There is a longstanding question in Public Economics on whether government can guide people's behaviors through the design of tax rates. For example, in 1985, the federal government increased the tax on alcohol substantially from 510.5 to 512.5 per proof gallon. One of their claims is that this can guide people to drink less alcohol, which is good for their health. (a) Suppose now you have data from 48 states on mortality rate and consumption on beer in year 1982. Someone runs the following regression {robust standard errors in pare nthesis): E1? = 846.29 + 4.16 beer, R2 = 0.36 (34.90) (1.89) where mr is the mortality rate in percentage points {deaths per 100,000 individuals}, and beer is the consumption of beer in dollars (per 100,000 individuals}. Can you interpret the results above? Based on the regression output, can you conclude that more beer consumption lead to higher mortality rate? (b) Since there was a tax increase in 1985, this can be considered a good \"natural experiment\" to explore. Suppose you have data from 48 states in between year 1982 and year 1988. In other words, you now have a panel dataset to work with. Suppose you want to run the following regression: been; = ,30 + ,81 tax\" + Syearn + an; t = [1982,1988] where beer is still the consumption of beer in dollars, tax is the total alcohol tax either in 1982 or 1988, year is a continuous variable for year from 1982 to 1988. What factors are captured by the year variable? Can you provide some examples? And what is your prediction on the sign of the coefcient in front of the year dummy variable? (c) Since you now have a panel data, one of your classmates suggests running a xedeffect regression as follows: been, = ai +31 tan, + anyeam + an; t = [1982, 1988] Where at is now is the fixed effect of state 1'. Econ 213a - Fall 2021 Prof. Pettenuzzo What is the dummy variable a; capturing here? Can you provide some examples? Which regression do you prefer, the one with of or without (If? Please motivate your answers