GRAPHICAL REPRESENTATION OF THE EFFECTS OF MULTICOLLINEARITY

This paper considers the effects of multicollinearity on the multiple coefficient of determination and on the standard errors of the estimated regression coefficients. Limiting results are well known for these problems, and some particular cases have been investigated. However, the limiting cases do not explain the nonmonotonic relationships that have been observed in practice. This paper explores these relationships and attempts to provide a unifying graphical explanation that includes the previous results as special cases. Implications for stepwise regression and for the interpretation of any multiple regression involving multicollinear independent variables are discussed.     

The Dynamics of Inequality

The past forty years have seen a rapid rise in top income inequality in the United States. While there is a large number of existing theories of the Pareto tail of the long‐run income distributions, almost none of these address the fast rise in top inequality observed in the data. We show that standard theories, which build on a random growth mechanism, generate transition dynamics that are too slow relative to those observed in the data. We then suggest two parsimonious deviations from the canonical model that can explain such changes: “scale dependence” that may arise from changes in skill prices, and “type dependence,” that is, the presence of some “high‐growth types.” These deviations are consistent with theories in which the increase in top income inequality is driven by the rise of “superstar” entrepreneurs or managers.