Lets derive the results in table 10.7. (a) Exercise 10.10a demonstrates that V(xi )=V(xi*) + V(i ).

Let’s derive the results in table 10.7.

(a) Exercise 10.10a demonstrates that V(xi )=V(xi*) + V(νi ).

Recall that V(xi*) = 8.5. Use the value for V(νi) to calculate V(xi) for each simulation in table 10.7. Recalling that σ = 25,000 for all simulations, use equation (10.44) to calculate the population value of SD

(b) for each simulation. Compare the result to the third column of table 10.7.

(b) We constructed our instrument, zi, in each of these simulations using the following formula:

zi = xi* + ηi , where ηi is a random variable with expected value zero and variance equal to V(νi) in that simulation. Use the result of exercise 10.10e to calculate CORR(zi, xi) for each simulation. Compare the result to the fourth column of table 10.7.

(c) Apply equation (10.45) to the results of parts a and b to derive the asymptotic value of SD(bIV) for each simulation. Compare the result to the fifth column of table 10.7.