Part 2 of Chapter 5

REGRESSION RESULTS

C. UNEMPLOYED PARENT PARTICIPATION EQUATIONS

1. Determining the Final Specifications

We present two sets of estimates for the UP participation models. In the first set -- the "full-period" 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 "post-mandate" 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 post-mandate 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 full-period 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 first-order (linear) instead of second (quadratic), and the maximum lag length is six instead of ten.

For the post-mandate estimates, we started with the final specification from the full-period 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 full-period model first, then present the post-mandate 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 "child-only" families are in the Basic program, which is consistent with our earlier interpretation that the finding for the Basic program captures the child-only phenomenon.

Exhibit 5.3

a. Expected participation variable is based on national age-specific participation rates for 1990 and estimated population of the state by age in the quarter.

b. T-statistics 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 [(T-K)/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 + a₁ j + a₂j² 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 long-run 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 time-series 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 cut-off 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

FSA-88 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 post-mandate 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 full-period model. We replicated that specification in our first set of post-mandate 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 cross-state 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 six-month 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 12-month programs.

We initially estimated models using changes for the full post-mandate 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 post-mandate 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 full-period 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 post-mandate period, although different in some respects from the full-period estimates. The long-run unemployment elasticity is 0.86 (compared to 0.97) and the long-run 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 post-mandate estimate of -1.7 for the 19 full-period states (Column 3). Hence, there is evidence of very strong business cycle effects, but there are differences in the findings for mandate and non-mandate 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 post-mandate estimates using just the 19 full-period states, the sign of the long-run 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 full-period estimates for the 19 full-period 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 full-period estimates for the 19 full-period 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

a. T-statistics 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 + a₁ j + a₂j² for j=0, 1, 2, ...L. Other variables are lagged the number of periods indicated.

c. Variable is amoving average of previous four quarters.

D. AVERAGE MONTHLY BENEFIT EQUATION

1. Determining the Final Specification

The selection of variables for the final average monthly benefit (AMB) equation was largely determined by the findings from the Basic and UP participation models (Exhibit 5.5). We began by including all of the variables that are included in either the final Basic or the final UP participation equations plus dummy variables for the existence and type of UP program (six-month, 12-month, and whether introduced as the result of requirements in FSA88). Except in the case of some program parameters, we then dropped all variables that had coefficients with t-statistics less than one in absolute value.

In interpreting the findings, it is important to keep the following in mind:

• The AMB variable is average monthly benefits for all cases in both the Basic and UP programs;
• The effects of explanatory variables on AMB may be of two types: effects on benefits received by existing AFDC families, and effects that work through changes in the composition of the AFDC caseload;
• The maximum monthly benefit variable in the AMB equation does not include the value of Food Stamps, whereas the same variable in the participation equations does. The reason for this is that the AMB equation itself refers to the AFDC benefits received only; and
• The sample period for this equation does not include the first two and the last four quarters of the period used to estimate the participation equations.

2. Year and Seasonal Effects

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

3. Demographic Variables

Population Growth and Aging

We did not include a variable for population growth and aging in the AMB equation.

Exhibit 5.5

a For the polynomial distributed lag (PDL) variables, the coefficient of the variable lagged j periods is a0 + a1 j + a2 j2 for j = 0, 1, 2, ... L. Other variables are lagged the number of periods indicated.

b. T-statistics in bold are at least 2.0 in absolute value.

c. All explanatory variables except quarter and year dummies are changes. Quarter and year dummies are equal to .25 in the quarters/years indicated so that coefficients can be interpreted as annualized rates of growth.

d Variables are moving averages of previous four quarters.

Vital Statistics

Only one of the vital statistics variables, out-of-wedlock births, appears in the final AMB specification and it has a significant, positive coefficient. More out-of-wedlock births among existing AFDC families would be expected to increase AMB, but families entering the caseload as the result of a first out-of-wedlock birth would presumably receive lower than average benefits.

Immigration

The IRCA legalizations variable appears in the final specification with a positive, but insignificant, coefficient. The positive coefficient seems at odds with the hypothesis that the large coefficients on this variable in the Basic participation models reflects child-only families; presumably such families would receive lower than average benefits unless the average number of children in such families is substantially larger than average.

4. Labor Market Variables

Unemployment Rate

A one percent increase in the unemployment rate, other things constant, reduces the AMB by an estimated 0.03 percent after 14 months. Equivalently, an increase in the unemployment rate from five to six percent reduces the AMB by 0.6. It seems likely that increases in unemployment, if anything, increase benefits among existing AFDC cases. The negative estimated effect presumably is the result of new cases that receive lower than average benefits -- due to fewer children and/or greater income from other sources.

Trade Employment per Capita

The long-run elasticity of AMB with respect to trade-employment is estimated to be -0.41. Presumably increases in trade employment reduce benefits for families that stay in the caseload, if they have any effect at all. Some families leave the caseload, however, and they may be receiving above or below average benefits. The negative long-run unemployment elasticity, discussed above, suggests that marginal families receive lower than average benefits, but the negative long-run elasticity for trade employment suggests the opposite.

5. AFDC Program Variables

Program Parameters

The variable with the most significant coefficient in the model is, not surprisingly, the current value of the maximum monthly benefit. The current coefficient is a highly significant 0.66, and the coefficients on the first and second lag are both negative, but not significant. The finding suggests that a one percent increase in MMB is immediately translated into an almost equal increase in the average benefits received by existing cases, but that the average benefit might fall as new families enter the caseload and receive lower than average benefits.

The estimated effects of a change in the average tax and benefit reduction rate (ATBRR) are somewhat puzzling and reminiscent of the puzzling findings for UP participation. The pattern of the coefficients would be consistent with the hypothesis that existing AFDC families initially lose benefits, but over time they either recover benefits by reducing other income or marginal families with low benefits leave the caseload -- but this conclusion may be too strong. After two quarters, any initial effects of a change in the ATBRR disappear.

A similar pattern appears in the coefficients of the current and lagged values of the AFDC earnings cut-off (ECO) relative to the gross income limit (GIL). They suggest that a reduction in the GIL, holding ECO constant (i.e., an increase in the ratio) initially reduces AMB, but after two quarters this negative effect is more than offset as, perhaps, some females reduce their other income, thereby increasing benefits, and marginal families with below average benefits leave the roles.

Federal Legislation

The estimated effects of OBRA81 on AMB depend on the coefficients on the OBRA81 variable, the 1981 and 1982 year dummies, and the program parameter coefficients, along with the magnitude of the changes in the parameters that resulted from OBRA81. The estimated impact of DEFRA84 is similarly complex. We discuss their effects in the context of the AMB simulations (Chapter 6).

The effect of the UP programs established in 1990.4 under the mandate of FSA88 depends on both the dummy for mandated programs and the dummies for six-month and twelve-month programs. About half of the 23 states affected introduced six-month programs. The combined coefficients for the 1990.4 dummy and the six-month dummy indicate these states experienced, if anything a small reduction in AMB as a result. The estimates suggest that states which introduced 12-month UP programs in 1990.4 experienced a reduction in AMB as a result, by 2.5 percent (based on the sum of the coefficients for the 1990.4 dummy and the 12-month dummy). This may be because UP families in six-month programs are only in the program in the months when their income from other sources is lowest.

1115 Waivers

The only waiver dummy that appears in the final AMB specification is the dummy for the family cap, and it has a significant coefficient that suggests that this type of restriction increases AMB by 5.5 percent. This is puzzling because we would expect such restrictions to, if anything, reduce benefits for families that would have been AFDC families anyway. It may be that the restrictions discourage small families, with below average benefits, from participating in AFDC, but it seems unlikely that the effect of such a change in the composition of the caseload would be so large. As with the finding in the Basic participation models, there are more likely explanations of this finding: other efforts to reduce caseloads in the three states that imposed family caps; migration of some AFDC families to other states; and chance.

6. Other Programs and Laws

Medicaid

We initially included the Medicaid expansion variable and interaction term in the AMB specification, just as in the final specification for the Basic model, but found that both terms had t-statistics well below one in absolute value. Hence, we dropped them in the final specification

SSI children

We also included the SSI child recipient variable in the initial AMB specification -- again because of the finding in the Basic participation model -- and subsequently dropped it from the specification because the t-statistic was below one in absolute value.

Unemployment Insurance

The log of the percent of unemployed persons who are insured has statistically significant, positive coefficients in the final specification. Given the positive relationship between the UI variable and participation in the Basic program found previously, a likely explanation is that unobserved factors such as administrative tightening of programs have common effects on both UI and AFDC.

Abortion Restrictions

The two abortion dummies have significant, and large, negative coefficients. They suggest that parental consent or notification laws and restrictions on Medicaid payments for abortion each reduce AMB by about 1.5 percent. Interpreting the Basic participation results at face value, these restrictions reduce the caseload by 0.2 and 0.3 percent, respectively, and reduce the number of child recipients by 0.3 and 0.5 percent, respectively. This implies that the number of children per AFDC family is reduced by 0.1 and 0.2 percent, respectively.⁽¹⁵⁾ We would expect this reduction to reduce AMB by a comparable percentage amount. A more plausible explanation of the large effects is one we suggested in the discussion of the participation findings: they may be due to other unobserved efforts in the states that adopted these restrictions to reduce fertility and AFDC participation.

SSA Allowance Rates

We included our measure of SSA's administrative tightening of disability requirements in 1977-78 in our initial AMB specification, but the t-statistic was less than one.

E. FURTHER DISCUSSION OF BUSINESS CYCLE ESTIMATES

In this section we examine the dynamics of the effects of changes in the unemployment rate on the caseload and compare our findings to findings reported by others. All of the findings reported in this section are based on Basic and UP caseload models in which we dropped the trade employment variable (Exhibit 5.6). This was done to simplify the analysis and presentation. The other studies we examine use only the unemployment rate as a business cycle variable, whereas in the models we have reported there are two important business cycle variables. Dropping trade employment increases the magnitude of the unemployment rate coefficients somewhat.

For comparison purposes, we consider the estimated effect of a one percentage point increase in the unemployment rate on the caseload, in percent. In the specification we use, the size of the effect depends on the initial unemployment rate. We assume the increase is from five percent to six percent.

1. The Dynamic Effects of an Unemployment Rate Increase

We consider below the dynamics of the effects of a one-percentage point increase in the unemployment rate (i.e., an increase from 5 percent to 6 percent--a 20 percent increase in the unemployment rate) on the caseload under the two hypothetical scenarios for the unemployment rate series. Under both scenarios, the unemployment rate is constant at 5.0 percent for at least 14 quarters before it increases by one percentage point, to 6.0 percent. Under the "temporary increase" scenario, the rate stays at 6.0 percent for one quarter then returns to 5.0 percent and remains there for at least the next 14 quarters. Under the "permanent increase" scenario, the rate stays at 6.0 percent for at least the next 14 quarters. Assume also that all other factors are constant during the relevant period.

Under both scenarios, the estimated initial effect of the one percentage point increase in the unemployment rate on the caseload is 0.7 percent for the Basic program and 3.7 percent for the UP caseload. Even if the unemployment rate increase is temporary, according to the estimates its effect on the caseload will be felt for the next three and one-half years (Exhibit 5.7). Both caseloads start to decline immediately.⁽¹⁶⁾ The decline is faster for the UP caseload than for the Basic caseload, but the UP caseload increased by much more in the first place. By the end of the second year after the temporary increase, both caseloads are above their original levels by about half the initial increase.

If the unemployment rate increase is permanent, the effects of the increase accumulate (Exhibit 5.8). One year after the change the Basic caseload is 2.8 percent higher than originally and the UP caseload is 14.5 percent higher. The increase continues, but at a decreasing rate. By the end of the second year the Basic caseload is 4.3 percent above its original level and the UP caseload is 20.4 percent higher. The caseloads continue to gradually increase, to 5.7 percent and 25.9 percent higher than their original levels after 3.5 years (14 quarters ).

Real recessions are different than either of these stylized scenarios. The increase in the unemployment rate is usually substantially greater than in this example. For instance, from 1989 to 1992 the unemployment rate increased by about two percentage points, and from 1979 to 1983 it increased by about four percentage points. Hence, the magnitude of a recession's effect may be two to four times as large as indicated here. Second, increases in the unemployment rate of substantial magnitude are seldom if ever as temporary as in the first scenario and do not increase and remain indefinitely constant at a higher level as in the second. Instead, they increase and decrease gradually over long periods. In both recessions in the sample period, they stayed close to their peak levels for about two years. This is well short of the 3.5 years in the permanent change scenario. At the same time, however, in each case the rate stayed above 6.0 percent for at least three years. In fact, for the seven years from 1980 to 1986 the average monthly unemployment rate was at or above 7.0 percent every year.

In summary, according to the estimates a recession can result in very large cumulative increases in both programs' caseloads, and higher caseloads are likely to remain above pre-recession levels for three or more years after the economy recovers.

2. Comparison of Business Cycle Effects to Findings in Previous Studies

The estimates we have obtained for business cycle effects are substantially stronger than those found in the literature. We compare the estimated effect of a one percentage point increase in the unemployment rate, from five to six percent, in our model to estimates obtained by others (Exhibit 5.9). For the Basic program, we also report our results when the vital statistics variables are dropped from the specification because variation in these variables may partly be due to business cycles.

We estimate that the specified increase in the unemployment rate increases the Basic caseload by 5.7 percent after 14 quarters. This increases somewhat when the vital statistic variables are omitted -- to 5.9 percent. The largest finding from other studies for the same unemployment rate change is from Cromwell, et al. (1986), a 1.8 percent increase after just three quarters. The difference is in substantial part due to the use of a longer lag length in our specification: our estimate of the effect after three quarters is much more comparable -- 2.4 percent. We estimate that the specified increase in the unemployment rate increases the UP caseload by about 26 percent after 14 quarters. This estimate is almost identical to the estimate reported by Cromwell et al. after just three quarters. By comparison, we estimate that the increase in the UP caseload is only 12.3 percent after three quarters.

Exhibit 5.6

a. Expected participation variable is based on national age-specific participation for 1990 and estimated population of the state by age in the quarter.

b. T-statistics 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 used is .41, computed as [(T - K)/T].5, where T is the number of quarters (60) and K is the number of explanatory variables (50).

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. For the polynomial distributed lag (PDL) variables, the coefficient of the variable lagged j periods is a0 + a1 j + a2 j2 for j = 0, 1, 2, ... L. Other variables are lagged the number of periods indicated.

d. Indicates whether vital statistics variables are included (with v.o.) or not (without v.o.). The vital statistics variables are ln(out-of-wedlock births) and ln(marriages).

e. Variables are moving averages of previous four quarters.

f. This variable is the change in the state's SSDI initial allowance rate from 1977 to 1978 times the 1979 year dummy. Special dummies for three states were included due to missing initial allowance data.

g. "Medicaid expansion" is the share of children in the state covered under the Medicaid expansions that began in 1988. "Share participating" is the share of children in the state who were in AFDC families in the year before the expansions began (1987 -- average monthly child recipients divided by population under 19).

Exhibit 5.7

Percent increase in the Caseload from a Temporary One Percentage Point Increase in the Unemployment Rate *

(Based on caseload models excluding trade employment variable.)

*Assumes unemployment rate increases from five percent to six percent for one quarter, then returns to its previous level. For the jth lag, the percent increase is calculated as b_jln(.06/.05), where b_j is the coefficient of the jth lag of the log of the unemployment rate.

Exhibit 5.8

Percent increase in the Caseload from a Permanent One Percentage Point Increase in the Unemployment Rate

(Based on models without trade employment)

*Assumes unemployment rate increases from five percent to six percent and remains at six percent for the next 14 quarters. For the jth lag, the percent increase is calculated as S ^j_i=0 b_jln(.06/.05)

a Estimate for total based on Basic and UP estimates, assuming 5 percent of total caseload is UP.

b Based on data for 44 states, for AFDC Medicaid enrollees. Estimate for Basic is based on results for states without an UP program; estimate for total is based on finding for states with an UP program; and UP estimate is based on the Basic and Total findings assuming that five percent of the caseload is UP.

c Based on specifications without trade employment per capita; inclusion of the later reduces the estimated effect of the unemployment rate, but increases the total effect of business cycles. Basic estimates use data for 50 states and the District of Columbia; UP estimates use data for 19 states with UP programs for the entire sample period. Vital statistics were only included in the Basic equation because of insignificance in the UP equation.

d Based on sample of nine years and an average of 27 states each year.

F. FURTHER DISCUSSION OF PROGRAM PARAMETER EFFECTS

In this section we compare our findings for the program parameters to findings from other studies. As with comparisons of business cycle effects across studies, these comparisons are problematic because of specification differences.

Our estimates of the effects of an increase in the maximum monthly benefit are among the highest found, but one study reports a much larger effect (Exhibit 5.10). We estimate that a one percent increase in this variable increases the Basic caseload by 2.7 percent and the UP caseload by 2.6 percent.⁽¹⁷⁾ Our estimates for the Basic program are larger than those reported by Moffit (1986) or CBO (1993), but Shroder (1995) finds a much larger effect than we do for the combined programs: a 16.7 percent caseload increase. Shroder also uses a pooled state time-series methodology, but with several important differences. One major difference is that he uses instruments for the maximum monthly benefit variable, on the grounds that growth in recipients is likely to cause states to reduce benefit levels. When he does not use the instruments, the estimated effect drops by more than two thirds, to 5.1 percent -- still almost twice as large as our own.

Exhibit 5.10

^a Basic model includes vital statistics variables; see Exhibit 5.1. Total estimates assume 95 percent of caseloads is in the Basic program.

^b Estimate changes may be complete only after several quarters.

^c Assumes need standard is identical to AFDC earnings cut off. The change in the gross income limit described is the change that was implemented under DEFRA84.

^d Results reported are for random effects estimator. Results for fixed state effects estimator are smaller in magnitude and not statistically significant. Means for the middle year of the sample period (1975) were used in the calculations.

^e Based on fixed effects specification with instrumental variables for the maximum monthly benefit variable. Estimate without instruments is about one-third as large.

^f Changes calculated at sample means.

We found only one other study that includes an average tax and benefit reduction rate in the specification, Moffitt (1986). Moffit estimates that a 10 percentage point increase in the rate reduces participation in the Basic program by 5.5 percent, compared to our finding of 1.5 percent.

While the reasons that we obtain a smaller effect for the MMB than Shroder and a smaller effect for the ATBRR than Moffitt are unclear, one possible explanation is that we include three benefit variables in our model compared to one for Shroder (MMB) and two for Moffitt (MMB and ATBRR). Neither study, nor any other we have seen, has included a variable for the gross income limit. The sample periods used by both Shroder and Moffitt include years when the GIL changed (twice in Shroder's sample), and it could be that their coefficients for other program parameters are biased away from zero because of this omission. We have not, however, tried to confirm this conjecture.⁽¹⁸⁾

References for Part 2 of Chapter 5

12. The UP caseload series obtained from ACF reported zero UP cases for the District of Columbia in 1992.2 and 1992.3 and for Mississippi in 1993.4.

13. There are eight states in the sample in addition to the 19 full-period states and the 22 mandate states. These states had UP programs during part, but not all, of the pre-mandate subperiod. Recall that Mississippi and the District of Columbia were dropped from the sample because of evident data errors that could not be corrected. See Chapter 4.

14. The full-period estimates (Column 1) differ from the results reported previously in both specification and estimation methodology. We inadvertently did not include the ratio of the ECO to the GIL in this model. Its exclusion may account for differences in the Park and WLS results for the ATBRR, but we have not had an opportunity to confirm this.

15. The change in the log of children per family (case) equals the change in the log of children minus the change in the log of families. Because small changes in logarithms are approximately equal to percentage changes in the variable itself, the percent change in children per AFDC family is approximately the difference between the percent change in children and the percent change in families.

16. The graph suggests that the effect on both caseloads will continue to be positive for some time after the 14-month period ends; in fact, the effect for the UP caseload appears to be increasing! We specified only a 14-quarter distributed lag because in models in which we included the trade-employment variable the distributed lag coefficients for the unemployment rate became slightly negative in the 15th quarter when we specified long maximum lag lengths. We did not try longer lag lengths without the trade employment variable.

17. The overall figure assumes that five percent of the caseload is in the UP program.

18. One piece of information we have is, at least, consistent with the conjecture. As previously mentioned, we inadvertently omitted the GIL variable from the UP specification when we re-estimated the full-period model using WLS (Exhibit 5.4). Both the MMB and ATBRR coefficients in these findings are much larger than those in the Parks estimates (Exhibit 5.3). Of course, other model and estimation differences could explain these differences. In the WLS results, the long-run MMB elasticity implies that a 10 percent increase results in an UP caseload increase of 4.2 percent -- close to Shroder's 5.1 percent finding when he does not correct for simultaneity, but well short of the 16.7 percent figure he obtains when he makes the correction. The estimated long-run ATBRR effect implies that a 10 percentage point increase in that variable reduces the caseload by 1.6 percent -- in line with our finding for the Basic program (1.5 percent), but well below Moffit's estimate (5.5 percent) for the Basic program.