Whether the "American Dream" is alive and well is a hot topic in current politics. One way the question is phrased is in terms of intergenerational mobility. The argument is that our incomes should not be too highly correlated with the incomes of our parents: it should be possible to succeed economically even if you were born to poor parents. Many studies have used simple regression analysis to measure the relation between our own income (Y, usually measured in logs) and our parents' incomes (X, also in logs), and have found that a 10% difference in parents' income (0.10 in logs) is associated with about a 4% (0.04 in logs) difference in the incomes of their children as adults. Thus the intergenerational income elasticity is about 0.4. Suppose we design a program that gives low-income parents a 10% increase in income during the years they are raising kids. Do you think that their children would indeed earn 4% more as adults, as the regression predicts? Why or why not? Explain, making reference to the ideas of ceteris paribus and omitted variables bias.