work as many hours to reach a particular level of income.⁽¹³⁾ Higher unearned income has only one effect and is expected to lower family hours spent in the wage labor market.⁽¹⁴⁾ Additional unearned income means family members can spend less time in the wage labor market and consume the same amount of goods. Additional adults in the family should increase family hours spent in the wage labor market by providing another potential wage earner and additional help with home production. The number of children in the family is expected to reduce hours spent in the wage labor market, due to the need for additional time spent caring for the child. This is particularly true for families with young children.

Human capital theory suggests that family labor should also vary with age. As described above, young adults are more likely to invest in human capital and so spend less time in the wage labor market, working-age adults will spend more hours as they reap the benefits of their investments, and adults nearing retirement age will spend fewer hours. Family members’ health status will affect hours worked if a family member misses work due to illness or is unable to work due to a disability. The economy captures demand side effects of the labor market, such as whether part-time, full-time, or over-time jobs are available. Family preferences such as taste for work, taste for government transfers (as it affects unearned income), and the value put on home production will also affect the amount of time family members spend in the wage labor market.

Determinants of wages: The wage rate is another important determinant of family earned income. The wage available to individuals in a family will depend primarily on their:

human capital (education level and on-the-job training level),
age,
gender,
race,
state of the economy, and
government policies.

Human capital theory predicts that individuals with higher levels of education and training will have higher wages. It also predicts wages will be affected by age, where young and older individuals are expected to have lower wage rates. Gender may affect wage rates to the extent that women have taken time out of the labor market to rear children and there is discrimination in the labor market. Similarly, we may see differences in wage rates by race to the extent that our measure of educational attainment does not capture the level of human capital (since school quality differs substantially across the country and minorities are more likely than non-minorities to attend low quality schools) and to the extent that discrimination exists in the labor market. The economy will affect wage rates—a strong economy and high demand for workers will result in higher wages. Finally, government policy such as the minimum wage may also affect wages.

As an individual’s earnings are simply the product of his/her labor market hours and wage, and family earned income is the sum of all individual earnings within a family, the determinants of a family’s earnings will be all the determinants of family wage labor hours and family members’ wages.

2. Determinants of Family Unearned Income

Family unearned income is the sum of government transfers, private transfers, and asset income. The amount of government and private transfers a family receives is in part a function of individuals’ preferences. All else equal, families with little taste for receiving transfers will have less unearned income from either government or private transfers than their counterparts who have more of a taste for transfers. The economy may also play a role in altering family unearned income as returns on investments will affect asset income.

With both the determinants of earned income and unearned income in hand, we have identified the determinants of family income. We now turn our attention to family size, the final component of poverty.

3. Determinants of Family Size

Family size is an important determinant of whether a family or individual is in poverty because the official poverty measure incorporates family size. Family size depends on:

family income,
cost of children,
wages,
government transfers, and
preferences.

Becker’s (1991) theory of the demand for children predicts that the number of children in a family will depend on family income and the costs of children. Income plays a role in determining family size because families with higher incomes are more able to afford additional children. In terms of the cost of children, direct costs associated with having children include, among others, food, clothing, and health-care expenses. In addition to these direct costs there is also the relative cost. The relative cost of having a child is affected by the opportunity cost of child rearing as measured by the female wage, to a lesser extent the male wage, and government transfers. Government transfers may affect the number of children and adults in a family by altering the relative cost of having a child and creating incentives or disincentives to marry. Finally, individual preferences will affect family size.

Putting It All Together—the Underlying Determinants of Poverty

Combining the determinants of family income and family size, we arrive at the determinants of poverty. Whether a family is in poverty is determined by:

health or disability status of family members,
age of adults,
race/ethnicity of adults,
human capital (education and on-the-job training level) of working age adults,
gender of adults,
number of adults,
number of children,
age of the children,
cost of children,
government policies,
state of the economy, and
family preferences.

Note that some of these factors, such as the number of children, are determined by the family, while others, such as the state of the economy, are not. These variables will be included in the empirical model that examines the relationship between family poverty status, family characteristics, and the events that families experience. We now turn to examine the events that may affect families' poverty status.

Events Hypothesized to Affect Poverty

The conceptual model identifies the types of events that might be associated with entries into and exits from poverty:

Changes in family composition
- the birth of a child—through its negative effect on wage labor hours and its effect on family size,
- a change in marital status—through its effect on wage labor hours,
- a young adult sets up her/his own family—through the effect of age and family composition on wage labor hours and wages;
Change in employment status—through its effect on earnings;
Changes in disability or health status—through their effect on wages or wage labor hours;
Changes in educational attainment—through their effect on the wage;
Changes in government policies—through their effect on earned income, unearned income, and family size; and
Changes in economic status—through their effect on the hours family members can choose to work (e.g., job loss) and wages

III.2. Poverty Rate

The poverty rate measures the percentage of the population living below the poverty line during some fixed time interval, usually a year. While the poverty rate itself is a static measure, much can be learned by decomposing the poverty rate to look at the dynamics behind its year to year changes. Equation 1 below provides such a poverty rate decomposition:

. [1]

The numerator of the decomposed poverty rate breaks down the number of people living in poverty at the time of interest, T. It says the number of people in poverty at time T is the number of people who were in poverty at some initial time (N_p,0), plus the number of people who have entered poverty since the initial time period, minus the number of people who have exited poverty since the initial time period. The denominator breaks down the number of people in the population at the time of interest, T, in a similar manner. It says the number of people in the population at time T is the number of people who were in the population at some initial time (N₀), plus the number of people who have entered the population (through births or immigration) since the initial time period, minus the number of people who have exited the population (through deaths or emigration) since the initial time period.

The decomposed poverty rate highlights the variables responsible for changes in the poverty rate: the number of people who enter and exit poverty and the number of people who enter and exit the population. It will be used to help us answer one of our primary research questions: What are the dynamics behind changes in the poverty rate over time? We now turn to the empirical model.