Voters care about the economy, often more than any other issue. It is not surprising, then, that politicians invariably argue that their party is best for the economy. Who is right? In this exercise, we'll look at the U.S economic and presidential party data in PresPartyEconGrowth.dta to test if there is any difference in economic performance between Republican and Democratic presidents. We will use two different dependent variables:

- ChangeGDPpc is the change in real per capita GDP in each year from 1962 to 2013 (in inflation-adjusted U.S. dollars, available from the World Bank).

- Unemployment is the unemployment rate each year from 1947 to 2013 (available from the U.S. Bureau of Labor Statistics).

Our independent variable is LagDemPres. This variable equals 1 if the president in the previous year was a Democrat and 0 if the president in the previous year was a Republican. The idea is that the president's policies do not take effect immediately, so the economic growth in a given year may be influenced by who was president the year before. 

(a) Estimate a model with Unemployment as the dependent variable and LagDemPres as the independent variable. Interpret the coefficients.

(b) Estimate a model with ChangeGDPpc as the dependent variableand LagDemPres as the independent variable. Interpret the coefficients. Explain why the sample size differs from the first model.

(c) Choose an \(\alpha\) level and alternative hypothesis, and indicate for each model above whether you accept or reject the null hypothesis.

(d) Explain in your own words what the \(\mathrm{p}\) value means for the LagDemPres variable in each model.

(e) Create a power curve for the model with ChangeGDPpc as the dependent variable for \(\alpha=0.01\) and a one-sided alternative hypothesis. Explain what the power curve means by indicating what the curve means for true \(\beta_{1}=200,400\), and 800 . Use the code in the Computing Corner, but with the actual standard error of \(\hat{\beta}_{1}\) from the regression output.

(f) Discuss the implications of the power curve for the interpretation of the results for the model in which ChangeGDPpc was the dependent variable.