
1. Determining the Final Specification

The selection of variables for the final average monthly benefit (AMB) equation was largely determined by the findings from the Basic and UP participation models (Exhibit 5.5). We began by including all of the variables that are included in either the final Basic or the final UP participation equations plus dummy variables for the existence and type of UP program (sixmonth, 12month, and whether introduced as the result of requirements in FSA88). Except in the case of some program parameters, we then dropped all variables that had coefficients with tstatistics less than one in absolute value.
In interpreting the findings, it is important to keep the following in mind:
 The AMB variable is average monthly benefits for all cases in both the Basic and UP programs;
 The effects of explanatory variables on AMB may be of two types: effects on benefits received by existing AFDC families, and effects that work through changes in the composition of the AFDC caseload;
 The maximum monthly benefit variable in the AMB equation does not include the value of Food Stamps, whereas the same variable in the participation equations does. The reason for this is that the AMB equation itself refers to the AFDC benefits received only; and
 The sample period for this equation does not include the first two and the last four quarters of the period used to estimate the participation equations.


2. Year and Seasonal Effects

As in the participation equations, the coefficients on the year dummies must be adjusted for seasonal effects to obtain estimates of growth not accounted for in each year by variables in the model. The adjustment factor in this case is positive, .036. Only one of the year coefficients is positive, even after the adjustment (.015 for 1985). In many years the negative coefficient is substantial, even after adjustment. The largest negative values are for 1980, 1981, and all years from 1986 to 1991. The largest adjusted value is .041, for 1980, the next largest is .028, for 1981 , and the next is .02, for 1990.


3. Demographic Variables

Population Growth and Aging
We did not include a variable for population growth and aging in the AMB equation.
Exhibit 5.5
Average Monthly Benefit Regression Results Sample: 51 states, 1980.2  1993.3 Dependent Variable is Change in ln(average monthly benefit) Explanatory Variables ^{c} Lag Coefficient Tstatistic ^{b} ln(unemployment rate) 100xa_{0} 0.656 3.7 (PDL: L = 14) ^{a} 100xa_{1} 0.338 6.6 1000xa_{2} 0.223 6.7 long run elasticity 0.030 ln(trade employment per cap.) a_{0} 0.127 14.7 (PDL: L = 10) ^{a} 10xa_{1} 0.615 24.9 100xa_{2} 0.410 13.4 long run elasticity 0.406 ln(maximum monthly benefit) current 0.663 73.0 1st lag 0.085 9.9 2nd lag 0.018 2.0 sum 0.596 average tax and benefit current 0.133 8.8 reduction rate 1st lag 0.142 9.4 2nd lag 0.166 11.3 sum 0.109 AFDC earnings cut off current 0.026 3.7 relative to gross income limit 1st lag 0.003 0.5 2nd lag 0.059 8.8 sum 0.030 OBRA81 current 0.080 9.9 1st lag 0.038 4.8 2nd lag 0.061 7.4 sum 0.056 DEFRA84 current 0.008 1.6 6month UP program current 0.035 4.6 12month UP program current 0.013 4.5 UP started in 1990.4 current 0.038 5.8 family cap 1st lag 0.055 3.5 IRCA immigrants per 100 1st lag * 0.007 1.4 ln(outofwedlock births) ^{d} * 0.074 3.6 ln(% insured unemployed) 1st lag 0.032 8.0 abortion: parental consent/notice. 1st lag 0.015 6.8 Medicaid restricted 1st lag 0.016 7.5 Spring 0.036 4.8 Summer 0.094 13.8 Fall 0.086 10.5 Calendar year 1980 0.077 9.1 1981 0.064 5.7 1982 0.022 2.3 1983 0.048 6.0 1984 0.041 4.4 1985 0.028 3.3 1986 0.049 6.0 1987 0.039 4.9 1988 0.052 6.5 1989 0.052 6.5 1990 0.056 6.8 1991 0.055 6.7 1992 0.050 6.1 1993 0.053 4.7 a For the polynomial distributed lag (PDL) variables, the coefficient of the variable lagged j periods is a0 + a1 j + a2 j2 for j = 0, 1, 2, ... L. Other variables are lagged the number of periods indicated.
b. Tstatistics in bold are at least 2.0 in absolute value.
c. All explanatory variables except quarter and year dummies are changes. Quarter and year dummies are equal to .25 in the quarters/years indicated so that coefficients can be interpreted as annualized rates of growth.
d Variables are moving averages of previous four quarters.
Vital Statistics
Only one of the vital statistics variables, outofwedlock births, appears in the final AMB specification and it has a significant, positive coefficient. More outofwedlock births among existing AFDC families would be expected to increase AMB, but families entering the caseload as the result of a first outofwedlock birth would presumably receive lower than average benefits.
Immigration
The IRCA legalizations variable appears in the final specification with a positive, but insignificant, coefficient. The positive coefficient seems at odds with the hypothesis that the large coefficients on this variable in the Basic participation models reflects childonly families; presumably such families would receive lower than average benefits unless the average number of children in such families is substantially larger than average.


4. Labor Market Variables

Unemployment Rate
A one percent increase in the unemployment rate, other things constant, reduces the AMB by an estimated 0.03 percent after 14 months. Equivalently, an increase in the unemployment rate from five to six percent reduces the AMB by 0.6. It seems likely that increases in unemployment, if anything, increase benefits among existing AFDC cases. The negative estimated effect presumably is the result of new cases that receive lower than average benefits  due to fewer children and/or greater income from other sources.
Trade Employment per Capita
The longrun elasticity of AMB with respect to tradeemployment is estimated to be 0.41. Presumably increases in trade employment reduce benefits for families that stay in the caseload, if they have any effect at all. Some families leave the caseload, however, and they may be receiving above or below average benefits. The negative longrun unemployment elasticity, discussed above, suggests that marginal families receive lower than average benefits, but the negative longrun elasticity for trade employment suggests the opposite.


5. AFDC Program Variables

Program Parameters
The variable with the most significant coefficient in the model is, not surprisingly, the current value of the maximum monthly benefit. The current coefficient is a highly significant 0.66, and the coefficients on the first and second lag are both negative, but not significant. The finding suggests that a one percent increase in MMB is immediately translated into an almost equal increase in the average benefits received by existing cases, but that the average benefit might fall as new families enter the caseload and receive lower than average benefits.
The estimated effects of a change in the average tax and benefit reduction rate (ATBRR) are somewhat puzzling and reminiscent of the puzzling findings for UP participation. The pattern of the coefficients would be consistent with the hypothesis that existing AFDC families initially lose benefits, but over time they either recover benefits by reducing other income or marginal families with low benefits leave the caseload  but this conclusion may be too strong. After two quarters, any initial effects of a change in the ATBRR disappear.
A similar pattern appears in the coefficients of the current and lagged values of the AFDC earnings cutoff (ECO) relative to the gross income limit (GIL). They suggest that a reduction in the GIL, holding ECO constant (i.e., an increase in the ratio) initially reduces AMB, but after two quarters this negative effect is more than offset as, perhaps, some females reduce their other income, thereby increasing benefits, and marginal families with below average benefits leave the roles.
Federal Legislation
The estimated effects of OBRA81 on AMB depend on the coefficients on the OBRA81 variable, the 1981 and 1982 year dummies, and the program parameter coefficients, along with the magnitude of the changes in the parameters that resulted from OBRA81. The estimated impact of DEFRA84 is similarly complex. We discuss their effects in the context of the AMB simulations (Chapter 6).
The effect of the UP programs established in 1990.4 under the mandate of FSA88 depends on both the dummy for mandated programs and the dummies for sixmonth and twelvemonth programs. About half of the 23 states affected introduced sixmonth programs. The combined coefficients for the 1990.4 dummy and the sixmonth dummy indicate these states experienced, if anything a small reduction in AMB as a result. The estimates suggest that states which introduced 12month UP programs in 1990.4 experienced a reduction in AMB as a result, by 2.5 percent (based on the sum of the coefficients for the 1990.4 dummy and the 12month dummy). This may be because UP families in sixmonth programs are only in the program in the months when their income from other sources is lowest.
1115 Waivers
The only waiver dummy that appears in the final AMB specification is the dummy for the family cap, and it has a significant coefficient that suggests that this type of restriction increases AMB by 5.5 percent. This is puzzling because we would expect such restrictions to, if anything, reduce benefits for families that would have been AFDC families anyway. It may be that the restrictions discourage small families, with below average benefits, from participating in AFDC, but it seems unlikely that the effect of such a change in the composition of the caseload would be so large. As with the finding in the Basic participation models, there are more likely explanations of this finding: other efforts to reduce caseloads in the three states that imposed family caps; migration of some AFDC families to other states; and chance.


6. Other Programs and Laws

Medicaid
We initially included the Medicaid expansion variable and interaction term in the AMB specification, just as in the final specification for the Basic model, but found that both terms had tstatistics well below one in absolute value. Hence, we dropped them in the final specification
SSI children
We also included the SSI child recipient variable in the initial AMB specification  again because of the finding in the Basic participation model  and subsequently dropped it from the specification because the tstatistic was below one in absolute value.
Unemployment Insurance
The log of the percent of unemployed persons who are insured has statistically significant, positive coefficients in the final specification. Given the positive relationship between the UI variable and participation in the Basic program found previously, a likely explanation is that unobserved factors such as administrative tightening of programs have common effects on both UI and AFDC.
Abortion Restrictions
The two abortion dummies have significant, and large, negative coefficients. They suggest that parental consent or notification laws and restrictions on Medicaid payments for abortion each reduce AMB by about 1.5 percent. Interpreting the Basic participation results at face value, these restrictions reduce the caseload by 0.2 and 0.3 percent, respectively, and reduce the number of child recipients by 0.3 and 0.5 percent, respectively. This implies that the number of children per AFDC family is reduced by 0.1 and 0.2 percent, respectively.^{(15)} We would expect this reduction to reduce AMB by a comparable percentage amount. A more plausible explanation of the large effects is one we suggested in the discussion of the participation findings: they may be due to other unobserved efforts in the states that adopted these restrictions to reduce fertility and AFDC participation.
SSA Allowance Rates
We included our measure of SSA's administrative tightening of disability requirements in 197778 in our initial AMB specification, but the tstatistic was less than one.
