1. Describe an econometric model, and distinguish it from an economic model. Why should the parameters of an econometric model be estimated rather than calculated? Explain carefully.
2. Suppose there are three alternative estimators for parameter ß – B1, B2, and B3. B2 is an unbiased estimator of ß, whereas B1 and B3 are biased. B1 is negatively biased, but B3 is positively biased. The bias in B3 is twice (in absolute value) the bias in B1. Draw the sampling distributions of the three estimators on the same graph. Assume the variance of B1 is smaller than the variances of B2 and B3 (which are equal), and the distributions are normal.
3. The Mean Square Error (MSE) criterion is said to make a trade-off between bias and efficiency. Using the following formula for MSE, show that MSE is a weighted average of “squared bias” and variance.
, where N is the number of estimates in repeated sampling.
4. The “Law of Supply” expresses quantity supplied (Q) of a product as a positive function of its price (P). Write the appropriate linear econometric model for this case, and use the following data to find the OLS estimates of the parameters of the Supply Line [Q = f (P)].
Q: 20 23 18 21 19 25 28 22 30 26
P: 8 9 7 8 6 10 12 9 13 10
The OLS estimators for the two parameters are as follows:
“P-bar” and “Q-bar” in the above formulas are the average of the values of P and Q, respectively.
5. Suppose you have programed a computer to do the following:
i. Draw randomly 25 values from a standard normal distribution.
ii. Multiply each of these values by 3 and add 2.
iii. Take their average and call it A1.
iv. Repeat this procedure to obtain 500 averages A1 through A500.
v. Compute the average of these 500 A values. Call it A-bar.
vi. Compute the variance of these 500 A values. Call it A-var.
a) What is this Monte Carlo study designed to investigate?
b) What number should A-bar be close to? Why?
c) What number should A-var be close to? Why?