Mathematics Homework Help

I need. sample answers. to all parts of question 2 and 5, attached it a more readable version of the. paper. IF YOU CANNOT ANSWER PLS DO NOT BID

QUESTION 2

. Do political protests affect election results? Consider the following model

Republican votei = β0 + β1T ea party protest turnouti + εi

where Republican votei is the vote for the Republican candidate for Congress in district i in 2010 and
Tea party protest turnouti measures the number of people who showed up at Tea Party protests in
district i on April 15, 2009, a day of planned protests across the United States.

(a) (10 pts) Explain why this regression may have an endogeneity problem.

(b) (10 pts) Consider local rainfall on April 15, 2009 as an instrument for Tea Party protest turnout.
Explain how to test whether the rain variable satisfies the first stage condition.

(c) (10 pts) Does the local rainfall variable satisfy the exclusion restriction? 5. A researcher has estimated a regression model of Williams student happiness as a function of two
variables: i) scoops of Likety Split ice cream (or sorbet) consumed; and ii) temperature in degrees
Farenheit. In the equation below, i indexes student and t indexes date.

QUESTION 5.

A researcher has estimated a regression model of Williams student happiness as a function of two
variables: i) scoops of Likety Split ice cream (or sorbet) consumed; and ii) temperature in degrees
Farenheit. In the equation below, i indexes student and t indexes date.

happinessit = α + βtemperaturet + γscoopsit + δtemperaturetscoopsit + εit

1. (a) (5 pts) Explain your intuition for the signs of the coe cients β and γ. (There is no right or wrong
   answer here; please just explain your thinking.)
2. (b) (5 pts) Explain your intuition for the sign of δ. Why might it be important to interact temperature
   and scoops in this model?
3. (c) (5 pts) Using partial di erentiation, obtain the formula for the marginal e ect of scoops on
   happiness. (The marginal e ect is the change in the outcome from a one-unit change in a given
   right-hand-side variable.)
4. (d) (5 pts) What is the marginal e ect of scoops when temperaturet = 0? Does your answer change
   your intuition about the sign of any of the model parameters?
5. (e) (5 pts) The average June high temperature in Williamstown is 83 degrees. What is the marginal
   e ect of scoops at this temperature?
6. (f) (10 pts) The researcher’s regression model fails to re ect one of the core results of economics:
   diminishing marginal utility. (This is a sad waste, as one of the advantages of economics relative
   to a eld like data science is that our theoretical models are sometimes a powerful guide for our
   empirical work.) How could the regression be modi ed to allow for diminishing marginal utility
   of scoops? (Hint: you may need to add terms to the regression, or substitute something else for
   the level of scoops.) Explain your choice. Again using partial di erentiation, nd the marginal
   e ect of scoops on happiness in your modi ed regression.