A. BACKGROUND AND PURPOSES

In recent years many states have made substantial changes to their Aid to Families with Dependent Children (AFDC) programs on Federal 1115 Waivers, and the recent enactment of the Personal Responsibility and Working Opportunity Reconciliation Act of 1996 ensures that many more, large changes will be implemented in the not too distant future. The anticipated growth in state-level experimentation makes it especially important to improve our understanding of state-level factors behind historical growth in AFDC caseloads, for several reasons.

First, a better understanding of the impact of changes in the state economy will help states better prepare for the fiscal implications of economic recessions and recoveries under block grants.

Second, a better understanding of state-level factors behind program growth will help states design, and understand the implications of, program changes. This analysis cannot provide significant insight on the impacts of reforms such at time limits, work requirements or various restrictions on benefits because there has been little historical experience relevant to these reforms. However, the analysis can provide valuable insights on the effects of changes in basic program parameters for cash assistance, and how changes in programs such as Medicaid, SSI and Food Stamps interact with AFDC. We have more historical experience with these changes and while some research has already been done in this area, the results have been mixed or inconclusive. This analysis will help determine how realistic it is to expect proposed program changes to substantially reduce welfare dependency without impoverishing children.

Third, a better understanding of state-level factors behind historical growth will also improve our ability to establish baseline levels of program participation in a state for comparison to actual levels of participation under a state reform. As states implement reforms under the new welfare law, it will be very important to separate the impacts of those reforms on caseloads from the effects of environmental factors. Currently, caseloads are declining in most states. Are these due to legislated and administrated reforms, improvement in the economy, or some combination?

For these reasons, the Office of the Assistant Secretary for Planning and Evaluation (ASPE) in the U.S. Department of Health and Human Services has a strong interest in promoting research aimed at better understanding the determinants of AFDC participation at the state level. As part of their effort in this area, ASPE has contracted with The Lewin Group, Inc. to analyze the relationship between state AFDC caseload growth and (1) the strength and structure of the state economy; (2) demographic trends; and (3) changes in the structure of AFDC and other public assistance programs using state-level data to estimate pooled time-series models of program participation. This is the project's final report.

It is important to keep in mind that the purpose of this effort was not to build a better forecasting model. Many efforts to model AFDC participation, especially using time-series data at the national or state level, are motivated by the need to project future caseloads and expenditures. Such efforts place a priority on building a model that fits the historical series well, using whatever predictors are available. They do not necessarily require a more fundamental understanding of the relationship between the predictors and the historical series. In contrast, we place greater emphasis on developing and assessing explanatory variables that derive from theoretical considerations on the overall fit of the model.

While our findings on AFDC participation are of interest in their own right, they also serve to illustrate the potential of the methodology we use, as well as its weaknesses. We have previously applied the methodology to studies of participation in SSA's disability programs, Social Security Disability Insurance (SSDI) and Supplemental Security Income (SSI), and obtained much stronger findings about the effects of labor markets and general assistance programs on program participation than had been found in earlier studies. The methodology could also be applied to state-level indicators of the well-being of children or other vulnerable groups. Tobin (1994) has, for instance, applied the methodology to understanding determinants of the poverty rate with some success.⁽¹⁾ Gaylin and McLanahan (1995) have applied the methodology to studying determinants of out-of-wedlock births. The approach we take views state-level events as "natural experiments" that allow the examination of their impacts on key outcome variables. For the AFDC program, the level of experimentation has increased markedly in recent years and is likely to mushroom in the next few years. Interest in this methodology is likely to grow as a result.

Our work builds on the strengths of several previous studies that have used the same general approach (see Chapter 2). With the assistance of staff at ASPE and the Administration for Children and Families (ACF), we undertook an ambitious effort to develop a quarterly, state-level data set for the 1979-94 period. This effort has been rewarded with some results that are substantially stronger than previous results, especially concerning the impact of business cycles and of changes in basic program parameters (maximum monthly benefits, the average tax and benefit reduction rate, and the gross income limit). In other ways, however, we have not made as much progress in understanding the determinants of caseload growth as we would have liked. While we better understand the substantial caseload fluctuations during the period studied, an underlying trend remains unexplained, and we have very limited new findings concerning the effects of other state programs and policies on AFDC participation. Nonetheless, our findings clearly demonstrate the promise of this approach, and they could no doubt be strengthened through: expansion of the database to the post-1994 period and to earlier years; further development of some explanatory variables; and further experimentation with the model's specification and methods of estimation.

We estimate separate participation models for the Basic and Unemployed Parent (UP) programs. We focus on caseload models for each program, but also estimate total recipient and child recipient models. In addition, we estimate an average monthly benefit model for the combined programs.

Because the focus of this study is participation at the state level, we have also used our "best" estimated model to analyze the history of program participation in four selected states over the sample period: California, Florida, Maryland, and Wisconsin. We chose these states in part because their caseload histories have been carefully analyzed by others. California and Florida are both large states with rates of caseload growth during the latter part of our sample period that are well above the national rate. Maryland's caseload declined substantially relative to the national caseload during the middle part of the period. Wisconsin's caseload was essentially stable in the last few years of the sample, when caseloads in most other states were growing substantially. This exercise serves two purposes: determining how well the model, built on the varied experiences of all states, fits individual state caseload series, and improving our understanding about the causes of caseload growth in these states.

B. NATIONAL CASELOAD TRENDS

Caseload growth rates have varied substantially since 1980. Exhibit 1.1 shows changes in AFDC caseload growth from 1980 through 1994, which is the period for this analysis. While absolute changes in participation have been much greater for the Basic program than for the much smaller Unemployed Parent (UP) program, relative changes have been greater for the latter. In order to illustrate this, we have plotted the national participation series for the two programs on the logarithmic scale; on this scale, the slope of a series at any point is equal to its rate of growth. Official periods of economic recession are also shown for reference purposes.

After peaking in 1981 at 3.6 million, the AFDC Basic caseload fell and then rose slowly until 1989, growing from 3.3 million to 3.5 million. Between 1989 and 1994, the Basic caseload rose by more than 40 percent, from 3.6 to 5.1 million. Recent data, not shown in Exhibit 1.1, show that the caseload has once again begun to decline, from 5.1 million in March 1994 to 4.1 million in January 1997.

Like the Basic program, the UP caseload grew rapidly from 1980 to 1981, but then, unlike the Basic caseload, it continued to rise through 1984. The average annual growth rate during this period was about 25 percent. The UP caseload peaked in 1984 at just over 300,000 and then fell gradually through 1990 -- again departing from the pattern observed for the Basic caseload. The Family Support Act of 1988 required all states operating AFDC programs to also have an UP program by 1990. Since 1990, the UP caseload has risen steadily, surpassing its previous peak in 1984, although it would not have reached that peak if only states with UP programs in place before 1990 were counted.

Based on the national time series, it would appear that the UP caseload is more sensitive to economic recessions than the Basic caseload--not surprising given the nature of the program. Another evident feature of the UP caseload series is its seasonal behavior, with higher caseloads in the winter and spring than in the summer and fall.

Exhibit 1.1

AFDC Basic and UP Caseloads, 1980-1994

Note: Basic caseloads (solid line) are in millions of cases and UP caseloads (broken line) are in thousands of cases. Both Basic and UP cases are graphed in logarithmic scale. The plus signs trace the growth of UP programs after October 1990 excluding caseloads from states that initiated UP programs in accordance with the Family Support Act of 1988. Vertical lines show official recession periods.

Source: Office of Family Assistance (various years) and CBO (1993).

C. CONCEPTUAL FRAMEWORK

1. The Participation Decision and Other Choices

We approach this project from an economic perspective. This perspective emphasizes the role of individuals making choices between various alternatives as key to understanding individual behaviors such as labor force participation, marriage, fertility, and participation in AFDC. It posits that there are many adults for whom modest changes in factors affecting the economic attractiveness of various alternatives will influence their behaviors in these areas, although it also recognizes that the behaviors of many others may be immune from even very large changes in these same factors.

It is important to recognize that an unmarried parent's (usually a mother's) decision to seek AFDC Basic benefits is not necessarily a decision that is made taking other critical aspects of her life as given. Instead, that decision may just be one dimension of a set of "life decisions" concerning fertility, marriage, employment, and many other things. Hence, showing that AFDC Basic participation is positively related to the number of female-headed households containing children under the age of 18 -- as many studies have done--begs the question of what determines the number of such households. To some extent the number of such households and AFDC participation are jointly determined by the same factors.

Because the decision to apply for benefits may be made in conjunction with other life decisions, any factor that influences the relative well-being of the (potential) parents under all of their various "life alternatives" is a potential determinant of AFDC participation. The most obvious economic factor is the strength of the economy. A decline in job opportunities will make AFDC participation relatively more attractive than work to an unmarried mother. It may also, for instance, make family formation less attractive because of reduced job opportunities for both herself and her potential partner.

Declines in job opportunities can also have an impact on fertility, although the direction of the effect depends on the relative strength of competing forces. On the one hand, if one has a child she will need to use a share of her reduced income to provide for the child. On the other hand the "opportunity cost" of time she devotes to having and raising a child is reduced; i.e., when her potential wage rate is lowered, she gives up less when she uses her time to raise children rather than work. An additional incentive in favor of having a child exists if the woman does not have children already: it gives her access to AFDC benefits, which may substantially offset the income losses due to her poorer job prospects. ⁽²⁾

Changes in programmatic factors, such as the level of benefits and eligibility criteria, also lead to changes in AFDC caseloads. Provisions of the Omnibus Budget Reconciliation Act of 1981 clearly reduced caseload growth. In more recent years, several important changes brought about by Federal legislation may also have had an effect on the AFDC caseload. The 1988 Family Support Act (FSA) created the Job Opportunities and Basic Skills (JOBS) program and mandated that all states operate a UP program. In addition, many states have received Federal waivers that allow them to experiment with various policies, often with the intended effect of moving people from welfare to work or reducing dependence on AFDC in other ways.

As with changes in job opportunities, the influence of changes in programmatic factors on participation may partly work through their impact on marital, fertility, and other decisions. For instance, introduction of the UP program was expected to reduce the number of unmarried mothers because it increased the availability of AFDC benefits to households with two parents. In theory, however, making AFDC benefits more available to two-parent families makes childbearing more attractive.

While there is much disagreement in the literature about the influence of economic factors on various life decisions, there is little doubt that these decisions are influenced by a common set of factors and, to some extent, are jointly made. Hence, it is critical to recognize the potentially joint nature of these decisions in research on AFDC participation.

Changes in other programs that provide benefits to the low-income population can also have an impact on AFDC participation. Perhaps most importantly, past changes in state Medicaid benefits are likely to have had an impact because almost all AFDC recipients have been automatically eligible for Medicaid. Changes in other programs, such as Food Stamps (FS), general assistance (GA), unemployment insurance (UI), workers compensation (WC), and Social Security Disability Insurance (SSDI) and Supplemental Security Income (SSI) can also have an impact. All of these programs are potential sources of benefits to at least some individuals who might be eligible for AFDC, either directly (e.g., SSI provides benefits for low income adults or children with qualifying disabilities) or indirectly (e.g., GA may provide support to members of an AFDC household who are not in the AFDC family unit, or to a relative of the AFDC family unit who lives in another household, including a non-custodial parent).⁽³⁾

2. The Budget Constraint for an AFDC Family

In order to understand how the structure, as well as the benefit value, of AFDC and other programs potentially affect AFDC participation, it is helpful to consider a stylized budget constraint--the trade-off between disposable income and "non-market time" (time spent in activities other than paid employment) -- for the current month that is faced by a single mother who is making the choice between participation and non-participation in that month (Exhibit 1.2).

We treat the value of the combined AFDC and Food Stamp benefit as a single benefit because, from the woman's perspective, a dollar's worth of food purchased with Food Stamps frees up a dollar of cash benefits or other income for spending on other goods and services. Point C represents the value of her combined AFDC and Food Stamp benefits if she does no market work--her maximum monthly benefit (MMB) from the combined programs, sometimes called her "guarantee." If she has earnings, the first dollars earned do not reduce her benefits, and her income increases by one dollar for every dollar earned--along the line segment CI. This ignores payroll taxes (FICA) and the earned income tax credit (EITC), which we will consider later, as well as in-kind benefits such as Medicaid and housing subsidies. At I, a share of each additional dollar she earns is lost through a reduction in AFDC benefits--the marginal benefit reduction rate (MBRR). The MBRR is currently very high--essentially 100% -- in most states. The slope of the line from point I to point D is her wage rate times one minus the MBRR. Point D is the point at which her combined benefits are entirely "taxed" away, and her income at that point is usually called her "break-even income" or "cut off earnings." The slope of dashed line CD is her wage rate times one minus the average benefit reduction rate (ABRR).

Exhibit 1.2

Stylized Budget Constraint for a (Potential) AFDC Family

The earnings of some AFDC mothers may reach the "gross income limit" (GIL) before they reach the break-even level. OBRA81 mandated a GIL of 150 percent of the state's need standard; households with pre-benefit income above this amount were declared ineligible for AFDC benefits even if the state's formula otherwise resulted in some benefit; DEFRA84 increased the GIL to 185 percent of the need standard. The GIL only affects the budget constraints of mothers with substantial disregards for work expenses or child care; the GIL has always been above the break-even income level in all states for families with minimum disregards. The effect of the GIL on a budget constraint with high disregards is illustrated by line KL in the exhibit. The level of the GIL is depicted by L. When L is less than the break-even income (the height of D in the diagram), as depicted, the GIL creates a "notch" in this household's budget constraint, depicted by MKD. If the GIL is sufficiently high relative to the cut off earnings of most households, it is irrelevant to the budget constraint.

The stylized budget constraint can be fully described with the wage rate and four "program parameters:" the MMB, the ABRR, the MBRR, and the GIL. That is, the full budget constraint is completely determined by these parameters and the wage rate. We use these parameters, slightly modified, to characterize the budget constraints of an AFDC family with one adult and two children in each state and each quarter of our sample, assuming minimum disregards. Modifications are made for the effects of the EITC and payroll taxes on net income for mothers with earnings, and to capture the fact that the GIL is only relevant to the budget constraint if it is sufficiently low relative to the earnings cut-off of a family with minimum disregards. The EITC and payroll taxes change the rate at which earnings are reduced at the margin, and on average. We take these into account and replace the MBRR and ABRR with the marginal and average tax and benefit reduction rates (ATBRR and MTBRR), respectively. Our measure for the restrictiveness of the GIL is AFDC cut off earnings for our hypothetical household divided by the GIL.

We also attempt to estimate the effects of Medicaid on participation. If the mother receives AFDC payments, she and her children will automatically qualify for Medicaid benefits. In the exhibit, the value of her Medicaid benefit is the distance from point C to point E; point E represents the combined value of her AFDC, Food Stamp, and Medicaid benefits if she performs no market work. Medicaid benefits are not implicitly taxed until her income reaches the "Medicaid need standard" (income at point H); if her income passes that level, she loses all of her benefits. Before OBRA89 the Medicaid need standard was the same as AFDC break-even income in most states. Changes mandated by OBRA89 and OBRA90 expanded Medicaid coverage to individuals with incomes above the AFDC break-even level including pregnant women and children under age six with family incomes below 133 percent of the federal poverty level and children under age 19 with family incomes below 100 percent of the federal poverty level.⁽⁴⁾ Thus, given the stylized AFDC budget constraint, two critical parameters determine the Medicaid "add-on" to the budget constraint: the value of Medicaid benefits and the Medicaid need standard. We attempt to capture both of these features in the model, through the use of an estimate of the value of Medicaid benefits to our hypothetical three-person family and a variable intended to capture the effects of the OBRA89 and OBRA90 Medicaid expansions.⁽⁵⁾

All of the following hypotheses are related to the budget constraint and are testable under the methodology:

• Increases in the mother's wage rate (or, more generally, job opportunities) reduce participation, other things constant;
• Increases in the MMB increase participation, other things constant;
• Increases in the ATBRR reduce participation, other things constant;
• Increases in the MTBRR reduce participation, other things constant:
• Increases in the GIL increases participation, other things constant:⁽⁶⁾
• Increases in the value of Medicaid benefits increase participation, other things constant; and
• The Medicaid expansions of OBRA89 and OBRA90 reduced participation.⁽⁷⁾

Changes in these factors have parallel effects on aggregate expenditures. The direction of effects of changes in the parameters on average benefits per person are less clear, however. Even though a change in a parameter that increases the incentive to participate will generally increase the value of benefits received by families that would be participating anyway, it also draws in families that are likely to receive benefits that are below average in value.

3. Other Program Factors

Many states have obtained and implemented waivers to federal rules under Section 1115 of the Social Security Act ("1115 Waivers") during the period under investigation, especially during the last few years, and some were expected to have an impact on program participation. Based on descriptions of all waivers granted during this period provided by ACF, we created a series of indicators for the following features of these waivers: reduction or elimination of AFDC benefits for children born or conceived while the family is receiving AFDC ("family cap"); requirements for participation in work, education, or training activities;⁽⁸⁾ extension of transitional Medicaid benefits; elimination of the 100-hour work limitation rule for UP families; and elimination of the work history requirement for UP families.

Many states also enacted laws during the period under investigation that may have had an impact on AFDC caseloads and expenditures. New laws in the areas of paternal identification, child support enforcement, and restrictions on abortion and Medicaid funding of abortions may have affected participation and expenditures through their effects on fertility and family income, in addition to their direct effects on participation.

D. OVERVIEW OF THE MODEL

As described previously, the model has six participation equations, three for each program (Basic and UP) and one quarterly average monthly benefit equation for the combined programs. The explanatory variables are classified into four broad groups:

Demographic Factors--We distinguish between two types of demographic factors:

• Size and age distribution of the adult population--we assume that these factors are influenced little by economic factors except through immigration or over very long periods of time. This is clearly true at the national level; changes in a state's economy may trigger changes in these factors, but we assume that current migration induced by current economic change is negligible;
• Family characteristics--the variables used to capture family characteristics are vital statistics (marriages, divorces, and out-of-wedlock births) and immigration measures.
• Labor Market Factors, including the unemployment rate and various measures of employment and wages;
• AFDC program factors, including the program parameters, federal legislation, and state waivers. The program parameter variables partly reflect the Food Stamp program, the EITC, and payroll taxes because these interact with the AFDC program rules to determine the relationship between recipient earnings and net income;
• Other program factors and legislation, including Medicaid, SSI, SSDI unemployment insurance, general assistance, paternity identification laws, child support enforcement, and restrictions on abortions and public funding of abortions.

Most other studies have assumed that the second set of demographic variables, family characteristics, are exogenous to AFDC participation. For the reasons given in the previous section, this assumption may be incorrect. Therefore, we investigate the extent to which this assumption is appropriate in a limited way, by estimating models with and without variables intended to capture the effects of changes in these family characteristics.

A schematic summary of the model appears in Exhibit 1.3

Exhibit 1.3: The Structure of the Model

E. SUMMARY OF THE FINDINGS

1. The estimates we obtain for the effects of the business cycle on participation in the Basic program are substantial, and last longer than any we have found in the literature.

The relationship between the unemployment rate and the AFDC caseload is complex. Current changes in the unemployment rate have lingering effects on caseload growth for many quarters to come. Similarly, current AFDC caseload growth is affected not only by current changes in the unemployment rate, but also by unemployment rate changes from many quarters in the past.

The estimates imply that if the unemployment rate rises by one percentage point and then remains constant for a year, the AFDC Basic caseload by the end of that year will be 2.4 percent higher than it would be if the unemployment rate had not changed. This effect is somewhat larger than the four-quarter effects reported in any previous study.⁽⁹⁾

More significantly, our estimates indicate that a current increase in the unemployment rate affects caseload growth for the next 14 quarters (3.5 years). Previous studies have not found significant unemployment rate change effects after 4 quarters. It appears that we are able to detect these long lags in business cycle effects because we have used the information provided by the individual business cycle experiences of all states over two major cycles.

According to our estimates, if the unemployment rate were to rise by one percentage point and then remain constant for the next 14 quarters, the total increase in the Basic caseload over 14 quarters would be nearly six percent. Of course, this stylized scenario is unlikely. The unemployment rate typically increases by well over one percentage point in a recession, the increase is gradual and erratic, and the peak may be sustained or brief. Below, we describe the estimated effects of the two recessions in our sample period on the caseloads.

We estimate that the poor performance of the economy from 1980 to 1982 resulted in an average annual increase in the Basic caseload of 2.1 percent from 1980 through 1983, and that the sustained recovery that followed reduced the caseload at an average annual rate of 3.3 percent from 1984 through 1989. The impact of the business cycle during this period is not evident in the national caseload, which was essentially the same in 1983 as in 1970 and grew at an average annual rate of 1.0 percent from 1984 through 1989. The reason is that program changes substantially offset the business cycle effects (see below). We estimate that the less severe recession of 1990-91 resulted in average annual caseload growth of 1.5 percent from 1990 through 1993, about 23 percent of the actual average annual growth rate of 6.5 percent. Although the caseload grew by 0.4 percent in the last year of the sample, the recovery from the recession was already having a negative effect, estimated to be 0.8 percent in the last year.

The estimated business cycle effects for the UP caseload are also substantial, and longer lasting than those found previously. According to the estimates, a one percentage point increase in the unemployment rate would increase the UP caseload by 17.3 percent by the end of the year. The effects of a current change in the unemployment rate continue to affect the UP program for 14 quarters, similar to the effects on the Basic program. Based on the estimates, if the unemployment rate increases by one percentage point and then remains constant, the UP caseload would increase by 26 percent after 14 quarters. Cromwell (1986) obtained estimates of a similar magnitude, but after just four quarters. Other studies have found substantially smaller effects. The estimates of the combined effects of the unemployment rate and trade employment per capita are larger.

Again, this hypothetical scenario is unlikely, and we look to historical examples to demonstrate the actual effect of changes in the unemployment rate on the UP caseload. In the 19 states that had UP programs throughout the sample period, we estimate that the poor performance of the economy from 1980 to 1982 resulted in an average annual increase in the UP caseload of 15.3 percent from 1980 through 1983, or about 60 percent of the average annual increase of 25.1 percent. According to our estimates, the subsequent recovery from 1984 through 1989 reduced the caseload at an average annual rate of 16.6 percent, when the actual average annual decline was 7.9 percent. We estimate that the 1990-91 recession resulted in average annual caseload growth of 12.8 percent from 1990 through 1993, essentially all of the average annual growth of 13.1 percent. There was no change in the caseload in 1994, but our results indicate that the recovery was already having a small negative effect, estimated at 0.3 percent.

2. We obtain strong evidence of the effects of changes in three important program parameters--the maximum monthly benefit (MMB), the average tax and benefit reduction rate (ATBRR), and the gross income limit (GIL)--on participation.

We estimate that a ten percent real increase in the MMB (e.g., from $400 to $440) increases the Basic caseload by 2.7 percent and the UP caseload by 2.6 percent. We also estimate that a 10 percentage point reduction in the ATBRR increases the Basic caseload by 1.5 percent, but, somewhat surprisingly, has no impact on the UP caseload. Finally, we estimate that the increase in the GIL enacted under DEFRA84, from 150 percent of the state's need standard to 185 percent, increased both the Basic and UP caseloads by a little over one percent.

Our simulations indicate that the combined effects of program cuts related to OBRA81 reduced the Basic caseload at an average annual rate of 4.6 percent from 1980 through 1983 (mostly in the last two years of that period), more than offsetting the positive effect of the poor economy. The effect on the UP caseload was comparable.

3. The estimated contribution of growth and aging of the at-risk population to AFDC participation was high during the early 1980s (about two percent per year), but declined throughout the period studied.

The reason for the observed pattern is that the youngest members of the baby boom generation--those born in the early 1960s--were entering the age group at highest risk in the early 1980s, while smaller post-boom cohorts were entering that age group by the end of the decade. From 1980 through 1983, we estimate that this factor contributed an average of 2.0 percentage points to annual growth in the Basic caseload. This contribution gradually declined throughout the period and was actually negative by 1994, at 0.4 percent. Results for the UP program were comparable.

4. Legalizations of illegal aliens under the Immigration Reform and Control Act (IRCA) of 1986 appear to have contributed substantially to Basic caseload growth in some states during the period from 1988 to 1993.

Even though individuals legalized under IRCA were not eligible for benefits during a five-year waiting period, many of their children were born in the United States and had been eligible all along, but were apparently not enrolled because of deportation fears. It appears that many "child-only" cases were opened when parents became legal aliens. We estimate that IRCA legalizations contributed about five percentage points to average annual growth in California's Basic caseload from 1990 to 1993, and about 1.5 percentage points to growth in the national Basic caseload.

5. Declines in marriage and increases in non-marital births contributed noticeably to Basic caseload growth throughout the period examined.

These "vital statistic" variables account for average annual growth in the Basic caseload of 0.5 percentage points from 1980 to 1994 which is a little more than one-quarter of the total average annual growth in the Basic caseload of just under 2 percent. We did not find a statistically significant effect for the UP caseload, but this is not surprising because UP cases are two-parent families.

We expected to find that omitting these variables from the models would increase the estimated effects of the labor market and AFDC benefit variables on participation, based on the hypothesis that changes in the latter have an impact on the former. Changes in estimated effects were in the anticipated direction, but proved to be trivial. Thus, it would appear that other major factors are behind the decline in marriage and the growth in non-marital births.

We had originally hoped to develop state-level estimates of female-headed households for use in our models, but our efforts were not successful. Vital statistics variables--marriages, divorces, and non-marital births--were substituted instead. It may be that better measures of female-headed households would lead to stronger estimated effects for this factor, but we do not know.

5. Many other factors we examined were not found to have statistically significant, substantial estimated effects.

We were especially surprised that the Medicaid variables used in the analysis yielded very weak findings, given strong findings that appear in the literature. According to our estimates, the Medicaid expansions for women and children who were not on AFDC had a small positive effect on AFDC caseloads in states where the share of children in AFDC was previously small, and a small negative effect in states where the share of children in AFDC was previously large. We did not find a statistically significant effect for changes in the estimated value of Medicaid benefits.

The following findings are not very strong, and are subject to interpretation. It should be kept in mind that we examined a large number of possible explanatory variables, and any such examination is bound to yield a few "statistically significant" effects by random chance alone.

• States that implemented "family caps"--limits on payments for children born to existing AFDC mothers--under 1115 Waivers experienced statistically significant reductions in their Basic caseloads according to some models we estimated, but not in their UP caseloads. These results are weak and it is not clear what conclusions should be drawn;
• States that imposed restrictions on Medicaid funding of abortions or required parental consent or notification for minors experienced statistically significant reductions in their Basic caseloads according to some models we estimated, but not in their UP caseloads. For abortion restrictions to have a negative impact on the Basic caseload, they would presumably have to reduce fertility among the target population by more than any increase they cause in the number of pregnancies ending in live births. While the findings for the Basic caseload would be consistent with such an effect and are intriguing, they are not rigorous enough to support it on their own. Again, these results are not conclusive;
• Administrative tightening of eligibility requirements for the Social Security Administration's disability programs (Social Security Disability Insurance and Supplemental Security Income) in 1977-78 had a statistically significant, positive impact on the Basic caseload a year later, but not on the UP caseload. As with the other factors described here, it is difficult to know to what extent these findings may be due to chance, or influenced by the effects of omitted variables;
• The share of unemployed persons who are covered by unemployment insurance has statistically significant, positive coefficients in the Basic participation equations. The sign is contrary to what might be expected, and may reflect factors that have been omitted from the model and that have positive effects on both participation and the share of unemployed persons who are insured; and
• The number of children receiving SSI benefits also has significant, positive coefficients in the Basic participation equations. The explanation of the counter-intuitive sign of this coefficient may be similar to that for the coefficient of the insured unemployment variable.

Other factors we tried that did not yield statistically significant findings are: average weekly wages in the trade industry; average weekly wages in manufacturing; total employment per capita; manufacturing employment per capita; dummy variables for other types of 1115 waivers (in addition to family caps); dummies for child support and paternity establishment laws; the ratio of employed men to the number of women of childbearing age; dummies for the existence and type of UP program (Basic participation equations only); a measure of cuts in state general assistance programs; SSI benefit levels, including state supplements; and the number of SSI children in the Zebley class.⁽¹⁰⁾

In many years, the changes in the state explanatory variables in the models account for most of the observed changes in the caseload, but there are important exceptions. We included "year effects"--dummy variables for each year to capture the average effects of omitted, or poorly measured, factors on the Basic and UP caseloads. For both caseloads, the coefficients are positive in most years and are statistically significant from 1985 to 1991, indicating that factors other than those captured in the state explanatory variables played a substantial role in determining caseload growth. For the UP caseload, the dummy coefficients are also positive and significant in 1980 and 1981. Possible reasons for these positive year effects include:

• Effects of federal legislation that applies equally to all states;
• Overestimation of the impact of the recovery from 1983 to 1989, and underestimation of the impact of the recession of 1990-91;
• Effects of the relative decline in wages for low-skill work;
• Underestimation of the contribution of immigration;
• Underestimation of the role of changes in household characteristics;
• Increases in the cost of health care and reductions in access to health insurance that were not captured with our Medicaid variables; and
• Declines in job prospects for low-skilled workers that are not reflected in the unemployment rate and/or the trade employment variable.

F. RESEARCH IMPLICATIONS

This study demonstrates both the promise and limitations of the pooled time-series approach to studying AFDC caseload participation, other state-level measures of program participation, welfare, and health. We have obtained what we believe to be the most accurate estimates of the effects of labor market factors on AFDC participation of any study to date,⁽¹¹⁾ and have also obtained strong findings for program parameters.

At the same time, however, we have not been able to reliably estimate the effects of several state-level factors that are believed to be important determinants of AFDC participation. While we obtained strong results for non-marital births and marriages, we do not know the extent to which these variables capture the effects of growth in female-headed households, which we could not measure satisfactorily at the state level. Other determinants to consider further are other characteristics of families, access to health care insurance, the value of Medicaid, wages in low-skill jobs and other aspects of local labor markets not captured in the current model, other aspects of immigration, and parameters of other programs (e.g., UI). Further progress in this area will require development of better measures of state-level variables.

Recent caseload declines and devolution have substantially heightened interest in measuring and understanding the determinants of the welfare and health of vulnerable populations at the state level as well as of program participation. The pooled time-series approach to modeling these variables at the state level may prove to be a useful tool in helping researchers and policymakers determine whether changes in such variables are due to state program changes or to environmental factors that are beyond the control of the states. The promise of this tool will be substantially enhanced if better measures of key state-level factors are developed--both prospectively, as welfare reform and other changes occur, and retrospectively, as is necessary to estimate and understand the impacts of these factors on the measures of interest.

The value of this tool will also depend, however, on the extent to which states vary in their approaches to welfare reform. While the AFDC program varied substantially across states during the sample period, it was still reasonable to say that there were 51 variants of the same program and to analyze them together. Reforms may be so radical and varied as to make such a statement unreasonable in the future. Over time, pre-devolution caseload behavior will become less and less relevant to post-devolution caseload behavior.⁽¹²⁾

G. FUTURE WORK

This effort has produced some important findings, but has also fallen short of its objectives in some respects. Future work that would build on the findings of this project may benefit from the following recommendations.

1. Refinement of the "expected participation" variables should be considered. The single most important explanatory variable in the participation model is the change in the logarithm of our "expected participation" measure. This measure is a weighted sum of the number of women in the state in age groups that are at-risk for participation, with weights equal to national participation rates by age-group in 1990 (see Chapter 3). This variable is intended to capture the size and age distributions of the population of women who are at-risk for participation. Michael Wiseman has suggested that the widening over the sample period between actual caseloads and predicted caseloads is in part due to the fact that this is an index with weights fixed by observed participation rates in one year. An alternative would be to compute the change for each state in each year using weights based on national participation by age group in the previous year--i.e., to update the weights when computing each year's change.⁽¹³⁾ Obtaining different weights for each year from SIPP may be problematic, but it should be possible to obtain weights for many other years. An even more desirable solution would be to use each state's own age-specific participation rates in the previous year to predict the change in participation due to population change, but the information needed to construct state-specific indices is not available.

2. Development of models with alternative dependent variables should be considered. Possibilities include:

• Openings and closings--we initially considered using case openings and closings as dependent variables, but elected not to in keeping with the mainstream of the existing literature and because of concerns about the openings and closings data. The extra effort needed to estimate such models given the existence of the database for the explanatory variables is small, however, and might well pay off.
• Disaggregated dependent variables--the ACF participation data are reported by program (Basic vs. UP), and cannot be directly disaggregated further. It might be possible, however, to use the ACF quality control (QC) data to estimate disaggregated caseloads. We think that disaggregation by citizenship, reason for deprivation, child-only vs. other, ethnicity, age, or sex of household head would be especially helpful if feasible. Disaggregation by state regions might also be very useful. Reviewers have provided three examples of how caseload behavior in some regions within states have varied substantially from those for the rest of the state.⁽¹⁴⁾
• Aggregated dependent variables--we developed separate participation models for the Basic and UP programs, but it may be that the separation of the two programs created some problems for the analysis. We have learned, for instance, that a large share of UP cases in California eventually convert to Basic cases. Such conversions might help explain caseload growth in the Basic program during the 1984 -1992 period following the large increases in the UP program during the earlier recession. While this could be modeled directly, it may be problematic to build models in which lagged participation measures for one program appear as explanatory variables in participation models for the other. Combining the caseloads and estimating a single model may be a more useful alternative.
• Joint AFDC/SSI models--we attempted to estimate the effect of changes in SSI child recipients on AFDC caseloads, but were not successful. The likely reason is that participation in both programs is, in part, determined by a common set of factors. It might be fruitful, instead, to develop models of "welfare recipients," including those on either AFDC or SSI. We think it would be feasible to develop a model for AFDC or SSI child recipients, and another for adults age 15 - 64. The adult model could be substantially improved by separating female and male recipients; this is possible for the SSI recipients, but may not be possible for the AFDC recipients--depending on the QC data. Garrett and Glied (1997) have pursued this approach.
• Alternative functional forms for the participation variables--we used the logarithm of the participation variable or the log of participation rates. The logarithmic specification implies that a change in an explanatory variable is proportional to the level of participation. Use of the level of the participation rate (caseload per adult in the relevant age group, say) is a defensible alternative.⁽¹⁵⁾ We have noticed that several states with relatively small UP caseload rates at the beginning of the sample period experienced extraordinarily large percent age increases in their UP caseload rates in the first three years of the sample period relative to the percent increases observed in other states; the percentage point changes in the caseload rates themselves, however, are much more comparable to those in other states. ⁽¹⁶⁾

3. Development of additional explanatory variables should be considered. Possibilities include:

• Wages for low-skill workers--one promising explanation of growth that is not accounted for over the sample period is the relative decline in wages for low-skill workers. Substantial research has been done by labor economists on understanding the causes of this decline, and some of that work has been done using state or regional data. Several economists familiar with this research have suggested that, with some effort, reasonably accurate state-level estimates of wages for low-skill workers could be constructed, following work that has already been done in this area.⁽¹⁷⁾ We did not pursue this under the current project because of the level of effort required;
• Unemployment insurance benefits--Dr. Jonathan Gruber (MIT) has developed a computer model for simulating UI benefits to workers with specified characteristics in each state for every year since 1968. This model could be used to construct a measure of each state's benefits that would be analogous in origin to the AFDC program parameters we used in our research. This would be a better measure of the generosity of the state programs than the UI measure we used in the estimates reported here;
• Immigration variables--we have not included a variable for refugees in our models. Even though the number of refugees is small, high participation rates among refugees may mean that they are an important explanation of caseload growth in some states. More generally, the strength of our findings for IRCA legalizations suggests that more effort in modeling the effects of immigration on caseloads may be fruitful;
• Female headed households--our efforts to produce state-level estimates of this explanatory variable were not very successful. We found that even subregional estimates based on the March CPS exhibited substantial random variation from one year to the next. We have not had time to examine the reasons for this variation--whether it is just sample size or whether it might be some other aspect of the CPS methodology. It may be that better estimates can be produced, but significant effort will be required to determine how this might be done. Ongoing efforts by ASPE and others to develop state-level estimates of many health and welfare indicators may prove useful here;
• Medicaid measures--we were surprised not to find more significant findings for the Medicaid variables we tried. It is puzzling that previous analyses of micro data have produced much stronger results. A substantial effort to understand the reason behind these inconsistent findings might produce better measures for use in the state-level analysis;
• Neighbor variables--Shroder (1995) used measures of labor market and AFDC program variables in neighboring states in his models. We did not have the time to construct such variables for this project, but they can be constructed from the data we have already assembled. Given concerns about states "racing to the bottom" under devolution, it may be especially valuable to examine how reductions in benefits in one state affect caseloads in neighboring states;
• Minimum wage--we did not include the minimum wage in our models. Most states use the federal minimum, but some states have had higher values in at least some years. A recent analysis by Burkhauser, Couch and Wittenburg (1996) of the effect of minimum wage increases on employment of "at-risk" youth in 1990 and 1991 suggests that this would be fruitful.

4. Simultaneous models of benefit levels and program participation should be considered. Shroder (1995) found much stronger results for the impact of increases in benefits on participation when he modeled them as simultaneously determined with participation levels. As he and others have argued, an increase in the burden of a state's welfare expenditures on taxpayers is likely to make cuts in benefits politically popular; i.e., higher participation results in legislated reductions in benefit levels. This negative, reverse relationship between benefits and participation may result in an underestimate of the presumably positive effect of benefits on participation. We are, however, concerned about the quality of possible instrumental variables needed to identify the effects of benefits on participation, especially because there are three benefit variables that would require instrumentation.⁽¹⁸⁾ Three instruments would be required at a minimum, and all three would need to be important determinants of the benefit parameters that do not have a direct impact on program participation. Additional resources would be needed to pursue this further.

5. Extension of the sample period should be considered. Data for the participation variables in our model are available from the fourth quarter of 1974 on. Data through the end of the federal program (third quarter of 1996) should soon be available. The sample period constraints we faced primarily came from the explanatory variables. Earlier and, especially, later data for many key variables can, however, be obtained or constructed, but may require substantial effort.

6. Further examination of the stability of the parameter estimates across subperiods should be considered. We were limited in our ability to produce subperiod estimates by both resources and software. More effort in this area would be helpful in determining whether changes in the program or the characteristics of participants have affected the sensitivity of participation to the business cycle, program parameters, or other factors. For instance, the introduction of the UP program could have reduced the sensitivity of participation in the Basic program to business cycles.⁽¹⁹⁾ Other major programmatic changes that occurred during the period under investigation could have had similar effects--especially the provisions of OBRA-81 and the introduction of JOBS.

7. Further examination of asymmetries in business cycle effects and, more generally, model dynamics should be considered. Many have suggested that the effects of business cycles on the caseload are asymmetric, with rapid growth during recessions and only gradual declines during recoveries. We explored this idea by estimating models with different distributed lags for unemployment in growth and recession periods, but found only very small, insignificant differences. Such models are known as "switching regression" models, with the applicable specification for a period depending on some decision rule. Our models were crude in this respect, with the applicable regression depending on whether or not the national unemployment rate was increasing in the current period. Steven Thompson recently developed a more sophisticated version of a switching regression model for his monthly time-series model of Maryland's caseload, with some success in identifying asymmetric effects (Regional Economic Studies Institute, 1994). Maryland's caseload (see Chapter 6) displays a pattern of rapid increases after recessions and gradual declines during the following recoveries. Thompson's initial experience was similar to our own; using the change in the current national or regional unemployment rate yielded results that did not seem to capture the asymmetric relationship very well. After some experimentation, however, he discovered that lagging the "switch" from the recession model to the recovery model by 8 to 12 months after the peak in the caseload yielded a much better fit for Maryland. We do not know whether a similar lag would fit other state experiences well.

Another reviewer, Michael Wiseman, has suggested developing a dynamic model in which the speed of adjustment of the caseload depends on the difference between the actual caseload and a long-run equilibrium level. Such a model would put a different structure on the lagged variables and include the lagged caseload variable as an explanatory variable. This seems to be echoed, but with a twist, in the comments of a third reviewer, Don Winstead, who suggests that lack of program capacity to deal with the large numbers filing for benefits during the Florida recession resulted in larger caseloads than would have been realized had capacity been greater.

Don Winstead also suggested that changes in the unemployment rate lag, rather than lead, caseload changes in a recession, but lead them in a recovery. The theory is that low-skill workers are the first fired in a downturn and last hired in a recovery.

8. More extensive analyses of actual and predicted series in individual states might be useful. The independent reviews of our findings for four selected states were useful in both understanding growth in those states and understanding the strengths and weaknesses of the model. We did not have an opportunity to revise the model to incorporate information we obtained from these reviews, but this would be feasible. For instance, Steven Thompson reported that he found a substantial interaction in his time-series model between an 1115 waiver for the "Up-Front Job Search" program and labor market variables. The estimated coefficients of the labor market variables increased substantially after the program's implementation. This essential elements of this specification could be implemented in the pooled model. Detailed assessments for additional states might also be very useful.

1. An important limiting factor in applying the methodology to indicators of well-being is that reliable state-level measures of many indicators do not exist. ASPE and others are promoting efforts to improve measurement of state-level indicators going forward, but these will not be helpful for supporting the type of modeling reported on here until at least several years into the future. Existing data may permit development of reasonably reliable estimates of some state-level indicators retrospectively.

2. A few recent studies have found evidence that suggests business cycles impact family structure. Moffitt (1994) includes the state unemployment rate and variables reflecting employment in specific sectors in his study of female headship that uses pooled CPS data from 1968 to 1989. Unemployment was significantly and positively related to female headship among black females, but not among white females. Blank and Ruggles (1996) include the state unemployment rate in duration models of AFDC eligibility and AFDC participation. Unemployment reduces the likelihood that a spell of AFDC eligibility will end due to a change in family composition. However, Moffitt (1995) finds little consistent evidence that AFDC benefits have had a substantial impact on out-of-wedlock childbearing.

3. Throughout this document we use the word "family" to refer to AFDC assistance units, as defined by Federal and state regulations, although some units contain individuals who are not legally related to each other.

4. This second requirement is currently being phased-in and holds true only for those children born after September 30, 1983.

5. We are grateful to Aaron Yelowitz for providing the Medicaid expansion variable. See Yelowitz (1994).

6. Note that "other things constant" implicitly includes the AFDC earnings cut-off, which is fully determined by wages and the other program parameters.

7. See Yelowitz (1994) and Moffitt (1992) for more complete discussion of these theoretical points.

8. This refers to requirements that are beyond those of the state's JOBS program.

9. Cromwell, et.al, (1986) found that the same change results in a 1.8 percent caseload increase after a year, using a similar methodology. The Congressional Budget Office estimates a 1.7 percent increase using a time-series model (CBO, 1993). The findings we report here are based on a model that uses changes in the unemployment rate as the only labor market variable. Adding another business cycle variable, trade employment per capita, essentially increases the estimated effect of the business cycle.

10. Since completing this work, we have become aware of very recent analyses of the impact of Zebley on SSI child participation and the share of SSI child participation growth accounted for by transfers from AFDC, by Garrett and Glied (1997). There preliminary results indicate that about half of the SSI child growth caused by Zebley is accounted for by transfers from AFDC.

11. Hoynes (1996) has also obtained strong and convincing results in a duration analysis of AFDC cases in California, using local labor market variables.

12. Tom Corbett is more pessimistic. In correspondence to us, he writes: "The reality is that the notion of a national program where a few relatively easily measured economic, demographic, and program parameters could predict caseload had virtually disappeared by the 1990s."

13. The problem is analogous to the problem with fixed weight price indices, such as the Consumer Price Index, which become a poorer and poorer measure of inflation as actual consumption bundles drift away from the market basket used to determine the weights. The proposed solution is equivalent to a Divisia ("chain-linked") price index.

14. The examples are California (northern vs. southern), Florida (Dade County -- Miami area -- vs. the rest of the state), and Maryland (Prince George's County vs. the rest of the state).

15. Another way to define the participation rate in a state would be to divide the caseload by a weighted sum of the population in various age groups, using national participation rates by age in a base year as weights. We use the logarithm of this denominator, which we call "expected participation" as an explanatory variable in our participation models.

16. For example, Nebraska's caseload increased by 260 percent from 1979.4 to 1980.4, but the base was very small (60 families) and the per capita increase was high, but not out of line with the experience in other states during the period.

17. Steven Thompson reported that Regional Financial Associates in West Chester, PA, has obtained data from state employment departments for all 50 states. We had previously explored wage data available by state and industry from the Department of Labor and determined that data for specific low-wage, low-skill industries were missing in many states and many years.

18. We originally had planned to estimate a simultaneous model for the maximum monthly benefit variable, following Shroder (see Lewin-VHI, 1996), but abandoned this effort after expanding the number of benefit parameters in the model. One idea for generating instruments is to use the share of adults (voters) in various age groups; presumably elderly voters are less supportive of benefits for young families than are younger voters. Another possibility is the Federal share of the AFDC payment; the higher the Federal share, the less would be the impact of a change in the caseload on taxpayers.

19. Testing whether the presence or absence of an UP program shifts the parameters for the Basic model merits further discussion because there are really three separate regimes to consider. All States have been required to have UP programs since October of 1990, and this period clearly represents one regime. Many States adopted UP programs voluntarily well before 1990. Pre-1990 observations for these States could be grouped with post-1990 observations for all States, but the fact that these States had voluntary programs, along with the fact that these State programs did not necessarily comply with Federal rules that came into effect in 1990, makes it possible that these two groups of observations are not comparable. Hence, we will begin by treating them as separate regimes. Observations for States with no UP programs constitute the third possible regime. For this study we examined the comparability of results for the UP programs across the first two regimes in an informal way.