LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

AC 47

M.Sc. DEGREE EXAMINATION – STATISTICS

SECOND SEMESTER – APRIL 2007

ST 2950/3950 – ECONOMETRICS

 

 

 

Date & Time: 28/04/2007 / 1:00 – 4:00      Dept. No.                                       Max. : 100 Marks

 

 

 

Section A

Answer all questions.                                                                        (10*2=20)

1. What is the difference between a linear and non-linear model?
2. Give any two reasons for the inclusion of the ‘disturbance term’ in an econometric model.
3. Interpret the following statement:

Pr{-0.25 < β₂ < 1.3} = 0.95.

1. Show that in a simple linear model the mean of the observed and estimated Y values are equal.
2. What is ‘cross – section ‘data? Give an example.
3. What is meant by ‘linear hypothesis’?
4.  “In a linear model involving dummy variable, if there are ‘m’ categories for the dummy variable, use only ‘m-1’ independent variables”. Justify the above statement.
5. Define the term ‘autocorrelation’.
6. For a four variable regression model, the observed and estimated (under OLS) values of Y are given below:

Observed Y:   10         14        13        12        17

Estimated Y:  10         13        11        14        15

Calculate the standard error of the estimate.

1. Mention any two consequences of multicollinearity.

 

Section B

Answer any five questions.                                                         (5*8=40)

 

1. Mention the assumptions in the classical linear regression model.
2. Suppose that a researcher is studying the relationship between gallons of milk consumed by a family per month (Y) and the price of milk each month (X in dollars per gallon). The sample consists of observations in 12 consecutive months. Analysis of the data reveals the following:

SY = 480;        SX=36;            Sxy=-440

Sx² = 20;         = 528, where x and y are deviates of X and Y from their respective means.

For this sample, find the following:

• Least squares intercept and slope
• Standard error of regression.
• Standard error of the slope.
• Test the hypothesis that the slope coefficient is zero at 5% level.

1. Calculate TSS, ESS, RSS and R² for the following data assuming a linear model of Y on X.

Y:        12        10        14        13        16        14

X:        2          4          7          10        12        13

1. Explain the concept of structural change with an example.
2. What is meant by interval estimation? Derive a 100(1-α) % confidence interval for the slope parameter in a simple linear model.
3. Explain the various methods of detecting multicollinearity.

 

 

 

1. Consider the following OLS regression results with standard errors in

parenthesis:

S = 12,000 – 3000X₁ + 8000(X₁ + X₂)

(1000)    (3000)                        n = 25

where S = annual salary of economists with B.A. or higher degree

X₁ = 1 if M.A. is highest degree; 0 otherwise

X₂ = 1 if Ph.D is highest degree; 0 otherwise

• What is S for economists with a M.A. degree?
• What is S for economists with a Ph.D degree?
• What is the difference in S between M.A.’s and Ph.D’s?
• At 5% level of significance, would you conclude that Ph.D’s earn more per year than M.A.’s?

1. Explain the method of estimating the regression parameters in the presence of heteroscedasticity.

 

Section C

Answer any two questions.                                                   (2*20=40)

 

1. a.) State and prove Gauss – Markov theorem.

b.) Show that for a ‘k’ variable regression model, the estimator

= (e¹e)/(n-k) is unbiased for σ^2.                                           (12+8).

1. a.) Derive a test procedure for testing the linear hypothesis Rβ = r where R

is a known matrix of order q x k with q ≤ k and r is a known q x 1

vector.

b.) Explain the procedure for testing the equality of the slope coefficients of

two simple linear models using dummy variables.          (10+10)

1. a.) Consider the following data on weekly income(Y), gender and status.

Y:        110      100      120      115      145      136      102      150

Gender:       1          1          0          1          0          0          1          0

Status:       0          0          1          1          1          0          1          0

where gender = 1 if male; 0 if female

Status = 1 if minor; 0 if major.

Assuming a linear model of Y on gender and status, estimate the

regression coefficients. Interpret the results.

b.) Define the following:

1.) Standard error of the estimate

2.) Ordinal data

3.) Variance Inflating Factor

4.) Coefficient of Determination.                                          (10+10)

22. a.) For the following data, use Spearman’s rank correlation test to for the

presence of heteroscedasticity.

Y:        10        14        20        25        13        19        10        35

X:        1.3       2.1       2.5       3.0       1.7       1.9       1.0       2.9

b.) Explain the Breusch – Pagan – Godfrey test.                          (10+10).

 

 

 

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