## ECON20003 Quantitative Methods 2

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ECON20003 Quantitative Methods 2

Second Semester, 2017

Assignment 3

Due date and time: Monday 9 October, 4:00PM

Please read the following instructions carefully before working on the assignment.

We cannot accept assignments where the instructions have not been followed.

The total number of marks in the assignment is 90. It is worth 5% of the final grade for QM2.

This assignment must be submitted online via the LMS by 4:00 PM on Monday October 9.

Any assignment not submitted by this due date and time will be given a mark of zero.

A group of two students (but no more than two students) may work together and submit one

set of assignment answers for the group. Both members of the group must be enrolled in the

same tutorial. Individuals may work alone if they wish, and submit their own assignment

answers, but I urge students to work in pairs.

Please note that the assignment submission process has two stages:

1. Registering your assignment group, and

2. Submitting the assignment online via the LMS.

To register your group, go to the link on the LMS and follow the instructions.

The deadline for registering your group is 5:00 PM on Tuesday 3 October.

Students making an individual submission do not have to register: single‐member groups

are created automatically after group registration has closed. If a pair fails to register their

group before the deadline for group registration, both students will need to make an

individual submission.

A separate link will be given to submit your assignment on 4 October, after the assignment

group registration process is completed.

For assignments submitted as a group, both group members will receive the same mark for

the assignment. Students should form their own groups. No credit can be given for group

assignments where members of the group do not come from the same tutorial, or where

there are more than two students in a group.

All assignments should be converted into PDF before submitting online via the LMS. Students

must preview their assignment after uploading on the LMS to ensure they have uploaded the

correct/complete assignment, and the formatting is in order as in their original document.

Submissions that are late because of formatting issues, or because a version is incomplete,

will not be accepted.

Please make sure to include a cover page with student IDs and names of both group

members.

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Question 1 (42 marks, 6 for each part)

The file nels.wf1 contains 1000 observations taken from a National Education Longitudinal

study in the U.S. for the year 1988. The study was taken over 1988-1994 and was concerned

with access and choice in post-secondary education. We wish to model the probability that an

individual who is finishing high school goes on to university. The variables that we focus on

are:

UNI = 1 if an individual went to university, and 0 otherwise.

GRADES = average high school grade in maths, English and social studies on a 13

point scale with 1 being the highest.

FAMINC = family income in $10,000 units.

PARUNI = 1 if the most educated parent had successfully completed a university

degree, and 0 otherwise.

FEMALE = 1 if the individual is female, and 0 otherwise.

(a) Estimate a logit model for UNI as a function of GRADES, FAMINC, PARUNI, and

FEMALE. Use these estimates to answer parts (b) to (e).

(b) Estimate the marginal effect of FAMINC on the probability of a son going to university

if he has GRADES = 6 and comes from a family with income $80,000 and a parent with

a University degree.

(c) Find a 95% interval estimate for the quantity in part (b).

(d) Consider a daughter who has GRADES = 3 and comes from the same family described in

part (b). Estimate the probability that she attends University.

(e) How would the estimated probability in part (d) change if neither parent had a

University degree.

(f) How does the probability in part (d) compare with that obtained using the linear

probability model?

(g) How does the probability in part (d) compare with that obtained using the probit model?

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Question 2 (48 marks, 6 for each part)

The file gwth.wf1 contains quarterly observations on Australian GDP growth (GWTH) from

1979Q4 to 2016Q1.

(a) Graph the observations against time using EViews’ View/Graph. Comment on whether

the mean and/or variance of the series appear to change over time.

(b) A recession is often defined as three or more successive quarters of negative growth.

Using the graph and/or the spreadsheet of observations, find the periods in which the

Australian economy was in recession.

(c) Find the sample autocorrelations

1 1 cor ,t t r GWTH GWTH , 2 2 cor ,t t r GWTH GWTH ,

3 3 cor ,t t r GWTH GWTH , 4 4 cor ,t t r GWTH GWTH

Are they significantly different from zero at a 5% level of significance?

(d) Estimate an AR(2) model for GWTH. Use it to obtain forecasts and standard errors of

forecast errors for growth in 2016Q2, 2016Q3, and 2016Q4.

(e) Is there evidence that the residuals from the AR(2) model in part (d) are autocorrelated?

If so, what are the implications of this correlation?

(f) Estimate an AR(5) model for GWTH. Use it to obtain forecasts and standard errors of

forecast errors for growth in 2016Q2, 2016Q3, and 2016Q4. How do these forecasts and

standard errors compare with those obtained in part (d)?

(g) Use the results from part (f) to find a 95% interval forecast for growth in 2016Q4.

(h) Is there evidence that the residuals from the AR(5) model in part (f) are autocorrelated?