Answer the following questions using the Winter Olympics data described in Table 15.1 that can be found in olympics_HW.dta

(a) Investigate whether each of the independent variables varies within unit. Discuss how whether a variable varies within unit matters for fixed effects and random effects models.

(b) Estimate a pooled OLS model where the dependent variable is medals and the independent variables are population, GDP, host country, average temperature, and maximum elevation. Briefly comment on the results.

(c) Estimate a random effects model with the same variables as in part (b). Briefly explain the results, noting in particular what happens to variables that have no within-unit variation.

(d) What is necessary to avoid bias for a random effects model? Do you think this condition is satisfied in this case? Why or why not?

Table 15.1:

Variable name ID Description Unique number for each country in the data set country Name of country year Year time A time variable equal to 1 for first Olympics in data set (1980), 2 for second Olympics (1984) and so forth; useful for time series analysis. medals Total number of combined medals won population Population of country (in millions) GDP host temp Per capita gross domestic product (GDP) (in $10,000 U.S. dollars) Equals if host nation and 0 otherwise Average high temperature (in Fahrenheit) in January if country is in Northern Hemisphere or July if Southern Hemisphere elevation Highest peak elevation in the country