STA312 Assignment 9

Quiz in Tutorial Friday Nov. 16th

In the readings and in the lecture, we have examined the instrumental variables trick for obtaining an identified model in measurment error regression: add a couple of extra dependent variables. So far we have looked at the case of two instrumental variables, for a total of three dependent variables in all. We did it with SAS for the poverty data.

1. Prove that the model is still identified if you add another dependent variable (error terms still uncorrelated), for a total of four.
2. What do you think would happen if you added several more? Would the model still be identified? Just answer Yes or No with no proof.
3. Now I want you to take and modify my program poverty2.sas. The program and data are available online HERE. You will add deathrate, and replace average life expectancy with the separate life expectancies for males and females. Thus, your independent variable is (true, latent) GNP, your dependent variables are (observed) birth rate, death rate, infant mortality rate, life expectancy for males and life expectancy for females. GNP measured with error is (observed) gnp2. Please use just this rescaled version, to avoid numerical problems.

   Again, you'll steal my program, with my blessing, and run proc calis once, not three times. Look at the test for each γ parameter. At the 0.05 level, do you reject the null hypothesis that γ=0? In plain English, what do you conclude? (For example, in richer countries, the infant mortality rate is lower.) Be prepared to answer questions like these on the quiz, but please do not write the answers on your printouts before the quiz.

Please bring your log file and your list file to the quiz. Note that the log file and the list file must be from the same SAS job. You will lose very substantial marks if there are any error messages or warnings.