Absolute mobility was measured using the difference of the log of the income for the two five-year periods (for simplicity we can think of these as the age 37 and age 47 incomes).
ln x is approximately x - 1, for values of x near 1 (eg ln 1.200 is 0.182). I'm not sure why the log is used rather than the percentage change (maybe Muon can explain). I think it reduces the effect of extreme changes, persons doubling income and persons who income goes down (inflation adjusted income was used).
I expect that they used the log to get rid of the exponential effect of income growth over a number of years. A constant percentage change in income would yield an exponential curve, but the log of a constant percentage change gives a straight line over time. That would make it easier for the researchers to extract an average, though one could do it with fitting functions as well.
This also occurs in the population growth rates of the states, which is why when I make apportionment projections I fit the state's growth to a constant exponential instead of a linear fit.
