
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 wellbeing (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 wellbeing, 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 tradeoffs 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 tradeoff may be between working in the wage labor market and working on home production. This tradeoff may be particularly important for singleparent 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 nonlabor) 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.


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 (N_{0}), 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.

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