The minimum (legal) drinking age in the United State is age 21 before age 21, individ- uals are not permitted to purchase or publicly consume alcohol. Underage drinking still occurs through either illegal purchase or consumption of alcohol purchase by older individ- uals. Suppose that you are interested in determining the effect of the minimum drinking age law upon alcohol consumption. The variables of interest are alcohol (the average number of alcoholic drinks that individual drinks in a week; continuous variable) and age (an individual's age in years; discrete variable). The general form of the conditional expectation is E(alcohol|age) = m(age), and you are particular interested in the difference between what happens at age 21 and what happens at age 20, i.e. m(21) m(20), but at the same time trying to control for a possible relationship between alcohol and age (a relationship that would exist even without a drinking age law). Assume that we focus on the population of ages between 16 and 25 (age {16, 17, ..., 25})

a) Explain why a linear model E(alcohol|age) = 1 + 2age is too simplistic here. b) Define a variable overage = 1(age 21) (equal to one if age 21, and equal to zero otherwise). i. Utilizing the overage variable, propose a linear model for E(alcohol|age) that has a common slope for both underage and overage individuals but that allows for a jump in the conditional expectation at age 21. ii. In terms of your model parameters, what is the effect of the drinking age law? What value(s) of the parameter(s) would correspond to a situation in which the drinking law has no effect? iii. In terms of your model parameters, what is the expected difference in average alcohol consumption between a 25 year old and a 22 year old? How about about between a 22 year old and a 19 year old.