Effects of Using Mean Scores in Regression Models: An Example From Environmental Psychology

Multiple regression analysis with grouped data is often used as a method for exploring environmental preferences, the preferred unit for measurement in such analyses is mean scores rather than individual scores.Although this procedure allows us to reduce the potential for error in measuring different variables and, as a consequence of this, improves the reliability of the technique, it also produces some additional, undesirable effects. The latter include artificial increases in R² values which give the impression that a high degree of fit has been achieved for the regression model. Indeed, this goodness fit often appears to be better than that which could have been achieved by using individual scores. Further, given that different studies operate with differing numbers of subjects in their groups, the R² scores which result from the analyses of these groups are not directly comparable.In the following discussion, we demonstrate how any value, other than zero for correlations between variables, can be increased, at will, by simply expanding the number of subjects in each group. We present the specialised formulae used for quantifying this increase and offer a warning about the purely relative nature of any study which bases its conclusions on models of regression analysis using grouped data.     

Optimal education and pensions in an endogenous growth model

In OLG economies with life-cycle saving and exogenous growth, competitive equilibria in general fail to achieve optimality because individuals accumulate amounts of physical capital that differ from the one that maximizes welfare along a balanced growth path (the Golden Rule). With human capital, a second potential source of departure from optimality arises, related to education decisions. We propose to recover the Golden Rule of physical and also human capital accumulation. We characterize the optimal policy to decentralize the Golden Rule balanced growth path when there are no constraints for individuals to finance their education investments, and show that it involves education taxes. Also, when the government subsidizes the repayment of education loans, optimal pensions are positive.