2. (20 points) In development economics, the Kuznets hypothesis is a theory about how income inequality changes as a country experiences economic growth. It is named for the economist Simon Kuznets, who first articulated it. He theorized that when a country's GDP per capita was low, most people would be poor, and income inequality would be low. As a country experienced economic growth and GDP per capita increased, income inequality would increase because some people would benefit from joining the higher-paying modern sectors of the economy while others would be stuck in the agricultural sectors. Eventually, once the process of industrialization was complete and GDP per capita was high, most or all of the population would be in the modern sectors of the economy, and income inequality would decrease. You can implement a very rough test of the Kuznets hypothesis by using data from different countries to study the relationship between income inequality and GDP per capita. You have data from the World Bank on 141 countries, and the data includes the following variables: gini is the country's Gini index, a measure of income inequality, scaled so that 0 represents no inequality and 100 represents the highest possible inequality; gdppc is the country's GDP per capita, in thousands of U.S. dollars; and gdppc2 is the square of gdppc. The mean of gdppc is about 12 (that is, $12,000) and the maximum is about 80 ($80,000). The mean Gini index is about 41, the minimum is 25, and the maximum is 74. You regress gini on a quadratic in gdppc and find the following estimates. gini = 44.69 (1.08) 0.405 (0.124) gdppc + 0.00273 (0.00235) gdppc2 , 2 = 0.185 (numbers in brackets are residuals) 2.1. What is the predicted Gini index for a country with a GDP per capita of $15,000 (be careful with the units, here and throughout the problem)? 2.2. What is the rate of change of the Gini index with respect to GDP per capita for a country with a GDP per capita of $30,000? 2.3. At what value of gdppc does the sign change on the relationship between the predicted Gini index and GDP per capita? 2.4. Are the regression estimates consistent with the Kuznets hypothesis? 2.5. What do the estimates imply about how the predicted Gini coefficient changes as GDP per capita changes, in this sample? In the answer choices below, "increasing rate" means getting steeper and "decreasing rate" means getting flatter. (a) decreasing at an increasing rate (b) decreasing at a decreasing rate (c) increasing at an increasing rate (d) increasing at a decreasing rate (e) decreasing, then increasing (U shape) (f) increasing, then decreasing (inverted U)