
1. Determining the Final Specifications

We present two sets of estimates for the UP participation models. In the first set  the "fullperiod" estimates  we use data for only the 19 states that have data for the whole sample period  a total of 19 x 60 = 1,140 observations. In the second set  the "postmandate" estimates  we use data for 49 states for the last 16 quarters of the sample period, during which all states were required to have UP programs  a total of 784 observations. The District of Columbia, which had an UP program for the entire period, is excluded from both samples due to questionable data for the dependent variable in two quarters. Mississippi is excluded from the postmandate sample for a similar reason.^{(12)} For the latter sample we only estimate a caseload model.
As with the Basic program, we searched through many specifications for the fullperiod models prior to the specification reported here. The search was conducted in parallel with the search for the Basic equations, for the caseload equation only. In general, we searched in the same way as for the Basic equations, except that we elected to retain the same program parameter specification as in the Basic equation for comparison purposes.
We focused our search efforts on the labor market variables because prior research has demonstrated that these variables are more important for the UP program than for the Basic program. Nonetheless, we settled on the same two variables, the unemployment rate and trade employment per capita, for the final specification. The only difference between the specification of these variables in the Basic and UP equations is that the distributed lag for trade employment in the UP equation is firstorder (linear) instead of second (quadratic), and the maximum lag length is six instead of ten.
For the postmandate estimates, we started with the final specification from the fullperiod estimates, minus the dummies for the early years. We subsequently changed the specification in a few respects, as discussed later, but the two models are very similar in specification. We could not use the Parks method to estimate this model because the sample period is too short, so we applied only the WLS method. We discuss the findings for the fullperiod model first, then present the postmandate estimates.


2. Year and Seasonal Effects

The estimated coefficients of the seasonal and calendar year dummies appear at the end of Exhibit 5.3. Seasonal variation in participation is much greater for the UP program than for the Basic program. As in the Basic models, conversion of the calendar year dummy coefficients to obtain annual growth not accounted for by the model's other variables is done by adding the mean of the four seasonal coefficients (zero for the first quarter) to each calendar year coefficient. This mean is 17.4 percent, i.e., 0.174 = ( 0  0.218  0.340  0.130)/4.
All of the calendar year coefficients are positive in the caseload equation after adjusting for the seasonal factor except five (1982, and 1991 through 1994). In all other years the adjusted coefficients are substantial positive numbers, indicating that significant growth in the caseload during this period is not accounted for by the variables in the model. The largest coefficient is for the first year, 1979, followed by the second largest in 1980 and the third largest in 1981; after adjustment these are 0.40, 0.31, and 0.24. The largest coefficient in any other year is for 1988, 0.11 after adjustment. The simulations presented later (Chapter 6) show a similar pattern of growth not accounted for, but at substantially lower levels. The difference is evidently because the model accounts for a larger share of growth in relatively large states, and these get more weight in the decomposition analysis.


3. Demographic Variables

Expected Participation
As in the Basic equation, the expected participation variable's coefficient was the most significant coefficient in early runs, and we could not usually reject the hypothesis that the coefficient is one. Hence, we again constrained the coefficient to be one by incorporating it in the dependent variable.
Vital Statistics
The coefficients of the vital statistics variable were not significant in the specifications we tried. Theory would suggest that the signs of these coefficients would, if anything, be opposite those found in the Basic equation. Given this, the small size of the program, and the smaller sample size, the lack of a significant finding is not surprising.
Immigration
The coefficient of the IRCA immigration variable was not significant in the specifications we tried, and usually had a negative coefficient. Hence, we have not included it in the final specification. Our understanding is that "childonly" families are in the Basic program, which is consistent with our earlier interpretation that the finding for the Basic program captures the childonly phenomenon.
Exhibit 5.3
Regression Results for Unemployed Parent Models Sample: 19 states, 1979.4  1994.3 Dependent Variable is change in ln(participation/expected participation) ^{a} Coefficients Tstatistics ^{b} Explanatory Child Child Variables^{c} lag^{a} Caseload Recipients Recipients Caseload Recipients Recipients ln(unemployment rate) a_{0} 0.180 0.171 0.177 9.0 9.0 9.0 (PDL: L = 14)^{a} 10xa_{1} 0.241 0.199 0.267 3.8 3.3 4.3 100xa_{2} 0.109 0.076 0.128 2.5 1.8 3.0 longrun elasticity 1.283 1.244 1.148 ln(trade employment per cap.) a_{0} 0.920 0.778 0.838 5.9 5.1 5.5 (PDL: L = 6)^{a} 10xa_{1} 2.083 1.740 1.652 5.2 4.4 4.2 longrun elasticity 2.068 1.794 2.397 ln(maximum monthly benefit) current 0.258 0.091 0.283 1.9 0.7 2.1 1st lag 0.054 0.125 0.089 0.4 0.9 0.6 2nd lag 0.053 0.055 0.028 0.4 0.4 0.2 longrun elasticity 0.258 0.161 0.344 average tax and benefit current 0.196 0.226 0.161 1.5 1.8 1.2 reduction rate 1st lag 0.109 0.160 0.074 0.8 1.2 0.5 2nd lag 0.083 0.145 0.051 0.7 1.3 0.4 longrun effect 0.004 0.080 0.036 AFDC earnings cut off current 0.015 0.011 0.027 0.3 0.2 0.5 relative to gross income limit 1st lag 0.048 0.046 0.066 0.9 0.9 1.2 2nd lag 0.030 0.051 0.020 0.9 1.5 0.6 longrun effect 0.093 0.086 0.113 OBRA81 current 0.091 0.045 0.083 1.5 0.8 1.5 1st lag 0.009 0.024 0.014 0.1 0.4 0.2 longrun effect 0.100 0.020 0.069 DEFRA84 current 0.004 0.008 0.007 0.1 0.3 0.3 Seasonal Dummies Spring 0.218 0.249 0.200 4.9 5.9 4.8 Summer 0.340 0.341 0.317 6.4 6.7 6.4 Fall 0.130 0.145 0.117 2.8 3.2 2.7 Calendar Year Dummies 1979 0.576 0.687 0.566 6.2 7.6 6.4 1980 0.477 0.482 0.476 6.3 6.5 6.7 1981 0.416 0.291 0.382 4.3 3.1 4.2 1982 0.114 0.151 0.121 1.4 1.9 1.6 1983 0.269 0.274 0.250 3.7 3.9 3.7 1984 0.200 0.204 0.210 2.6 2.7 2.8 1985 0.232 0.224 0.200 3.1 3.0 2.8 1986 0.239 0.271 0.234 3.2 3.8 3.3 1987 0.239 0.217 0.210 3.3 3.1 3.1 1988 0.284 0.279 0.247 3.9 3.9 3.6 1989 0.279 0.300 0.263 3.7 4.1 3.7 1990 0.259 0.296 0.241 3.5 4.1 3.5 1991 0.118 0.118 0.112 1.6 1.6 1.6 1992 0.086 0.105 0.091 1.2 1.5 1.3 1993 0.170 0.196 0.170 2.2 2.7 2.4 1994 0.141 0.106 0.179 1.3 1.0 1.7 a. Expected participation variable is based on national agespecific participation rates for 1990 and estimated population of the state by age in the quarter.
b. Tstatistics in bold are at least 2.0 in absolute value. These statistics were reduced from those calculated by SAS to make a correction for degrees of freedom that is not made by the procedure used (TSCSREG). The reduction factor is .61, computed as [(TK)/T]5, where T is the number of quarters (60) and K is the number of explanatory variables (38).
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.lagged the number of periods indicated. For the polynomial distributed lag (PDL) variables, the coefficient of the variable lagged j periods is a_{o} + a_{1} j + a_{2}j^{2} for j=0, 1, 2, ...L. Other variables are lagged the number of periods indicated.
d. Variables are moving average of previous four quarters.


4. Labor Market Variables

As mentioned above, the specification search led us to a specification that is very similar to the final specification for the Basic equations. The final distributed lag specification for the unemployment rate is identical, but the estimated coefficients are much larger. We estimate that a permanent increase in the unemployment rate of one percent (e.g., 5 percent to 5.05 percent) increases the UP caseload by 1.28 percent (.0128 = 1.283 * .01), compared to just 0.16 percent for the Basic caseload. We also estimate that after just six quarters a one percent increase in trade employment per capita reduces the UP caseload by 2.07 percent, compared to 1.00 percent for the Basic caseload. When we omit the trade variable from the specification (a specification not included in the exhibit), the longrun elasticity for the unemployment rate increases from 1.28 to 1.42. Findings for the other participation measures are very similar. We discuss these findings further in Section E, below.
Many have speculated that the effects of the business cycle on AFDC participation are asymmetric, with recessions having a large effect on participation but recoveries having a smaller, or perhaps more delayed, effect in the opposite direction. We tested for asymmetry by estimating a model in which we interacted the three distributed lag variables for the unemployment rate with a dummy variable for the direction of change of the unemployment rate in the current period, yielding separate distributed lags for increases and decreases in unemployment (a "switching" model). The two estimated distributed lags were very similar, and not statistically different. As discussed in the introduction, Steve Thompson has recently been able to find statistical evidence of asymmetry in a monthly timeseries model for a Maryland by lagging the switch point. We did not have the resources to experiment with alternative switching specifications. It could be that the estimates we report are a weighted average of stronger business cycle effects in recessions and weaker effects in recoveries.


5. AFDC Program Variables

Program Parameters
The findings for two of the three program parameters included in the specification are very similar to those found for the Basic program, but the findings for the third are a puzzle. We estimate that a one percent increase in maximum monthly benefits increases the caseload by 0.26 percent after two quarters, compared to 0.27 percent for the Basic caseload, and that an increase in the earnings cutoff relative to the gross income limit of 10 percentage points reduces the caseload by 0.9 percent, compared to 1.0 percent for the Basic caseload. The puzzling finding is that the current quarter coefficient for the average tax and benefit reduction rate has the wrong sign and is substantial, although insignificant. Perhaps more importantly, the sum of the coefficients on the current and two lagged values of the variable is essentially zero, compared to 0.15 in the Basic caseload model. Findings for the other participation measures are quite similar to those in the Basic caseload model.
Federal Legislation
The sum of the coefficients on the current and lagged OBRA81 dummy implies a 10 percent reduction in the caseload after one quarter in addition to any reductions due to changes in program parameters, compared to a reduction of seven percent for the Basic caseload. Hence, the point estimates for the two caseloads are very similar, even though the finding for the UP caseload is not statistically significant. The DEFRA84 coefficient is essentially zero, indicating that any effect of DEFRA84 on the caseload is captured by the program parameters and the year dummies. This finding also accords well with the finding for the Basic program.
1115 Waivers
We did not find any statistically significant coefficients for the 1115 waiver dummies in the UP equations.


6. Other Programs and Laws

Of the many variables tried in this category, we found none that were statistically significant. This is consistent with the lack of strong findings for these variables in the Basic equation, and the small number of states in the UP model for the full period.


7. UP Results for 1991  1994

FSA88 mandated that all states have UP programs from October 1990 on. In this section we present estimates of the UP caseload model using data for the postmandate period. Because the sample period is too short to use the Parks method, we use the alternative, weighted least squares (WLS) method.
The specification we report is somewhat different than the specification reported for the fullperiod model. We replicated that specification in our first set of postmandate estimates, but found that the coefficients for the ratio of the ECO to the GIL were very insignificant. The evident reason for this is that the definition of the GIL was not changed during the subperiod. We also added two variables that had been dropped in the full period model because much of the crossstate variation in changes of these variables occurred in the subperiod: the IRCA immigrant variable and the Medicaid expansion variable. In addition, we added interactions between the seasonal dummies and a dummy for sixmonth UP programs that were introduced in some of the states affected by the mandate, on the expectation that the seasonal pattern for the caseload would differ from the seasonal pattern in states with 12month programs.
We initially estimated models using changes for the full postmandate sample, (1991.1 to 1994.3), but obtained results that made little sense. The coefficient for the 1990 year dummy (which estimates the annualized rate of growth from 1990.4 to 1991.1 that is not explained by changes in other variables) was extremely large, and the value for the 1991 coefficient was also very large. We traced the reason for this to the states that began their programs under the mandate. Because they started at zero in 1990.3, they experienced very rapid rates of growth for the first year. This is evident by comparing postmandate estimates for the 19 states that had programs for the full period (Column 2 of Exhibit 5.4) to results obtained using just the 22 states that started their programs in 1990.4 (Column 4).^{(13)} Dropping the first full year from the sample yields much more credible findings in the mandate states (Column 5), although year dummy coefficients continue to differ substantially from those for the fullperiod states (compare to Column 3). Hence, when pooling the data for all states, we added an interaction between each year dummy and a dummy for whether or not the state started its program under the mandate.
For the remainder of this section, we focus on the results using data for 49 states for the period 1992.1 through 1994.3 (Column 5) and compare them to estimates for the same model using the full period for the 19 states with UP programs for the full period (Column 1).^{(14)}
The findings for the labor market variables are strong for the postmandate period, although different in some respects from the fullperiod estimates. The longrun unemployment elasticity is 0.86 (compared to 0.97) and the longrun trade employment elasticity is 5.7 (compared 2.8). The large trade elasticity is primarily influenced by the data for the mandate states; using that sample alone, the elasticity is 10.3 (Column 5), compared to a postmandate estimate of 1.7 for the 19 fullperiod states (Column 3). Hence, there is evidence of very strong business cycle effects, but there are differences in the findings for mandate and nonmandate states. We have not had an opportunity to explore these differences further.
The subperiod findings for the MMB and, especially, the ATBRR are puzzling. For the postmandate estimates using just the 19 fullperiod states, the sign of the longrun MMB elasticity is opposite that expected and its magnitude is large. For the 22 mandate states, the sign is positive, as expected, but the coefficient is exceptionally large. When all states are combined, the estimate is credible. The problem may be inadequate independent variation in this variable over the subperiod, especially among the two subsets of states.
We did find significant results for the IRCA immigrant variable, but predominantly in the mandate states. Note that the IRCA coefficient is also significant in the fullperiod estimates for the 19 fullperiod states, whereas it was not when we used the Parks method for the full period. This change may be related to other changes in the specification, but it also may be due to the large weight given to California in these estimates.
We did not find evidence of an effect of the Medicaid expansion except marginally in the fullperiod estimates for the 19 fullperiod states. Recall, however, that we dropped this variable from the UP specification reported earlier because of its insignificance when we used the Parks method.
Exhibit 5.4
Regression Results for Postmandate Unemployed Parent Caseload Models ^{a} Weighted Least Squares Dependent Variable is change in ln(participation/expected participation) 19 States with UP Programs 22 States with for the Full Sample Mandated UP Programs 49 States Explanatory 1979.4 1991.1 1992.1 1991.1 1992.1 1991.1 1992.1 Variables^{ }^{b} 1994.3 1994.3 1994.3 1994.3 1994.3 1994.3 1994.3 ln(unemployment rate) a_{0} 0.092 0.026 0.002 0.026 0.006 0.012 0.027 (PDL: L = 14) (6.06) (0.85) (0.05) (0.28) (0.07) (0.45) (1.04) 100xa_{1} 0.422 0.793 0.634 1.652 1.082 0.756 0.371 (2.47) (2.45) (1.77) (1.61) (1.31) (2.74) (1.40) 1000xa_{2} 0.013 0.038 0.055 0.052 0.004 0.006 0.029 (1.46) (2.63) (3.04) (0.93) (0.09) (0.44) (2.22) longrun elasticity 0.973 0.489 0.716 1.343 1.249 0.666 0.856 ln(trade employment per cap.) a_{0} 0.839 1.862 1.199 3.912 3.479 2.816 1.994 (PDL: L = 6) (5.85) (6.00) (3.11) (6.29) (6.76) (12.03) (8.61) a_{1} 0.144 0.394 0.317 0.757 0.669 0.542 0.394 (4.58) (5.18) (3.37) (5.24) (6.05) (9.78) (7.52) longrun elasticity 2.849 4.76 1.736 11.487 10.304 8.33 5.684 ln(maximum monthly benefit) current 0.235 0.287 0.080 0.048 1.429 0.448 0.789 (2.38) (0.81) (0.17) (0.05) (1.58) (1.42) (2.40) 1st lag 0.141 1.305 1.112 1.933 1.170 0.769 0.111 (1.31) (3.43) (2.39) (1.67) (1.30) (2.24) (0.31) 2nd lag 0.040 0.183 0.493 2.616 0.019 1.351 0.106 (0.41) (0.52) (1.19) (2.88) (0.03) (4.45) (0.36) longrun elasticity 0.416 1.201 1.685 0.730 2.618 1.030 1.006 average tax and benefit current 0.216 0.083 0.044 0.194 0.206 0.177 0.223 reduction rate (2.59) (0.64) (0.29) (0.39) (0.56) (1.49) (1.98) 1st lag 0.211 0.107 0.034 1.190 1.180 0.141 0.134 (2.56) (0.66) (0.18) (2.11) (2.78) (0.99) (1.06) 2nd lag 0.166 0.043 0.047 1.358 1.337 0.283 0.292 (2.82) (0.29) (0.28) (2.65) (3.53) (2.19) (2.50) longrun effect 0.160 0.233 0.057 2.742 2.311 0.246 0.203 OBRA81 current 0.064 (3.23) 1st lag 0.005 (0.26) longrun effect 0.069 DEFRA84 current 0.011 (0.85) IRCA immigrants per 100^{c} 1st lag 0.326 0.365 0.040 2.109 1.647 1.035 0.458 (2.40) (1.94) (0.17) (2.31) (1.77) (4.56) (1.97) Medicaid expansion current 0.192 0.151 0.139 1.149 0.408 0.133 0.082 (1.97) (1.21) (1.04) (0.80) (0.32) (0.98) (0.67) Seasonal Dummies Spring 0.220 0.006 0.109 0.029 0.093 0.062 0.045 (8.79) (0.11) (1.52) (0.12) (0.54) (1.14) (0.82) Summer 0.341 0.011 0.116 0.040 0.030 0.073 0.061 (10.71) (0.16) (1.22) (0.18) (0.19) (1.16) (0.98) Fall 0.140 0.147 0.002 0.143 0.159 0.210 0.069 (5.15) (2.72) (0.02) (0.73) (1.11) (4.17) (1.31) interaction of dummy for states Spring 0.240 0.192 0.170 0.240 with sixmonth UP programs and (1.55) (1.74) (1.69) (3.12) seasonal dummies Summer 0.343 0.079 0.392 0.169 (2.14) (0.66) (3.71) (2.08) Fall 0.484 0.668 0.188 0.392 (3.07) (6.00) (1.88) (5.09) interaction of dummy for states with 1991 4.954 UP programs mandated under (36.66) FSA88 and year dummies 1992 0.701 0.501 (7.73) (6.18) 1993 0.368 0.300 (4.06) (5.30) 1994 0.014 0.053 (0.16) (0.93) 1995 0.026 0.061 (0.25) (0.95) Calendar Year Dummies 1979 0.653 (13.25) 1980 0.496 (12.46) 1981 0.338 (7.56) 1982 0.159 (4.00) 1983 0.197 (5.96) 1984 0.170 (4.76) 1985 0.223 (6.63) 1986 0.230 (6.71) 1987 0.156 (4.84) 1988 0.199 (6.16) 1989 0.289 (8.25) 1990 0.298 0.319 5.330 0.314 (8.24) (4.27) (24.36) (4.59) 1991 0.141 0.013 0.026 0.706 0.151 0.068 0.159 (3.76) (0.22) (0.36) (4.14) (0.95) (1.34) (2.77) 1992 0.158 0.063 0.002 0.413 0.407 0.042 0.019 (4.26) (1.24) (0.04) (2.56) (3.59) (0.90) (0.41) 1993 0.225 0.084 0.012 0.113 0.027 0.050 0.005 (6.00) (1.41) (0.16) (0.59) (0.17) (0.92) (0.08) 1994 0.134 0.187 0.111 0.519 0.346 0.006 0.052 (3.31) (2.81) (1.29) (2.26) (1.88) (0.11) (0.83) AutoRegression Correction 1st Lag 0.233 0.257 0.266 0.227 0.340 0.271 0.324 (7.76) (4.27) (3.71) (4.02) (4.87) (7.45) (7.50) a. Tstatistics in bold are at least 2.0 in absolute value.
b. 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.lagged the number of periods indicated. For the polynomial distributed lag (PDL) variables, the coefficient of the variable lagged j periods is a_{o} + a_{1} j + a_{2}j^{2} for j=0, 1, 2, ...L. Other variables are lagged the number of periods indicated.
c. Variable is amoving average of previous four quarters.
