## Econometrics

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ECOM30002/90002 Econometrics Semester 2

ASSIGNMENT 3

Instructions and information

Weight: 7.5%

Submit online through LMS no later than 2pm Friday 22 September; submission instructions to follow on LMS.

Assignments can be completed individually (on your own) or by a group (of up to two students). Students in a group (pair) do not have to be from the same tute.

Before submission, pairs must register their group using the group registration link to be posted on LMS (individuals need not register). Group registration closes (strictly) at 10am Tuesday 19 September. Pairs missing the group registration deadline will have to submit individual assignments.

Each assignment must include a completed cover page listing every member of the group with student IDs and tutors’ names.

Equal marks will be awarded to each member of a group.

Assignments should be submitted as a fully typed document (pdf or Word). Question numbers should be clearly indicated.

Where indicated (see Notes below), regression output must be presented in clearly labelled tabular form. Raw R output is not sufficient for full marks.

All questions requiring explanation should be answered in no more than three sentences.

For all tests, use a 5% significance level, and for tests and confidence intervals, use heteroscedasticity-consistent standard errors (HCSEs). In answering questions about testing, as a minimum, report the p-value for the test, and state the decision (reject null or not) and conclusion (what that means in context). The only advantage of reporting more than the minimum is the possibility of getting partial credit if the p-value is incorrect.

Notes

This assignment has three questions (including an “Appendix Question”) comprising 15 parts and will be marked out of 75 (all question parts are worth 5 marks).

* indicates parts for which tabulated regression output is required (see Appendix Question (a))

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QUESTION 1

Consider the following simple structural-form economic model of labour supply and demand

for married women (slightly extended from question 1 of assignment 1):

(supply) (1)

(demand) (2)

where is hours worked by individual i, is her hourly wage rate, is the number of

children in her household and is her spouse’s income.

Recall from assignment 1 the data file mroz2.csv, which contains labour market data for 428

married working women on the following variables:

number of hours worked for the year ( )

wage rate, $ per hour ( )

number of children in the household ( )

age in years

years of education

years of work experience

years of work experience squared

spouse’s annual income ($000s) ( )

Using the data in the file:

(a)* Test for instrument relevance. Interpret the result.

(b)* Test any overidentifying restriction(s). Interpret the result.

(c) Might the result in (b) help explain any theoretically implausible estimates in assignment

1? If so, why? If not, why not?

(d)* Estimate a regression to predict labour hours demanded for someone earning $5 per

hour, and obtain a 95% confidence interval for that prediction Report the prediction and

interval.

Hint: the technique outlined on page 12 of Lecture 13 is not limited to time series data.

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QUESTION 2

The file HIS.csv contains monthly time series data from July 1983 to May 2001 (inclusive)

on the following variables:

housing starts, seasonally adjusted ( )

mortgage interest rates, % ( )

series ‘smoothed’ using the (Google-able) Hodrick–Prescott filter ( )

Note: for this question, the whole sample (July 1983 (1983/7) to May 2001 (2001/5)) is split

into an estimating sample (1983/7 to 2000/12) and a forecasting sample (2001/1 to 2001/5).

Ensure that you use the appropriate sample (shown in brackets below) for each part.

(a) (Whole sample) Plot and over time on the same graph.

(b) (Estimating sample) Plot the residuals from a regression of on and briefly

explain their behaviour over time.

(c) (Whole sample) Define as the ‘interest rate cycle’ and plot and

over time on the same graph.

(d) (Estimating sample) Plot the residuals from a regression of on and explain

why they behave differently over time to those in (b).

(e) (Estimating sample) Fit an AR( ) model to based on a maximum lag of 12,

where (the lag length) is chosen to minimise the AIC. Report the chosen lag length.

(f) (Forecasting sample) Use your model from (e) to forecast log housing from 2001/1 to

2001/5 (inclusive) and present your forecasts in a table as formatted below.

Forecast and actual values of log housing, January–May 2001

Date Forecast value Actual value

January 2001

February 2001

March 2001

April 2001

May 2001

(g) (Forecasting sample) Based on your regression results from (b) above, use Model 1 below

to forecast interest rates from 2001/1 to 2001/5 (inclusive) and present your forecasts in a

table as formatted below.

, (Model 1)

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Forecast and actual values of interest rates, January–May 2001 (Model 1)

Date Forecast value Actual value

January 2001

February 2001

March 2001

April 2001

May 2001

(h) (Forecasting sample) Based on your regression results from (d) above, use Model 2 below

to forecast interest rates from 2001/1 to 2001/5 (inclusive) and present your forecasts in a

table as formatted below.

(Model 2)

Forecast and actual values of interest rates, January–May 2001 (Model 2)

Date Forecast Forecast interest rate Actual interest rate

January 2001 7.4446

February 2001 7.4815

March 2001 7.5185

April 2001 7.5555

May 2001 7.5926

Note: The forecasts for were obtained by simply linearly interpolating the 2000 values.

(i) Which of Models 1 and 2 forecasts best and why?

APPENDIX QUESTION

(a) Tabulate your regression results for parts marked * as a penultimate-page “Appendix A:

Results”.

(b) Present your R code as a final-page(s) “Appendix B: R code”.