Fundamentals of Econometrics — DU B.A. (Prog.) with Statistics as Major Discipline Previous Year Question Papers

DSC: Fundamentals of Econometrics (NEP) 1. (a) Fill in the blanks. i. The ratio scale has a meaningful point, unlike the interval scale. ii. The adjusted j32 penalizes the addition of variables to the model. iii. The total sum of squares (TSS) can be decomposed into iv. Using oLs in the presence ofautocorre]ation leads to c)f R2 . v. When the determinant of the correlation matrix of explanatory variables is close to zero, it indicates (b) State whether True or False. The first step in building an econometric model is the e.stimation of parameters. The stochastic error term in a regression model accounts for the variables omitted from the model. iii. The assumption that error terms follow normal distribution is required for point estimation. R2 can never decrease when a new variable is added to the regression model. V. Model mis-specification (e.g., omitting a variable) can create apparent autocorrelation in residuals. (c) i. For the variable X2 and X3, R2(auxillary) is 0.90 and 0.85 respectively. Calculate Variance Inflation Factor, comment on severity and suggest remedies. ii. Forthe given models: - Interpret coefflcients p2 and cr2 according to model (I) and model (2) - Under what circumstances, we use model (1) and model (2). [5,5,5] 2. (a) Discuss, in brief, the methodology of developing an econometric model. (b) For a General linear model y„x] =X„xp 4px] +€„x, with usual assumptions. Develop the test of significance for individual regression coefficient. Also. obtain 100(1 -cr)% confidence interval for Pi. 3. Consider the general linear model I;,x] =X„xp 4py, +€„x, with E(€)=0 , 7'(£)=qr2 J„ and P(X)=fr < p < 7g . Let y=c'4 be an estimab]e function. Obtain the BLUE of y in the class of all linear unbiased estimators of y by the method of least squares. Also obtain an unbiased estimator of a.2. [15]. 4. (a) What is multicollinearity? Explain the consequences of multicollinearity for the least square estimation technique. (b) Develop a prediction interval for the future observation yo corresponding to a specified level xo of the regressor variable x in the simple linear regression model. [9,6] 5. (a) Define auto-correlation. Given the model y = or + Px + u. Discuss the consequences of autocorrelation assuming the first order autoregressive scheme ut = p ut.I + €t where st satisfies the assumptions of the classical linear regression model. (b) For the generalized least square model Y = XP + u, with E(uu') = o2Q, o2. being unknown and a being known, symmetric positive definite matrix, Compute Aitken's estimator for p, its variance and a2. [7]/2, 7%]` 6. (a) Describe Ferrar-Glaubar test for detecting the presence of multicollinearity. (b) Discuss the Goldfeld- Quandt test for heteroscedasticity. How do you proceed with the test when there is more than one variable in the model. [8,7] 7. For the simple linear regression model yi = Po + Pixi + ei, (i = I, 2 ,..., n), where €i~ NID