We have used Ray Fair's voting data, (data file fair5, throughout the book to predict presidential election outcomes with the linear regression model. Here we apply probit to predict the outcome of the 2016 U.S. Presidential election. Create the variable DEMWIN \(=1\) if VOTE \(\geq 50.0\) and DEMWIN \(=0\) otherwise. As of October 28, 2016, the values for the key economic variables were \(G R O W T H=0.97\), \(I N F L A T=1.42\), and \(G O O D N E W S=2\).

a. Estimate a probit model for DEMWIN as a function of GROWTH, INFLAT, GOODNEWS using data for years prior to 2016. Comment on the signs and significance of the estimated coefficients.

b. Using the probit model in part (a), and the given values of GROWTH, INFLAT, and GOODNEWS, predict the election outcome in 2016. What is the estimated probability that a democrat will win?

c. Add DPER, DUR, WAR, and INCUMB to the model used in (a). Reestimate the probit model. What happens to the signs and significance of the estimated coefficients?

d. Using the model in (c), obtain the estimated probability, PHAT, of a democrat winning for the sample period 1916-2012. Are any of the predicted values very close to 1.0 or 0.0 ? For how many observations is PHAT \(>0.99999\) ? For how many observations is PHAT \(<0.00001\) ?

e. Examine the values of \(D E M W I N\) when the following four-variable pattern exists in the data: \(D P E R=-1, D U R=0, W A R=0, I N C U M B=-1\). How many such observations are there?