Applied Econometrics Homework #1 1. You observe 1021 US households and obtain information about their income and savings rate during a given year. For the purpose of the analysis, household income ($1000/year) is classified into 10 income categories, while the savings rate is classified into 9 rate categories. The number of households observed in each savings rate-income category is reported in the following table: Annual Household Income ($1000/year) Savings Rate 0.5 1.5 2.5 3.5 4.5 5.5 6.7 8.8 12.5 17.5 (percent) -0.25 9 10 8 9 7 5 9 3 3 2. 13 7 6 9 8 8 8 6 2 -0.18 2 11 5 12 16 17 12 14 7 4 3 -0.05 0 13 13 4 2 1 0 0 0 0 0 32 23 33 31 41 10 47 39 42 10 9 9 16 20 42 54 0.05 0.15 0.25 2 24 21 12 7 6 2 4 10 13 20 19 13 8 1 2 6 7 0.4 10 7 9 8 8 7 1 11 7 4 6 5 8 0.5 9 14 A 4 Determine (using matrix notation) and evaluate empirically the following: 1/ the marginal frequencies of income and savings rate. Interpret. 2/ the conditional frequencies of income, conditional on savings. Interpret. 3/ the conditional frequencies of savings rate, conditional on income. Interpret. 4/ the marginal mean of income and savings rate. Interpret. 5/ the conditional mean of savings rate, conditional on income. Interpret. 6/ the marginal variance and standard deviation of income and savings rate. Interpret. 7/ the conditional variance and standard deviation of savings rate, conditional on income. Interpret. Applied Econometrics Homework #1 1. You observe 1021 US households and obtain information about their income and savings rate during a given year. For the purpose of the analysis, household income ($1000/year) is classified into 10 income categories, while the savings rate is classified into 9 rate categories. The number of households observed in each savings rate-income category is reported in the following table: Annual Household Income ($1000/year) Savings Rate 0.5 1.5 2.5 3.5 4.5 5.5 6.7 8.8 12.5 17.5 (percent) -0.25 9 10 8 9 7 5 9 3 3 2. 13 7 6 9 8 8 8 6 2 -0.18 2 11 5 12 16 17 12 14 7 4 3 -0.05 0 13 13 4 2 1 0 0 0 0 0 32 23 33 31 41 10 47 39 42 10 9 9 16 20 42 54 0.05 0.15 0.25 2 24 21 12 7 6 2 4 10 13 20 19 13 8 1 2 6 7 0.4 10 7 9 8 8 7 1 11 7 4 6 5 8 0.5 9 14 A 4 Determine (using matrix notation) and evaluate empirically the following: 1/ the marginal frequencies of income and savings rate. Interpret. 2/ the conditional frequencies of income, conditional on savings. Interpret. 3/ the conditional frequencies of savings rate, conditional on income. Interpret. 4/ the marginal mean of income and savings rate. Interpret. 5/ the conditional mean of savings rate, conditional on income. Interpret. 6/ the marginal variance and standard deviation of income and savings rate. Interpret. 7/ the conditional variance and standard deviation of savings rate, conditional on income. Interpret