Determinants of AFDC Caseload Growth. 7. Weighted Least Squares Results

07/01/1997

We conclude this section with a comparison of the Basic caseload results from the Parks method (Column 1 of both Exhibits 5.1 and 5.2), to estimates of the same model using a weighted least squares (WLS) method, with weights proportional to population size (Column 2 of Exhibit 5.3). Given the Parks specification, the latter method is presumably less efficient (higher standard errors) than the former. If the model specification is correct, both methods produce unbiased estimates. If the correct specification varies across states in a manner not captured by the specified model, then the coefficients could be substantially different. In that case the WLS coefficients would more accurately reflect the national caseload experience.

In general, the results from the two methods are very comparable. The long-run unemployment elasticity is 25 percent lower in the WLS results, but the trade employment elasticity is 13 percent higher. The MMB elasticity is slightly higher, and the ATBRR elasticity is almost unchanged. The change in the coefficient of the ratio of the ECO to the GIL is more substantial; it drops to about 60 percent of the value from the Parks model. The family cap coefficient changes very little. The IRCA immigrant coefficient increases somewhat, but the standard error is much larger so the t-statistic falls. The coefficients of the Medicaid expansion variable and its interaction with the share of children participating in AFDC both increase substantially in magnitude, as do their t-statistics, but these are offsetting changes when considering the actual effect on a specific state; the effect is negative if the share of children participating in AFDC is greater than 14.3 percent, compared to 14.6 in the Parks results. The magnitudes of the coefficients on both vital statistics variables are substantially reduced and no longer significant. The coefficients of the SSI child beneficiary variable, the percent insured unemployed variable, and the two abortion variables change very little. The coefficient of the SSDI initial allowance rate changes sign, however, and is essentially zero.

Exhibit 5.2

Comparison of Basic Caseload Results
under Alternative Estimation Methodologies
Dependent Variable is change in ln(participation/expected participation) a
51 states, 1979.4 - 1994.3
Explanatory   Parks Weighted
Variablesb   Model Least Squares
ln(unemployment rate) 10xa0 0.250 0.119
(PDL: L = 14)   (9.35) (4.30)
  100xa1 -0.343 -0.054
    (-3.73) (-1.77)
  1000xa2 0.148 0.002
    (2.36) (1.01)
  long-run elasticity 0.165 0.123
ln(trade employment per cap.) 10xa0 -0.650 -2.035
(PDL: L = 10)   (-3.88) (-8.62)
  100xa1 -2.427 4.278
    (-7.46) (4.26)
  1000xa2 2.721 -3.232
    (6.62) (-3.59)
  long-run elasticity -1.002 -1.129
ln(maximum monthly benefit) current 0.080 0.098
    (4.49) (5.50)
  1st lag 0.151 0.175
    (8.15) (8.81)
  2nd lag 0.039 0.029
    (2.16) (1.66)
  long-run elasticity 0.270 0.302
average tax and current -0.033 -0.019
benefit reduction rate   (-2.35) (-1.36)
  1st lag -0.080 -0.082
    (-5.45) (-5.53)
  2nd lag -0.041 -0.050
    (-2.83) (-3.78)
  long-run effect -0.153 -0.151
AFDC earnings cut off current -0.051 -0.036
relative to gross income limit   (-8.84) (-5.12)
  1st lag -0.038 -0.018
    (-6.22) (-2.52)
  2nd lag -0.011 -0.002
    (-1.85) (-0.33)
  long-run effect -0.100 -0.057
OBRA81 current -0.039 -0.041
    (-5.29) (-6.54)
  1st lag -0.02 -0.030
    (-2.54) (-4.43)
  2nd lag -0.01 -0.011
    (-1.39) (-1.76)
  long-run effect -0.069 -0.082
DEFRA84 current -0.006 -0.005
    (-1.29) (-2.10)
family cap 1st lag -0.023 -0.021
    (-3.21) (-2.89)
IRCA immigrants per 100c 1st lag 0.05 0.073
    (5.04) (1.77)
Medicaid expansione current 0.179 0.475
    (2.46) (5.99)
Med. exp. x share participatinge current -1.23 -3.324
    (-2.06) (-5.56)
ln(out-of-wedlock births)c   .101 0.053
    (3.84) (1.60)
ln(marriages)c   -0.097 -0.017
    (-3.35) (-0.51)
ln(SSI child beneficiaries) current 0.009 0.011
    (2.31) (2.26)
ln(% insured unemployed) 1st lag 0.013 0.011
    (3.67) (2.50)
abortion: parental consent/notice 1st lag -0.002 0.002
    (-0.99) (1.08)
Medicaid restricted 1st lag -0.003 -0.002
    (-1.79) (-1.06)
SSDI initial allowance rated   -0.053 0.001
    (-2.08) (0.03)
1979 dummies for: Alaska 0.018 0.040
    (0.11) (0.27)
  Hawaii 0.06 -0.005
    (0.68) (-0.07)
  D.C. -0.057 -0.060
    (-1.33) (-1.35)
Seasonal Dummies Spring -0.004 -1.00E-04
    (-1.36) (-0.02)
  Summer -0.01 -0.003
    (7.10) (-0.57)
  Fall 0.053 0.045
    (0.64) (8.83)
Calendar Year Dummies 1979 0.01 0.075
    (0.64) (5.29)
  1980 0.009 0.059
    (0.78) (5.84)
  1981 -0.04 -0.002
    (-2.88) (-0.18)
  1982 -0.022 -0.018
    (-1.86) (-2.15)
  1983 0.004 -0.005
    (0.35) (-0.70)
  1984 0.004 0.001
    (0.35) (0.10)
  1985 0.034 0.034
    (3.07) (4.48)
  1986 0.034 0.036
    (3.22) (5.24)
  1987 0.016 0.014
    (1.53) (2.13)
  1988 0.031 0.032
    (2.89) (4.84)
  1989 0.042 0.043
    (3.75) (5.89)
  1990 0.048 0.058
    (4.50) (8.18)
  1991 0.038 0.043
    (3.50) (6.22)
  1992 0.005 0.019
    (0.45) (2.82)
  1993 -0.006 0.001
    (-0.56) (0.21)
  1994 -0.018 -0.018
    (-1.15) (-2.26)
Autocorrelation coefficient 1st Lag f 0.345
      (19.76)

Numbers in parentheses are t-statistics.

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. 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.

c Variables are moving averages of previous four quarters.

d. 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.

e. "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).

f. Autocorrelation coefficients vary across states in this specification.

Except in the first three years of the sample, the year coefficients change little. The two exceptions are for the first two years, in which they are much larger in the WLS results. We do not understand the reason for the changes in the initial years. Note, however, that the first two of these years are the only two that provide information about the effect of the SSDI allowance rate change, so the change in the year coefficients may be related to the change in the SSDI coefficient.