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 onepercentage point increase in the unemployment rate (i.e., an increase from 5 percent to 6 percenta 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 onehalf 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 prerecession 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
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 Tstatistics ^{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) 10xa_{0} 0.037 0.038 0.205 16.7 18.0 11.2 (PDL: L = 14) 100xa_{1} 0.003 0.003 0.026 4.4 4.8 4.3 1000xa_{2} 0.000 0.000 0.001 2.0 2.1 0.3 longrun 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 longrun 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 longrun 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 longrun 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 longrun 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 expansion^{g} current 0.131 0.128 2.2 2.3 Med. exp. x share participating^{g} current 0.888 0.855 1.7 1.8 ln(outofwedlock 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 agespecific participation for 1990 and estimated population of the state by age in the quarter.
b. Tstatistics in bold are at least 2.0 in absolute value. These statistics were reduced from those calculated by SAS to make a correction for degrees of freedom that is not made by the procedure used (TSCSREG). The reduction factor 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(outofwedlock 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_{j}ln(.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_{j}ln(.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 timeseries quarterly 197391 1.7% 4 qtrs. 9.7% 6 qtrs. 2.1% 6 qtrs. Cromwell et. al. (1986)^{}^{b} pooled state timeseries quarterly 197682 1.8% 3 qtrs. 25.8% 3 qtrs. 3.0% 3 qtrs. Moffit (1986) ^{d} pooled state timeseries biennial 196783 0.0% current year n.a. n.a. n.a. n.a. Shroder (1995) pooled state timeseries annual 198288 n.a. n.a. n.a. n.a. 3.50% current year Lewin, with vital stats. ^{C} pooled state timeseries quarterly 197994 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 timeseries quarterly 197994 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.
