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Semester One Sample Mid-Semester Examinations, 2018

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ECON2300 Introductory Econometrics

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School of Economics EXAMINATION Semester One Sample Mid-Semester Examinations, 2018

ECON2300 Introductory Econometrics (Sample Only) This paper is for St Lucia Campus students Examination Duration:

60 minutes

Reading Time:

10 minutes

For Examiner Use Only Question

Exam Conditions: This is a School Examination This is a Closed Book Examination — specified materials permitted During reading time — write only on the rough paper provided This Examination paper will NOT be released to the Library Materials Permitted In The Exam Venue: (No electronic aids are permitted e.g. laptops, phones) An unmarked bilingual dictionary is permitted Calculators — Casio FX82 series or UQ approved (labelled) Materials To Be Supplied To Students: 1 × 6 Page Answer Booklet 1 × Multiple Choice Answer Sheet Instructions To Students: Answer all questions in Part A on the Multiple Choice Answer Sheet. Answer both questions in Part B in the separate answer booklet. Total Questions: 7 in Part A and 2 in Part B Total Marks: 100

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Mark

Semester One Sample Mid-Semester Examinations, 2018

ECON2300 Introductory Econometrics

THIS PAGE LEFT BLANK INTENTIONALLY

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Semester One Sample Mid-Semester Examinations, 2018

PART A. M ULTIPLE

ECON2300 Introductory Econometrics

CHOICE QUESTIONS

ANSWER ALL QUESTIONS ON THE MULTIPLE CHOICE ANSWER SHEET EACH QUESTION IS WORTH

5

MARKS

(TOTAL 35

MARKS )

(1) Why does the denominator of σˆ 2 need to be the same as the degrees of freedom in the model? (a) so we will know how the estimate is distributed if Ho is true (b) so we can extrapolate the results to other values of x (c) so that the root MSE will be a positive number (d) so the estimator will be unbiased (2) What does R2 , the coefficient of determination, measure? (a) the probability of the true value falling within the forecast interval (b) the p-value on the coefficient we are using to test our hypothesis of interest (c) the confidence interval of the error terms as determined by the coefficients (d) the proportion of the variation in y explained by x within the regression model (3) Which of the following is not a component of a hypothesis test? (a) null hypothesis (b) goodness-of-fit (c) test statistic (d) rejection region (4) What does a p-value NOT tell you? (a) The size of the largest rejection region that would not contain the observed test statistic (b) The probability you would observe a test statistic more extreme than the one observed (c) The highest value of α for which you cannot reject the null hypothesis based on the data (d) The probability that the null hypothesis is true

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Semester One Sample Mid-Semester Examinations, 2018

ECON2300 Introductory Econometrics

(5) How can you estimate non-linear functional forms using least squares? (a) estimate the linear approximation over small ranges at a time (b) transform, such as squaring or cubing, some explanatory variables. (c) use a very large sample so you do not have to assume the error terms are normally distributed (d) It cannot be done. You need to use another estimation technique. (6) A model estimated using a dataset with 125 observations generates the following results. Variable β Std Error t − stat p − value < |t| Constant 8.86016

1.766116

5.016749

0

x2

-0.01264

0.005519

-2.28937

0.022

x3

0.595792

0.014482

41.13934

0

x4

1.124589

0.877192

1.282032

0.2

x5

0.323742

0.060709

5.332661

0

What test statistic would you use to test the hypothesis β5 > .25? (a) 1.2147 (b) 5.3327 (c) 1.2948 (d) 0.0607 (7) When highly correlated variables are included in an econometric model coefficient estimates are (a) biased downward and have smaller standard errors (b) biased upward and have larger standard errors (c) biased and the bias can be negative or positive (d) unbiased but have larger standard errors

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Semester One Sample Mid-Semester Examinations, 2018

PART

ECON2300 Introductory Econometrics

B

ANSWER BOTH QUESTIONS IN THE ANSWER BOOKLET

(TOTAL 65 M ARKS ) (1) Does tax policy affect corporate capital structure? (30 Marks) R Pozdena, Economic Review published estimates of the following model for US manufacturing corporations for the period 1935-1982. yi = β1 + β2 x2,i + β3 x3,i + β4 x4,i + β5 x5,i + β6 x6,i + ei yi the leverage (=debt/equity) in percent x2,i the corporate tax rate x3,i the personal tax rate x4,i the capital gain tax rate x5,i nondebt-related tax shields x6,i the inflation rate The results reported by the author are presented in the table below. Explanatory Variable

Coefficient (t value in parenthesis)

Corporate tax rate

-2.4 (-10.5)

Personal tax rate

-1.2

Capital gain tax rate

(-4.8) -0.3 (-1.3)

Non debt shield

-2.4 (-4.8)

Inflation rate

-1.4 (-3)

N (number of observations) R2 SST

48 0.87 8463.08

(a) Are all individual variables significant at the 5% level? Explain your answer. (2 marks) (b) Most observers believe the leverage level was different during the War period (1939-1945) from that during peaceful times. Define a variable that can be included in the model to quantify this difference. (3 mark)

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Semester One Sample Mid-Semester Examinations, 2018

ECON2300 Introductory Econometrics

(c) How would you test that the leverage response to an increase in the inflation rate was different during the War period? (i) Write the model you would set up to test the hypothesis (3 marks) (ii) Write the null and alternative hypotheses and indicate the statistic you would compute (3 marks) (d) The overall F statistic for this model was not provided by the author but could be computed from the data provided. What is the computed value of F and is this model significant at the 5% level? Show your work. (3 marks) (e) Compute the standard errors for all the coefficients presented in the table. (2.5 marks) (f) Using a 95% confidence level. (i) Write the interval estimator for β2 and explain its relationship to the random b2 − β 2 variable t = (2.5 marks) se(b2 ) (ii) Compute the interval estimate for β2 (2 marks) (g) A test was conducted to find evidence that tax rates have a significant effect on leverage. The computed value was 21.04. (i) State the Null and Alternative Hypotheses used for the test (2 marks) (ii) Which test statistic would have been used? (A) Write the formula of the test-statistic including the distribution and degrees of freedom (2 marks) (B) Write the decision rule (2 mark) (iii) At the 5% level, state the critical value and your conclusion (3 marks)

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Semester One Sample Mid-Semester Examinations, 2018

ECON2300 Introductory Econometrics

(2) (35 Marks) An economist uses a random sample of individuals aged 18 and older to estimate the regression model ln(EXP EN DIT U RES) = β1 + β2 AGE + β3 ln(IN COME ) + e where ln(EXP EN DIT U RES) = logarithm of annual expenditure on FAST food (measured in dollars), AGE = age (in years), and ln(IN COME) = logarithm of annual income (in thousands of dollars). The economist uses EViews to obtain the results in Figures 3 and 4 (on the following pages). (a) Interpret the coefficient of ln(IN COME). (7 marks) (b) Estimate the marginal effect ∂E(EXP EN DIT U RES)/∂AGE for a 33 year old earning an income of $42,500 and spending $590 per year on fast food. (7 marks) (c) Predict the annual fast food expenditure of a 33 year old earning an income of $75,000. (7 marks) (d) Interpret the value of R2 for the estimated regression. How is it related to the Goodness-of-Fit for the implied non-linear relationship between EXP ENDIT U RES , AGE and IN COME? (7 marks) (e) A histogram of the residuals is depicted in Figure 4. Test the null hypothesis that the errors are normally distributed. Use a 5% level of significance. (7 marks)

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Semester One Sample Mid-Semester Examinations, 2018

ECON2300 Introductory Econometrics

F IGURE 1. Model 2 Estimates

F IGURE 2. Histogram of Residuals

END OF EXAMINATION Page 8 of 13

Semester One Sample Mid-Semester Examinations, 2018

ECON2300 Introductory Econometrics

Some Useful Formulas cov(b1 , b2 ) = σ 2

b1 = y¯ − b2 x¯ b2 = b2 = σˆ 2 =

P

N

(x x)(yi −¯ y) Pi −¯ (xi −¯ x)2 P

P P xi yi −( xi )( yi ) P 2 P N x i −( xi )2

P

eˆi2 N −K

SST =

var(b2 ) =

2 P σ (xi −¯ x)2

R¯2 = 1 −

SSE/(N −K) SST /(N −1)

AIC = ln

S2 +

Linear Model:

(K−3)2 4

i

2 ∼ χ(2)

∂y = β2 ∂x2

Log-Linear :

∂y = β2 y ∂x2

log-inverse:

∂y = −β2 (y/x22) ∂x2

SC = ln

 SSE  N

 SSE  N

Linear-log:

Log-log:

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\ + (x0 − x¯)2 var(b2 )

(SSER −SSEU )/J SSEU /(N −K)

F =

h

σ ˆ2 N

P (ˆ yi − y¯)2

SSE SST

N 6

x2i (xi −¯ x)2

N

SSR =

i

P

var(f ) = σˆ 2 +

P (yi − y¯)2

x P −¯ (xi −¯ x)2

var(b1 ) =

R2 = 1 −

JB =

σ2 P

h

+

+

∼ F(J,N−K) 2K N

K ln N N

∂y = β2 /x2 ∂x2

∂y = β2 (y/x2 ) ∂x2

Semester One Sample Mid-Semester Examinations, 2018

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ECON2300 Introductory Econometrics

Semester One Sample Mid-Semester Examinations, 2018

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ECON2300 Introductory Econometrics

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ECON2300 Introductory Econometrics...