annual average over states benefit for a family of two one adult and one child and the benefit reduction rate over the time period from 1967 to 2015. The figure shows the
fall in real benefits during the 1970s and 1980s. The benefit reduction rate is increas- ing during the 1970s and 1980s and is almost constant at about 0.30. Although not
shown, benefits are computed for a second child and a third or higher birth order child. Given information on the number of children, the state of residence, the year, and
the wage offer, these parameters are used to compute the family’s AFDC grant.
IV. Results
Table 4 presents the estimation results for two different models.
9
The two specifications help provide some understanding of the role children play in these
decisions. In “Model 2,” the utility of each choice depends on age, education, race, and the number of children younger than 18 years old. “Model 1” omits the number
of children from the nonpecuniary utility function. However, in all cases the num- ber of children is assumed to be known and determines eligibility for AFDC, the level
of benefits, and the share of family income. For each specification, the utility function parameters are found in Panel A and other parameters are found in Panel B.
The first five rows of Panel A in Table 4 are the estimates the parameters associated with the nonpecuniary utility of being married and working, the second five rows are
the estimates of the nonpecuniary utility of being single and working and so on. The table entries measure the marginal impact of the observed characteristic on the utility
in the state under consideration relative to the base state single, not working, no AFDC. For example, the fact that the coefficient on “children” for choice 2 in
Model 2 is 0.788 means that having an additional child while married and not work- ing increases utility by 0.788 relative to the base state of single, not working and not
participating in AFDC. Because income consumption is assumed to enter the model in log form and the coefficient on log income is fixed at one, the coefficients are in
terms of log income.
Several conclusions can be drawn from Table 4. First, the estimates imply that women are forward-looking see Panel B. The specific point estimate of the discount
factor depends on the model specification with estimates ranging from 0.81 to 0.84. These estimates are similar to Keane and Wolpin’s 1997 estimate of 0.78 for a
model of career choice by young men. They are important because, as discussed in the introduction, the degree to which women are forward-looking affects the size
and existence of the behavioral response to the policy change: If recipients are not forward-looking, there will be no behavioral response to a time limit.
The estimates in Panel A of Table 4 show a number of consistent results: 1 blacks receive significantly less utility in the married choices than whites; 2 education is
positively associated with each choice except for receiving AFDC while not working; and 3 for the model that includes the number of children in the utility function, the
nonpecuniary utility of children is highest for married women who do not work and
9. A third model that excluded all person-specific characteristics from the utility function was also esti- mated. The results were similar to the other models.
The Journal of Human Resources 44
Swann 45
Table 4 Panel A: Utility Function Parameters
Estimates of the Structural Model Model 1
Model 2 Standard Standard
Estimate Error
Estimate Error
Choice 2: Married, Not Working, No AFDC Constant
−7.727 0.481
−9.098 0.448
Age −0.010
0.008 −0.029
0.008 Education
0.172 0.034
0.189 0.034
Black −1.610
0.181 −1.730
0.188 Children
— —
0.788 0.062
Choice 3: Single, Working, No AFDC Constant
−13.825 0.592
−13.379 0.585
Age 0.005
0.007 −0.004
0.006 Education
0.238 0.037
0.216 0.035
Black −0.810
0.116 −0.783
0.108 Children
— —
0.246 0.040
Choice 4: Married, Working, No AFDC Constant
−13.140 0.581
−13.554 0.596
Age −0.006
0.009 −0.006
0.007 Education
0.259 0.037
0.240 0.036
Black −1.167
0.146 −1.138
0.138 Children
— —
0.341 0.041
Choice 5: Single, not working, AFDC Constant
−8.568 0.635
−9.770 0.612
Age −0.141
0.017 −0.135
0.017 Education
−0.083 0.040
−0.032 0.037
Black −0.295
0.188 −0.575
0.184 Children
— —
0.762 0.073
Choice 6: Single, Working, AFDC Constant
−13.799 1.146
−14.553 1.099
Age −0.227
0.027 −0.210
0.027 Education
0.159 0.073
0.179 0.068
Black −0.845
0.271 −1.061
0.257 Children
— —
0.763 0.103
State Variables AFDC tenure
1.724 0.143
1.470 0.134
Marriage tenure 0.233
0.059 0.260
0.055 Work tenure
1.299 0.100
1.141 0.098
for single women who receive AFDC. This last result occurs in spite of the fact that the effect of family size on benefits is incorporated in the model and may occur
because the value of AFDC used in the paper includes only the cash benefit and excludes the value of food stamps and Medicaid.
The Journal of Human Resources 46
Table 4 Panel B: Wages Equations and Other Parameters
Estimates of the Structural Model Model 1
Model 2 Standard Standard
Estimate Error
Estimate Error
Own wage equation Constant
0.103 0.015
−0.291 0.121
Age 0.005
0.0004 0.005
0.0004 Education
0.103 0.001
0.108 0.084
Black −0.067
0.004 −0.067
0.004 South
−0.153 0.004
−0.153 0.004
Work tenure 0.119
0.002 0.120
0.002 AFDC tenure
−0.065 0.002
−0.067 0.002
Variance 0.469
0.001 0.469
0.001 Husband’s wage equation
Constant 1.444
0.015 1.442
0.015 Education
0.048 0.001
0.048 0.001
Black −0.186
0.005 −0.187
0.005 South
−0.112 0.004
−0.111 0.004
Work tenure 0.033
0.002 0.033
0.002 Work tenure squared
−0.072 0.007
−0.070 0.007
AFDC tenure −0.048
0.002 −0.048
0.003 Variance
0.486 0.001
0.486 0.001
Marriage probability Constant
−0.383 0.116
−0.291 0.121
Age −0.026
0.003 −0.027
0.003 Education
0.014 0.008
0.011 0.008
Black −0.463
0.030 −0.465
0.030 AFDC tenure
−0.007 0.016
−0.013 0.016
Other variables β
0.814 0.014
0.835 0.013
τ 2.786
0.208 2.560
0.207 Likelihood
−38,251.63 −38,080.79
The coefficients on the tenure variables are all positive and statistically significant. For AFDC, this effect ranges in magnitude from 1.47 to 1.72. The consequence of this
positive effect is that, holding all else constant, women become increasingly unlikely to leave AFDC as they accumulate tenure on the program. There are a number of dif-
ferent interpretations of this duration effect. It may represent a woman’s changing cir- cumstances as she learns the rules of the welfare system, or it may serve as a proxy
for changing preferences if the stigma of receiving cash assistance diminishes with exposure to the program. There are similar though smaller effects for marriage and
employment duration.
It is well known, however, that duration dependence may also be the result of uncon- trolled unobserved heterogeneity for example, Heckman and Singer 1984; Blank
1989. Because the model does not control for unobserved differences across women, it is not possible to separate these two effects. If the model were extended to allow for
unobserved preferences for work, welfare, and marriage, one would expect that some of the persistence in choices across a person’s lifetime that is now attributed to duration
would be attributed to these unobserved preferences. Consequently, the observed dura- tion effect would be smaller if unobserved differences were allowed and significant.
The wage equation parameters are quite consistent across the two specifications. Education and work experience each increase wages, and being black andor living in
the south reduces wages. The coefficients in the husband’s wage equation show the effect of the woman’s characteristics on her potential husband’s wages. Again edu-
cation and experience have positive effects on wages though experience is qua- dratic, while being black lowers wages. Lifetime AFDC tenure reduces both own and
husband’s wages in each model.
Finally, the marriage offer parameters show that race is the most significant factor in determining the probability of a marriage offer. For example, the model predicts
that a 20 year old white woman with a high school education and no past AFDC receipt has a 23 percent chance of receiving a marriage offer while a black woman
with the same characteristics has an 11.4 percent chance. If this same black woman has five years of AFDC receipt, the probability falls to 10.7 percent.
V. Model Fit
