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Transition Matrix question. No math involved. I do not know how
to read a matrix table.. Please answer with a sentence for
each.

Question: Transition Matrix question. No math involved. I do not know howto read a matrix table.. Please a...

Show transcribed image text Table 1: More than 50 percent of taxpayers in the bottom quintile moved to a higher quintile within ten years 1996 Income 2005 income Quintil Quintile Lowest Second Middle Fourth Highest Total Top 10% Top 5% Top 1% Lowest 42.4 28.6 13.9 9.9 5.3 100.0 2.3 1.3 0.2 7.9 100.0 170 26.7 15.1 3.0 1.2 0.1 100.0 Middle 7.1 17.5 33.3 29.6 12.5 4.2 1.4 0.3 Fourth 4.1 7.3 18.3 40.22 30.2 100.0 8.6 2.7 0.3 100.0 Highest 2.6 3.2 7.1 17.8 4.4 69.4 43.4 22.5 Top 10% 2.6 2.2 4.9 11.8 78.6 100.0 61.1 37.6 8.3 Top 5% 2.6 1.8 3.9 8.6 83.1 100.0 71.6 54.4 15.2 Top 1% 3.2 1.3 2.2 82.7 75.00 4.9 88.4 100.0 42.6 All Income 13.2 16.8 19.6 23.3 27.1 100.0 134 6.4 1.2 Groups The rows sum to 100 percent across the five quintiles in the first five columns. The table uses the tax retums of primary and secondary non-dependent taxpayers who were age 25 or over in 1996 and filed for both 1996 and 2005. Income breaks for the quintiles and top percentiles are based on the full cross-sections of tax retums for each year, where the taxpayer is age 25 and over. Income is cash income in 2005 dollars as defined in the Technical Appendix. Source: Tabulations by the U.S. Department of the Treasury, Office of Tax Analys using data from IRS Statistics of Income. Individual Income Tax Files for tax years 1996 and 2005 Based on this matrix, what is the probability that an individual who starts in the lowest income quintile in 1996 moves to a higher income quintile by 2005? b) What is the probability that someone who starts in the top 1% in 1996 ends up in the top 1% in 2006? What would we expect it to be ifincomes for all individuals were completely uncorrelated from year to year? c) One of the arguments in the Mankiw reading is that we cannot necessarily interpret low rates of intergenerational mobility as evidence of inequality of opportunity. Briefly summarize his argument (1-2 sentences) d) The Chetty et al. work documents a high degree of geographic variation in rates of intergenerational mobility. Does this descriptive evidence on its own provide evidence against the Mankiw point? Fxplain (1-2 sentences)

Table 1: More than 50 percent of taxpayers in the bottom quintile moved to a higher quintile within ten years 1996 Income 2005 income Quintil Quintile Lowest Second Middle Fourth Highest Total Top 10% Top 5% Top 1% Lowest 42.4 28.6 13.9 9.9 5.3 100.0 2.3 1.3 0.2 7.9 100.0 170 26.7 15.1 3.0 1.2 0.1 100.0 Middle 7.1 17.5 33.3 29.6 12.5 4.2 1.4 0.3 Fourth 4.1 7.3 18.3 40.22 30.2 100.0 8.6 2.7 0.3 100.0 Highest 2.6 3.2 7.1 17.8 4.4 69.4 43.4 22.5 Top 10% 2.6 2.2 4.9 11.8 78.6 100.0 61.1 37.6 8.3 Top 5% 2.6 1.8 3.9 8.6 83.1 100.0 71.6 54.4 15.2 Top 1% 3.2 1.3 2.2 82.7 75.00 4.9 88.4 100.0 42.6 All Income 13.2 16.8 19.6 23.3 27.1 100.0 134 6.4 1.2 Groups The rows sum to 100 percent across the five quintiles in the first five columns. The table uses the tax retums of primary and secondary non-dependent taxpayers who were age 25 or over in 1996 and filed for both 1996 and 2005. Income breaks for the quintiles and top percentiles are based on the full cross-sections of tax retums for each year, where the taxpayer is age 25 and over. Income is cash income in 2005 dollars as defined in the Technical Appendix. Source: Tabulations by the U.S. Department of the Treasury, Office of Tax Analys using data from IRS Statistics of Income. Individual Income Tax Files for tax years 1996 and 2005 Based on this matrix, what is the probability that an individual who starts in the lowest income quintile in 1996 moves to a higher income quintile by 2005? b) What is the probability that someone who starts in the top 1% in 1996 ends up in the top 1% in 2006? What would we expect it to be ifincomes for all individuals were completely uncorrelated from year to year? c) One of the arguments in the Mankiw reading is that we cannot necessarily interpret low rates of intergenerational mobility as evidence of inequality of opportunity. Briefly summarize his argument (1-2 sentences) d) The Chetty et al. work documents a high degree of geographic variation in rates of intergenerational mobility. Does this descriptive evidence on its own provide evidence against the Mankiw point? Fxplain (1-2 sentences)