1) [midterm question, 2017] The table below is the same transition matrix that w

Question

1) [midterm question, 2017] The table below is the same transition matrix that we looked at in class. Based on this data, what is the probability that a person in the bottom income quintile will have a grandchild who is in the top quintile? You should just write out the equation you would use. You don't have to do the actual calculation Intergenerational Income Mobility in the United States Parent's Income Quintile Child's' Income 4th 1st (bottom) 2nd 3rd 5th Quintile 1st (bottom) 2nd 3rd 4th (top) 0.09 0.15 0.14 0.23 0.39 0.42 0.23 0.19 0.11 0.06 0.250.17 0.230.24 0.24 0.18 0.17 0.100.19 0.08 0.15 0.19 0.32 0.26 0.23 5th (top)

Explanation / Answer

answer:

what we need here is that given the parent is in bottom quintile his grandchild will be in top income quintile.

here parent quintile is fixed = bottom

grandchild quantile fixed = top

but the child'd quintile can be anything from 1st to 5th

so basically the second generation table for us will now become like :

parent equivalent to child

child equivalent to grandchild of parent

we have 5 possibilties:-

1.)so if child is in 1st quintile given parent is in bottom probabilty child's child will be in top = 0.42 *0.06 =0.0252

2.)so if child is in 2nd quintile given parent is in bottom probabilty child's child will be in top = 0.23 * 0.06 = 0.0138

3.) so if child is in 3rd quintile given parent is in bottom probabilty child's child will be in top = 0.19 * 0.06 = 0.0114

4.) so if child is in 4th quintile given parent is in bottom probabilty child's child will be in top = 0.11 * 0.06 = 0.0066

5.) so if child is in 5th quintile given parent is in bottom probabilty child's child will be in top = 0.06 * 0.06 = 0.0036

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