1. You have a regional country-year dataset over 10 years of 150 total observations, within this data you have 25 observations where the ruling party has lost power.
(a) Assuming a binomial distribution, what is the likelihood function for Π, the probability that a country's ruling party loses power over ten years?
(b) Calculate the MLE of Π
(c) Calculate the standard error and the 95% confidence interval for this estimate. How did you know what test/sampling distribution to use?
(d) What is the value of the log-likelihood for this estimate?
(e) Say that for another region the estimated probability of a ruling party losing power over a ten-year span is 25%, using your region's data, what is the value of the log-likelihood function for a .25 value of Π?
(f) Using a Wald test, test whether your region's rate of over turning power is significantly different from the other region's.