Using data on \(N=4,642\) infant births, we estimate a probit model with dependent variable \(L B W E I G H T=1\) if it is a low birthweight baby and 0 otherwise, MAGE is the mother's age, PRENATAL1 \(=1\) if first prenatal visit is in 1 trimester and 0 otherwise, and MBSMOKE \(=1\) if the mother smoked and 0 otherwise. The results are in Table 16.10.

a. In Model 1, comment on estimated signs and significance of the coefficients on PRENATAL1 and MBSMOKE.

b. Using Model 1, calculate the marginal effect on the probability of a low birthweight baby given an increase in the mother's age by 1 year, for a woman who is 20 years old with PRENATAL1 \(=0\) and \(M B S M O K E=0\). Repeat this calculation for a woman who is 50 years old. Do the results make sense?

c. Using Model 2, calculate the marginal effect on the probability of a low birthweight baby given an increase in the mother's age by 1 year, for a woman who is 20 years old with PRENATAL1 \(=0\) and \(M B S M O K E=0\). Repeat this calculation for a woman who is 50 years old. Compare these results to those in part (b).

d. Using Model 2, calculate the impact of a prenatal visit in the first trimester on the probability of having a low birthweight baby for a woman who is 30 years old and smokes.

e. Using Model 2, calculate the impact of a mother smoking on the probability having a low birthweight baby given that she is 30 years old and had a prenatal visit in the first trimester.

f. Using Model 2, calculate the age at which the probability of a low birthweight baby is a minimum.

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TABLE 16.10 Probit Estimates for Exercise 16.11 C MAGE PRENATALI MBSMOKE MAGE Model 1 -1.2581 -0.0103 -0.1568 0.3974 (se) (0.1436) (0.0054) (0.0710) (0.0670) Model 2 -0.1209 -0.1012 -0.1387 0.4061 0.0017 (se) (0.4972) (0.0385) (0.0716) (0.0672) (0.0007)