The Next Generation

Economic Inequality has been getting a lot of attention of late. The Rich are getting richer, the Poor arc getting poorer, and the gap between them is increasing at an ever accelerating rate. But while the class divide is getting economically worse, it is thought that this inequality is balanced by Economic Mobility. While it may be unfair that the Rich are becoming richer, as long as the Poor have an equal opportunity to become Rich, then they too have a chance to benefit from Inequality. (Less talked about are all the Rich that have the “opportunity” to become Poor.) This project will try to quantify some aspects of Economic Mobility.
Rather than look at the Economic Mobility of a single individual, we will consider the mobility of an entire population over multiple generations. You will need to find data on the change in economic status — measured in at least 3-5 categories – from one generation to the next. They should be in the form of probabilities or percentage rates. (As such be very careful about the possibility of rounding error, both in your calculations, and in the original data itself.) Use this data to create a Transition Matrix, T, which can be used to find the distribution of incomes from one generation to the next. (If P. represents the current distribution of incomes, then Net = TN.)
How does T appear? Are you able to assess how “Fair” it might be looking at the matrix?
What do T2, T3, …V’ represent? What trend or trends seem to occur as n —.co? What does this indicate?
Find the Eigenvalues and associated Eigen Vectors of T. (If you use technological aids, make sure to indicate which calculator functions, computer program, or web site.) What is the largest Eigenvalue? What is the corresponding Eigenvector? What does this tell us about the long term distribution of economic status? Approximately how many generations does it take to reach this distribution?]

Sample Solution