Introductory Econometrics

Problem 1 (8 points) Let the following model describe the true relationship between variables y, x and z: y = β0 + β1x + β2z + u (1) 1. (5 points) Assume availability of a sample (yi , xi , zi), i = 1, . . . , n. Discuss under which conditions the OLS estimates of β1 and β2 are unbiased. Answer: Key conditions for unbiasedeness of OLS estimates of β1 and β2 are: (i) linearity of the true conditional expectation (this is already assumed to be true in this example) (ii) (yi , xi , zi), i = 1, . . . , n needs to be a RANDOM sample from the population (iii) positive variance in the observed xi (iv) E[u|x, z] = 0. 2. (3 points) Suppose we are particularly interested in estimating β1 but we only have information on a random sample for (yi , xi), i = 1, . . . , n. Under which conditions would it be correct to estimate the model y = β0 + β1x + u? Answer: Two possibilities: (i) β2 = 0, in which case z is not relevant; (ii) z is uncorrelated with x, following from the fact that the OLS estimate of β1 in the simple model identifies β1 + β2 Cov(x,z) V ar(x) . 1 Problem 2 (12 points) The file VOTE contains information on Congressional campaign expenditures for the U.S. House of Representatives in 1988. For each of the 173 two-party races we know the percentage of votes received by candidate A (voteA), the logarithm of campaign expenditures (in thousands of US dollars) for both candidate A (lexpendA) and candidate B (lexpendB) and