# Determinants of AFDC Caseload Growth. 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

 Regression Results for Basic and UP Models without Trade Employment Variables Sample: 51 states, 1979.4 - 1994.3 Dependent Variable is change in ln(participation/expected participation) a Coefficients T-statistics b Explanatory Caseload Caseload Variables c Basic UP Basic UP w/ v.s.d w/o v.s.d w/o v.s.d w/ v.s.d w/o v.s.d w/o v.s.d ln(unemployment rate) 10xa0 0.037 0.038 0.205 16.7 18.0 11.2 (PDL: L = 14) 100xa1 -0.003 -0.003 -0.026 4.4 4.8 4.3 1000xa2 0.000 0.000 0.001 2.0 2.1 0.3 long-run elasticity 0.313 0.324 1.421 ln(maximum monthly benefit) current 0.083 0.086 0.293 5.7 6.5 2.3 1st lag 0.136 0.136 0.063 8.8 9.7 0.5 2nd lag 0.033 0.032 -0.027 2.2 2.4 0.2 long-run elasticity 0.252 0.255 0.328 average tax and current -0.024 -0.028 0.167 2.0 2.6 1.4 benefit reduction rate 1st lag -0.066 -0.068 -0.150 5.1 6.0 1.2 2nd lag -0.029 -0.030 -0.108 2.4 2.8 1.0 long-run effect -0.119 -0.127 -0.090 AFDC earnings cut off current -0.049 -0.050 -0.029 9.3 10.3 0.5 relative to gross income limit 1st lag -0.035 -0.036 -0.054 6.3 7.0 1.0 2nd lag -0.011 -0.010 -0.032 2.1 2.0 0.9 long-run effect -0.095 -0.095 -0.115 OBRA81 current -0.044 -0.043 -0.075 6.8 7.6 1.3 1st lag -0.030 -0.029 0.013 4.2 4.7 0.2 2nd lag -0.013 -0.014 2.0 2.5 long-run effect -0.087 -0.086 -0.063 DEFRA84 current -0.008 -0.009 -0.009 2.1 2.8 0.3 family cap 1st lag -0.026 -0.025 3.3 3.4 IRCA immigrants per 100 1st lag 0.063 0.057 6.0 6.0 Medicaid expansiong current 0.131 0.128 2.2 2.3 Med. exp. x share participatingg current -0.888 -0.855 1.7 1.8 ln(out-of-wedlock births)e 0.097 4.0 ln(marriages)e -0.129 4.7 ln(SSI child beneficiaries) current 0.009 0.009 2.2 2.5 ln(% insured unemployed) 1st lag 0.017 0.018 5.4 5.6 abortion: parental consent/notice 1st lag -0.003 -0.003 1.7 2.1 Medicaid restricted 1st lag -0.002 -0.002 1.4 0.2 SSDI initial allowance rate f -0.064 -0.057 2.9 2.6 1979 dummies for: Alaska -0.011 -0.023 0.1 0.2 Hawaii 0.055 0.042 0.8 0.6 D.C. -0.042 -0.048 1.3 1.6 Seasonal Dummies Spring -0.015 -0.014 -0.312 2.7 3.0 7.8 Summer -0.029 -0.027 -0.503 5.0 5.4 11.4 Fall 0.009 0.010 -0.239 1.7 2.3 5.8 Calendar Year Dummies 1979 0.016 0.028 0.721 1.1 2.1 8.0 1980 0.028 0.034 0.624 2.8 3.7 8.6 1981 -0.020 -0.019 0.479 1.5 1.6 5.1 1982 -0.016 -0.014 0.201 1.4 1.4 2.6 1983 0.007 0.009 0.250 0.7 1.0 3.5 1984 0.009 0.014 0.217 0.9 1.5 3.0 1985 0.037 0.046 0.292 3.7 5.3 4.1 1986 0.047 0.051 0.295 4.8 5.8 4.1 1987 0.023 0.030 0.284 2.4 3.5 4.1 1988 0.039 0.045 0.330 4.1 5.2 4.7 1989 0.049 0.055 0.362 4.8 6.2 5.1 1990 0.060 0.064 0.371 6.0 7.4 5.2 1991 0.051 0.058 0.232 5.1 6.7 3.3 1992 0.017 0.017 0.168 1.7 2.0 2.4 1993 0.008 0.012 0.224 0.8 1.3 3.1 1994 -0.009 -0.009 0.185 0.6 0.7 1.7

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 *

*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 bjln(.06/.05), where bj 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 ji=0 bjln(.06/.05)

 Exhibit 5.9 Estimated Effect of a Permanent One Point Percentage Point Increase in the Unemployment Rate on AFDC Caseloads Effect on Caseload after Number of Quarters Indicated Study Type Period Basic After UP After Total After CBO (1993) a national time-series quarterly 1973-91 1.7% 4 qtrs. 9.7% 6 qtrs. 2.1% 6 qtrs. Cromwell et. al. (1986)b pooled state time-series quarterly 1976-82 1.8% 3 qtrs. 25.8% 3 qtrs. 3.0% 3 qtrs. Moffit (1986) d pooled state time-series biennial 1967-83 0.0% current year n.a. n.a. n.a. n.a. Shroder (1995) pooled state time-series annual 1982-88 n.a. n.a. n.a. n.a. 3.50% current year Lewin, with vital stats. C pooled state time-series quarterly 1979-94 2.4% 5.7% 3 qtrs. 14 qtrs. 12.3% 25.9% 3 qtrs. 14 qtrs. 2.9% 6.7% 3 qtrs. 14 qtrs. Lewin, without vital stats. C pooled state time-series quarterly 1979-94 2.4% 5.9% 3 qtrs. 14 qtrs. 12.3% 25.9% 3 qtrs. 14 qtrs. 2.9% 6.9% 3 qtrs. 14 qtrs.

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.