
A. INTRODUCTION

We present and discuss the regression results in this chapter. The participation equation results for the Basic program are in Section B, those for the Unemployed Parent program are in Section C, and the average monthly benefit results for the combined programs are in Section D. We consider the estimated effects for the labor market variables in more detail in Section E, including comparisons to findings from other studies. We do the same for the estimated AFDC program parameter effects in Section F.


E. FURTHER DISCUSSION OF BUSINESS CYCLE ESTIMATES

In this section we examine the dynamics of the effects of changes in the unemployment rate on the caseload and compare our findings to findings reported by others. All of the findings reported in this section are based on Basic and UP caseload models in which we dropped the trade employment variable (Exhibit 5.6). This was done to simplify the analysis and presentation. The other studies we examine use only the unemployment rate as a business cycle variable, whereas in the models we have reported there are two important business cycle variables. Dropping trade employment increases the magnitude of the unemployment rate coefficients somewhat.
For comparison purposes, we consider the estimated effect of a one percentage point increase in the unemployment rate on the caseload, in percent. In the specification we use, the size of the effect depends on the initial unemployment rate. We assume the increase is from five percent to six percent.


F. FURTHER DISCUSSION OF PROGRAM PARAMETER EFFECTS

In this section we compare our findings for the program parameters to findings from other studies. As with comparisons of business cycle effects across studies, these comparisons are problematic because of specification differences.
Our estimates of the effects of an increase in the maximum monthly benefit are among the highest found, but one study reports a much larger effect (Exhibit 5.10). We estimate that a one percent increase in this variable increases the Basic caseload by 2.7 percent and the UP caseload by 2.6 percent.^{(17)} Our estimates for the Basic program are larger than those reported by Moffit (1986) or CBO (1993), but Shroder (1995) finds a much larger effect than we do for the combined programs: a 16.7 percent caseload increase. Shroder also uses a pooled state timeseries methodology, but with several important differences. One major difference is that he uses instruments for the maximum monthly benefit variable, on the grounds that growth in recipients is likely to cause states to reduce benefit levels. When he does not use the instruments, the estimated effect drops by more than two thirds, to 5.1 percent  still almost twice as large as our own.
Exhibit 5.10
Sample Percent Change in Participation b Study Type Period Basic UP Total Ten Percent Increase in Maximum Monthly Benefit CBO (1993)^{}^{f} national timeseries quarterly 197391 0.7% 4.4% 0.8% Shroder (1995) ^{e} pooled state timeseries annual 198288 n.a. n.a. 16.7% Moffit (1986) ^{d} pooled state timeseries biennial 196783 1.6% n.a. n.a. Cromwell et. al. (1986) pooled state timeseries quarterly 197682 n.a. n.a. 1.3% Lewin ^{a} pooled state timeseries quarterly 197994 2.7% 2.6% 2.7% Ten Percentage Point Decrease in Average Tax and Benefit Reduction Rate Moffit (1986) ^{d} pooled state timeseries biennial 196783 5.5% n.a. n.a. Lewin ^{a} pooled state timeseries quarterly 197994 1.5% 0.0% 1.4% Increase in Gross Income limit for 150% to 195% to Need Standard ^{c} Lewin a pooled state timeseries quarterly 197994 1.3% 1.2% 1.3% ^{a} Basic model includes vital statistics variables; see Exhibit 5.1. Total estimates assume 95 percent of caseloads is in the Basic program.
^{b} Estimate changes may be complete only after several quarters.
^{c} Assumes need standard is identical to AFDC earnings cut off. The change in the gross income limit described is the change that was implemented under DEFRA84.
^{d} Results reported are for random effects estimator. Results for fixed state effects estimator are smaller in magnitude and not statistically significant. Means for the middle year of the sample period (1975) were used in the calculations.
^{e} Based on fixed effects specification with instrumental variables for the maximum monthly benefit variable. Estimate without instruments is about onethird as large.
^{f} Changes calculated at sample means.
We found only one other study that includes an average tax and benefit reduction rate in the specification, Moffitt (1986). Moffit estimates that a 10 percentage point increase in the rate reduces participation in the Basic program by 5.5 percent, compared to our finding of 1.5 percent.
While the reasons that we obtain a smaller effect for the MMB than Shroder and a smaller effect for the ATBRR than Moffitt are unclear, one possible explanation is that we include three benefit variables in our model compared to one for Shroder (MMB) and two for Moffitt (MMB and ATBRR). Neither study, nor any other we have seen, has included a variable for the gross income limit. The sample periods used by both Shroder and Moffitt include years when the GIL changed (twice in Shroder's sample), and it could be that their coefficients for other program parameters are biased away from zero because of this omission. We have not, however, tried to confirm this conjecture.^{(18)}


Notes

1. This constraint could be eliminated through modification of the software or use of an alternative estimation methodology. We estimated some models with SASETS PROC MODEL, a seemingly unrelated regression procedure for estimating linear and nonlinear multivariate models. We found, however, that PROC MODEL ran very slowly for our 51 equation model, even though the specification is linear.
2. Like most of the explanatory variables, the vital statistics variables are specified as changes. Initially, however, we included these variables as the current value, based on the argument that they measured flows of families into the pool of families that might participate in AFDC. Multiple lags were included, and we consistently found that the coefficients of the first and second lags were both significant, of opposite signs, and approximately equal in magnitude. Hence, we converted to the change specification.
3. Some have suggested that growth in outofwedlock births and declines in marriages have been a more important contributor to caseload growth in the latter part of this period than in the former (see, for instance, CBO, 1993). If so, the coefficients of the vital statistics variables might be larger if estimated using data for the latter part of the period only. To test the idea, we estimated a variant of the final specification in which we included interactions between each of the two vital statistics variables and two dummy variables  one for the middle third of the sample and one for the last third. The only coefficient that was significant was on the interaction for the marriage variable with the dummy for the last third of the period, and its sign was opposite that expected (coefficient: 0.20; tstatistic: 2.0).
4. We use the level rather than change because legal immigration represents a flow of families into the pool of families that may be eligible for the program.
5. We started with fourthorder polynomials, but found that the third and fourth order coefficients were not significant and could be dropped with little reduction in the fit.
6. In a quadratic DL for a variable, X, the coefficient of the jth lag of the variable, b_{j}, equals a_{0} + a_{1 }j + _{2 }j^{2} for j = 0, 1, ..., L, where the alphas are parameters to be estimated and L is the maximum lag length. If the original model is Y_{st} = ... b_{0}X_{st} + b_{1}X_{st1} + ... + b_{L}X_{stL} ..., substitution of the quadratic equation and simplification yields the following alternative version of the model: Y_{st} = ... a_{0}Z0_{st} + a_{1}Z1_{st1} + a_{2}Z2_{st} ..., where: Z0_{st} = X_{st} + X_{st1} + ... + X_{stL}; Z1_{st} = X_{st1} + 2 X_{st2} + ... + L X_{stL}; Z2_{st} = X_{st1} + 4 X_{st2 }+ ... + L^{2} X_{stL}. Thus, the alphas can be estimated by replacing the Xs in the model with the Zs. Once the alphas are estimated, the betas can be recovered from the quadratic equation. See Greene (1990).
7. The calculation described in the text yields 3.3 percent, but this somewhat overstates the estimated effect of the assumed change in the unemployment rate because the method used to calculate the effect is only accurate for small percentage changes in the unemployment rate. The exact methodsee equation 3.7yields an estimated increase of 3.0 percent, obtained from .165(ln(.06)  ln(.05)) =.165ln(.06/.05 ) = .030 .
8. From 5.2 percent in 1989.3 to 7.6 percent in 1992.3.
9. The 5.7 percent figure was computed by the exact method, described in the previous footnote, i.e., 0.057 = .313ln(.06/.05).
10. As discussed in more detail in Chapter 2, Yelowitz estimates that increasing the Medicaid need standard by 25 percent of the poverty line reduces the AFDC participation rate of single mothers by 4.6 percent.
11. For a state in which the share of children on AFDC is P, the estimated effect of a change in the share of children eligible for Medicaid under the expanded benefit is .179  1.23 x P, which is negative for P >.145.
12. The UP caseload series obtained from ACF reported zero UP cases for the District of Columbia in 1992.2 and 1992.3 and for Mississippi in 1993.4.
13. There are eight states in the sample in addition to the 19 fullperiod states and the 22 mandate states. These states had UP programs during part, but not all, of the premandate subperiod. Recall that Mississippi and the District of Columbia were dropped from the sample because of evident data errors that could not be corrected. See Chapter 4.
14. The fullperiod estimates (Column 1) differ from the results reported previously in both specification and estimation methodology. We inadvertently did not include the ratio of the ECO to the GIL in this model. Its exclusion may account for differences in the Park and WLS results for the ATBRR, but we have not had an opportunity to confirm this.
15. The change in the log of children per family (case) equals the change in the log of children minus the change in the log of families. Because small changes in logarithms are approximately equal to percentage changes in the variable itself, the percent change in children per AFDC family is approximately the difference between the percent change in children and the percent change in families.
16. The graph suggests that the effect on both caseloads will continue to be positive for some time after the 14month period ends; in fact, the effect for the UP caseload appears to be increasing! We specified only a 14quarter distributed lag because in models in which we included the tradeemployment variable the distributed lag coefficients for the unemployment rate became slightly negative in the 15th quarter when we specified long maximum lag lengths. We did not try longer lag lengths without the trade employment variable.
17. The overall figure assumes that five percent of the caseload is in the UP program.
18. One piece of information we have is, at least, consistent with the conjecture. As previously mentioned, we inadvertently omitted the GIL variable from the UP specification when we reestimated the fullperiod model using WLS (Exhibit 5.4). Both the MMB and ATBRR coefficients in these findings are much larger than those in the Parks estimates (Exhibit 5.3). Of course, other model and estimation differences could explain these differences. In the WLS results, the longrun MMB elasticity implies that a 10 percent increase results in an UP caseload increase of 4.2 percent  close to Shroder's 5.1 percent finding when he does not correct for simultaneity, but well short of the 16.7 percent figure he obtains when he makes the correction. The estimated longrun ATBRR effect implies that a 10 percentage point increase in that variable reduces the caseload by 1.6 percent  in line with our finding for the Basic program (1.5 percent), but well below Moffit's estimate (5.5 percent) for the Basic program.
