Professor Ray C. Fair has for a number of years built and updated models that explain and predict the U.S. presidential elections. Visit his website at https://fairmodel.econ.yale.edu/vote2016/index2.htm. See in particular his paper entitled "Presidential and Congressional Vote-Share Equations: November 2010 Update." The basic premise of the model is that the Democratic Party's share of the two-party [Democratic and Republican] popular vote is affected by a number of factors relating to the economy, and variables relating to the politics, such as how long the incumbent party has been in power, and whether the President is running for reelection. Fair's data, 26 observations for the election years from 1916 to 2016, are in the data file fair5. The dependent variable is VOTE = percentage share of the popular vote won by the Democratic Party. Consider the effect of economic growth on VOTE. If Democrats are the incumbent party \((I N C U M B=1)\) then economic growth, the growth rate in real per capita GDP in the first three quarters of the election year (annual rate), should enhance their chances of winning. On the other hand, if the Republicans are the incumbent party (INCUMB \(=-1\) ), growth will diminish the Democrats' chances of winning. Consequently, we define the explanatory variable \(G R O W T H=I N C U M B \times\) growth rate.

a. Using the data for 1916-2012, plot a scatter diagram of VOTE against GROWTH. Does there appear to be a positive association?

b. Estimate the regression VOTE \(=\beta_{1}+\beta_{2} G R O W T H+e\) by least squares using the data from 1916 to 2012. Report and discuss the estimation result. Plot the fitted line on the scatter diagram from (a).

c. Using the model estimated in (b), predict the 2016 value of VOTE based on the actual 2016 value for GROWTH. How does the predicted vote for 2016 compare to the actual result?

d. Economy wide inflation may spell doom for the incumbent party in an election. The variable \(I N F L A T=I N C U M B \times\) inflation rate, where the inflation rate is the growth in prices over the first 15 quarters of an administration. Using the data from 1916 to 2012, plot VOTE against INFLAT.

e. Using the data from 1916 to 2012 , report and discuss the estimation results for the model VOTE \(=\) \(\alpha_{1}+\alpha_{2}\) INFLAT \(+e\)

f. Using the model estimated in (e), predict the 2016 value of VOTE based on the actual 2012 value for INFLAT. How does the predicted vote for 2016 compare to the actual result?