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Unformatted text preview: THE UNIVERSITY OF NEW SOUTH WALES
SCHOOL OF ECONOMICS
ECON 2206/ECON 3290 (ARTS) INTRODUCTORY ECONOMETRICS FINAL EXAMINATION SEMESTER 1, 2006 1. TIME ALLOWED  2 Hours.
2. TOTAL NUMBER OF QUESTIONS  6. 3. ANSWER ALL QUESTIONS. 4. ALL QUESTIONS ARE OF EQUAL VALUE (The marks awarded to each part of a question are indicated
 the total marks for this exam is 60). 5. CANDIDATES MAY BRING THEIR OWN CALCULATORS TO THE EXAM
6. STATISTICAL TABLES ARE PROVIDED AT THE END OF THE EXAM PAPER 7. ALL ANSWERS MUST BE WRITTEN IN PEN. PENCILS MAY BE USED ONLY FOR DRAWING,
SKETCHING OR GRAPHICAL WORK. ANSWER ALL SIX QUESTIONS REMINDER: When performing statistical tests, always state the null and alternative hypothe
ses, the test statistic and it’s distribution under the null hypothesis, the level of signiﬁcance
and the conclusion of the test. Question 1. (10 Marks). (i) What is the “spurious regression” problem, and how can this problem be avoided when using OLS with
timeseries data ? (4 marks) (ii) What is the meaning of the term “contemporaneous exogeneity” as used in the context of time series
data ? What is the difference between contemporaneous exogeneity and the zero conditional mean (ZCM)
assumption in the multiple regression model for time series data 7 (4 marks) (iii) Consider the following model used to explain the wages of workers: wage = ,60 + B1 educ + ,62 emper + 53 emper2 + u where wage is the hourly wage (measured in dollars), educ is years of education and emper is years of work
experience. In terms of the parameters of the population model, what is the effect on the expected wage of
an extra year of experience ? (2 marks) qo‘ Question 2. (10 Marks in total)
The following regression model was used to explain child birth weight (bwght — measured in kilograms): bwght = ,80 + ﬁlcigs + [32parity + ﬁ3faminc + B4motheduc + ﬁ5fatheduc + u (2.1) where cigszaverage number of cigarettes the mother smoked per day during pregnancy, parityzbirth order,
faminc=family income, motheduc=years of education for mother and fatheduc=years of education for father. Based on a sample of 1388 observation, the following estimates were obtained: cigs f ammo motheduc fatheduc 0.0054
(0.0022) intercept 3. 8059
(.0 0336) Obs 1388 1 SSR 1, 088.355 (i) What is the interpretation of the coefﬁcient on (2195? (2 marks)
(ii) Test whether the coefﬁcient on cigs is statistically signiﬁcant at the 1% level (using a 2sided alternative). Is the coefficient practically signiﬁcance ? Explain. {3 marks)
(iii) What is the piedicted difference in birthweight for a child with parents who both have 9 years of education compared to a child with parents who both have 16 years of education 7 (1 mark)
(iv) We are concerned that model (2.1) may be misspeciﬁed due to the omission of nonlinear terms in the
explanatory variables. Outline the steps involved in running the RESET test (remember to state the null and alternative hypotheses). (4 marks) Question 3. (10 Mar/ts in total) We are interested in analysing the effect of different house characteristics on the sale price of a house7 and
propose the following model: log(prz'ce) : ﬁg + H] log( area) + 52 log(bdrms) + 63 log(bthrms) + u (3.1) where price is the house price, area is the. floor area of the house (in square metres), bdrms is the number
of bedrooms and bthrms is the number of bathrooms. (i) What is the interpretation of the coefﬁcient on bthrms ? (2 marks) (ii) We are concerned that the homoskedasticity assumption may be violated for this model (that is, het—
eroskedasticity may be present). What is heteroskedasticity and what are the consequences of heteroskedas—
ticity for estimation and inference with the standard OLS procedures 7 (5’ marks ) (iii) Based on a sample of 935 observations, the Breusch—Pagan (BP) test statistic was calculated to be 4.21.
Carry out the Breusch—Pagan test using a 1 % signiﬁcance level. What do you conclude from this test 7 (2
marks). (iv) Outline the steps required to estimate model (3.1) using Feasible Generalised Least Squares FGLS (also
known as Weighted Least Squares) (5’ marks ) Question 4. (10 Marks in total). Let literacy denote the percentage of students at a high school who get a passing grade on a standardised
English Literacy test. We are interested in estimating the impact of school spending on the literacy skills of
students. A simple model is literacy 2 [30 + ﬁlexpend + 52enroll + B3faminc + u (4.1) where expend denotes school expenditures (per student) in $1000, enroll is the number of students enrolled
at the school and famine is the average family income of students at the school. The following table
contains OLS estimates for this model: Dependent Variable: literacy Independent Variable _ expend 7.75
—
enroll —1.26
_
f amine 0.324
_
intercept 23.14
—
Observations 428. (i) Construct a 99 % conﬁdence interval for the effect of expend on literacy. Is 0 in the 99 ‘70 conﬁdence
interval 7(3 marks) (ii) Suppose we were not able to measure the average family income of the students enrolled at the schools
in our sample. Outline the potential problems of estimating the relationship between literacy and expend
in (4.1) but with famine omitted. (3 marks) (iii) Suggest a potential proxy variable we may be able to use in place of famine, and briefly justify your suggestion based on economic theory or intuition. (2 marks )
(iv) Is the model of the determinants of literacy in (4.1) a good model 7 Brieﬂy explain. (2 marks) Question 5. (10 Marks in total).
(1) The following regression model was used to explain the growth in consumption (gcont) over time in terms
of the growth in income (ginct), the real interest rate (rintt) and the expected inﬂation rate (inflet): gcom 2 BO + 609mg + Blrintt + Bﬁnflet + u (5.1) Is this a “static” or “dynamic” model of the growth in consumption ? Brieﬂy explain. (2 marks).
(ii) The model in (5.1) was estimated with a sample of data covering the period 1965—19987 and the estimates
were: ll 0.010 + 0.586 91710; — 0.050 rintt + 0.0322'nflet (5.2)
(0.003) (0.073) (0.029) (0.014)
n = 34, R2 = 0.684, SSR : 0.0017 A
gcont Test the null hypothesis that the real interest rate has no effect on the growth in consumption, against the
one—sided alternative hypothesis that it has a negative effect, using a 5 percent signiﬁcance level. (2 marks).
(iii) We are interesting in testing the hypothesis that the real interest rate and the expected inﬂation rate have
exactly the opposite effect on consumption growth. That is, we are interested in testing the null hypothesis:
H0 : 01 + 52 = 07 against the alternative H1 : ,81 + ﬁz 75 0. Why is there not enough information in the
results presented in (5.2) to carry out this test ? Rewrite the model in (5.1) into a form which you could
estimate and directly test this hypothesis. What parameter in this transformed model would the test be
based on 7 (3 marks). (iv) Write down an expanded version of (5.1) which is a Finite Distribute Lag Model of order 2 in gtnc.
What is the Impact Propensity (IP) and the Long Run Propensity (LRP) in this model, and what is their
meaning 7 (5’ marks). 404’ Question 6. (10 Marks in total).
We are interested in analysing wage discrimination against women, and how it has Changed over time.
We have independent samples of data for the Australian workforce in 1990 and 2000. The two Cross—sections are pooled and the following model was estimated:
log(wage) = ,80 + 51312000 + ﬁgeduc + ,63female + u (6.1) where y2000 is a dummy variable equal to 1 if the observation is from the Year 2000 sample (and is equal
to 0 otherwise), educ is years of education and female is a dummy variable equal to 1 if the observation is
for a woman (and is equal to 0 for male). The estimates obtained from our pooled sample are: A log(wage) 0.9764 + 0.3716 y2000 + 0.0653 educ — 0.3022 female (6.2)
(0.679) (0.0279) (0.0051) (0.0282) n = 1084, R2 : 0.2954, SSR = 224.84 (i) What is the interpretation of the coefﬁcient on 312000 in model (6.1) ? (2 marks).
(ii) What is the expected log(wage) for a male with 12 years of education in 2000 7 (1 mark).
(iii) Propose a regression model that could be used obtain a conﬁdence interval for the expected log(wage) for a male with 12 years of education in 2000. {3 marks).
(iv) From the estimates in (6.2), what is the estimate of the exact percentage wage difference between men and women 7 (2 marks).
(v) From the estimation results in (6.2), would you conclude there is discrimination against women in the labour market ? Explain the reasons for your conclusion. (2 marks). NOTE: The F—test statistic is given by the formula: (SSR. — SSRqu SSR‘ur/(n _ k _ 1)
(Rir ~ RE)”; (1 *R%r)/(n—k* 1) ‘ F: where S S R is the sum of squared residuals, q is the number of restrictions, and ur and r stand for unrestricted
and restricted models, respectively. Table 1. Critical Values of the t Distribution Si  nificance Level 1Tailed: 0.10 0.05 0.025 0.01 0.005
2Tailed: 0.20 0.10 0.05 0.02 0.01 Example. The 1% critical value for a one tailed test with 25 df is 2.485. The 5% critical value for a twotailed
test with large (>120) df is 1.960. Table 2. 1% Critical Values of the F Distribution Numerator Decrees of Freedom 25
26
27
28
29
30
40
60
90
120 Example: The 1% critical value for numerator df=3 and denominator df=60 is 4.13. ...
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 Three '11
 berrick
 Econometrics

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