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
Regression Results for Unemployed Parent Models | |||||||
Sample: 19 states, 1979.4 - 1994.3 | |||||||
Dependent Variable is change in ln(participation/expected participation) ^{a} | |||||||
Coefficients | T-statistics ^{b} | ||||||
Explanatory | Child | Child | |||||
Variables^{c} | lag^{a} | Caseload | Recipients | Recipients | Caseload | Recipients | Recipients |
ln(unemployment rate) | a_{0} | 0.180 | 0.171 | 0.177 | 9.0 | 9.0 | 9.0 |
(PDL: L = 14)^{a} | 10xa_{1} | -0.241 | -0.199 | -0.267 | -3.8 | -3.3 | -4.3 |
100xa_{2} | 0.109 | 0.076 | 0.128 | 2.5 | 1.8 | 3.0 | |
long-run elasticity | 1.283 | 1.244 | 1.148 | ||||
ln(trade employment per cap.) | a_{0} | -0.920 | -0.778 | -0.838 | -5.9 | -5.1 | -5.5 |
(PDL: L = 6)^{a} | 10xa_{1} | 2.083 | 1.740 | 1.652 | 5.2 | 4.4 | 4.2 |
long-run elasticity | -2.068 | -1.794 | -2.397 | ||||
ln(maximum monthly benefit) | current | 0.258 | 0.091 | 0.283 | 1.9 | 0.7 | 2.1 |
1st lag | 0.054 | 0.125 | 0.089 | 0.4 | 0.9 | 0.6 | |
2nd lag | -0.053 | -0.055 | -0.028 | -0.4 | -0.4 | -0.2 | |
long-run elasticity | 0.258 | 0.161 | 0.344 | ||||
average tax and benefit | current | 0.196 | 0.226 | 0.161 | 1.5 | 1.8 | 1.2 |
reduction rate | 1st lag | -0.109 | -0.160 | -0.074 | -0.8 | -1.2 | -0.5 |
2nd lag | -0.083 | -0.145 | -0.051 | -0.7 | -1.3 | -0.4 | |
long-run effect | 0.004 | -0.080 | 0.036 | ||||
AFDC earnings cut off | current | -0.015 | 0.011 | -0.027 | -0.3 | 0.2 | -0.5 |
relative to gross income limit | 1st lag | -0.048 | -0.046 | -0.066 | -0.9 | -0.9 | -1.2 |
2nd lag | -0.030 | -0.051 | -0.020 | -0.9 | -1.5 | -0.6 | |
long-run effect | -0.093 | -0.086 | -0.113 | ||||
OBRA81 | current | -0.091 | -0.045 | -0.083 | -1.5 | -0.8 | -1.5 |
1st lag | -0.009 | 0.024 | 0.014 | -0.1 | 0.4 | 0.2 | |
long-run effect | -0.100 | -0.020 | -0.069 | ||||
DEFRA84 | current | -0.004 | 0.008 | 0.007 | -0.1 | 0.3 | 0.3 |
Seasonal Dummies | Spring | -0.218 | -0.249 | -0.200 | -4.9 | -5.9 | -4.8 |
Summer | -0.340 | -0.341 | -0.317 | -6.4 | -6.7 | -6.4 | |
Fall | -0.130 | -0.145 | -0.117 | -2.8 | -3.2 | -2.7 | |
Calendar Year Dummies | 1979 | 0.576 | 0.687 | 0.566 | 6.2 | 7.6 | 6.4 |
1980 | 0.477 | 0.482 | 0.476 | 6.3 | 6.5 | 6.7 | |
1981 | 0.416 | 0.291 | 0.382 | 4.3 | 3.1 | 4.2 | |
1982 | 0.114 | 0.151 | 0.121 | 1.4 | 1.9 | 1.6 | |
1983 | 0.269 | 0.274 | 0.250 | 3.7 | 3.9 | 3.7 | |
1984 | 0.200 | 0.204 | 0.210 | 2.6 | 2.7 | 2.8 | |
1985 | 0.232 | 0.224 | 0.200 | 3.1 | 3.0 | 2.8 | |
1986 | 0.239 | 0.271 | 0.234 | 3.2 | 3.8 | 3.3 | |
1987 | 0.239 | 0.217 | 0.210 | 3.3 | 3.1 | 3.1 | |
1988 | 0.284 | 0.279 | 0.247 | 3.9 | 3.9 | 3.6 | |
1989 | 0.279 | 0.300 | 0.263 | 3.7 | 4.1 | 3.7 | |
1990 | 0.259 | 0.296 | 0.241 | 3.5 | 4.1 | 3.5 | |
1991 | 0.118 | 0.118 | 0.112 | 1.6 | 1.6 | 1.6 | |
1992 | 0.086 | 0.105 | 0.091 | 1.2 | 1.5 | 1.3 | |
1993 | 0.170 | 0.196 | 0.170 | 2.2 | 2.7 | 2.4 | |
1994 | 0.141 | 0.106 | 0.179 | 1.3 | 1.0 | 1.7 |
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} + a_{1} j + a_{2}j^{2} for j=0, 1, 2, ...L. Other variables are lagged the number of periods indicated.
d. Variables are moving average of previous four quarters.