We propose a social welfare function to evaluate a proﬁle of income streams and compare the welfare gain of the actual proﬁle relative to the income proﬁle where the individual receives his ﬁrst period income in each period. We derive necessary and suﬃcient conditions for the welfare gain to be positive, and show how this welfare gain can be decomposed in a pure eﬀect of economic growth, a mobility eﬀect and a cost due to aversion to time ﬂuctuations given individuals’ ranks in the income distribution. The mobility eﬀect, generated by reranking in the income distribution has two components: a cost due to the time ﬂuctuations in incomes and a beneﬁt, due to the equalization in time averaged incomes. We illustrate the analysis using CNEF data for Australia, Korea, Germany and Switzerland. Our results indicate that the largest component of the welfare gain is the equalization of time averaged income, induced by reranking. After subtracting the cost of mobility due to the increase in time ﬂuctuations of individual income streams, the net eﬀect of mobility remains positive. In countries with high growth (Australia and Korea), the growth eﬀect is larger than the mobility eﬀect, but in countries with low growth (Germany and Switzerland), the opposite holds true.
Keywords: intertemporal growth; mobility; income streams; time horizon