Questions 1,2,3,4,5. Use R studio when necessary.

Please show screenshots of R commands and R outputs.

income_democracy.dta : https://drive.google.com/file/d/1rxCQ761hxUg3Ji6BU9xYPPavLSKmIF70/view?usp=sharing

Income_Democracy_Description.pdf : https://drive.google.com/file/d/14atWCLhft5sFalkTlbb_8A_R53--r51O/view?usp=sharing

Problem 2: Demand for Democracy (70 marks) Background: Do citizens demand more democracy and political freedom as their incomes grow? That is, is democ- racy a normal good? To investigate this issue, you will explore the dataset Income_Democracy. dta which contains a panel data set from 195 countries for the years 1960, 1965, ... , 2000. A detailed description is given in Income_Democracy_Description. pdf.' The dataset contains an index of politi- cal freedom/democracy for each country in each year, together with data on the country's income and various demographic controls. (The income and demographic controls are lagged five years relative to the democracy index to allow time for democracy to adjust to changes in these variables.) Research tasks: 1. Is the data set a balanced panel? Explain. (5 marks) 2. The index of political freedom/democracy is labeled dem_ind. (a) What is the value of dem_ind for the United States in 2000? What is the average of dem_ind for the United States over all years in the data set? (4 marks) Repeat this exercise for Libya (2 marks). (b) List five countries with an average value of dem_ind greater than 0.95; less than 0.10; and between 0.3 and 0.7. (5 marks) 3. The logarithm of per capita income is labeled log-gappc . (a) Regress dem_ind on log-gappc using standard errors that are clustered by country (3 marks). (b) How large is the estimated coefficient on log-gappc? Is the coefficient statistically signifi- cant? (2 marks) (c) If per capita income in a country increases by 20%, by how much is dem_ind predicted to increase? What is a 95% confidence interval for the prediction? Is the predicted increase in dem_ind large or small? Explain what you mean by large or small. (5 marks) (d) Why is it important to use clustered standard errors for the regression? Do the results change if you do not use clustered standard errors? (4 marks) 4. (a) Suggest a variable that varies across countries but plausibly varies little or not at all over time and that could cause omitted variable bias in the regression in Question 3 above. (5 marks) (b) Estimate the regression in Q3, allowing for country fixed effects. How do your answers to Q3(b) and Q3(c) change? (5 marks) (c) Exclude the data for Azerbaijan and rerun the regression. Do the results change? Why or why not? (5 marks) (d) Suggest a variable that varies over time but plausibly varies little or not at all-across coun- tries and that could cause omitted variable bias in the regression in Q3. (5 marks) (e) Estimate the regression in Q3, allowing for time and country fixed effects. How do your answers to Q3(b) and Q3(c) change? (5 marks) (f) There are addition demographic controls in the data set. Should these variables be included in the regression? If so, how do the results change when they are included? (5 marks) 5. Based on your analysis, what conclusions do you draw about the effects of income on democracy? (10 marks)