The value of the expected participation variable for a specific State and quarter is the level of participation we would expect if age-specific participation rates were the same as national monthly average age-specific participation rates in 1990. We chose 1990 as the base year because the national age-specific data needed to construct the variable is better in that year than in others, due to the Decennial Census.

For the Basic caseload, the age-specific participation rate is defined as the number households in the Basic program headed by women in the age group divided by the number of women in the age group. Age-specific participation rates for the UP caseload are defined analogously, but using the number of households in the UP caseload, the age of the adult male in the household, and male population data. For expected recipients and expected child recipients in each program, we used the same scheme to classify households into age groups. The age-specific participation rate for recipients is the number of recipients in households in the age category divided by the number of women (Basic) or men (UP) in the age group, and the age-specific participation rate for child recipients is defined in the same way, but only including children. National age-specific participation rates for 1990 were estimated using the 1990 Survey of Income and Program Participation (see Chapter Four).

We constructed annual expected participation variables for each state by computing a weighted sum of the 1990 national age-specific participation rates, with the weight for each age group equal to the State's population of the relevant sex in the age category in the current year:

Equation 3.3: A^{*}_{st} = S_{a} A_{a90} P_{ast}

where A^{*}_{st} is "expected" AFDC participation (i.e., expected caseload, recipients, or child recipients in one of the programs) in State s and year t, A_{a90} is the 1990 national AFDC participation rate in age group a, and P_{ast} is the size of the population of the relevant sex in State s and year t that is in age group a. The final step was to convert the annual series to quarterly series, using the methodology discussed in Section E, below.

The change in the logarithm of each expected participation variable is used as an explanatory variable in the relevant participation equation. The coefficient of this variable can be interpreted as the percent change in the caseload associated with a one percent increase in the size of the population, holding the age distribution of the population and other explanatory variables constant. Hence, we would expect them to be close to one. In the initial models we estimated the coefficients of these variables were very significant, but not significantly different from one. In the models reported here, we have constrained the coefficient of these variables to be one.