ECONOMETRICS — DU B.Sc (hons) Statistics Previous Year Question Papers

Attempt five more questions choosing at least two from each section. (iv) When supply of a commodity, for example agricultural commodities. react to price with a lag of one time period due to gestation period in production. such a phenomenon is referred to as Cobb-Web Phenomenon. (vi) Glejser's test requires re-ordering of the observations with respect to X variable. (c) You are given the following regression results: Find out the sample size underlying the above result? (d) What is the relationship between Von-Neumann ratio and Durbin Watson statistics. Suppose the value of Durbin Watson test statistic is 0.9374 based on 20 observations, then compute the corresponding value of Von-Neumann ratio. (5, 5, 2½, 2½) 2 (a) For the general linear model Y = XB+U, explain the process to test the hypothesis Ho: c B = r, where e is an appropriately specified vector of constants and r is a known constant. (b) The estimated equation below depicts the empirical relationship between demand for coke (D), its own price (PC), advertisement expenditure (ADV) and the price of substitute goods (PPC) i.e. Pepsi Cola. (the numbers in parentheses are t statistics), [p-value is given in square brackets] a) Briefly comment on the coefficient of determination. b) Do the parameter estimates bear the expected signs? Justify your answer. c) Can you tell whether the explanatory variables jointly affect demand for Coke at the 5% level of significance? d) Taken individually, do the variables have a significant influence on Coke demand at the 5% level of significance? (7,8) 3 (a) Estimate the coefficients of the relation Yi = B, + BzXzi + B3X3i + Ui on considering the restrictions, 2ß, + Bz - B3 = 3 and Bi + B3 = 2. It is given that X'X = X'Y = and the number of observations is 25. (b) Explain four remedial measures for addressing the problem of multicollinearity. 4 (a) A data set produces the following regression: But after adding variable G, to the above regression we get: Do you suspect that the data is suffering from some problem? If yes, what could be the possible cause of concern? Give reasons to support your conclusions. Also regressing G, on Cr, we get: Does above equation help you reach at a conclusion? Give reasons to support your conclusion. (b) For the regression model Yt = B1 + BzXzt + B3X3t + Ut; t = 1, 2, ..... n, with usual assumptions, examine the effect of multicollinearity on , V(B), V(B., B2 - B2. 5 (a) For the generalized least square model Y = X£ + u, with E(uu') = o'S. o' being unknown and 52 being known, symmetric positive definite matrix. Compute Aitken's estimator for B, its variance and o'. (b) For a two variable model, assume the first order autoregressive scheme Ut = p Uti + & where & satisfies the assumptions of the classical linear regression model. (i) Show that Var(ur) = 0/(1 - p'), where o' is the variance of &i-