2. Bias and Inconsistency and a Potential Solution .

a. Suppose that dmtspgm is an imperfect measure of the change in TSPs due to misreporting. In addition, suppose that this measurement error is classical in the sense that it is independently and identically distributed. What does this imply about the bias in the estimated effect of dmtspgm from the regression that we have been examining in question 1?

b. Suppose God has told us (or that we suspect) that there are many unmeasured/unobservable confounding factors that determining both dimr7271 and dmtspgm. Examples of these types of variables include: health insurance status, rates of smoking across mothers, and parents income. Explain how this could lead to omitted variables bias in the LS equation. Show this in the derivation of the LS parameter estimate of the influence of TSPs on IMR.

c. In 1970 the federal government passed the Clean Air Act Amendments. This legislation set air quality standards for TSPs that all counties are required to obtain. In counties that did not meet the standards, TSP emitters were subject to harsh regulations that required them to reduce their emissions of TSPs, while emitters in clean counties were relatively free from regulation. Previous researchers collected the information for whether a county was regulated heavily and coded it as a dummy variable that is equal to 1 for heavily regulated counties and 0 otherwise. The variable name is reg_tsp. Under what conditions would this variable qualify as a valid instrumental variable?

d. Present evidence that reg_tsp might be a valid instrumental variable. In particular, test whether TSPs declined more in heavily regulated counties. What was the effect of the Clean Air Act Amendments on TSP concentrations? Can you devise any suggestive evidence that reg_tsp meets the other condition required of an instrument? (Hint: Recall how Woodbury and Spiegelman showed that randomization was effective)