Suggested Answers to Odd-Numbered Questions [A Guide to Econometrics, 5th edition, 2003, by Peter Kennedy] A1(a) This Monte Carlo study examines the sampling distribution of the average of 25 numbers drawn from a distribution with mean 2 and variance 9.The average of N numbers drawn randomly from a distribution with mean  and variance 2 has a sampling distribution with mean  and variance 2/N. (b) Abar estimates the mean of this sampling distribution, so should be close to 2. (c) Avar estimates its variance, so should be close to 9/25 = 0.36. A3(a) This Monte Carlo study examines the sampling distribution of the fraction of successes h in a sample of size 50 where the probability of success is 20%. When the true probability of success is p, for a sample of size N then h has a sampling distribution with mean p and variance p(1-p)/N. (b) hav should be an estimate of 0.2. (c) hvar should be an estimate of p(1-p)/N which here is ( 0.2)(0.8)/50 = 0.0032 (d) wav estimates the mean of the sampling distribution of the estimated variance of h, and so should be approximately 0.0032. A5. Create 44 observations from a normal distribution with mean 6 and variance 4. Calculate their average A and their median B. Repeat to obtain , say, 1,000 As and 1,000 Bs. Find the mean of the 1,000 A values and the mean of the 1,000 B values and see which is closer to 6. Calculate the variance of the 1,000 A values and the variance of the 1,000 B values and see which is smaller. A7. i) Choose values for a and b, say 2 and 6 (be sure not to have zero fall between a and b because then an infinite value of 1/x2 would be possible and its distribution would not have a mean). ii) Get the computer to generate 25 drawings (x values) from U(2, 6). (If the computer can only draw from U(0,1), then multiply each of these values by 4 and add 2.) iii) Use the data to calculate A's estimate A* and B's estimate B*. Save them. iv) Repeat from ii) 499 times, say, to get 500 A*s and 500 B*s. v) Obtain the mean m of the