Metrics Exam - S1 2008

Metrics Exam - S1 2008 - THE UNIVERSITY OF NEW SOUTH WALES...

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Unformatted text preview: THE UNIVERSITY OF NEW SOUTH WALES SCHOOL OF ECONOMICS ECON 2206 INTRODUCTORY ECONOMETRICS FINAL EXAMINATION SESSION 1, 2008 1. TIME ALLOWED — 2 Hours. 2. READING TIME 2 10 Minutes 3. THIS EXAMATION PAPER HAS 9 PAGES 4. TOTAL NUMBER OF QUESTIONS - 6. 5. ANSWER ALL QUESTIONS. 6. ALL QUESTIONS ARE OF EQUAL VALUE 7. TOTAL MARKS AVAILABLE FOR THIS EXAMATION — 60. 8. THE MARKS AWARDED TO EACH PART OF A QUESTION ARE INDICATED. 9. CANDIDATES MAY BRING THEIR OWN CALCULATORS TO THE EXAM 10. STATISTICAL TABLES ARE PROVIDED AT THE END OF THE EXAM PAPER 11. ALL ANSWERS MUST BE WRITTEN IN PEN. PENCILS MAY BE USED ONLY FOR DRAWING, SKETCHING OR GRAPHICAL WORK. 12. THIS PAPER MAY BE RETAINED BY THE CANDIDATE Please see over PW 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 are the distinctive features of ‘panel data’ compared to ‘cross-section’ data 7 Explain. (2 marks (ii) In the model: price 2 flu + fil area + fizbdrms + ’83 area X bdrms + u what is the partial effect of bdrms on pace 7 {2 marks (iii) What is the ‘p-value’ for a test statistic ? SHAZAM reported the p-value for a test was 0.022; should I therefore reject the null hypothesis at the 1% level of significance ? (2 marks) (iv) Consider the following regression model explaining child birthweight (bwght): bwght = 50 + filcigs + flzfamz'nc + u where cigszaverage number of cigarettes the mother smoked per day during pregnancy and f aminczfamily income. In the sample of data I do not have a measure of family income. One option is to find a ‘proxy variable’ for family income. What are the desirable properties of a proxy variable ? Suggest one possible proxy for family income. {2 marks ) (v) What is meant by the ‘sampling distribution’ of an estimator 7 What is known about the sampling distribution of the OLS estimator under the first 4 Gauss-Markov assumptions ? (2 marks) Please see over Question 2. (10 Marks in total) The variable smokes is a binary variable equal to one if a person smokes, and zero otherwise. The estimates for the linear probability model explaining smokes are: 'sniokes = 0.301 — 0.093 log(prz'ce) — 0.029 log(income) — 0.031 educ + 0.020 age — 0.00024 age2 (0.132) (0.184) (0.009) (0.006) (0.006) (0.00006) [0.087] [0.187] [0.032] [0.004] [0.006] [0.00005] 71. = 220, R2 20.213 where price is the price of cigarettes, income is monthly income, educ is years of education, and age is the person’s age measured in years. The usual OLS standard errors are reported in parentheses and the heteroskedasticity-robust standard errors are reported in brackets (i) What is the interpretation of the coefficient on educ ? (2 marks ) (ii) What is ‘heteroskedasticity’ and what are the consequences of heteroskedasticity for: (a) the estimation of the regression model by OLS, and (b) conducting hypothesis tests with the usual t and F test statistics ? (5’ marks in total) (iii) Are there any important diHerences between the two sets of standard errors reported above 17 Does this provide evidence of whether heteroskedasticity is present ? Briefly explain. (3 marks) (iv) What is the partial effect of age on the probability of smoking ? Atwhat age is this partial effect reach a maximum ? (2 marks) Please see over Question 3. (10 Marks in total) We are interested in analysing the effect of different house characteristics on the sale price of a house, and propose the following population model: price 2 fio + [31 area + ,szdrms + 33 bthrms + a (3.1) Where price is the house price (in $100,000), area is the floor area of the house (in square metres)7 bdrms is the number of bedrooms and bthrms is the number of bathrooms. Estimates for the model based on a sample of 108 observations from Sydney are: pit}: =' 3.2481 + 0.2013area + 0.2363bdrms + 0.3207bthrms (3.2) (0.3945)(0.0093) (0.2092) (0.0395) n : 108, R2 = 0.3301 (i) What is the interpretation of the coefficient on bdrms in Model (3.2) ? (2 marks) (ii) Test the hypothesis that the coefficient on bdrms is equal to 0. Use a two-sided alternative and a 10% level of significance. (2 marks) (iii) We are concerned that the model may be misspecified due to the omission of non—linear terms in either area, bdrms or bthrms. Outline the steps involved in performing the RESET test7 and state the null and alternative hypotheses of the RESET test. (4 marks ) (iv) Do the model estimates in seem reasonable - or do the results provide evidence that it is a poor model 7 Explain. (2 marks ) Please see over Question 4. (10 Marks in total). The following model log(price) = fio + [31 log(nox) + [32 log(dist) + fl3rooms + u (4.1) relates median house prices in the community (price) to a range of community characteristics: 7109: which is the amount of nitrous oxide in the air (a measure of air pollution), dist which is the average distance of the community from major employment centres, and rooms which is the average number of rooms in houses in the community. (i) What is the interpretation of the coefficient Bl 7 (2 Marks) Based on a sample of 620 communities in a large city, the following estimation results were obtained: A log(price) = 13.08 — 0.454log(n0$) — 0.121log(dist) + 0.255rooms (4.2) (0.52) (0.317) (0.083) ' (0.019) n = 620, R2 =0.251 (ii) Test the overall explanatory power of the model (that is, test the null hypothesis H0 : [31 : 0,fi2 : 0, B3 = 0) using a 1% significance level. (3 Marks ) (iii) Test that the two features of the local community - log(no:c) and log(dist) - are jointly insignificant and should be excluded from the model. Use a 1% significance level. The R2 statistic for the model with these restrictions imposed is R2 = 0.125. What do you conclude ? (3 marks) (iv) Do you think that this model captures the causal effect of nor on house prices ? Explain. {2 Marks ) NOTE: The F—test statistic is given by the formula: (35R, — SSRm)/q SSRuT/(n — k — 1) (Bar — 39/61 (1 — REA/(n — k - 1) F : II 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. Please see over Question 5. (10 Marks in total}. To study the impact of the Australian government’s ‘Baby Bonus’ policy on the fertility rate of Australian, the following model was estimated using annual data for the period 1928 to 2007: ’ R = 124.09 + 0.114 Bonust — 35.88 ww2t — 2.53t + 0.12012 (5.1) (4.36) (0.040) (5.71) (0.39) (0.005) n = 80, R2 = 0.698 The variable fr is the fertility rate (number of children born to every 1000 women of child—bearing age)7 Bonus is the economic variable of interest which measures the real dollar value of the ‘Baby Bonus’ (which is a government payment to women for each child she gives birth to: the value of Bonus from $0 to $5000, with an average of $100 over the sample period), 1111122 is a dummy variable equal to one during the years of the second world war. The model includes a quadratic time trend, with the variable t indexing the year of each observation (ranging from a value of 1 for the observation for 1928 to a value of 80 for 2007 (i) What is the interpretation of the coefficient on Bonus ? (2 marks) (ii) Construct a 90% confidence interval for the effect of Bonus on fit. (2 marks). (iii) What is the purpose of including the terms t and t2 in model (5.1) 7 What are the potential problems of not including such terms ? (2 marks). (iv)To allow for the possibility that the fertility rate may respond to Bonus with a lag, the following Finite Distributed Lag model was estimated: fit 95.87 + 0.035 Bonust + 0.072 Bonust_1 + 0024301111514 — 35371111122; (5.2) (3.28) (0.126) (0.016) (0.011) (10.73) —2.21t+ 0.09012 (0.61) (0.006) n = 80, R2 20.811 What is the estimated Long Run Propensity (LRP) of Bonus on 3‘; in this model 7 What is the interpretation of the LRP 7 (2 marks). (v) There is not sufficient information reported for model (5.2) above to test whether the LRP is statistically significant. Represent the general form of model (5.2) as frt 2 a0 + 60 Bonus; + 6lBonust_1 + 62Bonust_2 + a1 ww2t + u (5.3) and derive the transformed equation you would need to estimate to obtain a direct estimate of the LRP and, most importantly, its standard error. Which coeflicient in the transformed model represents the LRP? (2 marks). Please see over 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) = fin + Bly2000 + Bzeduc + figfemale + B4female X y2000 + 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), edue 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 males). The estimates obtained from our pooled sample are: A log(wage) 0.9764 + 0.3716 3/2000 + 0.0653 educ — 0.3022 female + 0.1401female >< y2000 (6.2) (0.679) (0.0279) (0.0051) (0.0282) (0.0361) n = 1084, R2 = 0.3554, SSR = 224.84 (i) What is the interpretation of the coefficient on female in model (6.1) 7 (2 marks (ii) What is the expected log(wage) for a female with 16 years of education in 1990 ? (2 marks (iii) From the estimates in (6.2), what is the estimate of the exact percentage difference in expected wages between 1990 and 2000 ? (2 marks). (iv) Horn the estimates in (6.2), calculate an unbiased estimate of the variance of the error term, Var(u) = 02. (2 marks). (v) From the estimation results in (6.2), would you conclude there is discrimination against women in the labour market 7 Explain the reasons for your conclusion. (2 marks End of Paper Table 1. Critical Values of the t Distribution Si 0 nificance Level 1-Tailed: 0.10 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 De - rees of Freedom __ —nnunnnnnm 10 11 D e n o m i n a t o r 25 26 27 28 29 30 40 60 90 120 m0 mmmnmmu OQtDCDfi'H 3 Example: The 1% critical value for numerator df=3 and denominator dfiGO is 4.13. ...
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Metrics Exam - S1 2008 - THE UNIVERSITY OF NEW SOUTH WALES...

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