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THE UNIVERSITY OF NEW SOUTH WALES

I~ , .,,0 ~ SCHOO L OF ECONOt.. IICS

ECON 2206 / ECON 3290 (ARTS) INT RO DUCTORY ECONO~"ETRICS FI NAL EXAM INAT ION

SESSION 1, 2009

l. T Il\lE ALLOWED - 2 Hours .

2. REA DING TI1-.IE = 10 t. l inutcs

3. T HIS EXAl\HNATlON PAPER HAS 9 PAGES

4. TOTAL NUl\ IBER OF QUESTIONS - 6.

5. ANSWER ALL QUESTIONS. 6. ALL QUESTIONS ARE OF EQUAL VALUE

7. TOTAL MAJ.lKS AVA ILABLE FOR THIS EXM,II NATION - 60.

8. THE l\ IARKS AWARDED TO EACH PART OF A QUESTION ARE INDICATED.

9. CANDIDATES MAY BRING THEIR OWN CALCULATORS TO T HE EXAl\1

10. STATISTICA L TABLES ARE PROVIDED AT T HE END OF THE EXAt..1 PAPER

11. ALL ANSWERS I\ IUST BE WRITTEN I N PEN. PENCILS I\ IAY BE USED ONLY FOR DRAWING, SKETCHI NG OR GRAPHI CAL WORK.

12. THIS PAPER I\I AY BE RETAINED BY T HE CANDTDATE

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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. (lO Marks).

(i) Consider the multiple regression model:

y =fjo + PI Xl +fj'l:t2 +u Briefly explain the consequences of measurement error in the dependent variable, y, for the O LS estimators of fjl and fj2 when:

(a) the measurement error is uncorrelated with the independent variables XI and X'l (2 marks)

(b) the measurement error is correlated with the independent variable XI (2 marks)

(ii) Consider the following model used to the salary of chief executive officers:

salary = Po + 13) sales + fj2 mktva/ + fj3 sales x m1},-val + u where sales is the firm 's total sales revenue for the previous year (measured in Smillions) and 1HT},;val is the firm's market value (also measured in $millions) . III terms of the parameters of the population model, what is t he effect on salary of all extra $lmillion of sales in the previous year? (2 marks)

(ii i) What is the meaning of t he term "contemporaneous exogeneity" as used in the context of time series data? \Vhat is t he difference between contemporancous exogeneity and the zero conditional mean (ZCM) as~IIJJlPtion ill the multiple regres~ion model for time series data ? {2 marks}

(iv) What does it mean for an estimator to be "consistent" and does this differ from "ullbiasness" ? Explain . (2 marks).

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Question 2. (lO Marks in total) The variable heavyd is a binary variable equal to one if a person is a heavy drinker (of alcoho\) , and zero otherwise. T he estimates for the linear probability model explai ning heavyd was:

heavyd = 0.467 - 0.007 log(price) + 0.056 log(i71come) + 0.028educ - 0.000geduc2 - 0.014 age (0.210) (0.034) (0.029) (0.006) (0.0003) (0.06) [0.131[ [0.031[ [O.OI B[ [0.005] [0.0002] [0.05]

71 = 1403, n2 = 0.233 where price is the price of beer in the individual 's local a rea, income is monthly income, educ is years of education and age is measured ill years. The usual OLS standard errors are reported in parentheses (.), and t he heteroskedasticity-robust standard errors are reported in brackets [.].

(i) At what point (i.e. specific number of years) does anot her year of education reduce the probability of being a heavy drinker ? (l mark)

(ii) Are t here a ny important differences between the two sets of standard errors reported above? Briefl y explain. (2 marks)

(iii) Outline t he steps involved in performing the White Test fo r the presence of heteroskedastici ty. (3 marks) (iv) We know t hat heteroskedasticity is present in t he linear probability model. What a rc the advantages of using the Weighted Least Squares (WIS) estimator for the model rather than O LS (wit h robust standard errors)? (1 mark) (v) In t he linear probabili ty model t he condit ional variance of the dependent variable, y, is given by:

Va' (y lx ) _ p(x ll l - p(x) [ where p(x ) /30 + /3IXI + ... + f3"x/c

Outline t he procedure for estimating the linear probability model by WLS. (3 marks)

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Ques t ion 3. (10 Marks in total) Let Quant denote the percentage of students at a NSW high school who get a passing grade 011 a

standllrdised mathematics tests. We are interested in estimating the impact of school spending on the mathematical skills of students. A simple model is

(3.1) where expend denotes school expenditures (per student) in S1000, enroll is t he number of students enrolled a t the school and famine is the average family income of students at t he school. The following table contains OLS estimates for this model:

Dependent Variable: Quant Independent Variable expend 7.75

(3.04) enroll -1.26

(0.58) famine -0.324

(0.036) intercept -23. 14

(24.99) Observations 428 R' 0. 1893

(i) Construct a 99 % confidence inten'al for the effect of expend on Qtlant . Is 0 in the 99 % confidence interval ?(2 marks)

(ii) Suppose we were not able to measure the average family income of the students enrolled at t he schools in the sample. Discuss the potential problems of estimating the relationship between Quant and expend. in (3. 1) but with famine omitted. (9 marks)

(iii) Suggest a potential proxy variable we may be able to use in place of faminc, and briefly j\lstify your suggestion based on economic theo!}' or intuition. What conditions must a useful proxy variable satisfy? (9 marks)

(iv) Is the model of the determinants of Qu.ant ill (3. 1) a good model? Explain your rew;;oning. (2 marks)

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Question 4. (10 Marks in total) . Let sa.ve denote the amount of money a family savings during a year . \Ve are interested in determining

whether the rich save relatively more, other things equal. Consider the model

log(save) = f30 + f3 1age + f32 children + f33wealth + u (2.1) where age denotes the age of the 'family head' , children is the dependent children in t he household and wealth is the total wealth (total asset s minus liabilities) of t he family (in SIOO,OOO).

(i) The following table contains OLS estimates for Illodels with and without wealth as an explanatory variable:

Dependent Variable' log(save) Independent Variable ( I ) (2) age 0.062 0.038

(0.011) (0.017) child)"en -0.065 -0.125

(0.04 1) (0.051) W ealth 0.025

(0.001) int.crcept 0.042 0.039

(0.D03) (0.004) Ob8e1"1Ja"tion8 325 325 R' 0.057 0.226

Note. Sta ndard errors In () below t he coefficient estimates.

Why is the erred of children on log(save) larger in magnitude in model (2) than (I )? Do families with more children save less? Briefly explain. (2 marh)

(ii) Test whether model (2) has any explanatory power. Perform a test of the overall significance of the regression using a 1% level of significance. (2 marks)

(iii) J am concerned the model in column (2) Illay be misspecificd due to neglected Ilonlinearities. Outline the steps required to carry out the RESET test, and clearly state the null and alternative hypotheses of the test. (9 marks)

(iv) An alternative specification of the model in column (2) is to have the age and wealth variables enter in log (rather than level) form. Outline one procedure which may help determine which is the better specification of the model. What , if any, are the limitations of the procedure? (3 nW"k!)

NOTE: The F -test statistic is given by the formula:

p = (SSR, - SSR",)/q SSR",/(n k I)

(R;, - R~)/q ( I R;,)/(n k I )

where SSR is the sum of squared residuals, q is the number of restrictions, and ur and r stand for unrestricted and restricted models, respectively.

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Question 5. (10 Marks in total) . To study the im pact of a government policy on the fert ility rate of Australian women, the following static model was estimated using anmlal data for t he period 1913 to 1984:

124.09 + 0.348 pct - 35 .88ww2 1 (5.1) (4.36) (0.040) (5.71)

n ~ :2 - 2 -72, n = 0.727, R = 0.106

The variable fr is the ferti lity rate (number of ch ildren born to every 1000 women of child-bearing age) , pe is the economic variable of interest which measures t he real dollar value of t he ' personal exempt ion ' (which is an income tax deduction for each dependent child: t he value of pe ranges frolll SO to S244, with an average of S100 over the sample period), and 1l.;w2 is a dummy variable equal to one during t he years of t he second world war.

(i) What is the interpretation of the coefficient on pe? Is pe practically (or 'economically') significant ? (2 marks) .

(ii) To allow for the possi bility that t he fertility rate may respond to pe with a tag, the following t hird order Finite Distributed Lag model was estimated:

/r! = 95.87 + O.3 13 pej + 0.OO62 pet _1 + 0.Q44pet _:2 + 0.034pet _3 -35.37ww2t (5. 2) (3.28) (0. 126) (0.1557) (0. 126) (0.102) (10.73)

n = 70, n2 = 0.821 , fl2 = 0.773

What is the estimated Long Run Propensity (LRP ) of pc O il /T in this model ? What is the interpretation of the LRP ? (1 mmk).

(ii i) What does it mean for a time series process (such as 11", ) to be covariance stationary ? Explain . (2 marks ).

(iv) What does it mean fo r a t ime series process (such as /r, ) to be weakly d ep e nde n t , a nd how does this differ from covariance stationary ? (2 marks).

(v) \Vhat is the "spurious regression problem" ? How c/\11 I adjust t he model in (5. 1) to ensure the regression results are not spurious? (3 marks).

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Question 6. (10 Marks in total). We are interested ill allalysing t he effect of the NSW government's Worker Compensation Laws int roduced

in 1996 on the duration of t ime workers receh'ed compensat ion fo r workplace injuries. The new laws reduced the maximum amount of earnings that injured workers could be compensated for while off work. The maximum amount of lost weekly earnings that an injured worker could receive compensation for decreased from $2000 to $1000. The law had the effect of Illa king it more costly for high income earners to remain on workers compensation (since forgone income was now greater), while the law had no effect on lower income earners (who earot less than $1000 per week). Therefore workers with high weekly earnings represent the treatment group and workers with lower w~kly income represent a control group. \Ve have a random sample of data on workers in 1995 (the "before" period) and Mother random sample on workers in 1997 (the "after" period ). The hypothesis we wish to test is that the new laws caused workers to spend less t ime off work in receipt of \Vorkers Compensation .

The data for each year includes the number of weeks the workers spent o ff work and in receipt of workers compensation (duration) as well as the worker' (pre-inj ury) weekly earnings (earnings ) measured in S1995. The earnings information was used to construct the dummy variable highinc which is equal to one if the worker's weekly earnings were $1000 or more, and is equal to zero otherwise. The followi ng simple regression model was estimated using only the year 1997 sample of data

du~on = 14.1307 - 5.0688 highinc (0. 1241) (0.5314)

n = 2716, R'l = 0.0983

while t he following was estimated using only the 1995 sample of data

du~on 12.4517 - 3.0557 highinc (0.2045) (0.3071 )

n = 3018, n2 = 0.0906

(6.1)

(6.2)

(i) What is the interpretation of the coefficient on the intercept term in model (6.2) (that is, what does the value 12.4517 mean )? What is the interpretation of the coefficient on highi71c in model (6.2) ? (2 marks)

(ii) Explain why we cannot infer from t he estimates in (6.1) , based on the 1997 data, t hat the new Jaws caused the duration of lime injured workers received Workers Compensation to fall by all average of 5.0688 weeks? What evidence from model (6.2) supports this conclusion ? (2 marks) (iii) An alternati ve approach is to pool the data fo r both yea rs and estimate the follow ing mode!:

dUJ~(m = J 2.4517 + 1.6790 dl997 - 3.0557 highinc - 2.0131 d1997 x highinc (6.3) (0.0973) (0.071 ) (0.1248) (0.864)

n = 5734 , R1. = 0.0954

where d1997 is a dummy variable equal to one if t he observation is for the year 1997 (and is equal to zero if the observation is for the year 1995). What is t he estimated impact of the new laws on the duration of time injured .... ,orkers receive Workers Compensation based on the "difference-in~difference" estimator ? Is the e ffect significantly different from 0 at the 1% significance le .... el ? (use the I-sided alternative hypothesis that t he coefficient is negative). (2 marks) (iv) Suppose that we are concerned that the workforce ill NSW may have changed between 1995 and 1997. Outline how the mode! ill (6.3) may be adapted to allow for changes in the underlyi ng characteristics of the population ill 1995 and 1997. (2 marks) (v) What , if any, would be the advantages of collecting a nd using panel data to evaluate t he effect of the change in t he laws? Explain . (2 marks)

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Table 1 Critical Values ofthe t Distribution Significance Level

i-Tailed: 0.10 0.05 0.025 0.01 2-TalJed: 0.20 0.10 0.05 0.02

1 3.078 6.314 12.706 31.82 1 2 1.886 2.920 4.303 6.965 3 1.638 2.353 3.182 4.541 4 1.533 2.132 2.776 3.747

1.476 2.015 2.571 3.365 6 1.440 1.943 2.447 3.143 7 1.415 1.895 2.365 2.998 8 1.397 1.860 2.306 2.896 9 1.383 1.833 2.262 2.821

D 10 1.372 1.812 2.228 2.764 11 1.363 1.796 2.201 2.718 9 12 1.356 1.782 2.179 2.681 r 13 1.350 1.771 2. 160 2.650 14 1.345 1.761 2.145 2. 624 1. 1.341 1.753 2.131 2.602 5 16 1.337 1.746 2.120 2.583

17 1.333 1.740 2.110 2.567 0 18 1.330 1.734 2.101 2.552 f

19 1.328 1.729 2.093 2.539 F 20 1.325 1.725 2.086 2.528 r 21 1.323 1.721 2.080 2.518 e 22 1.32 1 1.717 2.074 2.508 e 23 1.319 1.714 2.069 2.500 d 24 1.3 18 1.711 2.064 2.492 0 2. 1.31 6 1.708 2.060 2.485 m 26 1.31 5 1.706 2.056 2.479

27 1.314 1.703 2.052 2.473 28 1.313 1.701 2.048 2.467 29 1.311 1.699 2.045 2.462 30 1.3 10 1.697 2.042 2.457 40 1.303 1.684 2.021 2.423 60 1.296 1.671 2.000 2.390 90 1.291 1.662 1.987 2.368

120 1.289 1.658 1.980 2.358 ~ 1.282 1.645 1.960 2.326

Example. The 1 % c:ntical value for a one tailed test 'NIth 25 rJf IS 2.485. The 5% a1~cal value for a I'No-ta lled test wi\tllarge (>120)df is 1.960.

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0.005 0.01

63.657 9,925 5.841 4.604 4.032 3.707 3.499 3.355 3.250 3.169 3.106 3.055 3.012 2.977 2 .947 2 .921 2.898 2.878 2.861 2.845 2.831 2.819 2.807 2 .797 2.787 2.779 2.771 2.763 2.756 2.750 2.704 2.660 2.632 2.617 2.576

Table 2. 1% Critica l Values of the F Distribution Numerator Degrees of Freedom

1 2 3 4 6 7 8 9 ,.

D ,. 10.04 7.56 6.55 5.99 5.64 5.39 5.20 5.06 4.94 4.85

11 9.65 7.21 6.22 5.67 5.32 5.07 4.89 4.74 4.63 4.54

" 12 9.33 6.93 5.95 5.41 5.06 4.82 4.64 4.50 4.39 4.30

0 13 9.07 6.70 5.74 5.21 4.86 4.62 4.44 4.30 4.19 4.10 m 14 8.86 6.51 5 .56 5.04 4.69 4.46 4.28 4.14 4.03 3.94 ;

"

1. 8.68 6.36 5.42 4.89 4.56 4.32 4.14 4.00 3.89 3.80 , 16 8.53 6.23 5.29 4.77 4.44 4.20 4.03 3.89 3.78 3.69 t 17 8.40 6.1 1 5.18 4.67 4.34 4.10 3.93 3.79 3.68 3.59 0 18 8.29 6.01 5.09 4.58 4.25 4.01 3.84 3.71 3.60 3.51 , 1. 8.18 5.93 5.01 4.50 4.17 3.94 3.77 3.63 3.52 3.43 D 2. 8.10 5.85 4.94 4.43 4.10 3.87 3.70 3.56 3.46 3.37

21 8.02 5.78 4.87 4.37 4.04 3.81 3.64 3.51 3.40 3.31 9 22 7.95 5.72 4.82 4.31 3.99 3.76 3.59 3.45 3.35 3.26 , 23 7.88 5.66 4.76 4.26 3.94 3.71 3.54 3.41 3.30 3.21 24 7.82 5.61 4.72 4.22 3.90 3.67 3.50 3.36 3.26 3.17 2. 7.77

5.57 4 .68 4.18 3.85 3.63 3.46 3.32 3.22 3.13 26 7.72 5.53 4.64 4.14 3 .82 3.59 3.42 3.29 3.18 3.09

0 27 7.68 5.49 4.60 4.11 3.78 3.56 3.39 3.26 3.15 3.06 f 28 7.64 5.45 4.57 4.07 3.75 3.53 3.36 3.23 3.12 3.03

29 7.60 5.42 4.54 4.04 3.73 3.50 3.33 3.20 3.09 3.00 F 3. 7.56 5.39 4.51 4.02 3.70 3.47 3.30 3.17 3.07 2.98 ,

4. 7.31 5.18 4.31 3.83 3.51 3.29 3 .12 2.99 2.89 2.80

6. 7.08 4.98 4.13 3.65 3.34 3.12 2.95 2.82 2.72 2.63 d 9. 6 .93 4.85 4.01 3.53 3.23 3.01 2.84 2.72 2.61 2.52 0 12. 6 .85 4.79 3.95 3.48 3 .17 2.96 2.79 2.66 2.56 2.47 m

6.63 4.61 3.78 3.32 3.02 2.80 2.64 2.51 2.41 2.32 . Examplo. The 1% cnUcal value fQ( numerator df 3 and denomlna!or (ff--60 IS 4.13 .

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