
1. Basic Caseload

1979.4  1983.3 Subperiod
For this fouryear subperiod, average annual growth of the Basic caseload was essentially zero, but zero growth was the net effect of very large, offsetting changes (Exhibit 6.1, top section). According to our estimates, the labor market variables account for average annual caseload growth of 2.1 percentage points per year and AFDC benefit reductions account for a decline of 4.6 percentage points per year. This probably understates the impact of benefit reductions associated with OBRA81 because the estimated effects of the benefit reductions do not include any effects of OBRA81 that are captured by the calendar year dummies for 1981 and 1982; after adjusting for seasonal factors, the coefficients of these dummies imply reductions of 2.8 and 1.0 percentage points that might also be attributable to OBRA81. In total, the findings imply that OBRA81 reduced the Basic caseload by approximately 20 percent, after controlling for other factors.
Another important, but less widely recognized, feature of this period is that the population in the age group most atrisk for participating in AFDC was growing at a rapid rate as the tailend of the baby boom generation  those born in the early 1960s  was entering the age group; those born in the year usually recognized as the last baby boom year, 1964, turned 16 in 1980. According to our estimates, this growth contributed 2.0 percentage points per year to average annual caseload growth during the period. Changes in the vital statistics variables and in other variables in the model made modest contributions to growth.
1983.4  1989.3 Subperiod
During this subperiod the caseload grew at an average annual rate of 1.0 percent. According to our estimates, economic growth reduced the annual growth rate of the caseload by approximately 3.3 percentage points. The AFDC benefit changes captured by the statelevel variables made a positive contribution of 0.2 percentage points per year. The effect of AFDC program changes are likely understated in the simulations, however, because the statelevel variables do not fully reflect changes mandated by DEFRA84 and other federal legislation that
partially reversed some of the changes of OBRA81. Growth accounted for by population growth and aging declined from 2.0 percentage points in the previous period to 0.5 percentage points as the smaller postbaby boom cohort began entering the atrisk age group. The vital statistics variables contributed 0.7 percentage points per year. The state level factors in the model accounted for nearly all the growth during this period.
Overall, the model predicts an average annual decline of 1.8 percent per year. Given actual average growth of 1.0 percent, growth of 2.8 percentage points was due to other factors not captured in the model.
Exhibit 6.1 Decomposition of National Caseload and Average Monthly Benefit Series Average Annual Growth Rate Annual Growth Rate Accounted for by: Program, Period, and Model Actual Accounted for by Model Not Accounted for by Model Population Growth and Aging Vital Statistics Variables Labor Market Variables AFDC Benefits Other Variables Basic 1979.4  1983.3 0.0% 0.1% 0.1% 2.0% 0.3% 2.1% 4.6% 0.2% 1983.4  1989.3 1.0% 1.8% 2.8% 0.5% 0.7% 3.3% 0.2% 0.1% 1989.4  1993.3 6.5% 3.8% 2.7% 0.1% 0.5% 1.5% 0.1% 1.7% 1993.4  1994.3 0.4% 0.8% 0.3% 0.4% 0.5% 0.8% 1.3% 0.2% 1979.4  1994.3 2.2% 0.4% 1.8% 0.8% 0.5% 0.4% 1.0% 0.5% Unemployed Parent^{ 1} 1979.4  1983.3 25.1% 12.2% 12.9% 1.7% n.a. 15.3% 4.9% n.a. 1983.4  1989.3 7.9% 15.4% 7.5% 1.2% n.a. 16.6% 0.6% n.a. 1989.4  1993.3 13.1% 13.0% 0.1% 0.7% n.a. 12.8% 0.4% n.a. 1993.4  1994.3 0.0% 1.7% 1.7% 0.3% n.a. 0.3% 1.1% n.a. 1979.4  1994.3 7.0% 0.9% 6.1% 1.4% n.a. 0.9% 1.4% n.a. Average Monthly Benefit 1980.4  1983.3 3.3% 0.8% 4.1% n.a. 0.2% 0.2% 1.1% 0.3% 1983.4  1989.3 0.2% 0.5% 0.7% n.a. 0.5% 0.1% 0.1% 0.0% 1989.4  1993.3 4.1% 1.7% 2.3% n.a. 0.3% 0.3% 1.9% 0.2% 1980.4  1993.3 2.0% 0.0% 1.9% n.a. 0.4% 0.1% 0.3% 0.0% 1. The UP caseload model does not include the vital statistic variables and the AMB model does not include a variable for population growth and aging. The UP caseload simulations are for the 19 states with UP programs throughout the sample period only. 1989.4  1993.3 Subperiod
This fouryear period is one of very rapid growth in the Basic caseload, at an average rate of 6.5 percent per year. According to the model, the deteriorating economy accounts for 1.5 percentage points of that growth, and the vital statistics variables account for another 0.5 percentage points. The variables in the "other" category contributed a substantial amount (1.7 points per years); this is primarily attributable to the IRCA immigration variable. AFDC benefit changes captured in the statelevel variables contributed just 0.1 percentage points to growth. Again, this neglects any effects of federal legislation that might be picked up by the year dummies. The contribution of population growth and aging continues to decline, to 0.1 percentage points per year. The estimated effects of all statelevel factors in the model account for 3.8 percentage points of annual growth, combined, leaving 2.7 percentage points attributable to other factors that could not be measured in the model .
1993.4  1994.3 Subperiod
Caseload growth decelerated sharply in the last year of the sample period, to just 0.4 percent. The model also predicts decelerated growth, although not as low as actual growth0.8% compared to 0.4%. Two factors account for the slow growth: an improving economy contributes 0.8 percentage points and a decline in the size of the atrisk population contributes 0.4 percentage points. These factors are offset by growth attributable to the vital statistics variables of 0.5 percentage points and by the AFDC benefit variables of 1.3 percentage points. The latter growth is attributed to the effect that the expansion of the EITC had on the average tax and benefit reduction rate. Additional factors that could not be measured by the model caused slight declines in the caseload, accounting for the difference between 0.4% and 0.8%
Full Period Findings
The average annual growth rate of the Basic caseload over the period was 2.2 percent. Of this growth, 0.4% per year is attributable to state level factors in the model. Thus, 1.8 percentage points per year of growth are due to factors outside of the model. This disguises the fact, however, the statelevel factors and the two federal legislation dummies (OBRA81 and DEFRA84) in the model substantially help explain the large cycles in growth during the period. It also hides the fact that some factors in the models made substantial positive contributions to growth over the period and others made offsetting negative contributions.
Positive contributions come from three identified sources. First, population growth and aging contributed an average of 0.8 percentage points per year. Second, declines in marriage and increases in outofwedlock births (the vital statistics variables) contributed average growth of 0.5 percentage points per year. Third, other variables  especially the IRCA immigration variable  account for average growth of 0.5 percentage points per year.
Offsetting the factors contributing to positive growth were improvements in the labor market and reductions in benefits. According to the model, these latter factors reduced growth by an average of 0.4 and 1.0 percentage points per year, respectively.
Most of the difference in growth between the predicted and actual series occurs between 1983.4 and 1991.4. This is evident in Exhibit 6.2 (top panel) where we plot the two series. As in Exhibit 1.1, we have graphed logarithms of the caseload, so the slope of each series plot represents the growth rate. The predicted series is normalized to equal the actual series in 1989.4. That is, we use 1989.4 as the base period for the predictions and predict forward and backward from that quarter We have also plotted series showing the contributions of the labor market variables and the IRCA variable.^{(3)} It seems likely that the cause of the substantial divergence in the actual and predicted series is the result of several factors not captured in the statelevel variables. We discuss this issue further in Section D, after examining the other simulations.


2. Unemployed Parent Caseload

1979.4  1983.3 Subperiod
Much of the UP caseload growth came in the first four years of the sample period, in which the average annual growth rate was just over 25 percent (middle section of Exhibit 6.1). The model accounts for just under half of that growth. As with the Basic caseload, growth accounted for by the model during this period is the result of offsetting factors. We estimate that the recession contributed 15.3 percentage points to annual growth, that population growth and aging contributed 1.7 percentage points, and that cuts in benefits reduced average growth by 4.9 percentage points. The last of these figures is almost identical to the corresponding figure for the Basic caseload: 4.6 points.
The exceptionally high growth of the UP caseload relative to predicted growth during this subperiod is a puzzle. We are not aware of any major factors that would account for such rapid expansion other than the doubledip recession. It may be that the estimated effects of labor market factors, although large, substantially understate the recession's impact.
1983.4  1989.3 Subperiod
During this period the UP caseload declined at an average annual rate of 7.9 percentage points, but the model predicts an even larger decline, of 15.4 percent. The model's prediction stems from the estimated impact of growth in the economy, 16.6 percentage points, offset by a 1.2 percentage point increase attributed to population growth and aging, and an 0.6 percentage point increase attributed to AFDC benefit expansions.
Exhibit 6.2
Actual and Predicted Caseloads, 1979.4  1994.3*
* The predicted caseload series in each graph is normalized to equal the actual series in 1989.4. That is, we use 1989.4 as the base quarter and predict forward and backward from that point. The highest of the "labor market" series above the 1989.4 caseload shows the contribution of labor market factors relative to their contribution in 1989.4. A similar interprediction applies to the IRCA86 series
1989.4  1993.3 Subperiod
During this period the UP caseload again increased very rapidly, an average of 13.1 percent per year. The model predicts growth of 13.0 percent per year  a surprisingly accurate prediction given the model's performance in the previous nine years. Predicted growth is primarily due to labor market factors (12.8 percentage points), augmented by 0.7 percentage points from population growth and aging and offset by 0.4 percentage points from AFDC benefit changes. Curiously, the estimated effects of AFDC benefit changes on the UP and Basic caseloads during this period and the last year of the full period are opposite in sign. We discuss this further below
1993.4  1994.3 Subperiod
There is essentially no growth in the actual UP caseload during the last year of the sample, although the model predicts negative growth of 1.7 percent. The prediction is a combination of negative contributions from three factors; population growth and aging of (0.3 percentage points), economic recovery (0.3 percentage points), and changes in the AFDC benefit variables ( 1.1 percentage points).
The large reduction attributed to the AFDC benefit variables is in sharp contrast to the positive 1.3 percentage points that we estimate these same factors contributed to Basic caseload growth during the same year. The reason for this difference is differences in the coefficients of the average tax and benefit reduction rate in the two models. We estimate essentially no longrun effect for the UP caseload, and a negative effect for the Basic caseload. The longrun finding for UP is, however, the result of substantial offsetting coefficients on the ATBRR variable in the first two quarters of the change. The timing of the EITC change is such that the model's predictions for this subperiod reflect the current quarter effect, but not the second quarter effect.
Full Period Findings
In the 19 states with UP programs, the UP caseload grew at an average annual rate of 7.0 percent over the full period, while the predicted caseload grew at an average rate of 0.9 percent. The divergence between the actual and predicted series differs in timing from that for the corresponding Basic series (Exhibit 6.2). Most of the divergence for the Basic series occurs between 1984 and 1991. The greatest divergence for the UP series occurs in the first two years of the sample, through 1981. The actual series continues to grow at a rate that is above that for the predicted series through 1989, but from 1990 on the series move roughly in parallel.


3. Average Monthly Benefits

Due to data constraints the AMB simulations (bottom section of Exhibit 6.1) are for a slightly different period than the caseload simulations  1980.4 to 1993.3 instead of 1979.4 to 1994.3. The first of the three subperiods examined differs from the corresponding subperiod for the caseload simulations  the first year of the fouryear period used in the latter is omitted in the former  and the last oneyear subperiod is omitted for lack of data.
1980.4  1983.3 Subperiod
This period includes the implementation of OBRA81. The model predicts that implementation of the various provisions of OBRA81 increased AMB substantially; the average annual percentage point increase in this period due to the AFDC benefit variables is 1.1 percent. Yet actual AMB declined, at an average annual rate of 3.3 percent. The labor market and other variables in the model predict small declines, but the model obviously misses the major source of the decline. According to the estimates, changes in the AFDC benefit variables increased, rather than decreased, AMB over the period. These variables, however, do not include the effects of OBRA81 that are captured by the year dummies. The dummy coefficient for 1981 is .048 (4.8 percent) after adjusting for seasonality. The adjusted coefficient for the previous year, however, is even larger in magnitude (.063) suggesting that the changes not captured by the model that account for the AMB decline during this period occurred in advance of OBRA81. These could be changes external to the program that affect the composition of the caseload or the benefits they receive, or program changes that are not picked up by the model (e.g., tightening of rules concerning disregards.)
1983.4  1989.3 Subperiod
Actual AMB fell slightly during this period, while the model predicts growth of 0.5 percent per year. The source of the predicted growth is primarily the vital statistics variables.
1989.4  1993.3 Subperiod
AMB also fell at a rapid rate during this period  4.1 percent per year. While the model predicts some decline, the size of the predicted decline (1.7 percent per year) is substantially smaller. The factor driving the model's predictions is changes in the AFDC benefit variables.
Full Period
Average monthly benefits declined substantially over the full period, at an average annual rate of 2.0 percent. This decline is not predicted by the statelevel variables in the model, however; instead, they predict no change.
One intriguing finding is that the average annual percent decline in AMB that is not accounted for by the statelevel variables is approximately equal to the average annual percent increase in the caseload that is not accounted for by the same variables.^{(4)} The implication of this finding is that the model accounts for essentially all of the longterm growth in total expenditures (i.e., in the product of the caseload and AMB). An analogous finding applies to the subperiod from 1989.4 to 1993.3, but not in other subperiods. While the finding is intriguing, we know of no reason to think that it is other than fortuitous.
