In the absence of becoming eligible, these individuals would have private coverage given by
26
NEWPRNESEL = 1
N
new
Pr priv_nelig
i
= 1| newelig
i
= 1
new=1
∑
= 1
N
new new=1
∑
Pr priv_nelig
i
= 1, newelig
i
= 1 Prnewelig
i
= 1 =
1 N
new
Pr X
i
ˆ␥
ne
+ u
nei
0, −Z
1i
ˆ␦ e
i
≤ −Z
0i
ˆ␦ Pr
−Z
1i
ˆ␦ e
i
≤ −Z
0i
ˆ␦
new=1
∑
= 1
N
new new=1
∑
⌽
2
X
i
ˆ␥
ne
, −Z
0i
ˆ␦, ˆ
23
− ⌽
2
X
i
ˆ␥
ne
, −Z
1i
ˆ␦, ˆ
24
⌽
1
−Z
0i
ˆ␦ − ⌽
1
−Z
1i
ˆ␦ ⎡
⎣⎢ ⎤
⎦⎥ .
Again note that one could also estimate NEWPRNESEL from the data. Thus crowd- out for the newly eligible while accounting for selection is given by the difference
NEWPRESEL minus NEWPRNESEL, or Equation 25 minus Equation 26. As before,
we can calculate the analogous effects including crowd- out for the currently eligible in the whole sample or in different demographic groups when we allow for selection;
the expressions for these calculations are available in the online Appendix.
VI. Comparison to Aakvik, Heckman, and Vytlacil 2005
Evaluating the effi cacy of a Norwegian vocational training program, AHV introduces an econometric model for estimating different policy parameters
the average treatment effect, the marginal treatment effect, and the average treat- ment effect for the treated when the outcome is discrete and the treatment effect is
heterogeneous. Its equation for whether an individual enters training is analogous to our Medicaid eligibility Equation 13, while its employment outcome is analogous to
our private insurance takeup Equations 9 and 10. Specifi cally, its likelihood function consists of employed trainees contributing a term for the joint probability of taking
training and being employed, nonemployed trainees contributing a term for the joint probability of taking training and not being employed, employed nontrainees con-
tributing a term for the joint probability of not participating in training and being employed, and nonemployed nontrainees contributing a term for the joint probability
of not participating in training and not being employed. It estimates the model by maximum likelihood assuming normally distributed error terms but one could also es-
timate its model by fi rst using Stata to estimate one equation determining trainee status and the employment outcome for trainees and another equation determining trainee
status and the employment outcome for nontrainees, and then optimally combining the parameter estimates using minimum distance.
As noted above, our approach differs from that of AHV in three key ways. First, we have two outcomes public coverage, private coverage while it only has one employ-
ment. Second, we calculate different policy effects than it does, and calculate our
policy effects for different groups in the population. Third, we can distinguish which individuals are affected by a nonmarginal increase in Medicaid income limits. We are
aided in the latter two contributions by the fact that conditional on family income, eli- gibility for a given child is observable. AHV cannot do this since the explicit rule for
being assigned to training, to the extent that one exists, is unavailable to researchers.
VII. Data
