4.1. Constructing Capital Stock Series (20 Points) Problem 1. Find annual time series data on real output, real investment for some country (other than the United States). Use the depreciation rate of capital 8 = 0.05 in what follows. (1) Use the data for real investment to construct a series for the capital stock following the rule Kt+1 = K (1-8) + 14 KT, = KT. where To is the first year for which you have data on output and investment. Choose Kro so that 1 . 10 Y: (2) Repeat part a, but choose Kt, so that Kro+1 KT9+10 to KT. (3) Compare the two series constructed in parts a and b. (That is, plot the two series on a graph) Are they similar? To+10 t=To+1 4.2. Growth Accounting (20 Points) Problem 2. Use the time series data on real output, real investment, employment, and working age population for some country (other than the US) in your previous exercise. Use the values 8 = 0.05 and a = 0.30 in what follows. (a) Perform a growth accounting exercise for this economy. That is, decompose the growth and fluctuations in real GDP per working-age person into three factors, one of which depends on total factor productivity, one of which depends on the capital/output ratio, and the third of which depends on employment/working-age-population ratio: K Lt N Y N, Print a graph showing the growth accounting exercise. Be sure to have clear labels and titles. (b) Discuss what happens during different time periods. (Write one or two paragraphs describing the patterns of growth. Is the growth coming from productivity, capital, or employment, or possibly all three? Are there any major recessions? etc.) 4+ ( 4.1. Constructing Capital Stock Series (20 Points) Problem 1. Find annual time series data on real output, real investment for some country (other than the United States). Use the depreciation rate of capital 8 = 0.05 in what follows. (1) Use the data for real investment to construct a series for the capital stock following the rule Kt+1 = K (1-8) + 14 KT, = KT. where To is the first year for which you have data on output and investment. Choose Kro so that 1 . 10 Y: (2) Repeat part a, but choose Kt, so that Kro+1 KT9+10 to KT. (3) Compare the two series constructed in parts a and b. (That is, plot the two series on a graph) Are they similar? To+10 t=To+1 4.2. Growth Accounting (20 Points) Problem 2. Use the time series data on real output, real investment, employment, and working age population for some country (other than the US) in your previous exercise. Use the values 8 = 0.05 and a = 0.30 in what follows. (a) Perform a growth accounting exercise for this economy. That is, decompose the growth and fluctuations in real GDP per working-age person into three factors, one of which depends on total factor productivity, one of which depends on the capital/output ratio, and the third of which depends on employment/working-age-population ratio: K Lt N Y N, Print a graph showing the growth accounting exercise. Be sure to have clear labels and titles. (b) Discuss what happens during different time periods. (Write one or two paragraphs describing the patterns of growth. Is the growth coming from productivity, capital, or employment, or possibly all three? Are there any major recessions? etc.) 4+ (