2 From Theory to Empirics A central question in development economics is why some nations are rich and other poor? An- swering this question has important implications for development polices, which aim to advance human wellbeing and eliminate poverty. Let's see how economics tackles this question (of course I cannot talk about every economic theory addressing this question here). 2.1 Production Function and Capital endowment The total production in country i depends on labor L, capital, K, and raw materials, R. We use the famous Cobb-Douglas function to model the relationship between production output and inputs. First lets define the value added of production as the value of total output Q minus the value of raw material, R: V = Q - R. Then we write the Cobb-Douglas using V. V=KOL- This equation tells us that the value-added measure of output in country i, Vi depends on K and L in country i. a is a positive parameter less than one. Usually, when we compare the economic perforce between countries we use GDP per capita (or value added per capita). Hence, we would like to write the Cobb Douglas in terms of value added per capital. V = K L L = ko V K K where and ki L 1. If equation 1 hods perfectly how would the scatter diagram plotting v against k look like? 2. In reality we know that equation 1 does not hold perfectly. Rewrite equation 1 to include all other variables that might affect v in addition to k. 3. Suppose you have data about v and k, how would you estimate equation 1. 4. Use the dataset hjoines.dta to plot a scatter diagram between v and k. 5. Estimate your model in (3). Interpret the coefficient of k 6. Add the regression line to the scatter figure. Make sure you label the scatter points in the diagram. (use mlabel option). 7. How much investment for capital per capita is needed in Tanzania to be as rich as USA? 8. Could you think of a method to test the normality assumption (u ~ N(0,0%)). Hint: obtain from the above regression and plot a histogram for . You might want check the commands: pormal and qnormal 9. Assumption 5 states that Var(uX) = E(u2|X) = 02 ( constant variance (homeskdacity)). Could you think of a way to test this empirically. Hint: the distribution of should not be correlated with X or Y. You might want try the command rufplot. 10. Discuss whether the model can tell why some countries are rich and others poor (hint: does the regression provide causal relationship between v and k). 11. Add human capital to your regression and estimate the model (note: use number of years of education divided by L as a measure of human capital). 2 From Theory to Empirics A central question in development economics is why some nations are rich and other poor? An- swering this question has important implications for development polices, which aim to advance human wellbeing and eliminate poverty. Let's see how economics tackles this question (of course I cannot talk about every economic theory addressing this question here). 2.1 Production Function and Capital endowment The total production in country i depends on labor L, capital, K, and raw materials, R. We use the famous Cobb-Douglas function to model the relationship between production output and inputs. First lets define the value added of production as the value of total output Q minus the value of raw material, R: V = Q - R. Then we write the Cobb-Douglas using V. V=KOL- This equation tells us that the value-added measure of output in country i, Vi depends on K and L in country i. a is a positive parameter less than one. Usually, when we compare the economic perforce between countries we use GDP per capita (or value added per capita). Hence, we would like to write the Cobb Douglas in terms of value added per capital. V = K L L = ko V K K where and ki L 1. If equation 1 hods perfectly how would the scatter diagram plotting v against k look like? 2. In reality we know that equation 1 does not hold perfectly. Rewrite equation 1 to include all other variables that might affect v in addition to k. 3. Suppose you have data about v and k, how would you estimate equation 1. 4. Use the dataset hjoines.dta to plot a scatter diagram between v and k. 5. Estimate your model in (3). Interpret the coefficient of k 6. Add the regression line to the scatter figure. Make sure you label the scatter points in the diagram. (use mlabel option). 7. How much investment for capital per capita is needed in Tanzania to be as rich as USA? 8. Could you think of a method to test the normality assumption (u ~ N(0,0%)). Hint: obtain from the above regression and plot a histogram for . You might want check the commands: pormal and qnormal 9. Assumption 5 states that Var(uX) = E(u2|X) = 02 ( constant variance (homeskdacity)). Could you think of a way to test this empirically. Hint: the distribution of should not be correlated with X or Y. You might want try the command rufplot. 10. Discuss whether the model can tell why some countries are rich and others poor (hint: does the regression provide causal relationship between v and k). 11. Add human capital to your regression and estimate the model (note: use number of years of education divided by L as a measure of human capital)