**Program Parameters**

We used four program parameters in some early specifications of the model: the maximum monthly benefit (MMB), the marginal tax and benefit reduction rate (MTBRR), the average tax and benefit reduction rate (ATBRR), and the AFDC earnings cut off (ECO) relative to the gross income limit (GIL). The MTBRR coefficient was never significant, even marginally, which we attribute to relatively little variation in changes across states in any given year during the sample period. Coefficients of the current and first lag of the other three parameters were very significant in virtually all specifications tried, and the second lag of each was sometimes as significant as well. Hence, the current and first two lags of each of MMB, ATBRR and the ratio of the ECO to the GIL are included in the specifications reported.

The estimated effects of increases in the MMB, the ATBRR, and the ratio of the ECO to the GIL are all statistically significant and consistent in sign with the predictions of the static participation model (Chapter 1). We estimate that a one-percent increase in the MMB increases the caseload by about 0.27 percent after two quarters. An increase in the ATBRR of 10 percentage points (e.g., 70 percent to 80 percent ) is estimated to reduce the caseload by about 1.5 percent after two quarters as some families receiving small benefits because of earnings or other income leave the caseload. An increase in the ratio of the ECO to the GIL of 10 percentage points is estimated to reduce the caseload by 1.0 percent. Estimated effects on recipients and child recipients are quite similar. We discuss the results for the program parameters further in Section F, below.

**Federal Legislation**

The only dummies for federal legislation that have statistically significant coefficients in any models are the OBRA81 and DEFRA84 dummies. The current and first two lags of the OBRA81 dummy are significant (the last only marginally so). It should be noted that the dummy coefficients do not capture the full effect of OBRA81. OBRA81 increased the ATBRR in most states and also introduced the GIL. The effects of these specific OBRA81 changes are presumably captured by the program parameter variables themselves. Further, the dummy variables for calendar years 1981 and 1982 imply annual caseload reductions of about 3.0 (i.e., -0.03 = -0.04 + (0 - 0.004 - 0.010 + 0.053)/4) and 1.2 percent, respectively, after controlling for other factors and adjusting for seasonal effects, which might also be attributable to OBRA81. The full estimated effects of OBRA81 on the Basic caseload are more apparent in the simulations (Chapter 6).

The coefficient for the DEFRA84 dummy lagged one period is negative, but not significant in the equations reported; it was negative and significant in many specifications we tried. Other lags had much smaller coefficients. We expected this coefficient to be positive if significant, because DEFRA84 partially reversed the changes of OBRA81. The full estimated effect of DEFRA84 includes the effects of resulting changes in program parameters, including the increase in the GIL from 150 percent of the state's need standard to 185 percent. Further, the calendar year coefficients in the caseload equation indicate a 1.4 percent unexplained increase in the caseload in 1984 (after adjusting for seasonality, i.e., 0.014 = 0.004 + (0 - 0.004 - 0.010 + 0.053)/4), and a 4.4 percent increase in the following year, which might at least partly be attributable to implementation of DEFRA84. It may also be that coefficients for other federal legislation dummies (for OBRA87, the provisions of FSA88, OBRA90, and OBRA93) are insignificant because the effects of the legislation are captured by the program parameters and the year dummies. These changes are one of several possible explanations of the substantial caseload growth not accounted for by state-level variables from 1985 to 1991.

We were somewhat surprised to find that the federally mandated introduction of UP programs in 1990 in states without existing UP programs did not have an identifiable impact on the Basic caseload. We had expected to find some shift from the Basic caseload to the UP caseload in these states, especially those with 12 month programs, but did not find any statistically significant shift.

**1115 Waivers**

Only one of the 1115 waiver dummies we tried had a statistically significant coefficient, the "family cap" dummy for restrictions on benefits for children born while the mother is an AFDC recipient. According to the estimate, such restrictions reduce the caseload by 2.3 percent after one quarter, but have no further effect. We did not expect such restrictions to have an impact on caseloads, at least so quickly. The most likely effect would be a reduction in child recipients, and perhaps only after several quarters (allowing nine months for gestation). The estimated effect on child recipients, however, is slightly smaller than the effect on the caseload.

While it could be that some one-parent families are deterred from welfare dependency by such restrictions, there are three more likely explanations. First, it may be that this waiver dummy is proxying for other administrative efforts in the waiver states to reduce caseloads. The three states that instituted family caps during the sample period are New Jersey (1992.4), Georgia (1994.1), and Wisconsin (1994.3), and the family caps are part of broader efforts to reduce welfare dependency in each state. Second, some AFDC families who have children subject to the cap may have migrated to other states without caps. Third, the finding may be due to random error; given the number of other variables we tried, it would be surprising if we didn't include at least one or two that really were not important in our final specification.

We had not expected to find strong effects for the waivers because each is implemented in only a small number of states and only for a short period before the end of the sample period. Hence, it would be premature to conclude that the requirements implemented under the waivers have little effect on caseloads or recipients.