Several studies have used cross-sectional data on individuals, pooled over a number of years, to estimate the impact of various factors on AFDC participation. This approach offers the advantage of being able to capture the effects of and control for detailed demographic characteristics of the household while also estimating the impact of changes in state-level factors such as programmatic and labor market variables. Thus, for instance, the researcher might specify a binary choice (logit, probit, or linear probability) model for AFDC participation of families, using some explanatory variables that are specific to the family and others that are specific to the family's state, which may vary over time, but not across families within a state and time period (e.g., the state's unemployment rate).
Another advantage of the approach is that it can use variation in variables across families within a state and time period to estimate coefficients for variables that vary across families within each state and time period -- variation that is lost when state aggregate data are used. In fact, the researcher can use or not use a variety of sources of variation in the data, depending on how the model is specified. Just as in pooled analysis of aggregate data, the researcher can include dummy variables for each state to capture and control for all effects of factors that vary across states but not over time or across individual's within a state. Symmetrically, time dummies can be included to capture and control for all effects of factors that vary over time, but not across states. In addition, state and time dummies can be interacted to capture and control for all factors that vary both across states and over time, but not across families within a state and time period. When this is done, coefficients of other explanatory variables reflect only variation and covariation of variables across families within both time periods and states -- i.e., all of the variation that is lost when state aggregate data are used. As with the pooled analysis of state data, results will depend on which specification is used and differences in findings across various specifications may provide information that is useful in interpreting the results.
Yelowitz (1993) pooled individual-level data from the CPS for the years 1989 to 1992 to estimate the impact of Medicaid availability on the labor force and AFDC participation of single mothers. He tests the hypothesis that Medicaid expansions for children mandated by OBRA89 and OBRA90, that severed the link between AFDC and Medicaid eligibility for some groups, had the effect of reducing AFDC participation and increasing labor force participation. This is because the expansions allowed single mothers, in some cases, to earn more and still retain Medicaid benefits.
The Medicaid eligibility changes made it possible to study the effects of Medicaid coverage on AFDC and labor force participation in a number of ways: analysis of within-state variation based on the age of children (mothers with children of different ages either were or were not subject to the new expansions); analysis within states over time, as the expansions occurred; and analysis across states and/or time, as states adopted the optional expansions. Yelowitz estimates a probit model in which the Medicaid expansions are captured in a single variable, "GAIN%," which represents the increase in the Medicaid need standard as a result of the eligibility expansion, measured as a percent of the family's poverty line. The value of this variable for a family depends on both the family's state of residence and the age of the family's children.
While Yelowitz controls for individual demographic characteristics such as age, education, marital status, and the age of children in the family, he does not include any state-specific economic variables, such as the average wage or unemployment rate, in his analysis. He assumes the effect of these factors are captured by his state, time, and state-time interaction variables. This assumption is clearly correct when state-time interactions are included, because they control for all factors that don't vary across individual's within a state and time period. Evidence from previous analyses of pooled state data suggest that the assumption is incorrect when the state-time interactions are not included.
Yelowitz finds that Medicaid coverage independent of AFDC eligibility has a significant effect on both AFDC and labor force participation. Using the models with both state dummies and state-time interactions, he estimates that increasing the Medicaid need standard by 25 percent of the poverty line decreases the proportion of single mothers between the ages of 18 and 55 who receive AFDC by 4.6 percent, and increases their labor force participation rate by 3.3 percent. Estimated AFDC participation effects are somewhat smaller when state dummies and time dummies alone are used, with no interactions, suggesting that smaller effects would have been found if he had used aggregate data alone. This finding may have changed, however, had he controlled for the unemployment rate and other state-level factors. While variation in the Medicaid variable across families within states and time periods clearly made a substantial contribution to the strength of Yelowitz' Medicaid findings, the fact that the findings are still significant when state-time interactions are omitted provides some reason for optimism that Medicaid eligibility expansion effects can be identified using aggregate level data.
Gabe (1992) uses data from the March 1988 and March 1992 CPS to examine the effect of demographic changes on AFDC participation over the 1987 to 1991 period; intermediate year data are ignored. Gabe's analysis decomposes the recent growth in the AFDC caseload into growth due to change in the number and type of mother-only families and that due to change in the rate of AFDC recipiency. Gabe examines the growth in AFDC participation within subsamples of mother-only families with specific marital status and living arrangement characteristics. This is equivalent to controlling for those characteristics by estimating a linear probability model of AFDC recipiency using dummy variables for all possible marital status/living arrangement combinations as explanatory variables.(17)
Gabe attributes most of the caseload growth over the period to the growing number and changing composition of mother-only families, rather than to a change in the rate at which mother-only families receive AFDC. Changes in living arrangements contribute little to the growth experienced over the period, while changes in the number of mother-only families by marital status account for a substantial share (93 percent) of the growth in the AFDC caseload between 1987 and 1991.
Gabe's analysis does not take into account economic factors and their potential effect both on the rate of AFDC recipiency within the various marital status/living arrangement subgroups, and the share of the total population within each subgroup. His results indicate, however, that the effect of economic factors on recipiency rates would have to be strong in order to account for much of the growth up to 1991. They do not provide any indication of the extent to which changes in marital status and living arrangements can be attributed to economic factors.
A case could be made for developing a pooled cross-section time series model with individual data rather than a state aggregate model. For instance, a probit model for family AFDC participation could be estimated, limiting observations to those families with children. Separate models for single and two parent households could be developed. If duration data exist, duration could also be modeled. The explanatory variables would be a combination of household demographic variables, state economic variables, and variables that combine state program and household demographics (e.g., the AFDC payment for a household with the demographic characteristics of the observation; the value of Medicaid benefit for average household of same size). We might, for instance, build a SIPP database for this.
As discussed previously, this approach has the advantage of being able to control for household demographic characteristics while estimating the impact of aggregate changes over time. This approach does, however, have a number of important limitations:
- It would require considerably more resources to develop than would a state-level model, and would not span as long a time period, particularly if SIPP data were used;
- The demographic variables that this approach allows us to include are mostly ones that may themselves be influenced by the economic factors we are considering. In fact, the existence of the family itself -- the basic unit of analysis -- may, in part, be determined by economic factors. Gabe's failure to find evidence of the impact of economic factors may be due this problem;
- Individual-level survey data are often annual in nature, and therefore would not capture important dynamics associated with AFDC participation; and
As with cross-sectional studies of individual data, the idiosyncratic behavior of individuals may obscure the effects of aggregate variables in the analysis unless sample sizes are extraordinarily large.