We group demographic variables into two subgroups: population characteristics and vital statistics. Population characteristics include the size of the population by age and sex, while vital statistics (e.g., outofwedlock births) refer to the structure of families. Population characteristics appear in all models. We have, however, explored the extent to which changes in economic factors affect AFDC caseloads and spending through their impact on family characteristics by including these characteristics in some models, but not in others

a. Population Characteristics

A general description of the methodology we use to capture the effects of population characteristics appears in Chapter Three. Recall that this requires the construction of "expected participation" variables, plus age adjustments to selected economic variables. We provide more details on the construction of expected participation variables here; details of the ageadjustments appear in later discussions of the variables to be adjusted. We also discuss the immigration variables here.
Expected Participation
The statelevel population characteristic estimates needed for constructing the expected participation variables are available only on an annual basis. Hence, we have constructed an annual average monthly participation series for each program and then expanded the series to a quarterly series, using the methodology described in Chapter Three.
The following is a description of the construction of the expected Basic and UP caseload variables. Calculation of the expected total recipient and child recipient variables follows this same methodology (see the Appendix).
We employ three types of data to construct the expected caseload variables. The first type is AFDC participation by type of family (oneparent versus twoparent) and age of head for 1990, estimated using the 1990 Survey of Income and Program Participation (SIPP).^{(4)} We use the SIPP data to compute initial national agespecific participation rates in the base period for the two programs. The rate for the Basic program in each specific age group is the proportion of women in an age group who head a oneparent AFDC family. The corresponding initial rate for the UP program is the number of men in the age group who are a parent in a twoparent AFDC family.^{(5)}
The second type of data is national Current Population Estimates by age and sex in 1990 from the Bureau of the Census, and were used to control our initial participation rate estimates to national totals. For the Basic program, we multiply the initial agespecific participation rates by the number of women in the corresponding age group and then add across age groups to get implied estimates of the national Basic caseload in the base period. We then adjust all of the initial agespecific participation rates by the ratio of the actual caseload average monthly caseload for the period (from ACF statistics) to the estimated caseload. We repeat this process for the UP program, but using agespecific estimates for the number of men.
The third type of data is state Current Population Estimates by age and sex, from the Bureau of the Census, used with agespecific participation rates to construct the expected participation series for each state. For the Basic program, we multiply the agespecific participation rates for the base period by the number of women in the corresponding age group for each state and quarter and then add across age groups to obtain the value for the expected Basic caseload in that state for that quarter. We follow this same procedure for the UP program, but using the population estimates for men.
Immigration
We employ two measures of immigration in our models: the total number of immigrants by state and the number of aliens per thousand population legalized under the Immigration Reform and Control Act (IRCA) of 1986. We obtained fiscal year data for both series from the Immigration and Naturalization Service (INS). INS data for total immigrants cover the period from FY1978 through FY1994 while data for IRCA legalizations cover the period from FY1989 through FY1994; no IRCA legalizations occurred before FY1989. We interpolate quarterly values for each variable from the fiscal year series to obtain the series used in the models. We experimented with several variants of the IRCA variable including lagged and lagged moving average constructions. The final construction included in the models is the movement of the four previous quarters.


b. Vital Statistics

The number of female headed households with children under the age of 18 has proven to be a strong predictor of AFDC Basic participation in previous studies. Unfortunately, reliable estimates of the number of female headed households at the state level are unavailable. Therefore, we relied on variables constructed from statelevel vital statistics on marriages, divorces, and outofwedlock births to proxy for femaleheaded households in our Basic models.^{(6)} The quarterly series used in the model are interpolated from the annual data provided by the Natality, Marriage, and Divorce Statistics Branch, National Center for Health Statistics. We also tried a "marriage market" variable in some models.
We expect the changes in the vital statistics variables to result in changes in the number of female headed households and, consequently, have an impact on the Basic caseload. We estimated Basic participation models with and without these data to determine whether the coefficients of business cycle variables are sensitive to their inclusion. It could be that business cycle effects work, in part, through their effects on formation of femaleheaded households. We also explore the effects of these factors in our UP models because changes in the number of twoparent households are expected to affect UP participation. In addition to the current values of these variables, we experimented with both multiple lag and lagged moving average specifications. In the results reported we use the moving average of the four previous quarters.
At least one previous study of participation in the AFDC has included a measure of "marriage market conditions" as an explanatory variable (Shroder, 1995). The variable used is a mixture of a demographic variable and an economic variable: the log of the number of women between the ages of 15 and 64 in the state divided by the number of employed men in the state. We obtained annual statelevel employment data by sex from the Bureau of Labor Statistics (BLS) and annual state population data by age and sex from the Bureau of the Census to create an annual series. The quarterly series included in the models is interpolated from this annual series. We experimented with a few variants of this variable, including lag specifications and the moving average of the last four quarters.
