Metrics Exam - S1 2006

# Metrics Exam - S1 2006 - THE UNIVERSITY OF NEW SOUTH WALES...

This preview shows pages 1–9. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

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 time-series 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 2-sided 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 non-linear 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 1-Tailed: 0.10 0.05 0.025 0.01 0.005 2-Tailed: 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 two-tailed 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. ...
View Full Document

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern