16.8 In Section 16.5.1w e describeda n ordinal probit model for post-secondarye ducatioo choice and estimated a simple model in which the choice depended simply on rhe student's GRADES.

(a) Using the estimates in Table 16.5, calculate the probability that a student *'ill choose no college, a 2-yeat college, and a 4-year college if the student's gradei are the median value, GRADES : 6.64. Recompute these probabilities assumine that GRADES :4.905. Discuss the probability changes. Are they what yor.r anticipated? Explain.

(b) Expand the ordered probit model to include family income (FAMINQ, family size (FAMSIQ, and the dummy variables BIA,CK and PARCOLL Discuss t}r estimates, their signs, and significance. (Hint: Recall that the sign indicates tlr direction of the effect for the highest category but is opposite for the loweg category).

(c) Test the joint significance of the variables added in

(b) using a likelihood ratio res-

(d) Compute the probability that a black student from a household of four membenincluding a parent who went to college, and household income of $52,000, will attend a A-year college if (i) GRADES : 6.64 and (ii) GRADES: 4.905.

(e) Repeat

(d) for a "non-black" student and discuss the differences in your findings.