Ollscoil na hÉireann, Gaillimh GX_____

National University of Ireland, Galway

Examinations 2010/2011

Exam Code(s) 3BA1, 3BA5, 3BA6, 4BA4, 4BA8, 1EM1, 1OA1, 3BC1,

4BC2, 4BC3, 4BC4, 4BC5, 1EK3, 1EK2, 1EK3, 3FM1

Exam(s) B.A., B.A. (ESS), B.A. (PSP), B.A. (Int’l), Erasmus,

Occasional, B.Comm., B.Comm. (Language),

H.Dip.Econ.Sc. 3rd B.Sc.(Fin. Maths & Economics)

Module Code(s) EC422

Module(s) Applied Econometrics

Paper No.

Repeat Paper 1

External Examiner(s) Dr Pat McGregor

Internal Examiner(s) Professor John McHale

Professor Ciaran O’Neill

Instructions: Answer any four questions

Duration 2 hours

No. of Pages

Department(s) Economics

Course Co-ordinator(s) Ciaran O’Neill

Requirements:

Statistical Tables

Graph Paper

EC422 Applied Econometrics Resit 2011

All questions carry equal marks.

Students answer four questions in 2 hours

1.

a. Briefly detail the steps involved in the conduct of an econometric study (8

marks)

b. Outline the principles underlying ordinary least squares regression

analysis (9 marks)

c. Distinguish between the coefficient of multiple determination and the

adjusted coefficient of multiple determination. Which would use when

assessing a regression function and why? (8 marks)

2a. Give an account of the desirable properties of an estimator (7 marks)

b. Construct the 95% confidence intervals for the predicted value of Y in the

following regression function when X = 262.5 and when X = 345. (10

marks)

^

Y = 7.6182 + 0.0814X1i

_^

Where n = 10, X = 262.5, σ2= 6.4864 and Σxi2= 51562

c. Interpret and comment on the confidence interval (8 marks)

3

You are given the following data based on 15 observations:

___

Y = 0.2033; X1= 1.2873; X2= 8.0; Σyi2= 0.016353

Σx1i2= 0.359609; Σx2i2= 280; Σx1iyi= 0.066196

Σx2iyi= 1.60400; Σx1ix2i = 9.82000

(Note, lower case letters denote deviations about the mean)

a. Estimate the intercept and partial slope coefficients (12 marks)

b. Test the statistical significance of each slope coefficient using α= 0.05 (8

marks)

c. Comment on the regression relationship (5 marks)

4a. What is multi-collinearity and what are its consequences for OLS

estimators (12 marks)

b. Detail how you ascertain whether a model suffered from multi-collinearity

(7 marks)

c. With use of examples briefly detail common sources of multi-collinearity

(6marks)

5a. Briefly discuss what is meant by “under” and “over” estimation in

regression analysis and outline the impact of each on OLS estimates (12

marks)

b. Detail the steps involved in the conduct of the WALD test (6 marks)

c. What, if any, impact will errors in measurement with respect to the

dependent or independent variable have on OLS estimators. (7 marks)

6a. What is heteroscedasticity and what are its consequences for OLS

estimators (8 marks)

b. Outline the method of weighted least squares as a means of addressing

heteroscedasticity (8 marks)

c. What is meant by autocorrelation, and how would you test for it? (9

marks)

Formulae Sheet EC422 Econometrics

Two variable model

^_^_

β0= Y – β1X

^

β1=Σxiyi

Σxi2

_ _

xi= (Xi– X) and lower case y = (Yi– Y)

^ ^

Variance of β0= Var(β0) = (ΣXi2/ n Σxi2) . σ2(note this involves upper and lower case

“x”

^ ^ ^

Standard error β0= SE (β0) = √Var(β0)

^ ^

Variance of β1= Var(β1) = σ2/Σxi2{as before lower case “x” is used to denote

deviations}

^ ^ ^

Standard error β1= SE (β1) = √Var(β1)

^

σ2is estimated by σ2= (Σei2) / n-2

^

Σei2=Σ(Yi– Yi)2

r2= 1 - Σei2/Σyi2

^

Σyi2=β1Σxi2+Σei2

Jarque-Berra test

JB = n/6 [S2+ (K – 3)2/4]

Where S is skewness and K kurtosis

Forecasting

Mean = E(Y│X0) = β0+β1X0

_

Var = σ2[1/n + (X0– X)2/Σxi2]

^

Where σ2is the variance of Ui(unknown) approximated by σ2

Confidence interval on forecast

^ ^ ^

β0+β1X0+ or - tα/2 SE(Y0)

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