Applied Econometrics
- (15 marks) As a researcher you have been given data on N = 4,642 infant births and are
asked to examine factors that determine the outcome of a low birthweight baby. Suppose
you estimate two probit models (Model 1 and 2) with dependent variable LBWEIGHT = 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 below (Note that C refers to a
constant and standard error are given in parantheses.)
Table 1: Estimates from model 1 and 2
C MAGE PRENATAL1 MBSMOKE MAGE2
Model 1 -1.2581 -0.0103 -0.1568 0.3974
(se) (0.1436) (0.0054) (0.071) (0.067)
Model 2 -0.1209 -0.1012 -0.1387 0.4061 0.0017
(se) (0.4972) (0.0385) (0.0716) (0.0672) (0.0007)
a. In Model 1, comment on estimated signs and significance of the coefficients on
PRENATAL1 and MBSMOKE (2 marks).
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 MBSMOKE = 0. Repeat this calculation for a woman
who is 50 years old. Do the results make sense? (3 marks).
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 MBSMOKE = 0. Repeat this calculation for a woman
who is 50 years old. Compare these results to those in part (b). (3 marks).
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. (2 marks).
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e. Using Model 2, calculate the impact of a mother smoking on the probability having
a low birth-weight baby given that she is 30 years old and had a prenatal visit in the
first trimester. (2 marks).
f. Using Model 2, calculate the age at which the probability of a low birthweight baby
is a minimum. (3 marks). - (10 marks) Suppose you are working as data scientist for the Deputy Premier and Minister for Education to the Victorian Parliament, the Hon. James Merlino. The Minister
is trying to understand the determinants of education choices of a random sample of individuals aged 18-24. According to your data, there are 3 types of possible choices they
have made: either individuals do not pursue a college degree, or they pursue a 3-year
college degree, or a 4-year (Honours) degree. You argue that the best way to approach
the problem is to estimate an ordered probit model which includes a few important determinants:
GRADES = the grades they got in high-school (which is an index ranging from 1.0,
highest level A+ grade, to 13.0, lowest level F)
FAMINC = family income (in $1000)
FAMSIZ = family size
ABR = 1 for aboriginal individual, and 0 otherwise
PARCOLL = 1 if a parent has at least a college degree, and 0 otherwise.
The estimates of your model are presented below.
Table 2: Estimates from model 1 and 2
Model 1 Model 2
PSECHOICE Coefficient Standard Error Coefficient Standard Error
GRADES -0.3066 0.0192 -0.2953 0.0202
FAMINC 0.0053 0.0013
FAMSIZ -0.0241 0.0302
ABR 0.7131 0.1768
PARCOLL 0.4236 0.1016
µˆ1 -2.9456 0.1468 -2.5958 0.2046
µˆ2 -2.09 0.1358 -1.6946 0.1971
ln L -875.8217 -839.8647
a. Using the estimates in the Table above, Model 1, calculate the probability that a
student will choose no college, a 3-year college, and a 4-year college if the student’s grades are GRADES = 7 (B-). Recompute these probabilities assuming that
GRADES= 3 (A-). Discuss the probability changes. Are they what you anticipated?
Explain using your economic intuition. (3 marks)
b. Discuss the Model 2 estimates, their signs and significance. Explain using your
economic intuition. [Hint: recall that the sign indicates the direction of the effect for
the highest category but is opposite for the lowest category]. What policy indication
would you suggest to the Victorian government? (2 marks)
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c. Test the joint significance of the variables added in (b) using a likelihood ratio test
at the 1% level of significance. Show how you do this. Explain the meaning of the
result in economic terms. (1 marks)
d. Compute the probability that an aboriginal student from a household of four members with $100,000 income, and with at least one parent having at least a college
degree, so that PARCOLL = 1, will attend a 4-year college if (i) GRADES = 7 and
(ii) GRADES = 3. What would be your policy conclusion from this? (2 marks)
e. Repeat (d) for a “non-aboriginal” student and discuss the economic differences in
your findings. What would be your policy conclusion from this? (2 marks)