Metrics Exam - S1 2007

# Metrics Exam - S1 2007 - 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, 2007 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 OIVN 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. FPS 137i 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) Suppose that the correct population regression model is: y=60+ﬁlx1+ﬁgx2+u (1-1) However we only have data only on y and \$1, and as a consequence we estimate the following model by OLS: y=BO+81m1+v (1.2) In what Circumstance will the OLS estimator for model (1.2): (a) provide an unbiased estimate of the true population parameter 61 7 (2 mar/cs) (b) provide an estimate of [31 that has positive (or upward) bias ? (2 marks) (ii) Outline the advantages of using larger samples of data in regression analysis. (2 marks) (iii) A model used analysing the effect of house characteristics on the sale price was: log(price) : 60 + )31 area + ,ngdrms + 53 area >< bdrms + u where price is the house price, area is the ﬂoor area of the house (measured in square metres), and bdrms A is the number of bedrooms. What is the partial effect on log(prz'ce) of increasing area by 1 square metre 7 ( 2 marks ). (iv) 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 “strict exogeneity” as used in multiple regression models for time series data 7 (2 marks) Question 2. (10 Marks in total) The following regression model explains the monthly wages as a function of years of education (educ), years of labour market experience (emper) and current job tenure (tenure): log(wage) : ,60 + ﬁledac + ﬂgezper + 53tenure + u (2.1) With a random sample of data the following output was obtained using SHAZAM: Welcome to SHAZAM - Version 10.0 |_sample 1 722 |_read wage educ exper tenure 4 VARIABLES AND 722 OBSERVATIONS STARTING AT OBS 1 Lgenr lnwage=log(wage) [_* Model estimates (_ols Inwage educ exper tenure REQUIRED MEMORY IS PAR= 81 CURRENT PAR= 2000 OLS ESTIMATION 722 OBSERVATIONS DEPENDENT VARIABLE= LNWAGE ...NOTE..SAMPLE RANGE SET TO: 1, 722 R-SQUARE = 0.1551 R-SQUARE ADJUSTED = 0.1524 VARIANCE OF THE ESTIMATE—SIGMA**2 = 0.19493 STANDARD ERROR OF THE ESTIMATE-SIGMA = 0.44151 SUM OF SQUARED ERRORS-SSE= 139.96 MEAN 0F DEPENDENT VARIABLE = 6.7790 LOG OF THE LIKELIHOOD FUNCTION = -438.839 VARIABLE ESTIMATED STANDARD T-RATIO PARTIAL STANDARDIZED ELASTICITY NAME COEFFICIENT ERROR 718 DF P-VALUE CORR. COEFFICIENT AT MEANS EDUC 0.74864E-01 0.6512E-02 11.50 0.000 0.353 0.3905 0.1487 EXPER 0.15328E-01 0.3370E-02 4.549 0.000 0.147 0.1592 0.0261 TENURE 0.13375E—01 0.2587E-02 5.170 0.000 0.167 0.1612 0.0143 CONSTANT 5.4967 0.1105 49.73 0.000 0.852 0.0000 0.8108 (i) What is the interpretation of the coefficient on education, [31 ? (2 marks). (ii) Calculate the exact percentage effect of another year of education on the predicted wage level. (2 marks). (iii) Test the null hypothesis that all the slope parameters in the model are jointly equal to zero using a 1 percent signiﬁcance level. What do you conclude ? (3 mark). Note: The F ~test statistic is given by the formula based on R2 is: (R’LZLT _< R72")/q (1— Rid/(TL * k — 1) where q is the number of restrictions, and ur and r stand for unrestricted and restricted models, respectively. F: (iv) We are interesting in constructing a conﬁdence interval for the (conditional) predicted log(wage) when educ : 13, exper = 11 and tenure = 7, To obtain the standard error for the prediction we need to estimate a transformed model that is equivalent to (2.1). Derive the transformed model which will give a direct estimate of the prediction and the standard error of the prediction. (3 marks). Question 3. (10 Marks in total) We are interested in analysing the effect of different house characteristics on the market price of the house in the Sydney, and consider the following regression model: log(prz'ce) = 50 + ﬁl log(lotsize) + 52 log(sqrft) + B3 log(bdrms) + u (3.1) where price is the sale price (measured in \$1000), lotsz'ze is land area (square metres), sqrmtr (is the floor area of the house (also measured in square metres), and bdrms is the number of bedrooms. Based on a sample of data from 2005 house sales in Sydney, the following regression estimates were Obtained: H 0.5481 + 0.7013 log(sqrmtr) + 0.1745 log(lotsize) + 0.0363 log(bdrms) (0.3945)(0.0323) (0.0353) (0.0932) n = 103, R2 2 0.551, R2 = 0.538 log/pace) (i) Construct a 90% conﬁdence interval for 03 (the coefﬁcient on log(bdrms)). Is zero within the conﬁdence interval ? (3 marks). (ii) Given the estimation results, would you conclude that this is a good econometric model 7 Explain. (5’ mar/cs) (iii) We are concerned that the model in (3.1) may be misspeciﬁed. An alternative model speciﬁcation where all the variables are in level form (rather than in log form) is: price 2 30 + ﬁllotsize + ﬁzsqrft + B3bdrms + u (3.2) Outline a procedure for testing whether model (3.1) or model (3.2) is a better specification. What are the limitations (if any) of the test ? Explain. {4 marks) Question 4. {10 Marks in total). In a recent study an economist examined the factors explaining whether a ﬁrm was taken over by another ﬁrm during a given year. The dependent variable in the analysis was Takeover — which is a binary variable equal to 1 if it was taken over (and 0 otherwise). The explanatory variables were profit which is the ﬁrm’s average proﬁt rate over the previous ﬁve years, mktval which is the market value of the ﬁrm (in \$100m), and debtearn which is the debt—to—earnings ratio. The table below presents coefﬁcient estimates (and standard errors) based on a sample of 177 ﬁrms in 2004. Table 4.1. Estimation Results for Takeover Models Dependent Variable: Takeover Variables debtearn constant Observations(n) R2 Note: The usual OLS standard errors in () below the coefﬁcient estimates. (i) What is the interpretation of the coefﬁcient on profit ? (2 mark) (ii) What is the predicted probability of Talaeooer for a firm with the following characteristics: profit : 0.05, mktval : 1.5 and debtearn = 6 7 Brieﬂy explain whether the result is sensible. (2 marks) (iii) We know the Linear Probability Model must contain “heteroskedaticity”. What is heteroskedasticity and what are the consequences of heteroskedasticity for: (a) estimation, and (b) inference with the standard OLS procedures ? (2 marks) (iv) Given that we know the model contains heteroskedasticity, what advice would you give an economist wishing to analyse the determinant of Takeover with regression methods ? (4 marks ) Question 5. {10 Marks m total). The following regression model was proposed for analyse the effect of the minimum wage on employment: log(emprtet) : ﬂo + 5110g(minwgt) + ﬁg log(minwgt41) + 53 log(GNPt) + 11; (5.1) where emprtet is the employment rate, minwg) is the minimum wage and GNP) is GNP (a proxy for labour demand) in year t. (i) What is the interpretation of the coefficient 51 7 (2 mark). (ii) Is this a “static” or “dynamic” model ? What is the purpose of including the lagged term mmng? Brieﬂy explain. (2 marks). Using annual data from 1950—1987, the following regression model estimates were obtained: A log(emprtet) ll ~7.05 — 0.072log(minwgt) — 0.06110g(minwgt_1) —~ 0.01210g(GNPt) (5.2) (0.77) (0.031) (0.015) (0.089) n : 38, R2 : 0.661, R2 = 0.641 (iii) Test the null hypothesis that the lagged term minwgt_1 is insignificant using a 10 percent signiﬁcance level and the one—sided alternative that the coefhcent is negative (H0 : 62 = 0. H1 : [32 < O ). (2 marks). (iv) There is not enough information in the results presented in (5.2) to construct a conﬁdence interval for the Long Run Propensity (LRP). Rewrite the model in (5.1) into a form which you give you a direct estimate of the LRP (and the standard error on the LRP). What parameter in this transformed model corresponds to the LRP ? (2 marks). (v) I am concerned that the model in (5.2) may suffer from the “spurious regression” problem. What is the spurious regression problem and what simple adjustment to the model would help reduce the possibility of this problem 7 (2 marks). Question 6. {10 Marks in total). We are interested in analysing the effect of locating a water desalination plant on local property prices. Desalination plants are large, industrial sites which can generate a lot of noise pollution and reduce amenities in the local area. The South Australian government built a desalination plant in the Adelaide area of South Beach in 1998. Discussion about building a desalination plant in South Beach began after 1994, and the plant was built and began operating in 1998. We have data on the prices of houses sold in South Beach in 1994 (the “before” period) and another sample on houses sold in 2002 (the “after” period). The hypothesis we wish to test is that the price of houses located near the site of the desalination plant would fall below the price of more distant houses. The data for each year includes the dummy variable nearplant which is equal to one if the house is located within 3 kilometres of the desalination plant. The variable hprice denotes the real house price (scaled by \$10,000). The following simple regression model was estimated using only the year 2002 sample of data: ll 21.311 v 6.198 nearplant (6.1) (0.618) (0.992) n = 353, R2 = 0.212 hp/rTce Using the 1994 sample, the following regression results were obtained: hzjrt'ce = 16.527—3679nea7'plant (6.2) (0.538) (0.615) n : 18212220172 (i) What is the interpretation of the coefﬁcient on the intercept term in model (6.2) (that is. what does the value 16.527 represent) ? What is the interpretation of the coefficient on nearplant in model (6.2) ? (2 marks) (ii) Can you infer from the estimates in (6.1), based on the year 2002 data, that the location of the plant caused the price of houses located nearby to fall by an average of \$61,980 ‘3 Explain . (2 marks) . (iii) An alternative approach is to pool the data for both years and estimate the following model: A hprz'ce : 16.527 + 4.7840 year2 — 3.679 nearplant ~ 2.519 year2 . nearplant (6.3) (0.793) (0.9471) (0.876) (1.128) n z 535, R2 : 0.202 where year2 is a dummy variable equal to one if the observation is for the year 2002 (and is equal to zero if the observation is for the year 1994). What is the estimated effect of the plant on neighbouring house prices based on the “difference-in-difference” estimator 7 Is the effect signiﬁcantly different from 0 at the 5% signiﬁcance level ? (use the one~sided alternative hypothesis that the coefﬁcient is negative). (3 marks) (iv) W hat, if any, would be the advantages of collecting and using panel data to evaluate the effect of the location of the desalination plant on local property prices ? Explain. (3 marks). Table 1. Critical Values of the t Distribution Si- nificance Level 0.10 0.05 0.025 0.01 0.005 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. Tabie 2. 1% Critical Values of the F Distribution Numerator Degrees of Freedom D e n o m i n a t o r *0 mmebwmmo OQQCDHTI 3 Example: The 1% criticai value for numerator df =3 and denominator df=60 is 413. ...
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