Beware of "good" outliers and overoptimistic conclusions

The main goal of this paper is to warn practitioners of the danger of neglecting outliers in regression analysis, in particular, good leverage points (i.e. points lying close to the regression hyperplane but outlying in the x-dimension). While the types of outliers which do influence regression estimates (vertical outliers and bad leverage points) have been extensively investigated, good leverage points have been largely ignored, probably because they do not affect the estimated regression parameters. However, their effect on inference is far from negligible. We propose a step-by-step procedure to identify and treat all types of outliers. The paper of Persson and Tabellini [American Economic Review (2004) Vol. 94, pp. 25–46] linking the degree of proportionality of an electoral system to the size of government is discussed to illustrate how the choice of a measure and the existence of atypical observations may substantially influence results.